ARTIFICIAL RAINFALL in LABORATORY HYDROLOGY By

ARTIFICIAL RAINFALL IN LABORATORY HYDROLOGY

M. J. HALL, D.I.C.

Thesis presented to the Faculty of Engineering in the University of London for the Degree of Doctor of Philosophy

Department of Civil Engineering, Imperial College of Science and Technology, London S.W.7.

May, 1967. 1.

ABSTRACT

A limited number of studies have been made of the response of artificial catchment areas in the laboratory to storms of simulated rainfall. To date, such studies have been restricted to investigations of the fluid mechanics of spatially-varied unsteady flow, the application of the principle of dynamic similarity in evaluating rainfall/ run-off relationships, and the examination of assumptions connected with linear and non-linear conceptual models of catchment behaviour. Little attempt has been made to study the time-distribution of the hydrological processes involved in transforming the rainfall over a catchment area into run-off and streamflow, even though this fundamental problem is directly amenable to treatment using a rainfall simulator and artificial catchment areas in the laboratory.

In the following work, the scope of such "microcatchment" studies is outlined in detail. The difficulties encountered and the assumptions made in setting-up an apparatus to generate storms of artificial rainfall for use in the proposed experiments are examined, and an appropriate specification is compiled. A design of apparatus, consisting of a network of swirl-type nozzles, is proposed, and an account of experimental work in connection with the selection of both suitable nozzles and their correct spacing in the network is presented. 2. A critical examination is made of methods of characterising the uniformity of the distribution of application depths from the nozzle network, and a method by which such distributions may be expressed in terms of both time and space co-ordinates (a "distributed parameter" representation) is suggested.

ACKNOWLEDGMENTS

The research described in the following pages was carried out in the Department of Civil Engineering of the Imperial College between October, 1963, and September, 1965. In reporting this work there are many people to thank for their assistance.

In particular, the writer wishes to acknowledge the valuable advice and encouragement given to him by his supervisor, Professor P. 0. Wolf, throughout the research.

He also wishes to thank Mr. T. O'Donnell for much helpful discussion during the preparation of the thesis.

The assistance given to the writer by Mr. D. Tait and the staff of the Hydraulics Laboratory in the design and erection of apparatus, and by Mr. R. Rapley of the Departmental Workshops in assembling the prototype nozzles is greatly appreciated.

In preparing the thesis, the writer also gratefully acknow- ledges the work of Miss Vanessa Grant, Miss Diana Watts and Miss Vivien White in typing the manuscript, Miss Sandra Rumble in drawing the diagrams and Miss Joyce Gurr in taking the photographs.

The laboratory studies connected with this work were undertaken with the support of a two-year Science Research Council Research Studentship.

3. CONTENTS Page

CHAPTER ONE Introduction - the microcatchment, 12

1.1 Hydromechanic prototypes. 14 1.2 Model catchments. 17 1.3 Prediction analysis prototypes. 25 1.4 The microcatchment. 37

CHAPTER TWO The development of rainfall simulation as an experimental technique. 41

2.1 Historical development. 41 2.2 The U. S. Soil Conservation Service experiments. 44 2.3 The dripolator or stalactometer-type of rainfall simulator. 47 2.4 Rainfall simulators involving the use of capillary tubes or hypodermic needles. 51 2.5 Rainfall simulators incorporating commercially available nozzles or sprinkler irrigation equipment. 56

CHAPTER THREE : Equipment specification for microcatchment studies. 75

3.1 Comparison between available methods of simulating rainfall. 75 3.2 The specification for a rainfall simulator for use in microcatchment experiments. 89

CHAPTER FOUR : Methods for evaluating the properties of nozzle systems. 98 4.1 The determination of spray distribution patterns. 98 4.2 Standards for the comparison of spray patterns. 104 4. Page

CHAPTER FIVE : Experimental work - phase I 122

5.1 Preliminary work. 122 5.2 Description of apparatus. 131 5.3 Procedure, 136 5.4 Discussion of results. 140

CHAPTER SIX Experimental work - phase II 173

6.1 The geometrical arrangement of nozzle networks. 173 6.2 The apparatus. 176 6.3 Procedure. 186 6.4 Discussion of results from the three- nozzle tests. 197 6.5 Discussion of results from the four-nozzle tests. 205 6.6 Comparison between the performance of the three and four-nozzle arrangements. 208

CHAPTER SEVEN : Experimental work - phase III 211

7.1 The apparatus. 211 7.2 Discussion of results from the 16 -nozzle tests. 221 7.3 A comparison between the different statistical measures of uniformity. 229

CHAPTER EIGHT : The measurement and analysis of drop size distributions. 242

8.1 Methods of measuring drop size distributions. 242 8,2 The stain method. 256 8.3 Sampling procedure. 264 8.4 The estimation of drop size distribution parameters from sampled data. 268 8.5 Methods of characterising drop size distributions in natural rainfall. 276 8.6 Discussion of results. 281 5. Page CHAPTER NINE : Summary, conclusions and recommendations for further study. 292

APPENDIX A Bibliography. 303

APPENDIX B The configuration of spray from swirl- type nozzles. 324

APPENDIX C : The behaviour of swirl-type nozzles fitted with triangular orifices. 328

APPENDIX D : The parametric representation of rainfall patterns. 338

APPENDIX E Computer programs. 347

6. LIST OF FIGURES Page, 1.2.1. : Measured and predicted hydrographs from a model catchment study of a drainage basin in Western Iowa. 20

1.2.2. : Measured and predicted hydrographs from a model catchment study of a drainage basin in New Mexico. 24

1.3.1. Schematic representation of the hydrological cycle. 27

1.3,2. Series of Unit Hydrographs corresponding to five different intensities of rainfall for a small catchment in Illinois. 33 1.3.3. : The response of a small laboratory catchment to three square-pulse inputs of artificial rainfall of equal intensity and 100 seconds duration applied at 50 second intervals. 36

245111 • : A comparison between the drop size distributions from the nozzles used by A. R. Bertrand and J. F. Parr (1960) for the Purdue sprinkling infiltrometer and from the empirical formulae for the drop size distributions of natural rainfall given by A. C. Best (1950a). 66

2.5.2. : A comparison between the drop size distributions from the sprinkler assemblies used by A. Shachori and I. Seginer (1962) and from the empirical formulae for the drop size distributions of natural rainfall given by A. C. Best (1950a). 72

3.1.1. : A comparison between the drop size distribution from the apparatus used by J. K. Basu and N. B. Puranik (1954) and from the empirical formulae for the drop size distributions of natural rainfall given by A. C. Best (1950a)-4 76

3.1.2. : Typical instantaneous sprinkler pattern used in the theoretical water distribution analysis presented by M. W. Bittinger and R. A. Longenbaugh (1962). 85 Page 3,2.1. : A typical example of an anomolous pip on the run- off hydrograph from a concrete channel having a 0.5 per cent slope subjected to a rainfall intensity of 0.851 in/h. 91 3.2.2. : The variation of resistance coefficient with Reynolds number for a concrete surface, for steady state conditions both with and without rainfall. 93

4.2.1. : Spray distribution pattern from four sprinklers spaced 2R x 2R. 106

4.2.2. : Spray distribution pattern from four sprinklers spaced,./2.R x ,./7.R. 106 4.2.3. : Spray distribution pattern from four sprinklers spaced R x R. 106 4.2.4. : A comparison between the uniformity coefficients (in percentages) for three single-sprinkler patterns combined at different spacings of units. 110

4.2.5* : Three patterns of sampled application depths expressed in arbitrary units. 113

5.1.1. : Prototype nozzle assembly. 125/6 5.4.1. -20: Patterns of application depths from five different nozzles at four different working pressures. 141/2 5.4.21. : Depth-area curves for nozzle types A/B and A/D. 145

5.4.22. : Depth-area curves for nozzle types A/E and A/F. 146 5.4.23 : Depth-area curves for nozzle type A/C. 148 5.4.24. : Comparison between diagonal cross sections from tests on nozzle type A/D. 151

3.4.25. : Comparison between head-discharge relationships for all test nozzles. 153 8. . Page 5.4.26. : Application depths from test number 16 plotted along with the measured differences obtained under the same working conditions in test number 17 (Nozzle type A/B; 10.01 ft. head). 160 5.4.27. Application depths from test number 48 plotted along with the measured differences obtained under the same working conditions in test number 49 (Nozzle type A/F; 9.99 ft. head). 160 5.4.28. Overlapped pattern analysis results for nozzle type A/D at square spacings. 169

6.1.1. The definition of geometrical arrangements used by J. E. Christiansen (1937). 174

6.1.2. Comparison between the highest uniformity coefficients available with square and triangular geometries of sprinklers. 175

6.2.1. The artificial catchment area. 177 6.3.1. : Head-discharge relationship for triangular nozzle arrangement. 192 6.3.2. : Head-discharge relationship for square nozzle arrangement. 194 6.4.1. Analysis of patterns of application depths from 3 -nozzle tests. 198 6.5.1. Analysis of patterns of application depths from 4-nozzle tests. 206

7 .1.1. Production nozzle assembly. 212/3 7.1.2. Head-discharge relationship for innermost four nozzles of the 16-nozzle apparatus. 220 7.2.1. Analysis of patterns of application depths from 16-nozzle tests (test numbers 124-134). 222 7.2.2. Analysis of patterns of application depths from 16•-nozzle tests (test numbers 135-146). 225 7.3.1. Plot of the Christiansen uniformity coefficient against the H.S.P.A. uniformity coefficient for mathematically overlapped patterns. 231 9. Page 7.3.2 • Plot of the Christiansen uniformity coefficient against the H.S.P.A. uniformity coefficient for the 4-nozzle and 16-nozzle tests. 232

7.3.3. Plot of U.S.D.A. pattern efficiency against coefficient of variation for mathematically overlapped patterns. 234 7.3.4. Plot of skewness (pi) against kurtosis (130 for the application patterns from the 4-nozzle and 16-nozzle tests. 237

7.3.5. The variation of the Christiansen uniformity coefficient with the ratio of the maximum to the minimum application depth. 241

8.4.1. The variation of terminal velocity with drop diameter - measurements and empirical relationships. 271 8.6.1. Typical cumulative water content curves from the distributions sampled from nozzle type A/D. 283

8.6.2. Plot of median volume drop diameter, dmv, against intensity of application, P, from filter paper samples compared with the empirical equation obtained by D. Atlas (1953) from the data of J. S. Marshall and W. McK, Palmer (1948). 285 8.6.3./4. : Drop size distribution measurements for nozzle type A/D compared with the Marshall-Palmer distribution for natural rainfall. 287/8

B.1. Three stages in the configuration of spray from a swirl-type nozzle. 325

C.1)-1 : Patterns of application depths from nozzle type B/B at four different working pressures. 330

C.5. Depth-area curves for nozzle type B/B. 333 C.6. : Drop size distribution measurements for nozzle type B/B. 337 10. EEEE D.1. Typical space-variation of intensity of application at any time, t. 342 D.2. : Typical time-variation of average application depth over an area. 342

E.1. : Schematic representation of the overlapping of an 8 x 8 single-nozzle pattern grid to form a 4 x 4 overlapped pattern. 349 E.2. : Subroutine PATERN. 351 E.3. : Subroutine UNIFCO. 352 E.4. : Subroutine EFFCO. 354 E.5. : Subroutine AVARA. 355 E.6. : Drop size distributions program. 356 E.7. : Subroutine XYMOM. 358 E.8. : Subroutine COEFS. 359 E,9. : Subroutine COSXY. 360 E.10. : Subroutine AVQUAD. 360 E.11. : Subroutine HARMCO. 361 E.12. : Subroutine ORDCAL. 362 11. LIST OF PLATES

Page

5.1.1. : General view of apparatus for the testing of 123 single nozzles.

6.2.1. : General view of apparatus for the testing of groups of 3 and 4 nozzles. 179 6.2.2. : Feeders and control system of 5/4 nozzle apparatus. 181 6.2.3. : Arrangement of 4 nozzles in a square geometry at 18-inch centres. 183 6.2.4. : Arrangement of 3 nozzles in an equilateral- triangle geometry at 18-inch centres. 184

7.1.1. Supporting system for 16-nozzle apparatus. 215 7.1.2. General view of apparatus for the testing of groups of 16 nozzles. 217 7.1.3. : Modified control system for 16-nozzle apparatus. 218

8.3.1. : Sampling device and ancillary equipment for the measurement of drop size distributions. 265

B.1. : Configuration of spray from nozzle type A/D at five different working pressures. 327 CHAPTER ONE 12.

Introduction - the microcatchment

In his book "Understanding Weather", O.G. Sutton (1960) wrote that "Rainfall is the most variable of all the quantities measured in meteorology". Although this statement may be considered more generalization than scientific fact, it reflects the embarrassment and frustration that the occurrence of rainfall can cause both layman and scientist.

Experiments in which natural rainfall, with its highly irregular properties of intensity and duration, is included as a major variable are notoriously inconvenient to design and execute. Such was the difficulty which faced the pioneer investigators of soil erosion problems in the United States of America. Their remedy was the development of mechanical methods for producing artificial rainfall.

Rainfall simulators have now become a standard item of research equipment for work on many other aspects of soil behaviour, but the extension of their use to more general hydrological problems has been slow. The possibility of studying the hydrological cycle of a laboratory-size artificial catchment area has remained no more than an exciting future development. The theoretical and practical problems presented by such experiments are manifold, and yet sufficient progress has been made during the last decade for J. Amorocho and W.E. Hart (1965) to propose a classification for this type of study.

According to Amorocho and Hart, a laboratory catchment is defined as "A physical system of comparatively small size in which * a bibliography is provided in Appendix A. 13. the input and output occur in the form of flowing water, and appropriate controls and measurement devices are provided to regulate the input as desired and to measure the output with adequate accuracy." Given this definition, laboratory catchments are considered by those authors to fall into the following categories

a)model catchments b)laboratory prototype systems 1)hydromechanic prototypes 2)prediction analysis prototypes

When the physical features of a natural catchment are reproduced to an appropriate scale in a laboratory model, from which predictions of prototype behaviour are obtained by the application of similarity criteria, the catchment is termed a "model catchment". In contrast, "laboratory prototype systems" are employed for the investigation of specific flow phenomena. "Hydromechanic prototypes" are used in the study of the laws of fluid motion over impervious surfaces, and "prediction analysis prototypes" for the testing of theories and methods of analysing hydrological input-output relationships.

This classification is adequate in covering all varieties of laboratory catchment that have been described previously in the literature. However, the advantages in the control of experimental conditions, which the use of a rainfall simulator permits, provides a flexibility to laboratory catchment studies belied by three such rigorous definitions. In particular, the laboratory prototype systems are capable of further subdivision. The prediction analysis prototype is intended primarily as a tool for analysis, i.e., the relationships between rainfall inputs and outputs of run-off are established by a mathematical process involving the use of the 14. measured input and output data only. The interest is not centred upon the form of the catchment used as the laboratory prototype system. The mathematical functions produced by the processes of analysis are not required to have a physical meaning in terms of the system that they represent.

The problem of predicting the run-off from a given rainfall is also capable of treatment by a synthesis approach in which the operation of the system is described by a series of components whose functions are known, and whose presence in the system is assumed initially by the investigator. In terms of a laboratory catchment study, experiments would proceed by manipulating the catchment characteristics to produce a predetermined output from a given input. The contrast between synthesis and analysis is sufficiently marked for the synthesis approach to be considered as a separate category of laboratory catchment study. The basis for the addition of this new subdivision may be illustrated most clearly by considering the progress made during the last thirty to thirty-five years in the fundamental hydrological problem of determining rainfall/run-off relationships, and the part that laboratory catchments have played in their development.

1.1 Hydromechanic prototypes. Historically, the first laboratory catchment studies were made with hydromechnnic prototypes. R.E. Horton (1938) discussed an analytical treatment of surface run-off from rectangular plots assuming constant rates of rainfall and infiltration, and conditions of 75 per cent turbulence, which amounted to a simplified study of the behaviour of a hydromechanic prototype. In 1942, work began in the United States on a co-operative project of the Public Roads Administration of the Federal Works :.gency and the Soil Conservation 15. Service of the Department of Agriculture, the object of which was to obtain basic data on the hydraulics of overland flow from paved and turfed surfaces. The results of the initial series of tests in this programme were reported by C.F. Izzard and M.T. Augustine (1943).

The experiments were carried out on a plot 6 ft wide and 72 ft long with a relatively smooth surface. Artificial rainfall was supplied from banks of type-F infiltrometer nozzles designed by the Soil Conservation Service (see section 2.2). The results presented by Izzard and Augustine included relationships between the amount of surface detention on the plot and the discharge from the. plot at various slopes and rainfall intensities, and equations for water surface profiles under equilibrium conditions. These equations were similar in form to those previously suggested by Horton, and were largely empirical. A further set of equations applicable to different types of surface were presented by W.I. Hicks (1944) in discussion.

A full mathematical treatment of the equation of motion of spatially-varied discharge over a sloping plane subjected to a constant rate of rainfall was given by G.H. Keulegan (1944). C.F. Izzard (1944) applied this equation to data from the project mentioned above, and obtained good agreement between measured and computed surface profiles under equilibrium flow conditions.

The final results from the Public Roads Administration/ Soil Conservation Service project were published in a paper by C.F. Izzard (1946). The principal feature of this paper was the presentation of a technique for synthesizing the overland flow hydrograph for any given constant intensity of rainfall. The method is applicable only if flow conditions are laminar and (according to the author) the.

* the names of units are abbreviated in accordance with the recommendations of B.S. 1991: part 1: 1954, letter symbols,signs and abbreviations, pp. 30-3. 16. product of rainfall intensity (in/h) and the length of overland flow (ft) does not exceed 500. Izzard showed that the rising limb of an overland flow hydrograph resulting from a constant intensity of rainfall could be adequately represented by a dimensionless chart giving the ratio of discharge at any time t less than the time to reach equilibrium conditions to the discharge at equilibrium. The recession side of the hydrograph was also found to be reproducible in the form of an empirical recession function. These dimensionless charts and graphs have been quoted widely in textbooks of hydraulics and hydrology, and need not be reproduced in detail again for the purpose of the present review. However, further reference may be made to works by R.K. Linsley, M.A. Kohler and J.L.H. Paulhus (1949,pp 275-82; 1959,pp209-11), American Society of Civil Engineers (1949,Pp92 -7) and Ven Te Chow (19591PP 543-6). More recent contributions in the same field have included papers by Dah-Cheng Woo and E.F. Brater (1962), Y.S. Yu and J.S. McNown (1964) and F.M. Henderson and R.A. Wooding (1964). Woo and Brater developed a more exact method of computing water surface profiles under equilibrium conditions. Yu and McNown presented a step-by-step method by which the run-off from the rainfall on an impervious surface could be predicted numerically. This method is capable of dealing with a wider range of conditions than previous treatments, and must be regarded as an outstanding and important contribution to knowledge. Henderson and Wooding approached the same physical situation as a kinematic wave problem, and presented a solution by the method of characteristics. Further bibliography on the same subject has been provided by Amorocho and Hart (loc.cit., 1965).

The contributions made by all the above-mentioned authors differ widely in both approach and emphasis. Their common 17. denominator is that where theory and experiment have been compared, the experimental data has been obtained by applying simulated rainfall onto a two-dimensional laboratory catchment. The transformation of rainfall into surface run-off has been studied in terms of detailed fluid mechanics as a steady or unsteady spatially-varied flow and not as a macroscopic natural process.

1.2. Model catchments.

The first model catchment study appears to have been the work of J.P. Mamisao (1952). The object of his study was the evaluation of the effect of cultural practices on the run-off from a 129-acre agricultural catchment in Western Iowa. A conformal scale model of the catchment was built up on a plaster board base with a mortar surface. A rainfall simulator capable of producing intensities of artificial rainfall up to 16 in/h was erected above the model. Provision was made for measuring outflow from the model by collecting the run-off at regular intervals in a series of small- capacity containers. Similitude criteria were developed as follows. Taking the run-off from a catchment to be affected firstly by the rainfall, and secondly by the condition of the catchment, twelve variables were chosen as pertinent to the analysis. These were (1) the rate of run -off, Q, (2) the rate of rainfall, I, (3) time, t, (4) length,. 1, (5) width, b, (6) height, h, (7) the roughness of the surface and resistance of the vegetation, r, (8) the infiltration capacity of the soil, i, (9) the density of water, p,(10) the viscosity,g (11) the surface tension,C, and (12) the acceleration due to gravity, g. Writing the run-off as a function of the other eleven variables, 18.

Q= fi (I,t,l,b,h,r,i,p,u,trI g) eq. 1.2.1. Buckingham's Pi theorem was applied to give nine Pi terms as expressed in the dimensionless equation

. 2 3 , = f 121 11, 1, P1 A r) eq. 1.2.2. 2 ` 1 h 1 I ut The first three terms on the right-hand side of equation 1.2.2 (the second of which has the structure of the Froude number) may be completely satisfied in a model. For reasons which are not at all clear from his writing., Mamisao chose to introduce a vertical scale distortion in the fourth term. As the model was based upon similarity between the ratio of inertia forces to gravitational forces (the Froude number) with the prototype, the sixth and seventh terms, having the form of the Reynolds number and the Weber number respectively, could not be satisfied simultaneously. In addition, variables such as the infiltration capacity and the surface roughness were obviously distorted in an impervious model. The prediction equation therefore contained a distortion factor, b:

QP 6. QM eq. 1.2.3. Ip.1p2 Im.1m2 Where the suffixes m and p denote model and prototype respectively. The factor 6 is in turn a function of five factors corresponding to the last five dimensionless terms on the right- hand side of equation 1.2.2, only the first of which is readily evaluated. The solution to the problem of assigning a value to b offered by Mamisao was to make the factor unity by adjusting the roughness distortion to compensate for the other four, i.e., the roughness of the model was to be modified until a correspondence was obtained between prototype and model values of Q and I. Mamisao also 19. chose to make the maximum intensity of storms measured over the prototype catchment correspond to the maximum of which the rainfall simulator was capable. Writing the ratio of prototype to model intensities of rainfall as M, and prototype to model lengths as n, equation 1.2.3 becomes 2 Qp = M.n . Qm eq. 1.2.4 a There were two reording raingauges on the prototype catchment. For the purpose of the study, the average of the catches from these gauges weighted with respect to area by the Thiessen method was assumed to fall uniformly over the catchment. A verification test of the model was carried out using data from three selected storms with roughly comparable frequencies of occurrence. The histogramme of rainfall for one of these storms has been plotted in figure 1.2.1 along with the corresponding hydrograph of discharge from the catchment. Also plotted in this figure are two discharge hydrographs obtained by applying equation 1.2.4 to measurements of discharge from the model corresponding to the same rainfall sequence. The first of the predicted hydrographs was obtained with the model in its original condition with a smooth mortar surface. As would be expected with an impervious model, the volume of run-off predicted by the model was considerably larger than that obtained on the prototype. The measured volume of run-off from the prototype was found to be 65 per cent of that predicted by the model. This figure compared well with the 62 per cent quoted for the proportion of rainfall on the prototype catchment which appeared as storm run-off. Another source of discrepancy was the very short time interval from the beginning of rainfall to the first peak of the predicted hydrograph compared with that of the prototype hydrograph. However, the general shape of the two was similarly, although corresponding rises '0 DISCHARGE HYDROGRAPH FROM MODEL WITH MORTAR SURFACE

0 HISTOGRAMME OF AVERAGE RAINFALL INTENSITY OVER 0 PROTOTYPE CATCHMENT.

DISCHARGE HYDROGRAPH FROM MODEL COVERED BY ONE IAYER OF DRY BURLAP.

MEASURED DISCHARGE HYDROGRAPH FROM PROTOTYPE CATCHMENT. •

) 19.00 19.30 20.00 2 .30 TIME SCALE. FIGURE. 1.2.1. Measured and predicted hydrographs from a model catchment study of a drainage basin in Western Iowa ( summarised from information provided by J. P. Mamisao , 1952.) 21. and falls in discharge were not reproduced at the same points on the time scale. Similar trends were observed with the second and third storms, one of which represented a different stage of growth, and both of which exhibited different rainfall patterns.

An obvious need was to provide additional roughness to delay the accretion side of the predicted hydrographs, and to retain a sufficient volume of the incident precipitation to lower the predicted peak rates of run-off. Three different treatments, consisting of the laying of various combinations of wet and dry layers of burlap over the surface of the model were tried. The most successful treatment was found to be one layer of dry material, and the predicted hydrograph obtained with the model modified in this manner has also been reproduced in figure 1.2.1.

Comparison between the hydrographs shows that this modification was only partially successful. The total volume of run- off from the catchment predicted by the model was 4.18 in, compared with the 4.42 in predicted by the unmodified model and the 2.87 in of the prototype hydrograph. The rising limb of the predicted hydrograph was delayed by the burlap, and showed improved agreement with that of the prototype hydrograph, but the recession side also appears to have been delayed, with the opposite result.

Mamisao concluded that the surface material would have had to have been modified to improve correspondence between predicted and prototype behaviour. Selected areas of additional roughness in certain parts of the model were also recommended as a solution to the problem of obtaining peaks at corresponding points on the time scale. Mamisao did not continue with the verification of the model, and so was unable to use the apparatus for quantitative hydrological studies. His further work on the effects of different geometries of terracing on the volume and time-distribution of run-off yielded only comparative results. 22. The work initiated by Mamisao does not appear to have been carried further until 1960, when an investigation based upon the same principles was started by Utah State University in co-operation with the U.S. Department of Agriculture, Agricultural Research Service. A comprehensive account of the apparatus developed for this project has recently been provided by D.L. Chery (1966). The model represented a 97.2 - acre semi-arid catchment in New gexico, which Chery described as rough, broken bad land. Nearly 77 per cent of the catchment is barren. The model was constructed from fibreglass to a length scale of 1:175, giving a time ratio by which one hour on the prototype catchment was equivalent to 4.5 minutes on the model. The rainfall simulator, which is described in greater detail in section 2.4, had far greater flexibility than that used by Mamisao, and was capable of reproducing different areal rainfall patterns and storm movements. A comparison between the principal scaling ratios used in both studies is given in table 1.2.1. TABLE 1.2.1 A comparison between the principal scaling ratios used in two model catchment experiments.

time author date of length ratio publication horizontal vertical ratio J.P. Mamisao 1952 1:450 1:240 1:21.21 D.L. Chery 1966 1:175 1:175 1:13.25

Chery also presented the results from a series of preliminary tests using a storm which occurred oter the prototype catchment on 4th October, 1946. This storm consisted of two pulses of essentially uniform rainfall intensity, the first of which (1.20 in/h for four minutes duration) occurred 45 minutes prior to the second and larger 23. burst (4.35 in/h for four minutes). The available records showed that the storm travelled over the area in a West-to-East direction, moving from the headwaters to the outfall of the catchment. These preliminary tests showed that no run-off could be obtained from the model when the scaled rainstorm was released onto a dry surface. The distilled water used was found to gather into small globules, scattered over the surface of the model. According to Chery, further tests indicated that at least 2250 cm3 of water could be retained in this manner. This volume would be equivalent to a depth of 1.2 inches over the whole of the prototype catchment. Two alternative operating procedures were tried in an attempt to eliminate this effect. The application of sufficient water to the model surface to compensate for the initial storage before reproducing the scaled storm provided a multi-peak model hydrograph totally different in form to the reduced prototype hydrograph (see figure 1.2.2). The total volume of run-off amounted to 69 per cent of the applied rainfall, compared with the 38 per cent obtained from the prototype. When the prototype intensities were magnified by a factor of 3 and applied to a dry model, the displacement in time of the run- off relative to the incidence of the storm was found to agree closely with that obtained by applying the appropriate scaling ratios to the prototype data. However, the distribution in time of the run-off from the model again exhibited a succession of peaks not produced by the prototype, and the total volume amounted to only 8 per cent of the rainfall. The agreement between the prototype and scaled-up model hydrographs presented by Mamisao appear all the more remarkable when compared with the results obtained by Chery. All the tests made by Mamisao were performed with prototype storms whose intensities were •

egd Input Roducad Prototypt. lipirogrcO, urface acme for all tests !ma Pulec rrzami tarots

12 Sealed input x) wet surface Ave. Runoff ratio = 69% Solid ling, flaw comma to all trials . 6 Input 4 2 0 7.1 U

14 Magnified Input Z 12 dry surtace Ava. Runoff u. 10 ratio„ a • 2c* 0 input

4 2 I 0 . . e 0 40 120 1-i0 200 240 280 320 360 400 TIME, IN SECONDS.

FIGURE .2.2. Measured and predicted hydrogrophs from a model catchment study of a drainage basin in New Mexico (after D. I.. Chery 1966 ) 25. magnified by a factor of M (see equation 1.2.4) as a matter of convenience in controlling variations in time. Furthermore, by using a topographic model having a vertical distortion of roughly 1:1.9, Mamisao was able to avoid the surface retention effect so apparent in Chery's results. As stated above, Mamisao did not provide the raY3ening which led to the introduction of a vertical distortion, and the present writer can only conclude that the choice was again made for experimental convenience.

Neither investigator pursued his studies beyond initial verification tests, and so the potential use of scale models in evaluating catchment behaviour remains a matter for personal conjecture. The theoretical basis of the method has been examined by Amorocho and Hart (loc. cit. 1965). The latter authors have rightly pointed out that (a) there is no assurance that the surface texture of a model may be adjusted over a sufficiently wide range of values for the correct correspondence between prototype and model behaviour to be obtained, and (b) once correspondence has been established, the system can only predict outflows, and cannot provide a replication of prototype behaviour in any other respect. The empirical treatment of the scaling laws which is necessary to provide a prediction equation, and the apparent need to apply separate scaling factors to the rainfall and the topographic model cast considerable doubt upon the validity of the whole method.

1.3. Prediction analysis prototypes. In a review of current methods in hydrological research, J. Amorocho and W.E. Hart (1964) commented upon the growth of two distinct and apparently conflicting approaches to the basic problem of establishing the relationship between rainfall and run-off. The first approach, which the authors referred to as "Physical 26. Hydrology", involves the investigation of the behaviour and inter- ' dependence of component phenomena within the hydrological cycle (see figure 1.3.1). The scope of individual studies may cover the working of only one component under a restricted range of conditions, but their long term objective is a complete synthesis of the cycle. Although the application of results to the solution of technological problems is recognised, such investigations are not made with the primary objective of providing data for this purpose. Interest is centred on the particular component process under study.

Physical hydrology is contrasted with another school of thought whose concern it is to provide solutions to engineering problems within limited periods of time. Historical sequences of measurements of only those variables within the hydrological cycle which appear significant to the overall result are used. Algebraic relationships are developed between these variables to provide a solution which it is hoped is applicable within the range of working conditions represented by the data. In this approach, to which Amorocho and Hart gave the name "System Investigation", interest is centred on the methods of solution rather than the behaviour of the physical processes involved.

Further consideration of the definition of system investigation given above soon shows that a strong interdependence ezists between the two approaches. Knowledge of the working of component processes is necessary for the selection of pertinent variables for system investigation. The interpretation of results from the latter also depends upon a clear understanding of the physical processes at work.

The system investigation approach arises logically from the unit-graph or unit hydrograph approach to determining streamflows from rainfall records proposed by L.K. Sherman (1932). The procedure MOiStWg Treatvor, oi* 140

bisPositioR Prccieet1611-

FIGURE.1.3.1. Schematic representation of the hydrological cycle ( after . D. Johnstone and W. P. Cross , 1949 ; P.11 ). Note that there is no significance in the. relative sizes of the segments. 28. originally described by Sherman was intended for use with daily rainfall totals published by the U.S. Weather Bureau and average daily flows taken from the Water Supply Papers of the U.S. Geological Survey, although the need to use time intervals less than 24 hours on smaller drainage basins than those considered in the paper was recognised by the author. The essential details of the method were contained in the first paragraph of Sherman's paper which read as follows:

"By making use of a single observed hydrograph, one due to a storm lasting one day, it is possible to compute for the same watershed the run-off history corresponding to a rainfall of any duration or degree of intensity. From the known hydrograph the "Unit" graph must be determined representing one inch of run-off from a 24 hour rainfall. The daily ordinates of the unit graph can then be combined in accordance with the variation in daily precipitation figures so as to show the run-off from a storm of any length."

The basic assumption upon which the method depends is that the unit hydrograph is a characteristic of the catchment. If, for example, a storm produces N inches of run-off from a fall lasting 24 hours, the run-off hydrograph would be obtained by multiplyirt the ordinates of the unit hydrograph by a factor of N. Similarly, the hydrograph of a storm which generated one inch of run-off on two successive days would be built up by adding the ordinates of two unit hydrographs, one of which was displaced from the other by 24 hours.

For such assumptions to hold, a number of other conditions are implied. The distribution of all storms over the catchment area must be either uniform or geometrically similar. Furthermore, the relationship between rainfall and run-off must not change with time. The validity of the former assumption that all rainfall distributions are space invariant decreases as the size of catchment increases. Orographic rainfall is said to produce consistent rainfall patterns 29. in some mountainous districts (see Linsley, Kohler and Paulhus, 1949, p.445). In contrast, the lack of validity in the latter condition that the rainfall/run-off relationship is time invariant is generally recognised. Sherman made some allowance for this fact by considering only the gross rainfall minus an allowance for infiltration and interception over the catchment area. The unit hydrograph is therefore the direct surface run-off produced by this "effective" (run-off producing) rainfall. The final streamflow hydrograph is obtained by superimposing the hydrograph of surface run-off upon a baseflow. The most important implied condition stems from the methods by which the run-off hydrograph from a specific storm event is built up from the unit hydrograph. The examples quoted above show that ordinates of run-off are assumed proportional to the volume of effective rainfall, and that the principle of superposition is taken to apply. To use the terminology introduced by J.E. Nash (1958), run-off is assumed to derive from rainfall by a "linear operation". In effect, the unit hydrograph provides a linear approximation to catchment behaviour in which such highly non-linear component processes as open-channel flow, overland flow and ground- water flow are allowed for by the arbitrary separation of total rainfall into effective rainfall, and streamflow into surface run-off and baseflow. The catchment is regarded as a "linear system" which produces an "output" of surface run-off from an "input" of effective rainfall. The system itself is a purely mathematical operation independent of catchment behaviour apart from the initial observations by which it is defined. Whether any or all these assumptions are justified in practic practice has been open to serious discussion since the method was first proposed. The difficulty in reaching a firm conclusion has 30. been accentuated by the almost complete absence of field studies in which the conditions have been adequately tested. The extent to which the results of an analysis approximate the behaviour of a natural catchment depends upon the degree of nonlinearity which exists in the natural system.

The assumption of linearity in the response of an artificial catchment was tested in a series of experiments carried out at the Hydraulics Research Station, Wallingford, in 1959 and described in an undated report by J.E. Nash. The meander area of the Station, a sand bed approximately 300 ft long, 100 ft wide and 4 ft deep was used as the catchment. Artificial rainfall was supplied from a system of oscillating spraylines, the details of which are described in section 2.5. The experiments began by bringing the sand bed to field capacity. The sprinklers were operated at approximately 0.1 in/h for between 24 and 48 hours, after which the discharge from the sand bed reached a constant value fractionally below the rainfall rate. The latter was then raised to a new constant value, and the test continued for another 24 hours until the discharge had become constant again. If the discharge Q is raised from a constant value Qi to another constant value Q2, the variation with time of the function

(t) = Qi- eq. 1.3.1 Q2- Q1

should be independent of the magnitude of Q2 - Q1 according to unit hydrograph theory. f(t) is generally referred to as the "S - curve", and in terms of system analysis may be considered as the response to a "step-function input". 31. The results from 19 test runs showed that the S - curves were totally unalike in shape. Nash commented that the curves obtained from nominally the same steps were almost as different from one another as the curves obtained from different steps. An attempt was made to study the differences between the S - curves by plotting the discharges 0.5 (Q1 + .2), 0.25 (3Q1 + Q2) and 0.25 (Q1 3Q2) against their times of occurrence. Again, from unit hydrograph theory, the times of occurrence of each should have been equal, and plotted as three vertical straight lines. Nash found a marked tendency for the points to be scattered about an oblique line with a 1:1 slope rather than any vertical.

The conditions under which these tests were carried out. was far from ideal. As the experiments were conducted in the open air, the spray patterns were subjected to wind interference. The diurr.al variations in evaporation rate during tests would provide another unestimated source of error in the analysis. Compaction of the sand surface by the impact of the artificial rainfall is yet another possibility. The results that were obtained led Nash to the conclusion that the time elements of the S - curve shortened with increasing discharge contrary to the implicit assumptions of unit hydrograph theory. The inaccuracies of the results prevented any further study of the shape of the S - curves.

It is not difficult to criticise these experiments. The rainfall simulator was made up from the cheapest variety of sprinkler irrigation equipment available, and no attempt was made to allow for the varying conditions inevitably encountered when per- forming tests in the open air over periods of from 24 to 72 hours. The added complication of a sandbed with an unknown degree of anisotropy was as unnecessary in testing unit hydrograph assumptions as was the areal extent of the artificial catchment. Greater 32. attention to these details would probably have improved the quality of the results.

Despite these criticisms, the present writer has been unable to find any account of similar experiments. Although tests were conducted in the open air, the artificial catchment may be considered to fall into the category of a laboratory prototype system. Because on analytical concept was examined rather than any detailed aspect of fluid motion, the catchment was used as a prediction analysis prototype rather than a hydromechanic prototype.

Evidence of essentially non-linear behaviour in a small natural catchment has been given in a paper by N.E. Minshall (1960). Working with data from a 27.2-acre cultivated catchment area in Illinois, Minshall derived a series of unit hydrographs from isolated storms of approximately the same duration but with widely varying intensities. By plotting values of the unit hydrograph peak and the time to peak against rainfall intensity, he was able to show that (a)the time to peak decreacalas the rainfall intensity increased, (b)the unit hydrograph peak did not increase in a 1:1 proportion with increase in rainfall intensity, and (c)that both of the above relationships were significantly different when the high intensity occurred at the beginning rather than at the end of the storm.

The unit hydrographs selected by Minshall to represent five different intensities of rainfall over the catchment have been reproduced in figure 1.3.2. Even when the inaccuracies arising from the calculation of loss rates in determining effective rainfall, and in separating baseflows from recorded streamflow hydrographs are taken into account, these results provide striking proof that the principles of proportionality and superposition are inapplicable to the catchment studied. MAY 27, 1948 (4-75 in/h )

1 SEPT. 21941 (2.65 inih ) 0 z 2 _-APRIL 17, 1941 (1,95 inn) ) LL 0 UJ --OCT. 22, 1941 (1.52 )

„....--JULY 20 , 1948 (0.95 in/h )

000,010 00 10 404 awaa telefeemsP"...... ,Artar.

0 20 40 60 80 120 140 TIME FROM BEGINNING OF EXCESS RAINFALL m n

FIGURE 1 . 3 . 2. Series of Unit Hydrographs corresponding to five different intensities of rainfall for a small catchment in Illinois (after N.E. Minshatt (1960); figure 6, p 30). 34. Since its conception, the unit hydrograph procedure has been the subject of incalculable man-years of study, debate and elaboration. A large proportion of this effort has concentrated on the development of mathematical refinements. The generalized theory of J.C.I. Dooge (1959), the application of the method of moments proposed by J.E. Nash (1959; 1960) and the use of harmonic analysis by T. O'Donnell (1960) have been significant among many others. However, the basic assumption of linearity implicit in unit hydrograph theory is a limitation which even the most sophisticated mathematics can do nothing to alter.

The employment of non-linear functions in predicting the response of a catchment area to rainfall would appear to form the obvious and logical alternative approach. Largely owing to their complexity, non-linear methods of analysis have been slow to develop, and their application to hydrological problems (see J. Amorocho and G.T. Orlob, 1961; J. Amorocho, 1963) has been a comparatively recent innovation. According to Amorocho and Hart (1964, p.316)

"In general, one outstanding characteristic of the processes of (general non-linear) analysis is that they permit relationships between partial inputs and partial outputs to be established independently, subject to certain conditions of mathematical continuity and boundedness. It is not necessary to satisfy physical continuity conditions among the total input, total output and inner storage."

The treatment of a hydrological system as one in which input and output are only partial forms of total input and total output respectively (i.e., an "open" system) has obvious advantages. The relationship between precipitation and streamflow may be evaluated without accounting for intermediate states of the hydrological cycle. In one of the first applications of non-linear analysis to hydrological systems, Amorocho and Orlob (loc.cit.1 1961) assumed 35. that the action of a non-linear system was equivalent to a summation of the actions of a number of elemental systems of progressively higher order. Having no field data to test their theory, the authors set up a prediction analysis prototype in the laboratory. This consisted of a simple two-dimensional rectangular basin with a sand and gravel surface which provided an elementary non-linear hydrological system from which inputs of artificial rainfall produced outputs in the form of run-off hydrographs. This apparatus was used to generate data against which the theory could be tested in the same way that Nash used data from the artificial catchment at Wallingford to examine the assumptions of linear analysis.

Details of the mathematics used by Amorocho and Orlob are incidental to the main purpose of the present review. However, in addition to their tests of individual step-function and square-pulse inputs, the authors presented results showing the response of their laboratory catchment to a succession of square-pulse inputs. One such result, which has also been quoted in the papers by Amorocho (1963) and Amorocho and Hart (1965), has been reproduced in figure 1.3.3. This figure shows the recorded outflow response to three 100- second pulses of equal intensity delivered at 50-second intervals. The predicted outflow obtained by superimposing the result from the first pulse on its own recession at the appropriate intervals is also shown. The latter curve underestimates the recorded peaks significantly, and does not reproduce the shape of the response at all closely.

This result serves to underline yet again the limitations of the well-established methods of linear analysis and the need for a fresh approadlto the problem. The development of non-linear analysis has presented the opportunity to fill this need, but such methods can 1.4 ACTUAL RUN ------LINEAR SUPERPOSITION 1.2 INITIAL RECESSION UNE // ./ 1•• / \ / / 1. / / / 1 / / \

I--

0.4

0. • mom. ••••• • •••••• au•••••••••• ••••••• ••••••• • 4 1 •••• • .••••• 0,11.E. • two a... 41•••••• ••••• ay.

40 80 120 160 200 240 280 320 360 400 440 480 TIME seconds

FIGURE 1. 3. 3 . The response of a small laboratory catchment to three square - pulse inputs of artificial rainfall of equal intensity and 100 seconds duration applied at 50 second intervals (after J.Amorocho and G.T . Ortob (1961) ; figure 31. p65 ) 37. contribute nothing to our understanding of the time-distribution of the hydrological processes involved in transforming rainfall into run-off. Considerable progress in the latter field of knowledge would be possible if the scope of laboratory catchment experiments were extended beyond the limited range of the classification proposed by Amorocho and Hart.

1.4 The microcatchment.

Once the assumption that rainfall patterns over a drainage basin are uniformly consistent or geometrically similar has been accepted, the shape of a run-off hydrograph from the area may be regarded as reflecting only the effects of certain characteristics of the catchment. Similarly, the shapes of hydrographs from catchments large enough for the effects of any local areal variations in rainfall intensity to be dampened out are determined solely by catchment characteristics. This logic has formed the basis of many methods for producing hydrographs for ungauged catchments, in which one or more parameters of the hydrographs from other basins in similar climatic areas have been correlated with one or more measurable catchment characteristics. A comprehensive account of such "Synthetic Unit Hydrograph" procedures has been given by D. Johnstone and W.P. Cross (1949, pp.212 -35).

P.E. Morgan and S.M. Johnston (1962) have given an interesting account of a study in which five such methods were applied to twelve catchments in Illinois between 10 and 101 square miles in area. The relative accuracies to which the methods reproduced unit hydrographs derived from recorded data were assessed. Their results showed that the estimated peak discharges ranged from 69 per cent below to 198 per cent above the derived unit hydrograph peaks according to the method used. The synthetic unit hydrograph 38. method developed specifically for Illinois did not give better results than the methods developed for other regions.

When the assumptions of unit hydrograph theory are added to the uncertainties of correlation analysis, the above results cannot be regarded as anything but commonplace. The fact remains that certain characteristics of a catchment have been found to exert a profound influence on its behaviour in times of flood. C.H. Dobbie and P.O. Wolf (1953) have given an account of an outstanding case. In their paper, the topographic features of the immature Lyn River catchment in Devon were discussed in relation to the catastrophic flood episode of August, 1952.

This catchment was described (loc.cit. p.529) as having "---- Gently rounded moors curving at ever increasing slopes down to streams which have carved deep valleys for themselves. The sides of the valleys are steep, and often precipitous, and never very far apart, so leaving little room for flood storage. The longitudinal slopes are steep, or moderately steep ----". In an appendix to a later paper, P.O. Wolf (1957) showed by the application of simple hydraulic conc,rts that the amount of surface storage was under- estimated, and the peak rate of flow overestimated unless the pronounced convexity of the catchment was taken into account. The Author commented that the Lynmouth catastrophe would have been even worse without the great breadth of the Exmoor plateaux.

Although the above example is exceptional in that the topography of the drainage basin is unusual for an English river, the evidence of catchment characteristics determining the magnitude and time-distribution of a flood event is clearly defined and typical of any area. To generalise, in the words of D.R. Dawdy and T.O'Donnell (1965, p.123), "The only reliable and accurate device for yielding the run-off resulting from a rainfall on a catchment is the catchment itself". 39. To study the time distribution of the various component phases of the hydrological cycle on natural catchments in relation to their surface topography, geometry and other hydraulic factors would present virtually insoluble problems in taking the necessary physical measurements. An alternative approach would be to investigate these same effects on laboratory catchments. With the intensity, duration and areal distribution of artificial rainfall controlled, the physical features of the laboratory catchment could be varied as required, and the different responses in outflow measured directly.

The operation of such laboratory catchments would not involve the application of similarity criteria. Whereas the prediction analysis prototypes used by Amorocho and his fellow investigators are simple, non-linear systems with controlled input parameters, the laboratory catchment experiments suggested above would involve the study of controlled catchment parameters. The latter type would be miniature catchments whose features could be varied to take the geometric and topographic forms of natural drainage basins. To distinguish between this type of laboratory catchment and those described in sections 1.1 - 3 above, the present writer proposes to refer to these miniature catchments as "Microcatchments."

The experiments would begin with the study of very simple cases in which the total volume of artifical rainfall applied to the microcatchzont would appear as direct run-off. In mathematical terms, the catchment would be a "closed system". The extension of studies to open systems could be undertaken once the basic case, which would correspond in all essential details to an urban catchment, had been fully understood.

If the classification of laboratory catchments proposed by Amorocho and Hart is re-examined in relation to the above discussion, Lfo. its restrictive nature is immediately apparent. In order to include the concept of microcatchments within the framework of their review, the present writer proposes that a third subsection be added under laboratory prototype systems to differentiate between the type of study outlined above and all previous work with laboratory catchments.

A problem which must be face immediately on beginning any laboratory catchment study is the choice of a suitable method of generating artificial storms. The available methods of simulating rainfall are therefore reviewed in the following chapter before further details of the specification for a microcatchment study are discussed in Chapter 3. 39. To study the time distribution of the various component phases of the hydrological cycle on natural catchments in relation to their surface topography, geometry and other hydraulic factors would present virtually insoluble problems in taking the necessary physical measurements. An alternative approach would be to investigate these same effects on laboratory catchments. With the intensity, duration and areal distribution of artificial rainfall controlled, the physical features of the laboratory catchment could be varied as required, and the different responses in outflow measured directly.

The experiments would begin with the study of very simple cases in which the total volume of artifical rainfall applied to the microcatchmont would appear as direct run-off. In mathematical terms, the catchment would be a "closed system". The extension of studies to open systems could be undertaken once the basic case, which would correspond in all essential details to an urban catchment, had been fully understood.

If the classification of laboratory catchments proposed by Amorocho and Hart is re-examined in relation to the above discussion, CHAPTER TWO 41.

The development of rainfall simulation as an experimental technique

2.1. Historical development.

The early development of research methods involving the use of artificial rainfall may be generally associated with the pioneer work on soil erosion problems in the United States of America.

The importance of natural rainfall as an agency in changing the physical properties of a soil was illustrated as early as 1874 in field experiments by a German scientist Ewald Wollny (see L.D. Bayer, 1938). The inconvenience of such experiments, which depend upon the occurrence of rainfall, with its highly variable properties of intensity and duration, is obvious. The early attempts to produce artificial rainfall under controlled conditions, both in the field and in the laboratory, were a logical development designed to overcome these difficulties.

According to C.O. Wisler and E.F. Brater (1959; p.111), even before World War I, R.E. Horton was using an apparatus in the determination of infiltration capacities of small plots which applied spray to an area in the manner of natural rainfall. However, it was not until the 1930s that references to investigations using such "artificial rainfall applicators" or "rainfall simulators" began to appear frequently in the technical press. Notable contributions were made by W.C. Lowdermilk (1930), M.L. Nichols and H.D. Sexton (1932), B.H. Hendrickson (1934) and J.H. Neal (1938).

A feature common to each of these investigations was the use of commercial sprinkler irrigation nozzles to generate the artificial rainfall. Nichols and Sexton reported examining a large number of such nozzles before finally adopting a system. Their comparison was 42.

based upon the relative depths of application sampled in small pans placed at regular intervals over the test area. Lowdermilk measured application depths in raingauges set up at various points over his installation, and used their readings to plot isohyetal maps for each test run from which estimates of the mean application rates were obtained.

The apparatus used by Neal consisted essentially of two spraylines, 15 ft in length and 0.5-in diameter with nozzles inserted at 9 - in centres. The nozzles were mounted so that the spray was thrown upwards before falling on to the test area. The lines were oscillated through an arc of up to 45 degrees every 2 - 4 seconds. In addition, they were moved forward one inch every 10 - 12 oscillations until a distance of 9 inches had been covered, whereupon the direction of movement was reversed. Both oscillation and horizontal movement were carried out manually.

The uniformity of distribution provided by this system was regarded as far from perfect by Neal. However, measurements of intensity of application given in his paper show that, by present-day- standards, his apparatus was quite successful. Table 2.1.1. shows tha'„ values of the H.S.P.A. uniformity coefficient calculated from these figures are remarkably high, and well within the accepted limits of uniformity (see Chapter 4).

In a description of further work involving the same apparatus, C.M. Woodruff (1947) stated that the sprinkler system had been re- designed with the nozzles oscillated by an electro-mechanical driving mechanism.

*see Chapter 4; the H.S.P.A. uniformity coefficient has a value of unity for absolutely uniform conditions, and lesser values for progressively more disturbed application patterns. 43. Table 2.1.1. Estimated uniformity coefficients for three different operating conditions in the experiments of J.H. Neal (1938).

average number sample estimate of uniformity rainfall of range standard coefficient intensity observations (in/h ) deviation- (in/h )

1.50 3 0.36 0.21 0.887 2.00 5 0.37 0.16 0.937 4.00 3 0.47 0.28 0.945

* taken from table 6 (p.7) of D.V. Lindley and J.C.P. Miller (1961).

It is apparent in all these early contributions that similarity between the artificial rainfall produced and natural rainfall was limited to the reproduction of a given intensity of application, regular in space only. At this time, little quantitative information was available on drop size distributions and the velocities of fall of drops in rainstorms. This lack of knowledge must be said to account for the use of what by modern standards is an elementary criterion. In fact, F.L. Duley and 0.E. Hays (1932) considered that their requirements were adequately met by careful use of a watering-can rather than by the development of a suitable system of nozzles.

During this period, scientists from both governmental agencies and university experimental stations began to devote increased attention to both direct measurement and indirect estimation of these additional rainfall characteristics and their effect on the behaviour of soils. In his introduction, Neal stated that "Since artificial rain was used in conducting these experiments, it was important to 44.

compare its characteristics with natural rain, especially in regard to the sizes and velocities of the respective drops." The only reference to measurements of the latter given by the same author was to the work of W.A. Bentley (1904), who conspicuously omitted to record intensities of rainfall in his investigation (see Chapter 8).

As part of his studies at the University of Missouri, Neal built an instrument, described in detail by J.H. Neal and L.D. Bayer (1937), which was designed to record the impact force of water drops directly. However, the authors were unable to perfect the apparatus, and Neal did not present any data on the relative behaviour of natural and artificial rains as he had originally intended. The U.S. Department of Agriculture also initiated a similar series of long-term experiments in the mid-1930s, and their studies were undoubtedly the most significant of any made in America at that time.

2.2 The U.S. Soil Conservation Service experiments.

In 1936, a group of U.S. Soil Conservation Service workers at the hydraulics laboratory of the National Bureau of Standards in Washington were commissioned to construct suitable sprinkling apparatus for the simulation of rainfall over experimental plots from 200 to 300 ft2 in area. The separate studies which this project entailed have been briefly sw)marised by D.A. Parsons (1943).

The project was planned in three phases. As there was an immediate need for such a device, phase one consisted of the selection and reproduction of the apparatus then in use which appeared to have the most desirable characteristics. The second and third phases, which run concurrently, involved the study of the drop size distributions and fall velocities of natural rainfall, and the construction of new devices to a tighter specification based upon this new information. Measurements of terminal velocities and the 45. variation in velocity with height of fall were reported by J.O. Laws 0 (1941). J,k. Laws and D.A. Parsons (1943) presented the results of a study of drop size distributions in rains of different intensity (see also Chapter 8). In addition, comparison tests were made of the erosion and infiltration properties of a standard soil subjected to sprays containing different ranges of drop sizes and fall velocities.

J.0. Laws (1940) reported on these comparison tests. Five different rainfall simulators, producing drop sizes ranging from 1-5 mm in diameter, were compared on the basis of the amount of erosion and infiltration resulting when each was applied separately to a tray of standard soil. Laws found that as the drop sizes increased from approximately 1.0 to 2.25 mm in diameter, the infiltration rate decreased by as much as 70 per cent, and the erosion losses (measured in terms of the cencentration of sediment in the run- off) increased by as much as 1200 per cent. These data showed con- clusively the importance of drop sizes in such studies, and underlined the requirement that rainfall simulators designed for that type of investigation should faithfully reproduce the correct drop spectra.

Of the new devices developed by the Soil Conservation Service, the first (type-B) was fitted with commercially-produced nozzles. The type-C apparatus, known as the "dripolator" or stalactometer", was a laboratory device which embodied an entirely different approach to the problem. The principal features of this type of apparatus, later described in detail by W.D. Ellison and W.H. Pomerene (1944), are fully discussed below.

The type-D apparatus also incorporated commercial nozzles. Similar equipment was used by E.L. Beutner, R.L. Gaebe and R.E. Horton (1940) in run-off and infiltration experiments in Arizona. The authors reported that the distribution of water was satisfactory, and that the drop sizes of the spray were comparable with those of natural rainfall. However, no quantitative measurements were published in 46. support of these statements.

The nozzles fitted to the type-E and type-F devices were developed in the laboratory by the Soil Conservation Service. C.F. Izzard (1942) described the type-F nozzles as consisting of ... an alternating series of discs with small orifices, enclosed and confined to definite positions by a cylindrical shell, which in turn is screwed into a threaded base designed for mounting on standard-type fittings. The base, in addition, acts as a housing for a standardised entrance arrangement, composed of a helix mounted rigidly within an entrance tube." The type-F apparatus was designed to produce a high-energy spray of low intensity with the minimum possible spray height. The nozzles were arranged to give an even distribution over a 6-ft wide area, with drops falling nearly vertically on impact.

The type-F design was undoubtedly the most successful of the Soil Conservation Service rainfall simulators. The apparatus was extensively employed for infiltration capacity measurements in the field (see H.G. Wilm, 1941; 1943). C.F. Izzard and M.T. Augustine (1943) used type-F nozzles in studying the hydraulics of run-off from impervious surfaces, as did W.N. Stammers and H.D. Ayers (1957). T.C. Peele and O.W. Beale (1955) carried out erosion experiments using similar equipment.

The type-F infiltrometer, designed for plots 72 ft2 in area, was cumbersome and expensive to operate, and a seventh device, designated type-FA, was also produced, having a working area of only 12 in by 30 in. According to the American Society of Civil Engineers (1949; p.42) this apparatus was built primarily to reduce working costs. Type-F nozzles were used, but the working pressure was altered, entirely changing the properties of the spray. 47. Such changes are the main weakness of this type of apparatus, for, as drop sizes decrease, the intensity of the simulated rainfall increase. The higher pressures necessary to produce high rates of application lower the chance of occurrence of larger diameter drops. For experiments in which drop sizes and the velocity of fall of drops were included as specific independent variables, other methods were subsequently developed to overcome this difficulty. Where spray nozzles and sprinklers continued to be used, measurements of drop size distribution were taken using standard techniques (see Chapter 8). Estimates of the velocities of fall of drops were made from the data published by Laws in 1941.

To summarise, the increased amount of quantitative information available as a direct result of the Soil Conservation Service's activities between 1936 and 1943 led to more precise standards for the production of artificial rainfall. The methods devised to meet these standards may be considered to fall into three distinct categories, namely -

1.the dripolator, or stalg%tometer type (following on from the S.C.S. type-C infiltrometer), 2. the use of large numbers of capillary tubes or hypodermic needles, each producing streams of individual drops, and 3. the use of readily-available commercial irrigation equipment.

The development of these methods over the last 25 years is reviewed in the following sections of this Chapter.

2.3 The dripolator, or ntalactometer-type of rainfall simulator.

As described above,this type of rainfall simulator was evolved during the Soil Conservation Service experiments in 1937, and was designated type-C in their laboratory programme. A modified version of this apparatus was constructed two years later at 48. Coshocton, Ohio, and subsequently described by Ellison and Pomerene (loc. cit., 1944).

The al:paratus was specifical.y designed so that the effects of different drop sizes, drop velocities and intensities of application could be studied independently. The artificial rain was formed in two stages. In the first, water was supplied from a galvaiized iron tank, 6 ft by 7 ft in plan. Half-inch diameter holes were drilled at 4-in centres in the bottom of the tank, and brass plates were soldered over each. In the centre of the brass plates, small holes were drilled and reamed to 0.042 in diameter. The depth of water in the tank was controlled by an adjustable overflow weir, and maintained by a constant supply. The intensity of application was changed by raising or lowering this weir, and further adjustments could be made by inserting copper wires in the 0.042-in diameter holes.

The water dripping from the supply tank was intercepted by the second stage of the apparatus which consisted of an inter- changeable screen of chicken wire covered with cheese cloth. The cloth was loosely laid over the screen, and depressed into each opening in the wire mesh. Lengths of woollen yarn were hung from the cheese cloth in the centre of each depression. Only 3.5 and 5.1 mm diameter drops were produced, the sizes of the wire mesh and the wool yarn being different for each. Variations in the size of drops were claimed to be within 6 per cent. The screen was arranged to lie on a plane parallel to the soil surface, and was kept in constant motion by a motor, ensuring a random scatter of drops over the test area. Intensities of from 4.8 to 14.8 in/h were obtainable.

Variations in the velocity of fall of the drops were obtained by changing the height of the screen above the soil surface. Estimates of the velocities of fall of the drops over different heights were 49. taken from the results reported by Laws in 1941. The duration of rainfall was controlled by the removal and replacement of a curtain of oilcloth from under the screen.

L. Sreenivas, J.R. Johnston and H.O. Hill (1947) used a similar, but smaller apparatus in which the supply was a convex shower nozzle, and the interceptor screen was not oscillated. The entire simulator was portable, and the area covered 9 ft2.

J.K. Basu and N.B. Puranik (1954) described another apparatus based upon the same principles. A similar sprinkling system to that described by Sreenivas et al was used. Three spherical shower nozzles were placed symmetrically above a plot 9 ft long and 3 ft wide, and supplied from a constant head tank. Two interceptor screens were suspended one below the other, some 18-24 in below the shower nozzles. These screens were made from expanded metal held in a wooden frame, 12 ft long and 4 ft wide, with a sheet of mosquito- net cloth attached to the lower sides of the screens, which were made convex towards the nozzles to avoid pooling. The frames were arranged to oscillate in mutually-opposing directions through an amplitude of 15 inches at a constant rate of 40 per minute controlled manually. The distance between the frames and the soil surface was maintained at 7 feet.

The use of two interceptor screens assisted the formation of a mixed droplet pattern, measurements of which were obtained using the filter paper technique (see section 8.2). Figures for intensities of application over 13 separate test runs quoted by the authors showed an average value of 3.38 in/h, with a maximum of 3.65 and a minimum of 3.07 in/h. Measurements of application depths at nine separate points over the plot during one test gave an avorage application rate of 3.87 in/h, and a sample range of 2.19 in/h. A similar analysis to that carried out for the data of Neal in section 2.1 above showed that 50. these figures are equivalent to an H.S.P.A. uniformity coefficient of 0.848.

The rainfall simulator used by L.J. Goodman (1952) in erosion-control experiments at Ohio State University was also, in certain features, identical with the apparatus described by Ellison and Pomerene. A smaller drip screen, measuring 5 ft by 5 ft was used, but the 2-in wire mesh and lengths of cotton yarn were the same size as those employed to produce 5.1 mm drops with the modified dripolator. A comparable drop size of 5.04 mm was reported by Goodman.

In contrast to the method used in the earlier apparatus, water was sprayed onto the drip screen from four garden nozzles held 12 inches above the screen on a 3/4-in diameter pipe frame. This frame was formed in a closed circuit, 5 feet square, with the nozzles mounted at the mid-points of each side. Rates of application of from 3 to 12 in/h were produced by varying supply pressure and the number of nozzles in use. The drops were allowed to fall 14 feet on to the target, which consisted of a series of samples arranged on the circumference of a rotating table. The drip screen was oscillated during tests, and exposure was controlled by a similar arrangement to that used by Ellison and Pomerene.

Dah-Cheng Woo and E.F. Brater (1962) adopted Goodman's design of nozzle in their investigation of water surface profiles during spatially-varied flow. A flume, 29 ft 7 in long and 6.25 in wide, was used for their experiments, and artificial rainfall was supplied from a dripolator-type apparatus. A drip screen with a 2 in wire mesh, covering an area 35 ft 2 in long and 2 ft 4 in wide was suspended horizontally above the flume. 33 nozzles were arranged at 4-ft centres, 13 inches above the screen, and operated at a pressure of 401b/in2. Intensities were changed by varying only the number of nozzles in use. The supply system consisted of four feeders arranged 51. so that a "light rain" (1.65 in/h ) was produced using one pipe supplying one quatter of the nozzles, a "medium rain" (2.95 in/h ) two pipes supplying half, and a "heavy rain" (5.04 in/h ) four pipes 2 using all nozzles. A pressure difference of 2 lb/in . was recorded between the first and last nozzles on any feeder. 4.5 mm diameter drops were produced, falling through distances of from 6 ft 5 in to 4 ft 8 in depending upon the slope of the flume.

2.4 Rainfall simulators involving the use of capillary tubes or hypodermic needles.

A large number of investigators have preferred to use batteries of hypodermic needles or capillary tubes as the drop- producing components of their rainfall simulators. Among the first were P.C. Ekern and R.J. Muckenhirn (1947), who carried out a laboratory investigation into the amount of sand transported at various slopes by water drops of known size and frequency.

Ekern and Muckenhirn mounted 36 hypodermic needles in the bottom of an aluminium container, with one needle to each square inch of area. The needles, which were 2.5 inches long and 22 gauge, produced drops of 2.75 mm diameter. Larger drop sizes up to 5.8 mm were obtained by enclosing the needles with glass tubing of appropriate diameter. The rate of flow through the needles was regulated by altering the depth of water in the container. Constant depths were maintained by providing a gravity overflow at the desired height, and supplying water in excess of the application rate. Distilled water at room temperature was used to approximate constant viscosity.

In order to obtain substantially correct terminal velocities, the drops were allowed to fall 35 feet before striking the target area. The authors noted that air currents caused a certain amount of deflection of the drops from a vertical path. This movement was 52. considered to be sufficient to ensure a random pattern of drops on the sand surface, and eliminated any need to rotate the needles or the target area. As the latter was extremely small (3 in by 6 in), the air currents also tended to reduce the intensity of application by scattering the drops over a wider area. The small secondary droplets, formed when large drops break away from the tip of a fine bore tube and sometimes referred to as Plateau's spherules (see V.N. Kelkar, 1959; p.127), were also found to drift outside the target area, further reducing this figure. Measurements of the intensity of application were made with a standard raingauge. Average figures for 6-minute periods before and after each test were taken, and values expressed to the nearest 0.1 in/h. Intensities of from 1.3 to 5.0 in/h were produced with this apparatus

The rainfall simulator used by J.P. Mamisao (1952) in his model catchment experiments was designed to cover an area approximately 8 feet by 4 feet and incorporated a much larger number of capillary tube "jets". These jets, of which 637 were used in the device, consisted of 3-in lengths of capillary tubing, 0.067 inches in internal diameter, into which lengths of 0.052-in diameter copper wire had been inserted. Preliminary studies had shown that the discharge of the capillary tubes was excessive even under very low pressures without the wire. The jets were mounted in rubber stoppers which were inserted into 9/16-in diameter holes in the bottom of a supply tank at 2.5 by 2.5-in centres.

The supply tank was supported 24 inches above the catchment model, and consisted essentially of two steel plates, approximately 5 ft 3 in wide and 8 ft long, separated by lengths of 2x1x1/4-in channel. 925 holes were bored in the lower plate to take the rainfall jets. Those which did not carry jets were sealed with plain rubber stoppers. The upper plate carried five 0.5-in diameter glass stand- 53. pipes to release entrapped air from the tank. Heads were measured on a one-inch diameter glass standpipe located at the opposite side of the tank to the supply. Rapid changes in the intensity of application were made possible by manipulating supply and overflow valves. A water meter was used in the calibration of intensity of application against head. Figures of from 1.27 to 15.95 in/h were obtained over a range of heads of from i.03 to 36.03 inches of water.

The principal features of the rainfall simulator designed by Mamisao were adopted by J.E. Adams (1956) in developing a portable rainfall simulator infiltrometer. This apparatus, later described in a paper by J.E. Adams, D. Kirkham and D.R. Nielsen (1957), was small enough to be carried, set up and operated by one person.

Drops were formed by one-inch lengths of glass capillary tubing of 0.060-inch internal diameter, inside which lengths of . 0.040-in diameter 80-20 nickel-chromium alloy wire were supported. The wire assisted in the formation of the drops, which were found to have an average size of 5.56-mm diameter. 100 such capillary tubes were mounted in the base of a 5.75-in diameter supply tank, one being on the axis, and the rest on concentric circles 0.5 inches apart. Water was supplied to this tank from a one-litre reservoir. A pressure regulator controlled the delivery rate from the reservoir to the supply tank.

The supply tank was located coaxially with, and on top of a wind shield one metre above the soil surface. According to the data presented by Laws in 1941 and later summarised by P.C. Ekern (1953), after falling through this distance, the simulated rain would possess a kinetic energy equivalent to a natural rainfall of 3.44 mm average drop diameter falling at terminal velocity. Using empirical formulae published by A.C. Best (1950a), Ekern calculated that a medium-volume drop diameter (as defined in section 8.4) of 3.47 mm corresponded to 54. a natural rainfall intensity of 4 in/h, and so in all experiments the pressure regulator was adjusted to give this rate of application.

A further design of rainfall simulator in which lengths of capillary tubing were used to form the drops has been described by C.K. Mutchler and W.C. Moldenhauer (1963). This design was also prepared in connection with a project concerned with the erodibility of soilr. The specification for the apparatus, compiled by a committee of experts in 1958, included the following points:

1. different sizes of small-bore stainless steel tubing, and hydro- static-head variations were to be used to control drop sizes and the rate of drop formation, 2. the applicator was to be "doughnut-shaped", and was to rotate at approximately 1 rev/min, 3. distilled water was to be used, and 4. sets of tubes to be installed with their tops at different elevations, so that higher intensities could be produced by increasing the head of water in the applicator to cover more tubes.

Before building the applicator an extensive investigation was carried out to find a suitable design of drop-former. A large amount of data was obtained on the sizes of drops delivered from various diameters of small-bore tubing under different flow rates. The design of drop-former finally adopted consisted of 4 one-inch lengths of hypodermic tubing, 19, 14, 12 and 9 gauge respectively, telescoped so that the smaller sizes overlapped the next larger by 3(4-inch.

The whole apparatus was mounted on a vertical one-inch diameter shaft some 8 to 10 feet above laboratory floor level. The applicator unit, in which the drop-formers were located was carried on radial arms attached to a seamless metal sleeve running in bearings on the shaft. The unit was divided into 8 triangular-shaped sections, giving the applicator the appearance of one large octagonal tank. A 55. water-supply tank was mounted on the sleeve above the applicator, and an overflow tank was attached to the shaft below it. The operation of the apparatus was only briefly described by the authors, but from diagrams and photographs given in their paper it would appear that both water-supply tank and applicator were rotated by an electric motor working through a speed reducer. The choice of a speed of rotation of one rev/min was stated to be completely arbitrary.

The authors attempted to provide a uniform distribution of drops by careful spacing of the drop-formers, and by rotating the applicator. The areal density of the drop-formers was calculated from their discharge characteristics and the desired application rate. The applicator was then divided into annuli of equal area with 8 drop- formers located in each, one to each section of the unit.

Another investigation of rainfall/run-off relationships, similar in both approach and design of equipment to that reported by Mamisao, has recently been concluded at Utah State University. The principal features of this work have been described by D.L. Chery (1966).

The catchment model occupied an area roughly 22 feet long and 10 feet wide. The rainfall simulator was divided into eleven independently-operated modules, each covering approximately the same area. Each module had 676 uniformly-positioned plastic tubes, 24 inches in length and 0.011-in internal diameter, located at 2-in centres and supplied from four brass distribution heads. Flow to the distribution heads was governed by small positive displacement pumps, each of which was driven by a 1/12 hp d.c. motor, and controlled by a potentiometer circuit. A "storm-programmer" was fitted to the apparatus which automatically switched different potentiometer settings into the motor controllers, thereby changing the intensity of the rainfall. 56. At the time of writing, the University of Illinois is also beginning an investigation on catchment hydraulics. The method of producing artificial rainfall adopted at Illinois has been described by Ven Te Chow and T.E. Harbaugh (1965). A modular type of construction has been employed. An individual unit consists of an air-tight fibreglass box, 24 inches square and one inch deep. 576 polyethylene tubes of 0.023-in internal diameter are positioned at one-inch centres in the bottom face of the unit, which is supplied from a 3/8-in opening in the centre of the top face. Each module represents the smallest area within which the rate of application can be varied. Chow and Harbaugh stated that 100 such modules, covering an area 40 feet square, are to be employed in the final experimentation. Instantaneous reaction to changes in inflow, corresponding to rainfall intensities of from 0.75 to 13.0 in/h, has been claimed for this apparatus.

2.5 Rainfall simulators incorporating commercially-available nozzles or sprinkler irrigation equipment.

Restrictions on drop size distributions and the velocities of fall of drops do not apply to all types of experiment in which rainfall simulation plays a part. For example, E.C. Childs (1953) has described a laboratory used by the Unit of Soil Physics at Cambridge University for studies of the flow in porous media. This installation consists essentially of a large tank, 33 feet square with an average depth of 5 feet, containing low-solubility Leighton Buzzard sand, to which artificial rainfall is applied from an overhead spray system at constant pressure. Flow problems with known boundary conditions in a structured soil may be solved by experiments with the structureless sand bed in the laboratory, provided that the same boundary conditions are reproduced and a condition of transference is satisfied. This condition is that the ratio of permeability to the velocity of flow at corresponding points must be the same in each case (see E.C. Childs, 1943). 57.

The use of a uniform sand medium avoids complications caused by the inhomogeneity of structured materials. Also, the sand bed requires proportionally higher flow velocities to reproduce a given flow net because of its permeability. The rates of simulated rainfall are correspondingly higher, and their uniformity and reproductivity of application are easier to control than at lower rates. Four separate grids of nozzles, each slightly offset from the other three, are used to provide the artificial rain. The nozzles are arranged in a square-mesh pattern at 50-in centres at a height of 8 ft 4 in above the sand surface. The grids provide application rates of 10.6, 4.6, 2.5 and 1.9 in/h respectively at working pressure. With this system, a range of from 1.9 to 19.6 in/h is produced in 15 separate stages. Further control is provided by regulating valves in each grid supply. A constant head of 35 feet is available at the nozzles from a 1000-gallon capacity water tower. Provisions have been made to subdivide the main tank into areas 22 feet square and 11 feet square, and valves have been included in the grid supply which reduce the size of the nozzle networks to give a proportional areal coverage.

The nozzles employed were adapted from a commercial swirl- type pattern. Under a working pressure of 35 feet of water, these nozzles were found to give an extremely fine spray which hardly com- pacted the sand surface. As the main emphasis of the studies was on the behaviour of flow within the sand bed, the important rainfall characteristics were the rates of application, and the uniformity and reproductivity of the depths of water applied.

An apparatus installed at the Road Research Laboratory, Harmondsworth was designed on similar considerations (see L.H. Watkins, 1963). There, the hydraulics of run-off from road surfaces was under study on a tilting platform, 36 feet long and 15 feet wide, to which artificial rainfall was applied from a system of spray bars. Two 58. identical sets of 5 bars were used to produce a range of application rates from 0.5 to 7.5 in/h. Vehicles could be driven over the platform when required, and the spraybars were extended some distance on either side of the platform so that cars arrived at the test section with wet tyres.

Oscillating spraylines were used by J.E. Nash during a series of catchment experiments carried out in the meander area of the Hydraulics Research Station at Wallingford during October and November, 1959. An account of this work, which was undertaken primarily to provide information on the linearity of response of an artificial catchment, was given in an undated H.R.S. report by Nash.

The meander area was 300 feet in length and 100 feet wide, and contained sand to a depth of 4 feet. The bed and enclosing banks of the area were formed from a reasonably watertight mixture of clay with some chalk. A drainage system was laid in the sand bed, and outflow measurements were made by means of a V-notch weir. Commercial reaction- driven oscillating spraylines were supported on metal stands at 40-ft centres across the area. Application rates up to one in/h were supplied from groups of nozzles mounted on the spraylines at 24Hin centres. The intensities of application were found to be constant, but the rate could only be altered by changing the nozzles, a procedure taking 20 minutes for all eight lines.

During the last twelve years, rainfall simulators have also been employed for investigations into the effects of various irrigation treatments on crop production. One of the first of these "precision plot irrigators" was described in an undated report by A.G.M. Bean, E.J. Winter and D.A. Wells. This particular apparatus was built for the National Vegetable Research Station at Wellesbourne by the National Institute of Agricultural Engineering. A plot size of 16 feet by 16 feet was chosen, with a minimum crop spacing of 9 inches by 9 inches. 59. An application rate not exceeding 0.25 in/h, distributed as uniformly as possible over each 9-inch square, was required. In addition, a tolerance of a: 2.5 per cent deviation from the mean application depth was specified.

The a::ove requirements could not be met by readily-available commercial equipment. Oscillating spraylines would not give such an accurate application because of the tendency for spray to drift under all but the calmest of field conditions. Rotating irrigation sprinklers are known to be affected similarly, and so a travelling nozzle line, carrying 192 trickle irrigation nozzles, moving across the plot on rails placed high enough to clear the crop, was adopted.

Under a pressure of 4 feet of water, the nozzles delivered a slow stream of large drops with little dispersion at a'rate of 0.25 gal/h. A spacing of one-inch centres was chosen. The sizes of drops were reduced to reasonable proportions by hanging a loop of copper wire to each nozzle. The line was driven across the plot at a speed of 15 in/min by a winch unit powered by a variable-speed electric motor., With the working pressure adjusted to give the above discharge from each nozzle, and the line travelling at this apeed, approximately 5/64- inch of water was applied on each 16-foot traverse. This figure was equivalent to an application rate in excess of that specified, but an operating technique was later devised to overcome this defect. A uniformity of application of 98 per cent on any 9-inch length along the line was claimed for this device.

A similar plot irrigator has been described by G.N. Sparrow, R.L. Carter and J.R. Stansell (1958). Their apparatus, used for experimental irrigation of tobacco in Georgia, was designed for much larger plots measuring 22 ft 6 in by 52 ft.

A spray boom 52 ft in length was suspended from a power-driven 6o. carriage running along a fixed, horizontal supporting beam. The beam spanned the shorter dimension of the plots in a direction normal to the boom at a height of 10 ft above the soil surface. The boom extended 26 ft on either side of a vertical pipe section serving both for water supply and as a suspension. The pipe was attached to the carriage by screw clamps which facilitated adjustments in the height of the spray boom. The carriage was powered by a one hp petrol engine, and the drive so arranged that the direction of movement was reversed automatically at the end of each traverse.

The spray boom carried 32 cpmmercial nozzles at 20-in centres, mounted so that the spray was ejected vertically downwards to minimize wind interference. The application Lrate was altered by changing the size of the nozzle orifices or by varying the water pressure. As the nozzles were designed for plant spraying, the force of the spray was not sufficient to cause damage to the crops. No quantitative measurements of uniformity of application were presented, but the authors noted that there were slight differences between depths recorded under a nozzle, and those recorded directly between nozzles. The variations were found to conform to a regular pattern, and were not considered to be serious.

Another more elaborate apparatus for use in soil erosion and run-off studies, which had many features similar to the Georgia irrigator, was developed by L.D. Meyer and D.L. McCune (1958). After extensive testing of commercial spray nozzles, sprinkler irrigation equipment and nozzles used on existing rainfall simulators, nozzles similar to those used by Sparrow et al were selected.

These nozzles produced an elliptical shape of spray pattern which decreased in intensity with increasing distance from the centre. Overlapping of adjacent patterns was necessary to obtain a reasonable intensity disleibution, and spacings of 5 feet parallel to and 6 feet 61. along the larger dimension of the individual spray patterns were adopted. Owing to the high flow rates of these nozzles at the adopted working pressure, arrangements were made to cut out each nozzle intermittently during an application. Intensities of 2,5 and 5.0 in/h were obtained with each nozzle spraying during only 20 and 40 per cent of the time respectively. In addition, the areal coVerage of the apparatus was increased by moving the nozzles backwards and forwards across the slope of the plots in a direction along the larger dimension of the spray pattern. The nozzles were positioned 8 feet above the plot and sprayed vertically downwards, as in the Georgia irrigator, to minimise wind distortion.

The above requirements for the operation of the chosen nozzles led to an interesting, but complex design of simulator. One basic unit of the apparatus covered an effective area 18 feet across and 15 feet down the slope of a plot. This area was obtained by using four rows of three nozzles mounted on a carriage moving the nozzles 6 feet during each complete half-cycle. The wheels of the carriage ran in channels attached to two I-beams, 22 ft long, joined by 10-ft lengths of angle and supported 7 ft 6 in above the plots on adjustable pipe legs. Aluminium was used for all parts of the frame and carriage for ease of handling.

3/4-in solenoid valves were used to control the supply to each of two sets of three nozzles in alternate rows of the unit. The nozzles began to operate immediately after the carriage reversed direction, sprayed over six feet and cut out before the carriage reversed direction again for the return trip. For an intensity of 2.5 in/h, alternate valves opened during alternate movements across the plot in one direction, whereas for 5.0 in/h, both operated together during one complete half-cycle. None of the nozzles discharged during the return trip, or when the carriage reversed direction at the extremities of its movement. The valves were controlled by DPST relays activated 62.

by the driving mechanism. Waste valves opened when the feed valves closed so that constant rates of flow were maintained. The variation in application rate within the 5 feet between rows of nozzles was reported to be less than 20 per cent. Further units could be added to the first to increase the area covered. Each additional upslope unit covered 20 feet as the adjacent outer rows of the units supplied the 5 feet in between them. The timing of the carriages of successive downhill units was staggered to avoid any unduly heavy forces on the frame caused by their simultaneous reversal. Two units required 25 and 50 gal/min to produce intensities of 2.5 and 5.0 in/h respectively. It is interesting to note that with this design of apparatus, two units have the same instantaneous water requirements as one operating alone. Meyer and McCune (loc.cit., 1958;p.664) presented a graphical comparison between the drop size characteristics of the spray from the apparatus and those of a natural rainfall of the same intensity. The median-volume drop diameter of the drop size distribution provided by the nozzles was shown to be fractionally smaller than that measured in a natural rainfall of 2.5 in/h by Laws and Parsons (see section 2.2). The nozzles gave a larger proportion of drops less than roughly 2.75 mm diameter, but a smaller proportion larger than the same figure. The kinetic energy of the spray was stated to be approximately 75 per cent of that calculated for a natural rainfall of the same intensity. These figures were considered to be satisfactory for most comparative studies. In subsequent papers, L.D. Meyer (1960) and L.D. Meyer and J.V. Mannering (1960) reported that 12 units of the apparatus, collectively referred to as the "rainulatorn, had been constructed. A specification and detail drawings were later provided by 63.

L.F. Hermomeier, L.D. Meyer, A.P. Barnett and R.A. Young (1963). Although the rainulator has proved to be a valuable aid to soil erosion research in the United States, N.P. Swanson (1965) has recently noted that the amount of time and effort required to move the apparatus from one place to another can be a serious problem. Accordingly, the U.S. Department of Agriculture have developed a smaller, less complex trailer-mounted rainfall simulator for experiments involving large numbers of plots. A full description of this device was provided by Swanson (loc. cit.) The type of nozzle chosen for the rainulator was also incorporated into the new apparatus. 30 nozzles were attached to ten 25-ft long booms rotating about a central stem supported on a trailer. The nozzles were positioned to spray directly downwards, and orientated so that the major axes of their elliptical application patterns were parallel to the axes of the booms upon which they were mounted. There were two nozzles at a radius of 5 feet, four at 10 feet, six at 15 feet, eight at 20 feet and ten at a radius of 25 feet of. from the axis/rotation. The stem and supporting structure were adapted from a commercially-available rotating boom irrigation sprinkler. The speed of rotation was maintained at 3.5 to 4.0 rev/ min by a small air-cooled engine.

This device was designed for simultaneous use on two 35-ft long plots whose combined overall width was not more than 40 feet. As the track of the trailer was eight feet, the plots had to be not less than nine feet apart to provide the necessary clearance for the wheels. Two units could be used to cover plots up to 75 feet in length. The booms were maintained in a horizontal position to avoid pressure differences at the nozzles. At the stem, their clearance was 9 feet.

An intensity of application of 5.0 in/h was provided by using 64. all 30 nozzles spraying continuously. 2.5 in/h was obtained by closing down half the number by means of manually-operated valves mounted immediately upstream of each nozzle. These intensities corresponded to flow rates of 130 and 65 gal/min respectively at a 2 delivery pressure of between 15 and 20 lb/in .

G.D. Bubenzer and L.D. Meyer (1965) have provided an account of another rainfall simulator using the same type of nozzles. This apparatus was designed specifically for laboratory use on plots 2 feet wide and 10 feet in length. Three nozzles were mounted at 5-ft intervals, 8 feet above the plot. The desired high-energy spray could only be obtained at a reasonable intensity of application by oscillating the nozzles across the width of the plot so that most of their discharge fell outside the test area. The plot was surrounded by metal shields to remove the excess spray.

The oscillating mechanism was similar to an eccentric drive with a delay between successive half-cycles. Because each nozzle crossed the plot every half-second, the time intervals without simulated rainfall were extremely short, and the different fall velocities of the different sizes of drops ensured almost continuous application. The rainfall intensity was changed by altering either the nozzle capacity or the critical dimensions of the driving mechanism. Application rates in the region of 1.5 in/h were produced with the 2 nozzles operating at 6 lb/in .

A.R. Bertrand and J.F. Parr (1960) also used standard commercial nozzles in developing a portable sprinkling infiltrometer at Purdue University. A specification was compiled involving both the uniform distribution of sprayover a plot and adjacent buffer area, and the production of realistic drop size distributions and drop velocities comparable with natural rainfall. Initial attention was concentrated on finding a nozzle producing a reasonably uniform spray distribution. 65.

24 nozzles were examined under laboratory conditions at various heights and working pressures. The nozzles were orientated to spray directly downwards, and uniformity was assessed on the basis of depth measurements with a grid of cans placed at one-foot intervals under the nozzles. Six of these nozzles were found to provide satisfactory intensities of application with reasonable uniformity in distribution, and were subjected to further tests involving measurements of drop sizes and drop velocities.

Drop size distributions were evaluated by the flour method as described by Laws and Parsons (see Chapter 8). Drop velocities were estimated from physical relationships based upon measurements of the average height to which drops rose with the nozzles spraying vertically upwards. Three nozzles with the properties outlined in table 2.5.1 were finally selected. An additional column, giving an estimate of the H.S.P.A uniformity coefficient based upon the assumption of 9 readings at one-foot centres within the 4-ft square area, has been added to the original data. These figures are seen to exceed 0.96, indicating that a high degree of uniformity was obtained.

Table 2.5.1 Summary of properties of nozzles used by A.R. Bertrand and J.F. Parr (1960) for the Purdue sprinkling infiltrometer (after ibid, p.436).

nozzle nozzle spray intensity off % Variation H.S.P.A. type pressure diameter application over 4-ft uniformity (lb/in2) (ft) (in/h ) sq. area coefficient, 4 4 7LA 6 13.6 4.67 4.04 0.978 53 6 9.6 2.5o 6.54 0.965 5D 9 10.0 3.25 7.28 0.961

The drop size distributions of the nozzles have been plotted in figure 2.5.1, along with those computed from the cumulative 40

NOZZLE 513 (2.5 IN/H .1 NOZZLE 50 (3.25 IN/H )

us NOZZLE 7LA (4.67 IN/H ) =20 Ui BESTS FORMULA BEST'S FORMULA BEST'S FORNIULA cc FOR SAIviE FOR SAME FOR SAME Lu INTENSITY INTENSITY INTENSITY aZt 10 /25

2.0 4.0 6.0 0 2.0 4.0 6.0 0 2.0 4.0 6.0 DROP DIAMETER, MM DROP DIAMETER , MM DROP DIAMETER , MM FIGURE 2.5.1. A comparison between the drop size distributions from the nozzles used by A.R. Bertrand and. J.F. Parr (1960) for the Purdue sprinkling infiltrometer (from data ibid ; table 1, p 436) and from the empirical formulae for the drop size distributions of naturcl rainfall given by A.C. Best (1050a) 67.

distribution formula for the same intensities of natural rainfall suggested by Best in 1950 (see Chapter 8). Even allowing for inaccuracies in this formula, the drop size distributions of the nozzles are seen to contain far too large a proportion of small drops.

With the nozzles providing a minimum wetted diameter of approximately 10 feet, a plot size of 3.81 by 3.81 feet (equivalent to 1/3000 th. acre) was selected to meet the specification. Under field conditions, the nozzles were supported 9 feet above the plot by a framework of 1.25-in diameter aluminium piping, built in the form of a tower with sloping sides to provide adequate stability. The base of the framework was 12 ft square, and the top of the frame 8 ft square. The legs of the tower telescoped to allow adjustment of heights and levels. Water was supplied to the nozzles from a 680-gallon mobile tank by a 1.5-in diameter petrol-driven centrifugal pump.

N.V. Hudson (1965) has described another portable apparatus designed for use in soil erodibility studies on small plots, 7 feet or less in diameter, in Central Africa. This rainfall simulator was intended to reproduce the characteristics of a 3.0 in/h subtropical rainstorm. Because drops of 4.0 to 5.0 mm in diameter are only obtainable from nozzles with large-diameter orifices, which also provide heavy rates of discharge, some form of intermittent application was required. For simplicity, a rotary movement was adopted, and a commercial rotary lawn sprinkler turned upside down was used as the basis of the apparatus.

A simple type of nozzle made from a short length of 0.5-in diameter tubing was designed for attachment to the rotating arm. A jet of water passing through a 0.25-in diameter axial hole in the tube impinged upon a flat, machined surface at 45 degrees to the axis, and spread out into a flat fan of spray. A gap of 0.125-in was provided 68. between the orifice and the machined flat.' Only one nozzle was attached to the rotating arm, the other being replaced by a counter- weight. The nngle of twist of the nozzle in a vertical plane at right angles to the arm of the sprayer was 35 degrees. The complete unit was mounted on the barrel of an irrigation sprinkler.

As the water requirement for a ten minute test on a small plot was only ten gallons, pressure was provided by a small constant head tank. The tank was mounted on a tubular mast to which a horizontal arm carrying the sprayer was also attached. This arm could be rotated about the mast, allowing several replications to be made for one setting of the apparatus.

This rainfall simulator gave 92 per cent of the required erosivity over the plots and was therefore considered to be satisfactory. Measurements of the drop size distribution of the spray by the flour method (see Chapter 8) showed an excess of large diameter drops compared with natural rainfall of the same intensity, but their effect was compensated for by velocities of impact being less than terminal velocity. The speed of rotation was approximately 20 to 25 rev/Min, making the frequency of application at any point on the plot once every 2.4 to 3.0 seconds. The height of the sprayer above the plots 2 was 12 feet, and the working pressure at the nozzle 1.5 lb/in .

The only apparent defect in this design was the uniformity of distribution. Measurements of intensity of application along a radius of the test area summarised by Hudson yielded a Christiansen uniformity coefficient of only 0.729. The author commented that uniformity could not be improved without introducing less desirable

* see Chapter 4; the H.S.P.A. uniformity coefficient and the Christiansen uniformity coefficient may be shown to be identical if a Gaussian distribution of application depths is assumed. 69. characteristics into the design. Results were assumed to reflect a composite measure of erosivity under a range of rainfall intensities rather than a measure under one constant rate of rainfall.

A. Shachori and I. Seginer (1962) also used standard items of sprinkler irrigation equipment in developing apparatus for a range of duties similar to that for which Meyer and McCune built the rainulator. Three different types of sprinkling assembly were evolved, the designs of which depended primarily upon specific experimental requirements. These devices were known as the "strip assembly", the "simultaneous assembly" and the "low-intensity portable assembly".

Two-arm rotary sprinklers, operating at from 80 to 200 rev/min and pressures of from 0.6 to 1.2 atm, were used as a basis for all three types. The first, as its name suggests, was used in studies involving long strip plots. The sprinklers were mounted 2 metres above the ground on pipe frames spanning the plots. Six units Were carried on 6-metre wide frames placed at 3-metre centres along each plot. Alternate frames were connected to separate supply pipes, 2 inches and 4 inches in diameter,, running parallel to the sides of the plot. Various application rates from approximately 0.25 to 4.75 .2:_n/h were obtainable by changing the working pressure and the number of sprinklers operated.

The simultaneous assembly was an essentially similar arrangement by which spray could be applied to several adjacent plots at the same time. In the example quoted by Shachori and Seginer, seven plots, 25 metres long and 4 metres wide, were covered by groups of four sprinklers mounted on 4-metre wide frames at 6-metre centres along each strip, with a 3-metre stagger between frames on adjacent strips. The frames were connected to a 2-in supply pipe on one side of the plot, and to a 4-in pipe on the other. The pipes ran inside sheet metal troughs along the borders of the plots. Various application rates were 70. produced as outlined above.

The third type of apparatus was designed for use where water had to be supplied from a mobile tanker. The sprinklers were mounted on standpipes 2.75 metres high, located alternately on separate 2-in supply pipes running along the borders of 6-metre wide plots. The standpipes were set up at 6-metre centres along each supply line, with a 3-metre stagger between those on adjacent pipes. Intensities of application varied between 0.25 and 1.0 in/h.

The description of these devices given by Shachori and Seginer is notable for their comparison between characteristics of the simulated rainfall and those of natural storms. The uniformity of application, reproduction of intensities, angles of impact of drops, drop size distributions and impact velocities of drops were all considered in detail.

The Christiansen uniformity coefficients for most of the tests performed with the sprinkler assemblies were found to lie between 0.8 and 0.95. The average value for 76 experimental runs was stated to be 0.871. The coefficient of variation of measurements of total application depths over 47 tests was given as 0.06. The comparable figure for intensities of application over 55 tests was 0.12, although Shachori and Seginer stated that with improvements in experimental technique, the coefficient of variation had been reduced to 0.07 for the last 23 runs.

Commenting upon the angle of impact of drops, the authors noted that the size of the angle depends upon the drop size and the wind velocity. A study was made of the trajectories of drops thrown from a rotary sprinkler 2 metres above ground level. The sprinkler was set up near a smooth wall so that drops striking the wall left marks indicating their direction upon impact. 2 mm and 3 mm diameter 71. drops were estimated to reach the ground at angles of 68 degrees and 60 degrees to the horizontal respectively. Shachori and Seginer calculated that these angles of impact would have been obtained in wind velocities of 10 km/h (2mm drops) and 17 km/h (3 mm drops), values which were considered to be average for natural storms. The main difference between the simulated and the natural conditions was that, under the former, drops from different sprinklers reached the same point from different directions. As surface run-off was considered to be the main transporting agent in the experiments made with the sprinkler assemblies, this effect was ignored.

No drop size distribution measurements were available for local high-intensity storms (the authors worked in Israel), and so drop size spectra were compared using Best's formula for the cumulative distribution of drops in the air. The filter paper technique was used to determine the drop size distributions of the simulated rainfall. The distributions provided by the sprinkler assemblies simulating intensities of approximately 0.5 and 2.0 in/h have been plotted in figure 2.5.2 along with those calculated from Best's formula for the same rates of natural rainfall. On comparison, the measured and computed distributions show basically similar shapes, although the sprinkler assemblies are seen to provide excessive numbers of drops less than 2 mm in diameter, and are deficient in drops between 2 and 4 mm in diameter.

Indirect estimates were made of the impact velocities of drops from the sprinklers by assuming only gravitational and drag forces affected the drop, and calculating the velocity from the shape of its trajectory (see also I. Seginer, 1965). Using these data, figures for the kinetic energy and momentum per unit mass of drops at impact were obtained, and compared with values for a natural storm of the same intensity. The kinetic energy for the 2.0-in/h simulated storm was SPRINKLER ASSEMBLY AT 1.0 ATMOS. PRESSURE

20-

SPRINKLER ASSEMBLEY AT 0.8 ATMOS. PRESSURE.

BEST'S FORMULA FOR BEST'S FORMULA FOR z 12 MM/ H NATURAL 50 MM/H NATURAL RAINFALL. RAINFALL.

< 10 ." fp-- zw tU a.

0 1.0 2.0 3-0 14 5.0 0 1.0 2-0 3.0 4-0 5.0 6.0 DROP DIAMETER , MM DROP DIAMETER MM FIGURE. 2.5.2 , A comparison between the drop size distributions from the sprinkler assemblies used by A. Shachori and I . Seginer (1962) and from the empirical formulae for the drop size distributions of natural rainfall given by A. C. Best (1950a). (Data from Shachori and Seginer, 1962 ; table 2 , p66.1 73. found to be 39 per cent too low, and the momentum 29 per cent too low. Corresponding figures for the 0.5-in/h storm were 25 and 20 per cent too low respectively.

These data emphasise the difficulties encountered in using sprinkler irrigation equipment for erosion studies. An increase in working pressure for a given number of sprinklers increases their rate of application, but modifies the drop size distribution in a manner which tends to decrease the energy of the spray. For experiments in which such parameters may be highly significant, this effect should be avoided. The solution offered by Shachori and Seginer was to hold the pressure and therefore the energy delivered by each sprinkler constant, and to increase the number of sprinklers within the test area. This procedure increases the application rate, but also increases the energy value to correspond with the particular storm intensity that is to be simulated.

Finally., the amount of equipment involved in the rainulator and the Israeli sprinkler assemblies may be contrasted with that used by J. Amorocho and G.T. Orlob (1961) in their study of a prediction analysis prototype (see Chapter 1). The laboratory catchment was 120 cm long and 9.9 cm wide. Two sets of 19 commercial "fog-nozzles", mounted on parallel 2-in diameter manifolds running on either side of the catchment, supplied the artificial rainfall. The manifolds were fed from both ends to minimise friction losses, and an inlet pressure 2 of 13.2 lb/in was maintained by a constant-head supply.

The spray pattern was adjusted by rotating the manifolds and by cutting out some of the nozzles. An optimum uniformity condition was obtained with the nozzles spraying upwards at an angle of 10 degrees to the vertical. An array of 49 glass gauges, 1.66 inches in diameter, marked off in 5 cm3 divisions were used to measure the spray patterns. 74.

The average of ten 6-minute tests was taken for each pattern. A set of typical measurements given by Amorocho and Orlob (loc. cit, 1961; p.41) was found to give an average application rate of 10.8 in/h with a Christiansen uniformity coefficient of only 0.708. However, the authors also stated that this method of measurement was not used when any great accuracy was required, and that intensities of application were generally estimated from equilibrium outflow rates.

As changes in manifold pressure were found to alter the spray patterns significantly, proportional variations in input were obtained by introducing an interceptor screen between the spray source and the catchment. This screen consisted of a number of equally-spaced stainless steel channels. Intensities were varied by altering their spacing. Step function inputs were produced by two screens attached to spring-loaded rollers, which were used to cover the catchment until the spray system reached an equilibrium condition. The ends of the screens overlapped at the centre of the test area, and were held in place by a solenoid-operated connecting mechanism. The screens could be retracted in less than half a second. The input could be stopped almost instantaneously by a quick-acting valve in the supply systerp.

The above apparatus was regarded as unsatisfactory for the purposes of the experiments, and in a subsequent paper, J. Amorocho and W.E. Hart (1965) stated that another was under development. The new device consisted of a modular arrangement of rectangular "input cells", similar to those described by Chow and Harbaugh. Drop formers consisting of stainless steel tubes of 0.047-in internal diameter were mounted in the base of the cells. Each unit covered an area of one square foot. No details were provided of the arrangement and spacing of drop formers in each cell. CHAPTER THREE 75.

Equipment specification for microcatchment studies.

3.1 Comparison between available methods of simulating rainfall.

The dripolator-type of apparatus was designed specifically to provide a single drop size over a wide range of application rates. The figure of 1 6 per cent for the variation in the size of drops quoted by Ellison and Pomerene showed that this objective had sly been achieved successfully. Hokever, for more general purposes the production of one drop size for all intensities of application is unduly restrictive. Basu and Puranik showed that a mixed droplet pattern could be generated by using two drip screens moving in mutually-opposing directions, but were unable to reproduce the correct drop size distribution for the intensity of application provided by their apparatus. The distribution obtained has been plotted in figure 3.1.1. along with the empirical curve derived from the cumulative distribution formula published by Best (see Chapter 8). In the absence of local size distribution measurements for Sholapur, the mean values of the parameters in the formula that were quoted by Best have been used in the calculations. There were significant differences in the performance figures given by Ellison and Pomerene, and those reported by Basu and Puranik. These figures have been presented for comparison in table 3.1.1. The essential differences between these two devices lay in the first stage of simulation, the supply system to the drip screens. Ellison and Pomerene obtained a regular distribution of water over 40

SHOLAPUR RAINFALL SIMULATOR

w w

1.5 20 z t1.1 a. BEST'S FORMULA FOR 3.38 IN/1-1 NATURAL RF.

1.•••••••••••••••••••••••••=7...m* 1.0 2.0 3.0 4.0 5.0 6.0 DROP DIAMETER MM. FIGURE 3.1.1 A comparison between the drop size distribution from the apparatus used by .1. K . Basu and N. B. Puranik (1954) and from the empirical formulae for the drop size distribution of natural rainfall given by A.C. Best (1950a). (Sholapur data from Basu and Puranik, 1954 , table 3, p 184) 77.

Table 3.1.1 A comparison between the performance of the apparatus described by W.D. Ellison and W.H. Pomerene (1944) and that of J.K. Basu and N.B. Puranik (1945)

max variation reproduction source location in distribution of application, over plot during rates fromruni one run. to run. Ellison/Pomerene Coshocton, U.S.A = 10 % + 3 % Basu/Puranik Sholapur, India = 29 % z 9 %

the screen by using a large tank with small orifices at 4—in centres in the base. By present-day standards, this method was inelegant, and probably raised the cost of the apparatus considerably. However, it is doubtful whether the three spherical shower nozzles used by Basu and Puranik could provide a comparable distribution even under ideal test conditions. There were additional differences in experimental procedure. The drip screens of both devices were oscillated to produce a random distribution of drops over the plot. One, that of Basu and Puranik, was manually controlled, whereas the other was motor-driven. Even allowing for these differences, the use of two drip screens should have tended to smooth out the distribution of water from the shower heads.

Woo and Brater also presented data from which figures for the reproduction of application rates could be deduced. Their light rain showed a maximum variation from the average application rate from run to run of approximately 13 per cent. The comparable figures for the medium and heavy rains were 9 per cent and 8 per cent respectively. These values are of the same order as those obtained by Basu and Puranik, although it is apparent from their paper that Woo and Brater took extreme care to ensure an even distribution of spray over their drip screen. As the working pressure of the nozzle system used by 78. the latter authors was 40 lb/in2, any small perturbations in pressure could have significantly affected the distribution pattern. Also, the method of estimating Vhe application rates from the steady discharge of the flume after 15 minutes could be subject to some error.

For general purposes, the fundamental weakness of this type of apparatus is the two-stage drop-producing process. Some method of applying a uniform distribution of water to the drip screen is always required. In four of the five examples quoted in section 2.3, a system of nozzles has been used. If the first stage of the apparatus can provide an adequate uniformity of distribution, the disturbing effect of the second stage can only be justified if it produces a drop size distribution more in accordance with specification.

The devices in which lengths of capillary tubing and hypodermic needles are used are also limited to the production of single drop sizes. A major disadvantage of this method of rainfall simulation has been that drop-formers, discharging streams of individual drops, must be considered to provide a uniform application to elemental areas depending upon their spacing. Mamisao commented that the discharge of even the smallest diameter of capillary tubing was high compared with his requirements. The larger the discharge from a drop-former, the wider the spacing necessary to provide a given intensity of application. The absence of any guidance from the originators of this type of apparatus on the choice of suitable spacings of drop formers to provide what might be considered to be a uniform application of water has been conspicuous. Spacings of from 0.5 to 2.5 inches have been used, although one inch appears to have been the most popular figure. Unless the simulator or the test area is rotated or oscillated in some way, such devices provide a large number of "point sources" of drops rather than a spray. This statement also 79. applies to dripolator-type apparatus.

This aspect of performance appears to have been largely ignored, although Ekern and Muckenhinadid observe that air movement in the laboratory produced an essentially random pattern of drops within the target area. The drops produced from lengths of capillary tubing can generally be observed to drift horizontally rather than to fall in an absolutely vertical direction. R. Gunn (1949b) stated that only drops of less than 1.0 mm in diameter drifted when falling freely under stagnant air conditions. More recent work by C.K. Mutchler (1965) has contradicted this statement.

Mutchler carried out a series of experiments in which drops were allowed to fall 9.75 metres on to a fibreglass insulation board target. The board was marked out with a 0.635 cm reference grid of fine wire. Drops falling on to the target area made distinct stains, which allowed their position to be determined to the nearest 0.32 cm. 3.5, 4.2, 4.8 and 5.6-mm diameter drops were used in the experiments. Their points of impact were recorded in rectangular co-ordinates, and the average co-ordinates of each impact pattern were taken as the origin.

Mutchler wrote that "Because the drift of falling waterdrops in still air was believed to be due to the release of turbulent eddies, which is a random phenomenon, random drop impact was also hypothesized. Therefore, the impact-point distribution should be uniform in angle and normal on a line through the pattern centre." Analysis of the data obtained by Mutchler, transformed into cylindrical co-ordinates, showed that the assumption of a normal distribution of impact points about the geometrical centre of the impact-point patterns was valid. The standard deviations of the curves for the 3.5, 4.2, 4.8 and 5.6 mm diameter drops were found to be 1.04, 1.27, 1.22 and 1.32 cm respectively.

80. Mutchler then extended his study to show how the results could be used to select appropriate spacings for drop-formers in a rainfall simulator, illustrating the procedure with an example. An equilateral-triangle arrangement of drop-formers was assumed with a spacing between units of Ko, where cr is equal to the standard deviation of the distribution for any drop size, and K is a constant. For any one drop-former, the frequency of drops, F, at any point (X,Y) may be written in terms of the normal distribution as

N 2 F - exp f (X-ivt) +(Y- v02i eq 3.1.1. - 20-2

Where the position of the drop-former is represented by co- ordinates (12,1Z), and N is equal to the total number of impact points within the pattern. X1Y,µ12 may all be expressed in terms of Ka, so that, for constant values of N and a , equation 3.1.1. may be written as

F = C exp 1,K2 eq 3.1.2. ( 2

Using equation 3.1.2., the intensity of application at any point (X,Y) under a number of drop-formers, each producing the same size of drops, may be expressed as I'4 2=1; F = C.IDexp LiK1 eq 3.1.3. i=1 rt 2 ) Where i =i, M denotes the location of the drop-formers.

Mutchler demonstrated the relationship between K and the uniformity of application by calculating coefficients of variation over a rectangle containing three drop-formers at intervals of 0.1K with C equal to unity. All frequencies less than 5 x 10 -5 were 81.

neglected, but the effects of adjacent drop-formers were considered. His results have been summarised in table 3.1.2. For purposes of comparison, an additional column, giving the corresponding values of the H.S.P.A. uniformity coefficient has been added to the original data given by Mutchler.

Table 3.1.2. Uniformity coefficients and extreme values of intensities of application over a representative area covered by an equilateral-triangle arrangement of drop-formers (after C.K. Mutchler, 1965; p. 3902).

extremes of intensity of coeff. H.S.P.A. K a. lication (,,e, of average) of uniformity max, min. variation coeff.

2,0 100.8 99.6 0.003 0.998 2.2 102.5 98.7 0.011 0.991 2.4 105,9 96.9 0.026 0.979 2,6 111.6 94.0 0.051 0.959 2.8 119.1 89.7 0.087 0.930 3,0 130.5 84.2 0.134 0.893 3.5 166.9 66.5 0„290 0.768 4.o 213.1 47.o 0.478 o.618

Mutchler concluded by stating that "Selection of an appropriate K value would be a decision for the individual researcher. However, a K giving Cv (coeffilent of variation) values up to 30 per cent should give an acceptable simulated drop-distribution, since wind currents for an operating situation would contribute to a more uniform impact distribution".

This criterion of a coefficient of variation of 0.3 (or a 82.

uniformity coefficient of 0.76) represents a relatively disturbed pattern and a value of 0.2 (0.84) is generally found to be more acceptable (see Chapter 4). The latter figure would correspond to a K -:-alue of between 3.0 and 3.5. Unfortunately, table 3.1.2. is applicable only to triangular arrangements of drop-formers, and cannot be used to compare all the various designs described in section 2.4. The only apparatus with such an arrangement of drop-formers was that of Adams et al., which produced drops 5.56 mm in diameter. Mutchler stated that drops 5.60 ram in diameter provided an impact-point distribution the standard deviation of which was 1.32 cm. Using this figure, and selecting a uniformity coefficient of approximately 0.90, a K value of 3.0 is obtained from table 3.1.2 leading to a spacing of 3.96 cm (roughly 1.5 inches). The spacing chosen by Adams et al, was 0.5 inches.

Capillary tubes are susceptible to blockage by fine grit carried in suspension. Their quality tends to deteriorate with time. Small variations in the diameter of individual drop-formers may cause significant differences in their discharge under identical head conditions. To date, this method of rainfall simulation has been confined to relatively small test areas. The use of nearly 60,000 drop-formers in one apparatus as proposed by Chow and Harbaugh could well provide troublesome maintenance problems.

Most writers on rainfall simulation, (for example, N.W. Hudson, 1964b,C.K. Mutchler and L.F. Hermsmeier, 1965) agree that spray nozzles and sprinkler irrigation equipmnnt present the only practicable method of producing a drop size distribution comparable with any in natural rainfall. The use of readily-obtainable commercial items can effect a considerable saving in time and research effort, although the initial selection process can be tedious without extensive knowledge of what equipment is available. Unfortunately, the operating characteristics 83. of spray nozzles and sprinklers generally differ in some respect from project requirements. As Mutchler and Hermsmeier noted, there are many nozzles with drop size distributions similar to those in natural rainfall, but with discharges giving application rates much higher than the natural rainfall intensity associated with that size distribution.

This incompatibility has led to two separate approaches to the problem. As the optimum condition of simulated rainfall intensities with correct drop size distributions and all drops falling at their terminal velocity is unobtainable, a search has begun for reliable parameters proportional to rainfall erosivity. L.D. Meyer (1965; p.64) has listed a number including kinetic energy, momentum and interactions of these variables with rainfall intensity. Perhaps the most frequently quoted of the latter category is the "erosion index" defined by W.H. Wischmeier and D.D.Smith (1958) as the product of the kinetic energy and the maximum thirty-minute rainfall intensity. At the time of writing, there appears to be no clear evidence in favour of any one parameter, and as Meyer concluded, "The decision of which parameter or other means to use must remain with each investigator."

Alternatively, conventional apparatus has been modified to make the drop size distribution and simulated application rate correspond. The modifications have consisted of either electro- mechanical control systems which close down the nozzles at regular intervals during a test, or driving mechanisms which move the nozzles so that larger areas are covered, or both. The rainulator provides the outstanding example of a device in which both features were found to be necessary. The laboratory apparatus described by Bubenzer and Meyer incorporated an oscillating mechanism for the same purpose. Swanson used a rotating-boom type of device. 84.

The rotating-boom type of sprinkler presents problems in field operation peculiar only to itself. According to R.E. Machmeier and E.R. Allred (1962), this type of sprinkler was introduced commercially about 1950, and has proved to be extremely popular in American agricultural practice. The labour requirements of rotating- boom sprinklers have been found to be considerably less than the conventional irrigation system with rotary sprinklers attached to portable lines.

The large wetted diameters of boom sprinklers make the overlapping of patterns difficult, and their performance is extremely susceptible to wind interference. An analysis of field tests with a typical unit by Machmeier and Allred showed that Christiansen uniformity coefficients of above 0.80 were only obtained at the optimum spacing when the wind velocity was less than 4 mile/h. Wind forces were found to exert a drag on the boom arms which caused the unit to rotate with uneven angular velocity. In turn, this uneven rotation caused distortion of the application pattern in addition to that resulting from the wind acting on the spray in the air. A theoretical analysis of the effects of wind resistance on boom sprinklers has been given by R. Allred and R.E. Machmeier (1962).

With a rotating boom rainfall simulator, the boom must remain horizontal to avoid unequal pressures at the nozzles. Therefore on a sloping plot, the clearance of the boom is less at the upper end of the slope than at the lower end. Also, large circular application patterns are difficult to fit into rectangular test areas without creating zones with deficiencies or excess application depths.

The rotation of a line of nozzles in a circular path, as with the boom-type sprinklers, or the movement of the line in a direction perpendicular to its length, as with the precision plot irrigators described in section 2.5, tends to distort the shape of individual

85.

nozzle patterns. M.W. Bittinger and R.A. Longenbaugh (1962) have given a theoretical analysis of these effects for two different shapes of single nozzle pattern. As an example, figure 3.1.2. shows the plan and elevation of an assumed distribution of application depths produced instantaneously by a nozzle which is also assumed to move in a straight line with constant velocity, V.

I. I

Velocity V. // MEVATION.

PLAN. 4 /

FIGURE 3.1.2. Typical instantaneous sprinkler pattern used in the theoretical water distribution analysis presented by M.W. Bittinger and R.A. Longenbaugh (1962).

Let at the rate of application at any point X distance s from the nozzle be Ix. Then

Ix = H (.11;72.) eq. 3.1.4.

where H is the rate of application directly below the nozzle, and r is the wetted radius of the pattern. Let m equal the ratio of the distance of the point X from the line of travel of the nozzle to the pattern radius, r. Then, by the geometry,

= ,Am2r24,y2) eq. 3.1.5.

86.

where y is the distance travelled by the nozzle in time t, i.e., y is equal to the product Vt.

The total depth of water applied during one pass of the nozzle may be written as rT D = 2j Ix dt. eq. 3.1.6.

where T is the total time for one half of the sprinkler pattern to pass X. Note that

T = ,,,/( 1 -m2). eq. 3.1.7. V

Equation 3.1.5 may be substituted in equation 3.1.4. to give an expression for Ix in terms of t, which may be integrated according to equation 3.1.6. Replacing T according to equation 3.1.7. and simplifying, the following equation for total depth is obtained:

Hr D = / (1-m2) - m2. In eq. 3.1.8. V m fi

The tendency therefore is for the spray to be concentrated near to the nozzle, making the moving cross section bell-shaped according to equation 3.1.8. When the same application pattern is rotated in a circular path, Bittinger and Longenbaugh found that nozzles located near the centre of rotation produced skewed depth distributions, and those at larger radii were subject to lesser distortion, similar to that for straight line travel.

Bean et al commented that a moving grid of nozzles could be considered as an infinite number of spraylines. As the above analysis shows, the effects are not the same because of the pattern distortion introduced by the movement. The instantaneous patterns of application depth from each nozzle would not exhibit the regularity of that shown 87. in figure 3.1.2 , and field measurements of the total depths applied at all points would be necessary for complete definition of the distortion.

Where discharges are intermittent, or applications are supplied from horizontal lines of nozzles moving across a study plot at right angles to their length, as with the precision plot irrigators, or rotating about central pivots, as with rotating boom sprinklers, the depths of water supplied at individual points within the study area will be roughly equal when considered over the full elapsed test time. At any instant of time during the test however, the total depths being applied at these same points may be widely different. The instantaneous application rates will vary from zero to many times the rate based upon the full elapsed test time. The applied depths are therefore "uniform in space" but not "uniform in time".

Uniformity in space, but not in time is also a feature of the operation of rotating irrigation sprinklers. P.E. Schleusener and E.H. Kidder (1960) noted that true water application rates, based upon the total time during which spray was applied to specified points within the application pattern of a rotating sprinkler, were as high as 50 to 90 times as large as the apparent application rate based upon total elapsed time. Shachori and Seginer (loc.cit. 1962) also commented on the way in which slowly rotating lever-type irrigation sprinklers gave short, high-intensity bursts over sections of their circle of influence.

The extent to which intermittent applications of water affect experimental results has been largely ignored in the existing literature. Of the few investigators who have considered this problem in relation to soil erosion studies, Hudson (1965) has commented that soil particles are unlikely to slake or puddles of water to infiltrate during the short time intervals between successive applications with a rotating sprinkler 88.

head. Hydrological systems varying in size from field plots to catchments of many thousands of square miles are known to be "highly damped", so that perturbations in the time-distribution of input intensity have little or no effect on output. Where the system consists of smooth, impervious surfaces such as those used in laboratory catchment experiments, the effects cannot be deduced with the same assurance.

Uniformity of application depths coupled with uniformity of application rates in time can only be obtained when the nozzle system is stationary, and the spraying is continuous. Of the eleven different devices described in section 2.5, only four, those of Childs, Bertrand and Parr, Amorocho and Orlob, and Watkins, fulfil these conditions. The apparatus devised by Bertrand and Parr was designed for use on limited areas, and incorporated only one nozzle. Amorocho and Orlob also operated with very small test areas, although their arrangement of parallel manifolds was similar to that of the spraylines described by Watkins.

With both of the latter devices, spray was discharged at a small angle to the vertical so that the fall path of individual droplets was lengthened. Although this procedure may be necessary to obtain the required level of uniformity of diritribution, the spray is subject to air currents and turbulence which may radically alter the application pattern during experiments. The provision of screens does not remove this source of error completely, as the entrainment of air by the spray is sufficient to create turbulent conditions over the test area.

The amount of available headroom in the laboratory may also severely restrict the use of this type of apparatus for indoor experiments. In the present investigation, clearances were limited to less than 10 feet, far too small a distance to contemplate the employ- 89. ment of spraylines. Of the alternative methods, a system of nozzles discharging vertically downwards, similar to that used by Childs, offered the more reasonable solution.

3.2 The specification for a rainfall simulator for use in microcatchment experiments.

L.D. Meyer (1965) appears to have been the most recent contributor among many to discuss overall specifications for rainfall simulators used in soil erosion research investigations. In his paper, Meyer listed nine separate criteria which should be-talumcinto account when designing such equipment. Two of these criteria, relating to portability and to satisfactory operation in winds of appreciable velocity, would apply only to field research apparatus. Of the remaining seven, one was concerned with the choice of a representative size of test area, and the rest with the reproduction of natural rainstorms by the equipment. These included

(1)intensities of artificial rainfall in the range of natural storms producing medium to high rates of run-off and erosion, (2)accurate reproduction of storms, (3)rainfall application nearly continuous throughout the study area, (4)drop size distribution and fall velocities near those of natural rainfall at comparable intensities, (5)uniformity of intensity and drop characteristics throughout the study area, and (6)angle of impact not greatly different from the vertical for most drops.

As the above criteria are intended to relate to soil erosion research, the simulated storms must necessarily reproduce the conditions which experience has proved to be critical in such work. The first and second criteria listed above may be summarised in general terms by stating that the equipment must provide intensities 90. of simulated rainfall over the particular range of conditions dictated by experimental requirements. A criterion of the latter form must ap-pear in any specification.

The third condition listed above refers to "nearly continuous" rainfall application within the study area. This qualification arises directly from the conflicting properties of nozzle systems, already discussed in section 3.1 , which make intermittent interruption of discharges necessary for the matching of intensities of application and drop size distributions. The higher the frequency of interruption, the closer the simulated conditions approach a continuous application.

The uniformity of application throughout the study area included in the fifth criterion listed above is directly linked to the problem of continuous and discontinuous applications. By specifying continuous applications, uniformity of both total application depths and instantaneous application rates are automatically implied.

The remaining criteria proposed by Meyer relate to the matching of intensities of application with correct drop size distributions having correct terminal velocities of fall for all drops. The question which immediately arises in connection with the present work is the applicability of these criteria to laboratory catchment studies. Unlike the problem of continuous and discontinuous applications, the effect of rainfall on sheet flow over plane surfaces has received some attention in recent years, and the available literature does allow some tentative conclusions to be drawn on this topic.

A well-known phenomenon associated with the run-off from plane, impervious surfaces to which uniform intensities of artificial rainfall have been applied is a momentary increase in discharge above equilibrium discharge obtained immediately after rainfall ceases (see figure 3.2.1). This "anomolous pip" was noted in the results obtained 0.012

0.0 W

FT 0.006 S/ EC S

CU 0.004 N I

AR 002 H C S DI 16 24 32 TIME IN MINUTES ----Ix-

A typical example of an anomolous pip on the run-off hydrograph from Q concrete channel having a 0.5 per cent slope subjected to a rainfall intensity of 0.851 in ih (after Y. S. Yu and J. S. McNown (1964), figure 5; p 17 ) 92.

by Izzard from the project described in section 1.1. The explanation given by Izzard and Augustine (1943, pp 502-3) was that, "---- This increase in the rate of discharge was due to the discharge of the quantity of water necessary to provide additional head to overcome the resistance caused by the impact of raindrops on the sheet flow."

In a more recent study of the flow over impervious surfaces, Yu and McNown (1964) were able to show that the pip is not caused by the removal of the retarding effect of the rainfall, but occurs as a consequence of turbulent flow becoming laminar. Their studies showed that the magnitude of the retardation to flow of the rainfall was far too small to cause the increases in discharge up to 20 per cent larger than equilibrium discharge that some of their experimental results exhibited. The authors found that where pips occurred, their height depended loosely on the Reynolds number at the outfall of the test area (a concrete channel). They continued

"No pips occurred for Reynolds numbers larger than 2200 nor less than 150. In contrast, pips always occurred for Reynolds numbers between 350 and 1150. Clearly, the pip is related to a transition from turbulent to laminar flow near the downstream end of the channel. No simple relationship exists because the Reynolds number varies along the channel and the degree of disturbance depends also on the rate of rainfall and the depth."

In this same connection, Yu and McNown presented data on the variation of resistance coefficients for a concrete surface with Reynolds number obtained from steady-state runs both with and without rainfall. For convenience, their results have been reproduced in figure 3.2.2. Despite considerable scatter the data do show that in the transition zone, the resistance coefficients obtained with rainfall * are higher than those for similar flows without rainfall. In the fully

* The low points on the right-hand side of the diagram were attributed to a faulty instrument, and may be ignored for present purposes. 9.

1.0 I 0 NO 0,6 RAINFALL z u.) 0 WITH L) RAINFALL U- Ui u02 NCE STA I 0.08

RES 0-06

0-04

0.02

0.0 1 4 6 8 103 2 4 6 8 104 REYNOLDS NUMBER

F GURE. 32. 2. The variation of resistance coefficient with Reynolds number for a concrete surface for steady state conditions both with and without rainfall ( after Y. S. Yu and J. S. McNown (1964) ; figure 1 p 7 ), 94. turbulent region, the coefficients were essentially the same with or without rainfall.

Although Yu and McNown regarded their explanation as "---- plausible rather than conclusive," their remarks confirm the opinion previously expressed by Woo and Brater (1962, p 45) that "--- the raindrop impact disturbs and hastens the change from laminar to turbulent flow, thus producing a condition for which no fundamental rule has been developed." The latter authors also recommended that the effect of droplet impact should be included in any analysis by making adjustments in the value of the resistance coefficient.

The studies performed by W.D. Ellison (1945), P.C. Ekern (1950), G.R. Free (1960) and many others have shown that the effects of drop impact on soils are directly proportional to functions of drop size and the fall velocity of the drop. If attention is centred on the relationship between rainfall and run-off as in a laboratory catchment experiment and not on the effects of impact forces as in soil erosion studies, the drop size distribution of the simulated rainfall can be taken into account by adjusting the values of the resistance coefficients. If the variation of tho resistance coefficient with Reynolds number and rainfall intensity can be obtained, the rainfall/ run-off relationship becomes independent of drop size distributions and variations in the fall velocities of the drops. As a first approximation therefore, such considerations need not enter into the specification.

The final requirement listed by Meyer was for angles of impact not greatly different from the vertical for most drops. In field installations, if no special precautions are taken to shield the test area, wind interference may cause angles of impact to depart considerably from the vertical. With nozzles that are mounted with the plane of their orifices horizontal and which exhibit a conical 95. dispersion, the angle at which drops reach the target area depends upon the angle of dispersion and their height of fall. The height at which a rainfall simulator may be erected in a laboratory study is primarily a function of the site.

The range of application rates to be provided for the present purpose was finally chosen to run from a lower limit roughly between 0.5 and 1.0 in/h to an upper limit of at least 10.0 in/h. The choice of the upper limit was not based upon any particular recorded mayimum, but upon the need to devise a versatile apparatus which would be able to provide a wide range of experimental conditions. According to the table of World record rainfalls given by A.H. Jennings (1950), depths of rainfall have been observed during intervals of less than 60 minutes which correspond to average intensities far larger than this figure, so that the choice is within the bounds of physical possibility.

A further requirement of advantage to the proposed experiments would be the ability to vary a,,plication rates continuously over the working range of intensities. Previous designs of rainfall simulator have incorporated duplicate nozzle networks to provide changes in application rate. In others, the nozzles themselves have had to be changed. If one apparatus could be provided to supply a range of intensities over which characteristics of the application, such as the uniformity of distribution, could be maintained at an acceptable level, then operation would be greatly simplified and considerable economy in construction costs effected.

A second requirement, which would also increase the flexibility of the apparatus, would be to provide some means of reproducing moving storm patterns, and inputs which were functions of the space co- ordinates of the system as well as time (i.e., "distributed" as opposed to "lumped" parameter inputs). A refinement of this nature depends largely upon the control system adopted rather than the basic design 96.

of equipment. However, the requirement is sufficiently important to be entered in the general specification.

Taking into account all points in the above discussion, details of the specification finally adopted were as follows:

(a)the application should be continuous over the test area, i.e., depths and rates of application should be uniform in time and in space as defined in section 3.1., (b)depths of application should be reproducible under identical experimental conditions, (c)rates of application should be continuously variable, if possible over a range of 10:1 or larger, subject to conditions (a) and (b) above, (d)the maximum application rate provided should be at least 10.0 in/h, and (0) provision should be made for the construction of moving storm or distributed parameter patterns, subject to the condition that depths should be reproducible,.

As stated in section 3.1 , a system of nozzles discharging vertically downwards appeared the most appropriate method of simulating rainfall for the proposed microcatchment studies. However, the use of separate grids of nozzles to supply different application rates under constant head could provide only discontinuous changes in rainfall intensity. This system would not produce the flexibility in operation required by the above specification. Some investigators (Woo and Brater, for example) have expressed the opinion that changes in the working pressure of a nozzle system cannot be used to alter its rate of application because the application pattern also changes its configuration with head. The present writer has yet to find convincing quantitative evidence that such changes are so marked that the significant features of the pattern cannot be assumed to change only with time and not with the space co-ordinates over at least a small 97• range of heads. Accordingly, experimental work was undertaken to evaluate the changes in the application patterns from a correctly- designed system of nozzles over a range of working pressures.

In the following chapter, the methods by which the patterns of application depths from a nozzle or system of nozzles may be evaluated are discussed along with standards for comparison and analysis.

CHAPTER FOUR 98.

Methods for evaluating the properties of nozzle systems

4.1 The determination of spray distribution patterns The measurement of variations in the uniformity of spray distributions is of fundamental importance in all problems involving the application of liquids from a nozzle, or group of nozzles. The methods by which such variability can be assessed generally differ according to the volumes discharged by the nozzles.

Qualitative comparisons between the distribution patterns of low-volume spray nozzles of the type used in applying herbicides and insecticides can be made using an apparatus known as a "sprayograph". The term "sprayograpHt was introduced by H. W. Riley (1909) to describe an apparatus consisting essentially of a framework 15 ft high and 7 ft wide. Four rollers were mounted in pairs 18 in apart at the top and bottom of this framework. A waterproof curtain was stretched over the rollers so that a 12-in wide slot was left across its entire width at the joint between its ends. Sprocket wheels attached to both ends of each roller carried two driving chains on to which the curtain was attached by special links. Sheets of newspaper on a wire screen backing were suspended from pulleys which ran on a track leading inside the framework.

A nozzle under test was mounted with its axis horizontal in front of the curtain. Further gearing on one of the rollers transmitted the drive from a petrol engine, allowing the slot in the curtain to be moved across the newspaper at any predetermine(' speed. With the curtain moving at a constant speed, the slit acted in a manner similar to a focal-plane camera shutter. The 99. resultant patterns on the newspaper approximated to instantaneous "pictures" of the areal spray distribution. These spray patterns were made permanent by the addition of a small quantity of red analine dye to the liquid discharged.

The Riley sprayograph was reconstructed in a simplified form by G. L. Shanks and J. J. Paterson (1952) in connection with studies of chemical weed-control methods carried out at the University of Manitoba. Their apparatus consisted of a framework 6 ft long and 3 ft wide, supporting two 6-in rollers. A canvas belt, spliced so that a 3-in wide slit was left between its ends, ran over the rollers, one of which was turned at constant speed by a small electric motor. A shallow drawer, carrying a sheet of plain, white paper, fitted into the framework between the upper and lower portions of the belt. Spray from the nozzle under test was directed vertically downward on to the paper. The apparatus was found to be particularly useful in rapidly detecting variations in performance of individual nozzles caused by abnormalities in their manufacture.

Most chemical spray systems used in agricultural practice consist of one line of nozzles, mounted at regular intervals along a pipeline or spray boom, which is moved slowly across the crop in a direction perpendicular to its length (see N. B. Akesson and W. A. Harvey, 1948). With such a system, the variations between fixed points along a line parallel to the spray boom, after a complete passage of the nozzle system, are of primary importance. The distribution patterns obtained with the Sprayo- graph are undistorted, as both nozzle and sampling surface are stationary. Other methods have been devised to evaluate variability under conditions involving movement of the nozzles.

E. L. Barger, E. V. Collins, R. A. Norton and 100. J. B. Liljedahl (1948) carried out a large number of quantitative distribution tests on chemical weed control equipment using apparatus in which the nozzles were arranged to discharge vertically downwards on to a large sheet of corrugated aluminium roofing. The sheet was inclined in the longitudinal direction of the corrugations, and at right angles to the line of nozzles. Drain- age from the corrugations was collected in graduated cylinders, placed at regular intervals along the bottom of the slope. The position of the nozzles was fixed in space, but the corrugated sheet served to integrate the total volume applied in successive cross sections of the distribution pattern, parallel to the supposed direction of movement of the system.

G. L. Shanks and J. J. Paterson (1948) devised another apparatus with which variations in spray distributions from moving nozzle systems could be simulated and examined qualitatively. The apparatus consisted of a securely-braced framework, 12 ft long and 18 in wide, which supported two lengths of 1-in angle iron, forming the track for a small four-wheeled trolley. The trolley was linked to a 2-in rubber belt, which ran at approximately track level, mid-way between the angles. The belt was carried on pulleys attached to parallel shafts, located at each end of the track. One shaft was driven by an electric motor through reduction gearing designed to produce a belt speed comparable to the rate of movement of a tractor-mounted spray boom. The nozzles were aligned in a direction at right angles to the track at a point half-way along its length.

Sheets of white paper were pinned on to the trolley, which was then driven through the spray. At a point beyond the influence of the nozzles, a limit switch was contacted, bringing the trolley to rest within the remaining distance. As for the sprayograph, permanent records of distribution patterns were 101. obtained by spraying an ink-water, or dye-water mixture from the nozzles.

Quantitative estimates of distribution intensity could be made from spray patterns obtained with both the above apparatus and the Sprayograph if a set of standard patterns, made under known application rates, were available for purposes of comparison. Such comparisons would be possible only under strictly controlled conditions. The exposure times for all samples would have to be the same, and the spray patterns themselves sufficiently clear to make estimates of areal density possible, i.e., they should be composed of large numbers of discrete stains made by individual droplets.

According to D. A. Isler (1963) this procedure has been used extensively by both the U.S. Department of Agriculture and the Canadian Department of Agriculture to evaluate the coverage of aerial insecticide spraying operations. Spray deposits were collected on sheets of card coated with an oil-soluble dye. The cards were laid out at regular intervals along a line roughly at right angles to the flight path. This technique is easy to use in the field, but the quantitative estimates obtained are necessarily subject to the personal judgement of the individual comparing the samples with the standard patterns. Even if the average of two or more opinions is taken, this source of error is never completely removed.

Isler stated that, prior to the introduction of dye- coated cards, a colorimetric method was used. Spray deposits were collected on 6-in square glass or aluminium plates arranged in the same way as the cards. The deposits were washed off the plates, and a sample of the solution placed in a spectro- photometer. The amount of light transmitted by the sample was 102.

measured, and quantitative values assigned by comparing the reading with those obtained from solutions of known dilution.

A relatively large staff is required to operate a colorimetric method successfully. The procedures are time- consuming, and additional laboratory facilities are necessary. For large measurement programmes, the method becomes uneconomical.

None of the above techniques can be applied when larger discharges are involved, but more direct methods of measurement can be used. For example, the variations in the distribution pattern from a group of irrigation sprinklers are most easily obtained by measuring application depths in cans or jars placed at regular intervals over the area covered. This method has the merit of extreme simplicity, although it can become tedious in operation when a large number of measuring vessels is used, or when a large number of tests is required. Despite these qualifications, the technique has been applied in a number of long-term studies. The work carried out by the University of California in the mid-1930's into the factors affecting the distribution of water from rotary irrigation sprinklers is probably the most outstanding example. J. E. Christiansen (1942) stated that over 300 separate tests, some of which involved the use of as many as 280 cans, were made during this investigation. The same procedure was used by J. C. Wilcox and G. E. Swailes (1947) in comparing the performance of a number of undertree orchard sprinklers. W. D. Criddle, S. Davis, C. H. Pair and D. G. Shockley (1956) also recommended the method.

A semi-automatic testing station for irrigation sprinklers has recently been set up by the University of Adelaide. This station, which has been described in detail by R. Culver and R. F. Sinker (1966) is situated in flat, open countryside 103 adjacent to an airport. There are no buildings within a quarter- mile radius of the station, and the unhindered wind run in the direction of the prevailing wind is two miles. 160 specially- designed raingauges were set up in a radial pattern with 20 gauges at 5-ft centres along each of eight equally-spaced radii. The gauges, which were manufactured from high density polythene, are clamped on to angle iron stakes driven firmly into the ground. The lip of each gauge was grooved to take an accurately-machined, 3-in diameter calibration ring on to which a dust cover is fitted when the gauge is not in use.

Each gauge is connected by a length of 17-in diameter P.V.C. tubing to its own manometer, housed in a control room located at the centre of the test area. Each raingauge and manometer may also be connected to an equalising chamber in the control room, allowing an observer both to bring all manometer levels to a common reading, and to vary the absolute level in the whole system. The control room.which measures 12 ft by 12 ft internally, stands with its concrete roof some 18 in above ground level. The sprinklers under test are mounted on risers securely bolted to a tripod set into the roof. Water is supplied under pressure to the sprinkler head from a pump located outside the test area, but controlled from within the control room. The total quantity of water used in each test is measured by an oscillating-disc type integrating water meter located in the supply line from the pump. Wind speed and wind direction are also recorded automatically inside the control room. 104.

4.2 Standards for the comparison of spray patterns The methods outlined above cover a wide range of working conditions, and can be used to evaluate distribution patterns from most types of spray system. The shape of pattern required from a group of nozzles or irrigation sprinklers varies according to the purpose of the spraying operations. Most chemical weed control systems, for example, are designed to direct spray between the rows of a crop, and not on to the plants themselves. Cross-sections of their distribution patterns should be discontinuous, with the application depth falling off rapidly at regular intervals corresponding to the spacing of rows, but maintained as uniform as possible at all points in between. In contrast, a sprinkler irrigation system is required to apply depths of water uniformly over the whole of a given area.

Having obtained a series of distribution patterns from different types of nozzles or sprinklers, or from one type under different working conditions, the designer of any spray system is faced with the problem of matching the patterns with his specification. He must decide on what basis the comparison should be made. A purely visual method is subject to errors of personal interpretation. Arbitrary criteria can be misleading. J. E. Christiansen (1941) referred to an investigation by F. E. Staebner (1931) in which the spray patterns from a number of German and American sprinklers were compared. Staebner considered the distribution from a single sprinkler to be adequate if, disregarding the edges of the pattern, the maximum depth of application within the area covered did not exceed twice the minimum depth.

In effect, this rule imposed a standard for the uniformity of the distribution pattern from a single sprinkler. However, when a number of sprinklers are used to irrigate an area, their 105. patterns must be integrated to provide adequate coverage.

As an illustration, consider the hypothetical case of an infinitely large network of sprinklers set out at regular intervals in equally-spaced rows and columns. The smallest representative element of this network would be a square "cell" of side S (say) formed by four adjacent units. If the total discharge from each nozzle, Q, is distributed over a circular area of radius R from each unit, and if R is less than or equal to S, consideration of the geometry shows that the mean depth of water applied by the network, X, may be calculated knowing only Q and S. A quarter of the distribution pattern from each sprinkler falls inside the cell, so that the total volume discharged into the cell per unit time is equal, to Q. The elemental area is S2, giving an X equal to 2. S The calculation of X is therefore independent of the manner in which the total discharge from each sprinkler is distributed over its wetted radius, R, and of the ratio R to S. However, in order to provide an adequate and uniform coverage, a value of S must be chosen for which the application depths at all points over the cell approach a common value. Both the ratio of R to S and the shape of the single-nozzle patterns in both cross- section and plan are fundamental in determining the spacing which gives the best overall performance.

The importance of the ratio of R to S may be illustrated by three simple cases as shown in figures 4.2;1,-3. When S is greater than 2R, a considerable area of the cell remains dry. When S is equal to 2R, i.e., when the edges of the single- sprinkler patterns touch, but do not overlap (see figure 4.2.1), only 78.54 per cent of the cell receives an application of water. sprinkler sprinkti.q. • \ \ \ •‘ \ • \ • . R\ . 2.1. spray distribution pattern from tour sprinklers \ spaced 2R x 2R.

sprinkler sprinkler sprinl

\ \ Fia. 4 .2.2. spray distribution pattern \ from four sprinklers spaced R x/ff.R

\ „ • `\ s , \ \ \

4.:,prinktk:r sprinkler sprinkler sprinkler Fig.4.2.3. spray distribution pattern from four sprinklers spaced R x R.

Egy. to figures 4.2.1 —3. coverage by - no sprinklers \ one sprinkler two sprinklers

sprinkler three sprinklers four sprinklers 107. As the spacing of units is decreased, the proportion of dry area is reduced and finally eliminated. When S is equal to ,/7.R (figure 4.2.2), all points lie within the radius of influence of at least one sprinkler. A limiting case is reached when S is equal to R, with all points over the cell receiving an aggregate application depth from at least two units (see figure 4.2.3). The variations in the proportion of the area of the cell covered by a given number of the sprinklers with changes in the ratio of R to S are summarised in table 4.2.1.

TABLE 4.2.1: Variations in the proportion of the area of a cell covered by a given number of sprinklers for different values of the ratio ,of R to S

proportion of cell for different number values of R/S of sprinklers 0.50 0.707 1.00

0 21.46 1 78.54 42.92 2 57.08 17.35 3 51.14 4 31.51

total 100.00 100.00 100.00

An increase in the ratio of R to S above 1.0 leads to a situation in which the sprinklers on any one row or column discharge into the cells beyond adjacent rows and columns. This apparent nloss" is normally made up by other lines discharging back into the cell under consideration, providing greater multiple coverage (up to seven-fold when R/S is equal to ‘/7). For all cells apart from those at the extreme edges of the network therefore, the value of X over a cell may still be calculated 108. knowing only Q and S.

To summarise, uniformity of application depths over the whole of an area covered by a fixed spray system is only approached when single-sprinkler patterns are overlapped. The designer must select the spacing of units giving the best overall performance. In there circumstances, a uniformity criterion for a single- sprinkler pattern is only partly relevant to the analysis, as the shape of the single-sprinkler pattern, both in cross-section and plan, together with the geometry and spacing of units, decides the overall degree of uniformity.

The importance of the shape of single-sprinkler patterns in designing irrigation systems was illustrated by J. E. Christiansen (1941). Using data obtained during the work at the University of California referred to in section 4.1 (see also J. E. Christiansen, 1937), Christiansen carried out analyses in which single-sprinkler patterns were combined at various spacings to give group-distribution patterns. As the single- sprinkler data consisted of measurements of application depths over a grid of equally-spaced points, the spacings of units for the group-distribution patterns were limited to multiples of the interval between observation points. Christiansen introduced a standard procedure for analysing this type of data by which the uniformity of the resultant group-distributions could be expressed in terms of a single, numerical parameter. This "uniformity coefficient" was defined by the expression

uc = 1 Eq. 4.2.1 A7

a_ where is the arithmetic mean of N observations of 7 - A 109. depth,Xil eachofwhichrepresentsanelementalarea,a.,of the total area of a cell, A, and U is the "Christiansen c uniformitycoefficient".IfallvaluesofLcarry equal weight,i.e.a.=A/N, the above equation may be written

7:1 x.-7 uc = 1 Eq. 4.2.2

In statistical terms, this uniformity coefficient is calculated by computing the sum of the absolute deviations of a set of observed depths, dividing this by the sum of the dep-E4P and subtracting the result from unity. The subtraction is made so that a fully uniform condition is represented by a coefficient of one, and irregular conditions by fractions proportionally less than one. The coefficient may also be expressed conveniently as a percentage.

Cross-sections of three typical single-sprinkler patterns obtained by Christiansen are shown in figure 4.2.4. The deposition of a large proportion of the discharge into an annulus, 35 to 40 ft in diameter, in pattern (A) was caused by operating the sprinkler at too low a pressure. Patterns (B) and (C) were recorded under more favourable pressure conditions, with the wind velocity less than 3 mile/h, and the sprinklers rotating at slow, uniform speeds. Tables of uniformity coefficients for group- distribution patterns, formed by combining each of the single- sprinkler patterns at various spacings both along and between lines, are also presented in figure 4.2.4. Owing to the asymmetry of the sprinkler patterns, the uniformity coefficients quoted are the mean values of those obtained from separate analyses using the patterns orientated in two mutually-perpendicular directions. These directions are labelled "north-south" and "east-west" in the diagrams.

LLC

FIGURE 4...2.4„ A Comparison between the Uniformity Coefficients (in percentages) for three single sprinkler patterns combined . at affluent spacings of units (alter data presented by J.E. Christiansen , 1037 ; 1941 ; 1942)

0.50in (A) E-W cross section l _ r 0.25in .... ---" N-S cross section 1 l 40 20 20 40ft 0 spacing Spacing betwecn tines t f t along line,ft 40 50 60 70 80 90 100 10 90 77 69 76 89 81 20 79 77 65 65 72 66 30 86 73 68 72 78 70. 40 76 56 45 50 57 52 6.1 7 53 45 49 42 0.25in (B) 60 40 20 0 20 40 600f t *••••,, .F.,•••••• 10 96 95 69 88 93 92 82 20 95 95 89 80 93 92 81 30 93 9/. 89 88 91 90 81 40 94 92 88 88 91 89 81 60 84 82 83 83 82 74 80 a 80 78 75 70

[ 10.3 98 96 95 91 81 69 59 20 97 96 95 92 80 69 59 30 97 96 94 91 00 69 59 40 96 95 9/. 90 80 69 58 60 94 93 89 80 69 58 Q 79 79 75 66 57 The influence of pattern shape on the uniformity of the group-distribution pattern is immediately apparent from the tables. For example, increasing the spacing of units up to 60 ft along a line, with a constant distance between lines, made relatively little difference to the performance of systems based on patterns (B) and (C), but caused a sharp decrease in Uc-values for those of pattern (A). ''/hen the spacing along a line was held constant, and the distance between lines increased from 40 to 100 ft, the coefficients for groupings of pattern (C) remained sensibly constant up to 70 ft, but then decreased rapidly. In contrast, systems based on pattern (A) gave values which decreased as the distance between lines opened up to 60 ft, and then increased at larger spacings up to 90 ft. A similar, but less extreme variation was obtained with pattern (B)-data. The extremely high values of uniformity coefficient calculated for close spacings of patterns (B) and (C) resulted from multiple overlapping.

In an attempt to include some consideration of the uniformity of distribution in calculating the efficiency of an irrigation system, V. E. Hansen (1960) proposed that the Christiansen uniformity coefficient should be adopted as a 'water distribution efficiency". If all observations of depth are of equal weight, the term EXi in equation 4.2.2 is equivalent to the total volume of water delivered by the system. Similarly, IETE-71 represents the volume applied in excess of the mean depth, plus the amount which should have been applied to the area in deficit. If the right-hand side of equation 4.2.2 is re-arranged into a single fraction, the expression is seen to provide a measure of the extent to which the water distributed by the system is uniformly applied. The use of Uc as an efficiency term has also been discussed by G. 0. Woodward 112. (1959, Chapter V) and C. W. Israelsen and V. E. Hansen (1962; Chapter 13).

J. C. Wilcox and G. E. Swailes (1947) examined the performance of a number of commercial irrigation sprinklers using an almost identical procedure to that laid down by Christiansen. Their analysis differed only in the definition of their uniformity coefficient, which was based upon the standard deviation of the data rather than the mean deviation:

1 Z(X.-p )2 U = 1 Eq. 4.2.3 X where U denotes the uniformity coefficient and the other rftTIN are as defined above. The ratio of the standard deviation of a set of figures to their arithmetic mean is referred to in most textbooks of statistics as the "coefficient of variation". Denoting the latter quantity by the symbol V, equation 4.2.3 becomes

U = 1 - V Eq. 4.2.4

Again, the subtraction from unity ensures that a value of one (or 100 per cent) is equivalent to an entirely uniform distribution, and figures less than one (or 100 per cent) to proportionally disturbed conditions. It may be noted that both U and U may become negative. However, there does not appear to c be any theoretical significance to the transition through zero of either coefficient, and, for practical purposes, interest is centred on obtaining values approaching unity.

The principal effect of using the standard deviation in preference to the mean deviation is to lay emphasis on the extreme values of the pattern data. For this reason, W. C. Strong (1961) has also recommended that the coefficient of variation should be used as a criterion of uniformity. Strong 113.

illustrated his proposal with three sets of figures, representing different patterns of sampled application depths, as shown in figure 4.2.5.

FIGURE 4.2.5: Three patterns of sampled application depths expressed in arbitrary units (after W. C. Strong, 1961)

PATTERN 1 PATTERN 2 PATTERN 3

12 8 12 15 10 10 5 20 10 10 10

12 8 8 12 10 10 10 0 10 10 10 10

10 12 8 8 12 10 _5 5 0 10 0 0

12 8 8 12 10 5 0 10 10 10 10

12 8 12 15 10 10 5 10 10 10 i 0

Each of the patterns shown in figure 4.2.5 has a mean depth of 10 units and a mean deviation of 2 units. All three patterns therefore have a Christiansen uniformity coefficient of 0.80. By giving weight to the extreme values, the coefficient of variation brings out the difference between them. Values of V for patterns one to three are 0.20, 0.32 and 0.45 respectively.

In the opinion of the present writer, the significance of the above figures should not be exaggerated. The example illustrates the need for caution in using uniformity coefficients rather than the weakness of one form of criterion compared with another. Uniformity coefficients assist the designer in summarising a distribution in terms of a single parameter which has a physical interpretation. Given the above patterns with ilk. equal values of Ue, the most suitable can be chosen by inspection without recourse to other criteria, such as U or V, which involve the computation of a higher statistical moment. Parameters such as the coefficient of variation, the skewness and the kurtosis, which are based upon the second, third and fourth statistical moments respectively, are invaluable in expressing a pattern of application depths as a statistical distribution. However, for purposes of comparison, sophisticated criteria are necessary only when the differences in the significant features of a limited number of patterns are minimal. Ultimately, the data are more important then the coefficients.

Another type of uniformity criterion has been suggested by the U.S. Department of Agriculture, W. D. Griddle, S. Davis, C. H. Pair and D. G. Shockley (1956) defined a "pattern efficiency", Pe according to the equation N/4 (xi) i=1 min P e ..5-C Eq. 4.2.5 N/ where (X.)are the i min 4 observations forming the lowest quartile of the sample, and TC: is the arithmetic mean of all N observations as before. The pattern efficiency was proposed primarily as a standard for the satisfaction of irrigation requirements, and draws attention to the drier portions of an application pattern. However, Hansen (loc.cit; 1960) has criticised the expression because it does not posa:ss'the same physical significance as the Christiansen uniformity coefficient.

Yet another form of uniformity criterion, depending upon two coefficients has been suggested by A. D:obos and P. Salamin (1960). These coefficients may be written as 115.

A Xmax e P = ; a Eq. 4.2.6

j3 is known as the uniformity coefficient, and X the area coefficient. Xmax is the maximum depth of application within a pattern whose mean depth is X. A is the total area covered by the pattern, and Ae is the "effectively irrigated area". Ae is further defined as the area receiving an application depth X such X that 0.67ic X ;1.35. Dobos and Salamin state that, if possible, the value of p should not exceed 1.50, and the value of X should lie between 0.60 and 0.70 for single-nozzle patterns.

By assuming that observations of application depths within the overlapped patterns from a group of irrigation sprinklers followed the Gaussian, or normal distribution law, W. E. Hart (1961) was able to demonstrate a relationship between the Christiansen uniformity coefficient and the U.S.D.A. pattern efficiency. For a normal distribution curve,

Eq. 4.2.7 where //k is the arithmetic mean, and a- the standard deviation of the universe of values, and the other symbols are as previously defined. Using this equolity, and substituting forAL, and S, the standard deviation of the sample, for a-, the Christiansen uniformity coefficient may be rewritten as

U Eq. 4.2.8 h 1 - 0.798 X

The symbol Uh is used to distinguish values calculated by equation 4.2.8 from those obtained from equation 4.2.1, and is referred to as the "Hawaiian Sugar Planters' Association (H.S.P.A.) uniformity coefficient". 116.

The U.S.D.A. pattern efficiency may also be expressed in terms of the normal distribution. According to Hart, the average of the lowest quartile of the observations within a sample corresponds to a value of 5r: - 1.27S on the normal distribution curve. Approximately 90 per cent of the observations are higher, and about 10 per cent lower than this point on the curve. Substituting this value into equation 4.2.5, we obtain

P = 1 - 1.27 . Eq. 4.2.9 h 7 denotes the "H.S.P.A. pattern efficiency". where Ph Hart checked Yhs assumption of a Gaussian distribution A of observations using pattern data from a large number of single- sprinkler tests carried out in winds up to 20 mile/h. These data were overlapped at various spacings to give a total of 2024 calculated group-distributions. Equations 4.2.1, 4.2.5, 4.2.8 and 4.2.9 were used to calculate pattern efficiencies and uniformity coefficients for these patterns. Chriq_ansen uniformity coefficients were compared with H.S.P.A. pattern efficiendes by linear regression analysis, giving the equation

U = 0.3859 + 0.6022 P Eq. 4.2.10 c e

Using equations 4.2.8, 4.2.9 and 4.2.10, an equation was derived relating Uc and Uh:

U = 0.0300 + 0.358 U Eq. 4.2.11 c h

Another linear regression analysis was performed with Pe and P using only the data obtained from small sprinklers, h delivering between 4 and 12 gal/min (1558 patterns), giving

P = 0.0782 + P Eq. 4.2.12 e 0.935 h 117.

Values of the coefficients of correlation squared for equations 4.2.10 and 4.2.12 were stated to be 0.888 and 0.914 respectively. These figures indicated to Hart that the above and P , expressions for Uh and Ph form reliable estimates of Uc e and that the assumption of a normal distribution of observations was justified.

This assumption allows the designer to place a more useful interpretation on the value of the uniformity coefficient in terms of the performance of the spray system. To illustrate this point, equations 4.2.8 and 4.2.9 may be re-written as

0.798S Eq. 4.2.13 Uh . X = X - 1..27S Eq. 4.2.14 Ph . x . x -

79 per cent of the total area under a normal error curve is contained between the ordinate at the point X - 0.798S and plus infinity. The minimum value of Xi over this proportion When considering the distribution of the area will be Uh . X. pattern from a spray system, the designer is able to state therefore that 79 per cent of the total area irrigated will receive an application equal to, or greater than Uh.X. Similarly, 90 per cent of the area would receive an application equal to, or greater than Pe .X. Hart extended the scope of this type of analysis by creating a new parameter, Pa, the "area pattern efficiency", which he defined by the equation

Eq. 4.2.15 P a= 1 - b .

The suffix a is a fraction chosen so that 100(1-a) per cent of the area has an ap-olication greater than, or equal to 118.

.T, and 100(1-2a) per cent of the area receives an application Pa between P ).Y.b is a factor depending upon a, and is a.7 and (2-Pa determined by normal distribution relationships. Corresponding values of b and a, calculated by the present writer from the tables of D. V. Lindley and J. C. P. Miller (1961), are given in table 4.2.2. TABLE 4.2.2: Corresponding values of the parameters b and a in equation 4.2.15 (from table 5 of D. V. Lindley and J. C. P. Miller, 1961)

a 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50 b 1.64 1.28 1.04 o.84 0.67 0.52 0.39 0.25 0.13 0.0

Given the mean application depth and standard deviation of a distribution pattern, equation 4.2.15 can be used to calculate the minimum application on any proportion of the total area covered, or the area receiving an application between two specific limits. Since Hart first made the proposal, the assumption that application depths within overlapped patterns from a number of irrigation sprinklers follow a Gaussian distribution has remained a matter of contention. D. T. Howell (1964b) has written that: "The distributions of application depth resulting from sprinkler irrigation observed by the writer have generally been unlike any standard statistical distributions, and they exhibit a wide variety of dispersion, skewness and kurtosis". More recently, J. E. Christiansen (1965) has quoted the results of another analysis by B. J. Dabbous (1962), similar to that by Hart, in which approximate relationships between the various uniformity coefficients were derived for a more limited range of data. Dabbous used 14 sprinkler patterns from the tests carried out 1'19. by Christiansen during the experiments at the University of California begun in 1932. In the present notation, the relationships were equivalent to

LT = 1.25Uc - 0.25 Eq. 4.2.16

= 1.45U - 0.45 Eq. 4.2.17 Pe c

These equations may be re-arranged to compare. with the equations derived by Hart. Substituting equation 4.2.4 into equation 4.2.16 we obtain

= 1 - 0.80V Eq. 4.2.18 Uc which is equivalent to equation 4.2.3, and re-arranging equation 4.2.17 we have

Eq. 4.2.19 Uc = 0.31 + 0.69Pe which gives reasonable agreement with equation 4.2.10.

The area coefficient proposed by Dobos and Salamin may also be examined within the framework of a normal distribution of observations. Dobos and Salamin defined an effectively irrigated area as that receiving an application of 0.67Y Xi Comparison between this inequality and that included in the definition of the area pattern efficiency above shows that, if a normal distribution of observations is assumed, Pa may be taken to equal 0.67. For single-sprinkler patterns, an area coefficient of between 0.6 and 0.7 w/s recommended by the authors, i.e. 60 to 70 per cent of the area should receive an application between the prescribed limits. These figures may be equated to the quantity 100(1-2a) per cent to give values of the suffix a of 0.15 and 0.20 resnectively. The corresponding values of b may be read from table 4.2.2 as 0.84 and 1.04. 120. Knowing Ra and b, coefficients of variation may be calculated from equation 4.2.15. An area coefficient of 0.6 is seen to be equivalent to a coefficient of variation of 0.397 and a uniformity coefficient (Uh) of 0.683. The corresponding figures for K equal to 0.7 are found to be 0.32 and 0.744. These uniformity coefficients would be low for application patterns from a group of nozzles, but in the single-nozzle case, the figures are comparatively high. L. H. Schoenleber (1944) analysed single- sprinkler patterns for four different types of unit, but in no case obtained Uc-values above 0.63. F. Liptak (1962) used p and d coefficients in comparing application patterns from various geometrical arrangements of nozzles, but did not appear to give any guidance on acceptable values for such cases. In his 1961 paper, Hart quoted Sprinkler Irrigation Association recommendations that coefficients of variation of less than 0.2 and Christiansen uniformity coefficients greater than 0.84 should be taken to define acceptable uniformities of distribution. According to Christiansen, Dabbous took a Uc value of 0.8 as a criterion on his analysis. Wilcox and Swailes set a minimum uniformity requirement equivalent to a coefficient of variation of 0.3 and a Uc of 0.76 in their studies. Criddle et al. stated that a U.S.D.A. pattern efficiency of 0.82 indicated good sprinkler performance. By equations 4.2.10 and 4.2.12, the latter figure is equivalent to a Christiansen uniformity coefficient of 0.864.

Finally, in addition to the above, a graphical method of characterising uniformity has been proposed by M. H. Dan, an officer of the Israeli Ministry of Agriculture Field Extension Service. Details of the Dan Method have been given by S. Elhalani and J. Kraus (1956) and S. Elhalani (1961). As far as the present writer is aware, this technique has not been applied outside Israel. 121. In this method, the average of all readings within a distribution pattern is designated as 100 per cent. The pattern is then divided into three zones;

(a) an average zone, in which the readings fall between 90 and 110 per cent, (b) a deficient zone, in which the readings are less than 90 per cent of the average application depth, and, (c) a surplus zone, in which the readings are greater than 110 per cent of the average depth.

The outlines of these zones are plotted by interpolation, and the total area of each measured with a planimeter. The average application depth within each zone is also calculated.

This method is laborious, but yields useful quantitative information about distribution patterns, and involves no assumption of any statistical distribution. However, if Hart's proposals are accepted, the calculations involved in the Dan method can be done more efficiently by using the area pattern efficiency. CHAPTER FIVE 122. Experimental Work - Phase I

5.1 Preliminary work Having adopted the specification outlined in Chapter 3, the possibility of adapting existing commercial nozzles was examined. Several firms marketing large ranges of sprinkler irrigation equipment in Great Britain were contacted. The general response to inquiries was found to be both helpful and generous. One firm, British Overhead Irrigation Ltd., sent a number of market garden nozzles for closer examination. These nozzles were small, brass diffuser nozzles designed for mounting on B.O.I.L. spray lines. One of these nozzles, identified by the manufacturers as type H, provided a circular application pattern. The dispersion was obtained from four slots cut into the head of the nozzle. According to the specification received, this nozzle discharged 40 gal/h at a pressure of 30 lb/in2, covering an area 9 ft in diameter. Its properties were subjected to closer examination under laboratory conditions.

During the academic year 1962-3, the Department of Mechanical Engineering at Imperial College ran an investigation into the dispersion properties of coking tower nozzles. A working space approximately 15 ft in diameter was allocated to this project in the Hawksley Hydraulic Engineering Laboratory. In July 1963, the contents of this laboratory were moved into the Hydraulic Engineering Laboratory of the new Civil Engineering Block. Owing to the time delay involved before the latter was available for postgraduate research work, the initial tests had to be carried out in the space vacated by the Department of Mechanical Engineering. A general view of the apparatus erected is given in plate 5.1.1. 123,

PLATE 5.1.1. GENERAL VIEW OF Al:TARATUS F02 THE TESTING OF SINGLE NOZZLES. 124. The area was surrounded by a brick wall approximately 22 in high, the lower two courses of which were waterproofed. A 3-in diameter pipe was welded into a 6-in laboratory ring main running across the area. This pipe ran out along a diameter of the area, and carried a tee-piece (2-in off 3-in diameter) at its extremity 5 ft 9 in from the junction with the ring main. The nozzles tested were attached to the tee-piece approximately 7 ft 8 in above laboratory floor level. Flow to the nozzles was controlled initially by a 3-in gate valve mounted immediately downstream of the junction with the ring main. An extension arm was attached to the wheel of this valve allowing discharges to be altered without the operator entering the test area. The 3-in pipe was of sufficient length to position the nozzles roughly over the geometrical centre of the area.

The B.O.I.L. type H nozzle was screwed into a brass plate which fitted on to 3 short lengths of studding attached to the tee-piece. The nozzle was oriented to spray directly downwards. Its behaviour was examined qualitatively at various working pressures. Changes in pressure were found to cause abrupt changes in the dispersion properties of the nozzle. Also, the rates of application dictated by agricultural and horticultural practice are well below the maximum anticipated for the laboratory catchment experiments.

B.O.I.L. nozzles are typical of those generally available. Other nozzles could have been obtained from another manufacturer, but the possibility of finding one which met the initial criteria was felt to be remote. Accordingly, the writer designed a simple basic nozzle which could be made without difficulty in the College workshops, and was capable of indefinite variation in detail dimensions. Details of the prototype nozzle are given in figures 5.1.1(a) and (b). 125.

2 k-16 i, AM

5" 8

5" 0:375n 8

5,4 0.1110111.01, 41.1111.• Ombra... 13" 1" 16 16

8 GENERAL ARRANGEMENT (HALF SECTION) SCALE : 2 x FULL SIZE .

PART.NO. NAME OF PART. MATERIAL NO.OFF.

0 NOZZLE BODY BRASS 1

0 COLLAR BRASS 1

0 SWIRL PLATE BRASS 1

SPACER BRASS 1 1111 ORIFICE PLATE BRASS

ELQULZE;14141(21, Prototype nozzle assembly — general arrangement .

1°8 .3 \\.1.\(.0/ z A SECTION AA Tr T 8

ORIFICE

11 I I— 0/O B Of ID 8 pi

0 SWIRL PLATE 0 ORIFICE PLATE FIGURE 5.1.1(b) Prototype nozzle assembly - detail of typical swirl plate ( type E) , and orifice plate (type A) to a scale of 2 x full size. 127. The principal element of this nozzle consisted of two thick brass plates separated by a -;-j-in1 thick brass ring. This "sandwich" fitted into a recess in the bottom of the nozzle body and was held in place by a collar as shown in figure 5.1.1(a). The inner plate, referred to as the "swirl plate" 741 carried a number of slots around its perifery designed to impart a circulatory motion to the flow. The outer, or "orifice plate" contained a single centrally-placed, sharp-edged orifice which acted as a sink for the chamber formed by the ring between the plates. Initially, two different types of swirl plate and two different orifice plates were tried out. The type A orifice plate had a single centrally-placed, sharp-edged orifice 1-in in diameter. The type A swirl plate had twenty-four 1/16-in. diameter vertical holes equally spaced around its perifery at a radius of 7/16-in. The type B swirl plate had 8 equally-spaced 45 degree slots. The cross-section of the slots was approximately 2,- by 1/16-in. The swirl plate was made in two separate pieces. The slots were cut in a disc, one inch in diameter, and a ring with an overall diameter of inches and an inner tadius fractionally under Q-in was sweated on to its outer edge.

The type B orifice plate had a centrally-placed equilateral-triangle profile orifice of equal area to that of type A. The use of non-circular orifices for irrigation sprinklers has been discussed by W. A. Hall and P. A. Boving (1956). According to their paper, triangular-shaped orifices tended to produce improved water distribution characteristics and more uniform droplet sizes. Favourable conclusions on non-circular orifices have also been published by W. K. Bilanski and B. H. Kidder (1958) and I. Seginer (1963), and so the opportunity was taken to build a further appraisal of triangular orifices into the present study. 128.

A convention was adopted for identification of the nozzles in which each combination of orifice and swirl plates was known as a different "type" of nozzle. Nozzle type A/B, for example, consisted of a type A orifice plate below a type B swirl plate. A qualitative comparison was made between nozzle types A/A, A/B, B/A and B/B with the following results.

At a level 6 ft below the plane of the orifice, nozzle type A/A covered an area roughly 18 in.in diameter. There was a pronounced central portion to the jet, and relatively little dispersion occurred. In contrast, the same orifice plate paired with the type B swirl plate covered an area of over three times the diameter of that provided by type A/A. An interesting behaviour pattern was observed in the flow within the first few inches immediately below the nozzle with changes in the working pressure. This phenomenon is illustrated and discussed in detail in Appendix B. Extensive dispersion of the jet was obtained with nozzle type A/B.

When paired with a type B orifice plate, the type A swirl plate was found to give a similar performance to nozzle type A/A. Again, changing the swirl plate to a type B improved the dispersion of the jet, but the general shape of pattern 6 ft below the orifice tended to be triangular and not circular. The behaviour of nozzles with triangular orifices is discussed more fully in Appendix C.

The conclusion that the type A swirl plate was inefficient compared with the type B is obvious. In order to produce rates of application in accordance with the specification, further investigation was confined to variations of the latter type. If the nozzle is considered in terms of the sandwich of plates, the following dimensions may be regarded as variable: 129. 1. The swirl plate (a) the thickness of the plate, and (b) the area of cross-section, angle, length-to- width ratio and number of the slots. 2. The chamber the depth of chamber 3. The orifice plate (a) the thickness of plate, and (b) the diameter and geometry of orifice, including the provision of chamfers or sharp edges

Numbers (la), (2), (3a) and (3b) along with the dimensions of the nozzle body and its roughness May be regarded as constant factors in the nozzle design without imposing severe restrictions on the variations that can be obtained from the same basic unit. Attention was therefore confined to evaluating the extent to which the items listed under (1b) above effected the dispersion characteristics of the basic nozzle. From this list, the number, angle and radial measurement of the slots were selected as the most appropriate variables. Slot width, the dimension perpendicular to the faces of a slot, was assumed to be another constant factor in the design. Seven additional swirl plates were made, allowing a possible choice of eight nozzles. Details of these nozzles are given in table 5.1.1. 130. TABLE 5.1.1. Principal dimensions and details of test nozzles

swirl plate details nozzle type angle of number radial mmt slot width slot (degrees) of slots of slot (in) (in) A/B 45 8 1/8 A/c 45 8 1/4

A/D 45 4 1/8 h

A/t 45 4 1/4 inc 6 A/F 60 8 1/8 1 A/G 60 8 1/4 ll 1/ A/H 6o 4 1/8 A A/J 60 4 1/4

NB. Angle of slot refers to the angle between the slot and the plate surfaces.

S. Elhanani (1961; pp.22-4) outlined three distinct methods for evaluating the distribution patterns from sprinklers and nozzles. These were:

1. The testing of single units, 2. The testing of single laterals with units set at a given spacing, and 3. The testing of a complete network of units at predetermined spacings.

Method (1) is the most flexible of the above alternatives, as a single-nozzle pattern can be used to build up an indefinite number of group-application patterns as described in section 4.2. However, theoretical overlapping takes no account of interference effects between the sprays from adjacent nozzles, or defects in manufacture, which alter the dispersion properties of what are essentially similar units. Method (3), and to a limited 131. extent method (2), would not be subject to these sources of error, but both involve changing the apparatus to obtain different spacings of units. The test area required for method (3) would be at least four times that required for method (1). As the space available in the Hawksley Laboratory was restricted, method (1) was adopted for the present series of experiments.

Time would not permit a full investigation of the application patterns from each of the nozzles in table 5.1.1 at a large number of working pressures. In addition, the question of the variability between patterns from successive tests under identical working conditions was of considerable, if not equal importance. Accordingly, a programme of experiments was undertaken in which patterns of application depth were obtained from each of the first five nozzles operating under heads of 5, 10, 15 and 20 feet of water. Each test under this set of conditions was repeated once.

This programme, involving 40 separate tests began on 29th November 1963, and was completed on 21st January 1964. Before running these experiments, the existing pilot apparatus underwent further development.

5.2 Description of apparatus The principal features of the apparatus have already been described in section 5.1 above. However, the existing method of controlling the working pressure at the nozzle was found to be totally inadequate. The discharges of individual nozzles were extremely low. At a head of 20 ft of water, nozzle type A/B delivered only 0.07 ft3/min. The fine control required to reproduce the required test conditions under such low rates of discharge could not be obtained with the 3-in valve. A bypass was installed with a *-in valve upstream of the main valve connected 132. by a length of polythene tubing to a tapping on the downstream side. Subsequent investigation showed that this system was equally unreliable. Conditions could not be guaranteed to remain sensibly constant. On one occasion, an initial head of 19.55 ft of water fell to 19.28 ft after 20 minutes, and then recovered to 19.40 ft after a further 60 minutes.

This problem was lessened considerably by substituting a suitably modified gas-cock for the 27-in valve. The modification consisted of the opening out of one side of the aperture in the plug into a "V" running part-way round the circumference. This change in profile of the plug allowed progressively finer control of flow as the discharge was reduced. The arrangement was found to be extremely successful, and was incorporated in all subsequent apparatus in which the same difficulties were encountered.

The variations in application depth over the area covered by each nozzle were measured using a grid of metal cans as described in section 4.1. An attempt was made to define a reliable size of sampling vessel. Four "spray gauges", 14 in. in diameter were soldered up from tin sheet. Their heights varied from 3 to 6 inches in increments of one inch. The gauges were placed at random on the laboratory floor within the cone of influence of nozzle type A/B. Each gauge was exposed for a period of ten minutes at each of the four points, and the catch measured in a 100 ml measuring cylinder. The results are presented in table 5.2.1. 133.

TABLE 5.2.1 A comparison between the catch obtained in four different heights of spraygauge at four points chosen at random within the cone of influence of nozzle type A/B

catch recorded in spraygauge (ml) position 3" high 4" high 5u high 6" high

first 23 24 25 25 second 29 32 34 35 third 28 30 36 ' 36 fourth 25 25 24 26

The differences in catch recorded between the various heights of gauge were extremely small. The results can only be compared if absolute reproduction of conditions is assumed between the successive exposures. As uncontrolled minor variations are always present, the differences cannot be regarded as significant. A height of 6 inches was finally chosen, as the splashing readily observed from large drops falling into the shallower gauges was minimal with this size of gauge. Taller gauges tended to be unsteady and easily disturbed. According to W. C. Strong (1961; p.198) the diameter of measuring vessels can be varied five-fold and only cause one percent differences in the recorded catch. The choice of 111 inches as the diameter for the spray gauges used in the present experiments was completely arbitrary.

75 drawn metal cans, 14 inches in diameter, were made to special order by the Metal Box Company Ltd. at Sutton-in-Ashfield. As originally delivered, the cans were 9 in deep and fitted with screw tops. These screw tops were removed when the height was trimmed to 6 in, leaving sharp edges on each gauge. 134.

A sampling frame was assembled from Handy Angle. The frame was mounted on castors, and its height above floor level adjusted so that the moutl7of the gauges stood exactly 72 inches below the nozzle orifice. The gauges were placed at 6 by 6-in centres on the sampling frame, and held in place by 2-in Lewis Springs. The frame was designed to carry a maximum of 64 gauges.

This sampling system was not the same as that used by the Department of Mechanica3 Engineering for the evaluation of patterns from cooling tower nozzles. The method used in that project consisted of a radial arm carrying gauges at equal intervals. This method has the advantage that the spacing of gauges is more dense within the area in which the variations in application depths are generally large. The disadvantage, which in the opinion of the present writer far outweighs the advantage, lies in repeating the sampling procedure for a number of different radii. In order to plot a pattern with any certainty, at least eight radii would be required, and such a sequence of samples would inevitably mask any possible variations between patterns under seemingly identical working conditions.

Having obtained a large number of samples of application depth, the problem arises of measuring the contents of each gauge both quickly and accurately. A chemical balance was tried and found to be too slow to operate. A Mettler K.7 electrical balance, reading directly to 0.01g was also tried. Using the latter, catch weights could be obtained in less than half the time required with the chemical balance.

The source of error in obtaining a full series of depth readings is primarily one of evaporation. Air temperature in the laboratory averaged 67°F. An attempt was made to evaluate this error by intermittently weighing a spraygauge over an extended time interval after a test. A figure of 0.10 cm3/h was obtained which 135. is equivalent to approximately 0.003 inches depth of catch per hour. Part of this loss can probably be attributed to the evaporation of moisture from the outside of the gauge rather than from the catch. The gauges were wiped with a dry cloth before weighing, thereby removing all but a thin film of moisture from their outer surfaces. From test number 24 (9th December 1963) onwards, air temperature was measured and recorded during each laboratory session. As temperature provides a crude index to the amount of evaporation, the consistency of the loss could be examined even though its exact magnitude remained a matter for speculation.

Another standard measurement taken during the programme of tests was pressure at the nozzle. A'1/16-in diameter pressure tapping was inserted in the nozzle body 13/32-in above the swirl plate, and conre'cted directly to a mercury manometer. A vernier attachment was fitted on to the scale of the manometer, allowing the head to be measured to 0.01 cmHg. The head in feet of water was obtained from the reading in cmHg by dividing by a factor of 2.242. Care was taken to clear the connecting line of entrapped air before taking each reading.

The total discharge from each nozzle was estimated directly from the time interval taken for the water level in a tank of known dimensions to rise by a predetermined amount. An 8-in plastic funnel was suspended immediately below the tee-piece carrying the nozzle, allowing sufficient airspace around the nozzle to prevent interference with the initial dispersion. A length of thin-walled rubber tubing led from the neck of the funnel into a small 1-ft diameter tank. A metre rule, constrained to move between two cross-pieces of Handy Angle placed back-to-back, was used to measure depths of water in the tank. If the water level rose H inches in T seconds, the discharge 136. Q in ft3/min was given by

Q = 3.927 Eq. 5.2.1

5.3 Procedure Before beginning the comparison tests between the various nozzles, a number of trial runs were made to perfect the experimental procedure, and prove the apparatus. These tests, numbered 1 to 13, drew attention to the problem of controlling the working conditions discussed in section 5.2. They also showed that a full sampling grid of 64 gauges was not necessary for all tests, and "reduced grids" of 24, 28, 36, 48 and 56 gauges were adopted for most of the subsequent work. The latter were arranged so that the central area of the grid receiving the larger proportion of spray had a dense network of gauges, whereas their spacing was increased at larger radii from the nozzle.

The sampling frame was positioned so that a plumb line dropped from the nozzle orifice lay directly between the innermost four gauge positions on the frame. A datum line was drawn out on the laboratory floor, passing through the plump centre from the nozzle and running roughly at right angles to the line of the supply pipe, to assist in locating the sampling frame for each test.

The test procedure adopted was as follows:

1. The sampling frame was located in its correct position with respect to the nozzle, and the appropriate number of gauges clipped into place. A sheet of polythene, supported by a frame of Handy Angle running on castors, was wheeled into place over the grid of gauges. 137. 2. The working conditions were set up using the bypass valve and paying strict attention to the pressure read off the mercury manometer. When conditions were sensibly constant, a measurement of total discharge from the nozzle was taken.

3. The cover was rolled away from the sampling frame, and the gauges exposed for a standard interval of ten minutes. The length of exposure was recorded on a stopwatch. The time interval was shortened to.as little as three minutes in particular cases owing to the occurrence of exceptionally high application depths. At the end of the exposure, the cover was rolled back over the sampling frame from the opposite side to that from which it was removed. This procedure ensured that each gauge received the same length of exposure. When the standard exposure was used, the time spent in moving the cover was extremely small compared with the total exposure time, being less than one per cent. In the case of the three minute exposures the possible error increased to about three per cent.

4. The manometer reading was checked, and then another measurement of total discharge taken. The nozzle was closed down, and the gauges removed from the sampling frame, wiped dry and weighed on the electrical balance.

During the following laboratory session, the test was repeated under identical working conditions, and the two results compared. 138. The total weight of each gauge and its contents were recorded immediately after exposure, along with the number of the gauge and its position on the sampling frame. The grid positions were identified by a letter-number combination corresponding to eight rows, numbered one to eight, of eight columns lottered A to H. The columns of the grid were taken to run parallel to the pipe carrying the nozzle. The dry weight of each gauge was subtracted from the total weight recorded to give the catch weight. The depth of application in inches, assumed to occur at the centre of each gauge, was obtained from the catch weight in grammes by dividing by a factor of 59.42.

These depths were subsequently used to plot the application pattern for the nozzle under the particular working condition. Isohyets, or contours of equal application depth, were drawn out at minimum intervals of 0.25 inches per standard exposure time. Where the data indicated sharp increases in depth over relatively short horizontal distances, the intervals were extended to maintain the clarity of the diagrams. Only one application pattern was plotted for each pair of tests under similar working conditions. All patterns plotted were adjusted to a common base of ten minutes exposure for purposes of comparison.

In plotting the single-nozzle application patterns, the following rules were observed:

1. Linear gradients in application depth were assumed between the measurements made over the sampling grid.

2. The positions of the isohyets were determined solely by interpolating along the rows and columns of the sampling grid, and not diagonally across the grid between values lying in both different rows and different columns. 139. Rule (1) can be justified on the basis of the saving effected in both time and labour by its use. The positions of the isohyets could have been determined to a greater degree of accuracy if cross-sections, taken along the rows and columns of the sampling grid, had been plotted before drawing each pattern. The positions of the isohyets could have been marked off on each cross- section and then transferred to the application pattern. As a smooth curve could have been drawn through the points in each cross-section, the method would not have involved assumptions similar to rule (1). However, the drawing of the curve would have involved subjective judgement, which is generally found to alter after many repetitions of the same procedure. Rule (1) served also to avoid this type of influence.

Rule (2) was adopted after preliminary trials had shown that the use of additional points, obtained by interpolating diagonally across the sampling grid, produced unrealistic distortions in the shape of the isohyets. Two additional points could be plotted for every four adjacent readings on the sampling grid. Invariably, these points did not coincide, and a compromise position had to be used. In general, the assumption of a linear gradient along the diagonals of the sampling grid tended to place each additional point too far towards the higher depth reading when the pattern surface was concave downwards, and towards the opposite extreme when its shape was convex. In other words, the interpolation should have been carried out using pattern cross-sections as described above. The same argument against their use applied in support of rule (1) may also be used here. The distortions introduced by interpolating linearly along the diagonals of the sampling grid were obviously the result of the plotting procedure, and to avoid unnecessary confusion, the additional points were omitted altogether from the patterns. 140. 5.4 Discussion of results The application patterns obtained for each of the five nozzles operating under four different working pressures are given in figures 5.4.1 to 5.4.20.

In general, the grid spacing of 6 in by 6 in was found to be adequate to define variations within these patterns. Some difficulty was encountered with nozzle type A/C owing to the high discharges obtained. Variations in depth as large as 4 in were recorded between adjacent points on the sampling grid at the centre of the 15 ft head pattern for this nozzle, even though the exposure time had been reduced to 3 minutes. Where variations of this order were encountered, linear interpolation placed the isohyets falling between the sampling points at equal intervals. The resultant patterns were deceptively conical in shape, unless examined with the original measurements clearly indicated.

The "zero" isohyets of the application patterns have been purposely omitted from figures 5.4.1 to 5.4.20. The depths recorded along the edges of the sampling grid were generally extremely small. In many cases, the total volume of the catch could be attributed to the collection of a small number of larger drops thrown out at random from the cone of influence of the nozzle. The extra gauges needed to define the pattern edge with certainty would have increased the time and labour required for each test run out of all proportion to the content of the additional information. The 0.25-in isohyet could be drawn reliably on most of the patterns, and this value was chosen to mark their periphery.

If the application patterns made by the single nozzles could have been examined under ideal conditions in which both nozzles and sampling system were correctly levelled and aligned, the isohyets would have plotted as concentric circles. The

CiQ)

1.·0 5 30 0 1· 10 0·2 0·5 0 ·5 05 0·5 025 02 0·25 025 NOZZLE POSITION +

FIGURE . 5. 1. 3. FIGURE 5 . 1..7 . FIGURE. 5 . I. . 11 FIGURE. 5. 1. . 15 FIGURE . 5 . I. 19 . Application pattern for nozzle type A I B under Application pattern for nozzle type A / C under Application pattern for nozzle type A I 0 under Application pattern for nozzle type A I E under Application pattern for nozzle type A I F under a head of 15·00 It water Itest number 18) a head of 15.03 It water I test number 26) a head of 15·01. It water I test number 31.) a head of 15·03 ft water I test nu mber 1.2) a head of 15·01. It water Itest number 50 )

+ to + 0 3.5 5· 1.0 3·0 2· 3·0 2 0 2· 0 1- a 1'0 0·2 05 0·5 0·5 025 a 2 025 025

F IGURE 5. 1. . 1. . FIGURE 5 . 1. .8. FIGURE . 5 . 1. . 12 . FIGURE . 5 . 416. FIGURE . 5.1.. 20. Application pattern for nozzle type A I B under Application pattern for nozzle type A I C under Applicat ion pattern for nOZZle type A 10 under Application pattern for nozzle type AI E under Application pattern for nozzle type A I F under a head of 20·00 ft water Itest number 21) a head of 20·00 ft water I test number 28) a head of 19 ·95ft water Itest number 36) a head of 20·07 ft water I test number 41.) a head of 20·01. ft water I te st number 53 J 143. variations in application depth could have been defined fully by a cross-section along any radius which, when rotated through 360 degrees, would generate the whole pattern. No doubt the sampling system used by the Department of Mechanical Engineering at Imperial College to evaluate the patterns from their cooling tower nozzles by sampling on a polar coordinate basis was devised to take advantage of any symmetry. Unfortunately, some degree of asymmetry was present in every one of the application patterns obtained in the present investigation. If the nozzles were as little as one degree out of their true vertical alignment, the centre of the application patterns would fall roughly 1.25 inches away from the plumb centre from the nozzle 72 inches below. Even allowing for inaccuracies in the sampling and plotting procedures, this movement was sufficient to distort the general shape of the isohyets.

The extent to which the single-nozzle apparatus was misaligned, may be judged from the patterns shown in figures 5.4.1 to 5.4.20. The geometrical centre of the sampling grid, which corresponds to the position of the .nozzle, has been marked on each. From these diagrams, the magnitude and direction of the movement would appear to be consistent, making the patterns obtained from different nozzles comparable one with another. Despite the interference caused by this misalignment, the general mode of behaviour of the nozzles over the chosen range of working heads may be inferrzed without undue difficulty.

Comparisons between patterns obtained from the same nozzle under different working conditions, and those for different nozzles under the same working conditions, could be made with greater certainty if the information contained in figures 5.4.1 to 5.4.20 were expressed in a more convenient form. The essential differences between the patterns obviously lay in the 144. extent of areal coverage up to predetermined depths of application. The areas contained within each contour in figures 5.4.1 to 5.4.20 were therefore measured using a planimeter, and the results plotted as families of depth-area curves for each nozzle as shown in figures 5.4.21 to 5.4.23. Basic similarities existed between the patterns from nozzle types A/B and A/D, and between types A/E and A/F, and their families of curves have been plotted together in figures 5.4.21 and 5.4.22 respectively. Nozzle type A/C demonstrated an entirely different mode of behaviour, and its family of curves has been shown separately in figure 5.4.23.

At a head of 5.00 feet of water, nozzle types A/B, A/D, A/E and A/F were all found to exhibit patterns in which the highest application depths occurred at a radius of from 12 to 18 in from the nozzle. Had the misalignments in the apparatus been absent, and the sampling mesh fine enough to show those part of the pattern in greater detail, the isolated points of high application depth would almost certainly have appeared as complete annuli. This effect is less obvious in figures 5.4.21 and 5.4.22, but the way in which the 5.00-ft head test curves (test numbers 15, 30, 38 and 46) lie apart from the curve for the other three working conditions may be noted.

Increasing the working head to 10.00 ft for each of the same four nozzles produced a complete change in the shape of their application patterns. The largest application depths were recorded at the four sampling points nearest the nozzle position in each case, although their values varied considerably from nozzle to nozzle. The 1.25-in contour was the maximum that could be drawn on the pattern for nozzle type A/D, whereas the corresponding values for types A/B, A/E and A/F were 3.0, 5.0 and 4.0 in respectively. Of the depth-area curves for the four nozzles at this working condition, only that of nozzle type A/D (test number 32) showed a 1.0 2.0 3.0 4.0 5.0 6.0 AREA SCALE (FT2) TEST 34 TEST 21

5 3.0 -3.0

TEST 36 TEST 18

TEST 16 io 4 TEST 32

0 U./ sr0 0 til NOZZLE TYPE A/ 0 NOZZLE TYPE A/ 8 . 1 0 1-0 2.0 3.0 4.0 5.0 6.0 AREA RECEIVING DEPTH >f RECORDED AFPtJCATION FT 4 ) FIGURE 5 i4. 1. Depth-area curves for nozzle types A/B and A/ 0 . 1.0 2.0 3.0 4.0 5.0 6.0

Et7 7.0 IX AREA SCALE (FT2 ) U)

6.0 6.0 z TEST 42 TEST 50

CD 5.0 z U) w I 4.0 zto TEST 40 vow* TH TEST 48 DEP

TION NOZZLE TYPE A/ E NOZZLE TYPE A/F 2.0 20 LICA TEST 44 TEST 53 PP A D 1.0 1.0 DE ST 46 OR C E R

0 1.0 2.0 3.0 4.0 5.0 k0 AREA RECEIVING DEPTH >, RECORDED APPLICATION (FT 4) FIGURE 5. 4. 22. Depth - area curves for nozzle types Al E and A I F 147. distinct intermediate result between the 5-ft and the 15-ft head curves. With each of the other nozzles, the 10-ft head curves were similar in shape and lay closer to the 15-ft head curves. The total area bounded by the 0.25-in contour was largest with nozzle type A/D (5.60 ft2), with types A/B (4.80), A/F (4.57) and A/E (4.20 ft2) next in decreasing order of magnitude. In each case, these values were smaller than the corresponding figures at the 5-ft head condition.

A further increase in head to 15.00 feet brought increases in the maximum depths recorded from each nozzle. The patterns obtained were again roughly conical in shape, with the largest readings occurring near the nozzle position. The maximum contour that could be drawn in for both nozzle types A/B and A/D was 3.5 in. Nozzle types A/E and A/F had maxima of 7.0 and 6.0 in respectively. The area enclosed by the 0.25-in contour increased by 0.62 ft2 for nozzle type A/B, and by 0.24 ft2 for type A/E. That of nozzle type A/F remained constant, and the area covered by type A/D decreased by 1.46 ft2. Finally, at a head of 20.00 ft of water, although the general shape of the patterns remained conical, another change in behaviour was noticeable. The values of the maximum contours recorded for nozzle types A/D, A/E and A/F decreased by 0.5, 2.0 and 1.0 in respectively. That of nozzle type A/B remained constant. In all four cases, the areas enclosed by the 0.25-in contours were substantially increased, nozzle type A/B by 0.63 ft2, A/D by 0.64, A/B by 1.80 and A/F by 1.03 ft2. The results obtained from nozzle type A/C were sufficiently dissimilar to the other four for them to warrant separate discussion. The total cross-section area presented to the flow by the type C swirl plate was twice as large as that of types B, B and F, and four times that of type D (see table 5.1.1). Consequently, at a DEPTH (INCHES PER10 MIN EX POSURE.) 0 FIGURE. 5.4.23. Depth -artacurves fornozzletypeA/C.

AREA RECEIVINGDEPTH>,RECORDEDAPPLICATION (FT 1.0 2.0

3:0

4.0 •••••••••tsi l• 2 ) 149. head of 5.00 ft, nozzle type A/C gave a fractionally larger discharge than nozzle type A/D gave at a head of 20.00 ft. The necessity to reduce the exposure times when evaluating the patterns from the former at heads of 10.0, 15.0 and 20.0 ft has already been referred to in section 5.3. The most significant change observed through having these high discharges with nozzle type A/C was the total absence of a similar pattern shape to the other four nozzles at a head of 5.00 ft. The pattern obtained with nozzle type A/C at this head was conical in shape and not annular. The type of pattern exhibited by the other nozzles at a head of 5.00 ft of water was similar to that shown by J. E. Christiansen (1937; p.534) for an irrigation sprinkler operating at a pressure less than its optimum working head (see also figure 4.2.4(a)). Owing to the design of nozzle type A/C, the same type of "low pressure" conditions would probably only occur at heads of one ft or less.

A small decrease in the area bounded by the 0.25-in con- 2 tour from 4.18 to 4.04 ft was obtained as the head was increased from 5.00 to 10.0 ft, and another of 0.66 ft2 was recorded between 2 10.0 and 15.0 ft. An increase of 0.66 ft was observed between the 15.0 and 20.0-ft patterns. The values of the highest contours that could be drawn on each pattern were 4.0, 7.0, 14.0 and 12.0 in at the 5.0, 10.0, 15.0 and 20.0-ft heads respectively. In showing a slight decrease in the value of the highest contour between the 15.0 and 20.0-ft heads, nozzle type A/C behaved in a similar manner to the other four nozzles.

If the results obtained with nozzle type A/C are disregarded, the general pattern of behaviour of the nozzles that were examined can be summarised as follows.

At heads less than or equal to 5.0 ft of water, a "low pressure" condition exists in which the greater proportion of the 150.

discharge from the nozzle is deposited at a radius of some 12 to 18 in from the nozzle. This type of dispersion results in an application pattern whose cross-section along any diameter is typically illustrated by that of nozzle type A/D shown in figure 5.4.24(a). A further increase in pressure at the nozzle results in the filling-up of the "plateau" left in the centre of the 5.00-ft head pattern. The centre portion of the cross-section is built up at the expense of the annulus until a conical pattern is obtained. This stage in development is represented by (b) in figure 5.4.24. The area covered by the pattern is slightly less than that at the previous stage. It is interesting to note that, in order to maintain this development the pattern must be uniform in depth over most of its cross-section at some intermediate head.

Another increase in nozzle pressure had the effect of increasing the peak depth of the pattern. The area of coverage may either remain approximately the same, or decrease as shown by (c) in figure 5.4.24. With further increases, a head is reached at which the peak depth arrives at a maximum from which it begins to decrease in value as the head increases. The decrease is accompanied by an increase in the area of coverage, giving a pattern cross-section such as (d) in figure 5.4.24.

As stages (a) to (d) represent equal increments in pressure, the corresponding increments in total discharge will not be equal. The head-discharge relationships of the nozzles may be written as power laws of the general form

Q = x (H)n Eq. 5.4.1 in which Q denotes the total discharge in ft3/min at a head of H ft of water, and K and n a constant and exponent respectively. The increase in discharge between stages (b) and (a) is therefore 1.0 - TEST 30 5.00 FT HEAD.

1.0 - TEST 32 9.97 FT HEAD

3.0 TEST 34 15.04 FT HEAD. z

2.0 z

(r) u s 1.0 Cs) a. 0 0 3.0 (d) TEST 36 19.95 FT HEAD.

2.0

1.0

Al 62 C3 D4 ES F6 G7 H8 GRID POSITION. FIGURE . 5. 4.24. Comparison between diagonal cross sections from tests on nozzle type A/D. 152.

greater than that between (c) and (b), which in turn is greater than that between (d) and (c), i.e.

Eq. 5.4.2 Qb Qa Qc -Q13 Qc

The largest increment Qb Qa accounts for the rapid change of the annular pattern into a conical shape. The development through stages (c) and (d) takes place at a relatively slower pace, until at (d), the increase in discharge per unit increase in head is so small, that, as the dispersion becomes stronger, the area of coverage increases at the expense of the maximum application depth.

The head-discharge relationships of all the nozzles described in table 5.1.1 are shown in figure 5.4.25. With the exception of nozzle types A/B, A/G, A/H and A/J, only the routine discharge measurements from each test run were available to plot this diagram. Nozzle type A/B was used during the preliminary trials (test numbers 1 to 13) and a larger number of readings was obtained. Nozzle types A/G, A/H, A/J were not included in the main test programme, and their head-discharge measurements were carried out separately. The relationship for nozzle type B/B has also been included in figure 5.4.25, although its behaviour is discussed separately in Appendix C.

Four points were considered to be insufficient to plot relationships corresponding to equation 5.4.1, and so figure 5.4.25 has been plotted with logarithmic scales. When transformed to logarithms, equation 5.4.1 becomes

log Q = n log H + log K Eq. 5.4.3

an expression corresponding to a straight line of gradient n and intercept on the log Q axis of log K, which can be drawn with greater certainty. Again, because of the small number of points 15,;.

0.11

U) 0.10 z

0.075 I.

tit N N Z 005

0.04 A/

B/ 0.03 A/ A/O : x A/C : A/D 0 A/ E : • &IF : A/G : ° 0.02 A/H : A/i : 0 B/B : '1

0416 2.5 50 10.0 15.0 20.0 25.0 HEAD AT NOZZLE ( FT WATER ) FIGURE. 5. 4, 26 Comparison between head-discharge relationships for all test nozzles 154. available, no attempt was made to evaluate the constant K and exponent n by regression analysis, and the lines drawn in figure 5.4.25 have been fitted by eye. On the limited evidence available from this figure, the data from the nozzled4having 60-degree slots in their swirl plates appear to lie at a fractionally steeper gradient than those from nozzles having 45-degree slots, i.e. the exponent n is larger for the former than the latter.

A number of interesting points emerge from figure 5.4.25. These points are conveniently illustrated by listing the nozzles in increasing order of magnitude of their total discharges as in table 5.4.1.

TABLE 5.4.1: Test nozzles with circular orifices, listed in increasing order of magnitude of their total discharges, along with their principal dimensions and details

SWIRL PLATE DETAILS

nozzle angle numbel type radial REMARKS of slots of mmt.of (degrees) slots slots (in)

AID 45 4 1/8 ) )equal cross-section area A/1-1 6o 4 1/8 ) A/B 45 8 1/8 ) ) A/P 60 8 1/8 )equal cross-section area, )twice that of types A,' A/E 45 4 1/4 )and A/H ) A/J 6o 4 1/4 )

A/c 45 8 1/4 )equal cross-section area, )four times that of types A/G 60 8 1/4 1)A/D and A/H 155. The nozzles can be considered to fall into three distinct groups according to the total cross-section area of the slots in their swirl plates. The larger the cross-section area, the larger the total discharge obtained from the nozzles at any given head. The latter statement is obvious, but when the list of nozzles is considered on the basis of the geometry of the swirl plates, two important trends can be seen, namely:

1. The total discharge of any nozzle with a given geometry of slots was always larger when the slots had been cut at an angle of 60 degrees instead of 45. This effect was greater when the total cross-section area of the slots in the swirl plate was small. The head-discharge relationships for nozzle types A/C and A/G were virtually identical, whereas the discharges of type A/H were always approximately 10 per cent larger than those of type A/D.

2. The larger the radial dimension of the slots in the swirl plate, the larger was the total discharge. Nozzle types A/B and A/E had the same angle of slot, and the same total cross section area through their swirl plates, but the nozzle with the longer radial dimension of slots delivered the greater discharge. The same comparison may be made between nozzle types A/F and A/J.

For the purposes of the present investigation, the dispersion properties of the individual nozzles are of greater significance than their total discharges. If the application patterns shown in figures 5.4.1 to 5.4.20 are also examined in relation to the geometry of the swirl plate in each nozzle, similar trends can be observed. If, for example, the performance of nozzle type A/C is compared with that of type A/E, the effect 156. of halving the number of identical slots may be examined. For the three heads at which this comparison is possible, the maximum application depth is considerably reduced (by 50 per cent in one case) and the area of coverage increased. When a similar contrast is attempted between nozzle type A/B and type A/D, for which the geometrical relationship between swirl plates is the same, the influence on maximum application depths is found to be less pronounced. In respect of the areal coverage, the effects are entirely opposite at 15.0 and 20.0-ft heads.

The effect of increasing the angle of the slots in the swirl plate from 45 to 60 degrees, obtained by comparing the patterns from nozzle types A/B and A/F, would appear to be to increase the maximum application depths. The total areal coverage of nozzle type A/F was smaller than that of type A/B at all heads.

The patterns from nozzle types A/B and A/C give some indication of the effect of doubling the radial length of the slots, keeping their number and angle constant. For the three sets of patterns which are comparable, doubling their length caused a considerable reduction in the area covered, and the maximum application depths increased. Similarly, the maximum depths recorded on the patterns from nozzle type A/F are greater than those for type A/D, although the conclusions regarding areal coverage are reversed at the 15.0 and 20.0-ft heads.

To summarise the above, better dispersion properties were obtained with the slots in the swirl plate cut at 45 and not 60 degrees. A similar effect was obtained by halving the radial dimension of the slots. The ratio of the width of a slot to its ralial length was more critical in regard to the dispersion properties of the nozzle than the total cross-section presented to the flow through the swirl plate. The latter was more significant in terms of the total discharge from the nozzles. 157.

In section 5.1, the statement was made that the variability between patterns from successive tests under identical working conditions was of considerable, if not equal importance to the differences in performance between the different types of nozzle listed in table 5.1.1. The ability of the nozzles to reproduce their application patterns at each of the four test conditions was examined by repeating the tests once under the same working conditions for each nozzle. Then, the measurements of depth at specific points on the sampling grid from the original test could be compared directly with the corresponding depths from the second test.

Here, the difficulty of expressing the reproductivity of depths at all points over the sampling grid in terms of a single index was encountered. The differences between corresponding measurements of depth between successive tests could be written either as a straightforward difference in inches of depth, or as a percentage of one of the measurements. The differences in depth varied greatly in magnitude, and tended to be randomly distributed over the sampling grid. An average of the recorded differences would have been meaningless in terms of reproductivity. The expression of differences in percentages is also open to mis- interpretation. Small differences in depth yield unduly large percentages when the original measurements are also small, i.e., 0.005-in.in 0.050-in represents a figure of 10 per cent, although in physical terms the difference is minimal.

For want of a more suitable index to reproductivity, percentages were finally adopted for the present purposes. In order to avoid anomalies caused by small differences in the smaller readings at the pattern edges, only those measurements greater than 0.040-in (approximately 0.25 in/h) were considered in the following analysis. 158. The differences between corresponding depths from successive tests under the same working conditions were expressed as percentages of the original measurements. In all, 539 pairs of readings were compared. The numbers of pairs used for each test condition for each of the five nozzles are shown in table 5.4.2.

TABLE 5.4.2: Summary of data used in reproductivity analysis

number of pairs of measurements used in analysis head ft.water type A/B type A/C type A/D type A/E type A/F

5.0 33 24 33 24 24 10.0 24 22 28 24 24 15.0 44 16 28 24 24 20.0 21 24 28 24 36

total 122 86 117 96 108

The figures were then grouped irrespective of sign into classes of per cent for differences between 0 and 15 per cent, one per cent from 15 to 20 per cent and five per cent for 20 per cent and above. The numbers falling within these intervals for each of the five nozzles were then added to form an overall picture of reprodudtivity for the complete programme of tests. These results have been summarised in table 5.4.3.

Examination of the figures also showed that reproductivity improved during the course of the test programme. The results from the testing of nozzle types A/D, A/E and A/F were also grouped together and tabulated alongside those for all five nozzles in table 5.4.3. These figures show the extent of the difference, which must be attributed to improvements in the experimental method as experience with the apparatus accumulated. 159.

The best reproductivity was obtained with nozzle type A/D, and the results from this nozzle have also been shown in table 5.4.3.

TABLE 5.4.3: Reproductivity analysis (uncorrected figures)

maximum difference (5) between proportion of corresponding measurements for that pro- total number of portion of the total number of readings pairs used in analysis (%) all nozzles types A/D, A/E, A/F type A/D 25 2.5 2.0 2.5 50 5.0 4.5 4.5 75 8.5 7.5 7.0 95 20.0 12.5 10.0 98 30.0 15.0 13.0

There were three definable sources of error in the reproductivity figures shown in table 5.4.3. These were

1. movement in the position of the sampling grid between successive tests, so that gauges at the same points on the grid were in effect in a slightly different position relative to the nozzle,

2. interference effects caused by either air movements in the laboratory, or fluctuations in supply pressure caused by other users of the laboratory constant head system operating simultaneously, and

3. differences in the length of exposure of the sampling grid between successive tests.

The presence of the first source of error was easily detected by plotting the readings and differences according to their grid position, The comparison between test numbers 16 and 17 shown in figure 5.4.26 illustrated a typical case. The depths

0.233{70-019) _ 0. 231{4).006) ALL FU.."-..AFYINGS 0 i"C RE-:AS D

0.672f-0.1i121_11.5?7_1:0.1641 !-- ‘.006) 0.6531-0-022)

0-204(70.Q10) 3-2251-0-015 13-335 (+0.125) 1.262M-006) 0-223(+0403)

0.(re4+0,...002,1 0.q40(+0•051.42.325 (+0-020) 12.3831A179i 0723(4-0.036110.122 (+0.005) ALL READINGS INCREASED. Q497(4-0.000)040 ".-L101. 5) 10-64240.029LO-2.5 (+0,017)

0...1?rjilf..001-.11_10.100(+0.CC9)

FIC,I.JRE. 5.1.. 26 Application depths from test number 16 piottcd along, with the measured differences obtained under the same working conditions in test number 17. (Nozzte type A/13 10.01 ft head )

0.1c.f9(4,0.011) 0.155(4-0.001)

0.507(+0.002) 1.435 -0.005 0.9L7( • 0.219(+0. 003)

0.128(-0.002) 1.11U0.0401 4.315‘-0.045) ?,..`-illi) 0.03 (4-0.002' 0.123(+0.001)

[0.114(-0,003) 11020 (-0-028 ) j4.065(-0.05"3 . 1...),...0.055) .9900.022LI 0 .143 (+0.003

if1701-0.004) )-c; , 0) 0.6, 71,4-0 0051_ 0.259(+0.006)

E0 .11 1'7. 10.031(-0.002) RCURE . 5.4. 27. Apptication depth from test number 6 plotted along with the measured differences obtained under 1..1z. sam W31rlg concitions in test number 49 (Nozzle. type A/F 0.09 ft "nead) 161. recorded in test number 16 are shown, along with the sign and difference in magnitude of the corresponding readings from test number 17. The point to note from figure 5.4.26 is the manner in which the positive and negative differences lie on opposite sides of a definable boundary drawn across the grid. Bearing in mind the pattern shape, a small movement in the grid position roughly at right angles to this boundary would obviously be sufficient to restore the recorded differences.

An example of a result in which the signs of the recorded differences were randomly distributed over the sampling grid has been plotted for comparison in figure 5.4.27. None of the recorded differences between depths from this pair of tests (test numbers 48 and 49) exceeded 6 per cent in magnitude. Corrections for differences in position of the measuring grid could not be applied very readily. However, where pairs of readings which differed by less than 0.020-in represented percentages above ten, and a well-defined boundary of the type shown in figure 5.4.26 was obtained, the readings could safely be omitted from the analysis. Fluctuations in supply pressure and air movement in the laboratory could easily be detected during the tests, and any such occurrences were noted in recording the experiments. In one particular case (test number 19; 4th December 1963), subsequent examination showed that the result had been effected by a fall in supply pressure during the course of the experiment. The figures obtained from pairing test numbers 18 and 19 were therefore entirely misleading and could be discarded.

No correction was possible for differences in the length of exposure of the sampling grid, but the probable magnitude of the error has already been discussed in section 5.3. Only those tests having exposures less than ten minutes were likely to be 162. affected significantly.

When the above adjustments were made, a new set of reproductivity figures were obtained for the three groupings of results considered in table 5.4.3. These corrected figures are shown in table 5.4.4.

TABLE 5.4.4: Reproductivity analysis (corrected figures)

proportion of maximum difference (%) between total number of , corresponding measurements for that pro- pairs used in portion of the total number of readings analysis (%) all nozzles types A/D, A/E, A/F type A/D

25 2.5 2.0 2.5 50 4.5 4.o 4.o 75 7.5 6.5 6.5 95 13.5 9.5 9.o 98 20.0 12.5 9.5

During the last fifty years, there have been many papers describing methods of simulating rainfall, and yet few investigators have troubled to discuss reproductivity, and many have failed to comment upon it altogether. Those who have quoted figures for reproductivity have done so for average application rates over a number of successive tests under the same working conditions. The above figures, for pairs of readings at individual points, within application patterns where depths varied from zero to tens of in/h, represent a far more severe test of nozzle performance. When compared with the figures in table 3.1.1, or those quoted by Dah-Cheng Woo and E. F. Brater (1962) for example, the reproductivity of readings during the present programme of experiments must be regarded at least as adequate if not as satisfactory. 163.

When selecting an appropriate nozzle for further study in connection with the present investigation, the following points were borne in mind. Firstly, the dispersion properties of the single nozzles should be sufficient to provide a wide areal coverage at the sampling level. There are two benefits which accrue from having a wide areal coverage. The optimum spacings of nozzle within a grouping are wider when the spray from each is dispersed over a larger area, and fewer units are required to give the necessary coverage. Also, given similar pattern shapes and the same total discharges, the larger the area covered by a nozzle, the lower the maximum depth in its application pattern. It is the average integrated depth of application supplied by the grouping of nozzles which is of primary concern, and if the single-nozzle patterns are fully overlapped, this depth cannot be less than the recorded maximum in the single-nozzle pattern.

One of the stated objectives of the present series of experiments was the extension of the use of nozzle networks to provide rates of application over a range of values within which the uniformity of distribution is maintained at an acceptable level, rather than to superimpose distributions from physically separate systems to produce the same effects. This objective leads to a second criterion of performance for the single-nozzle patterns; namely, that their changes in shape under varying head, both in cross-section and in plan, must be sufficiently small to cause only minor variations in the uniformity of distribution from a network of the same type of nozzle.

If the single-nozzle patterns shown in figures 5.4.1 to 5.4.20 are examined in regard to the above criteria, nozzle types A/C, A/E and A/F can be rejected immediately on the grounds of their high maximum application depths. When overlapped to give an 164. optimum uniformity condition, the average application depths from the grouping would far exceed those laid down in Chapter 3. Of the two remaining nozzles, type A/D showed both better dispersion properties and larger areal coverages at the lower heads than type A/B. Nozzle type A/D had the further advantage of giving the best reproductivity figures out of the five nozzles tested. Nozzle type A/D was therefore adopted for further study.

The results obtained from nozzle type A/D (test numbers 30, 32, 34 and 36) were subsequently analysed to determine the network dimensions that would provide the best uniformity of application over the range of working conditions represented by the patterns. The methods by which single-nozzle patterns can be theoretically overlapped at spacings equal to multiples of the sampling grid interval to provide information on uniformity of distribution have already been discussed in section 4.2.

The analysis of test numbers 30, 32, 34 and 36 was carried out by means of a computer program written in Fortran IV language for running on the Imperial College Computer Unit IBM 7090/1401 computers. Values of both the equivalent average application rate and the Christiansen uniformity coefficient were derived for each overlapped pattern. Spacings of 12, 18, 24 and 30 inches in each of two mutually-perpendicular directions parallel to the rows and columns of the single-nozzle pattern data were considered, making a total of sixteen different combinations of nozzles for each of the four patterns analysed. Full details of this and other programs written specifically for the present investigation are presented separately in Appendix E. The complete set of results obtained from the overlapped pattern analysis are given in table 5.4.5.

J. E. Christiansen (1941) carried out a similar analysis for patterns from irrigation sprinklers, concentrating solely on 165. the uniformity coefficients, and completely omitting any reference to changes in the average application depths as spacings were varied. Table 5.4.5 shows how misleading such an omission can be to the selection of appropriate spacings. The results obtained represent a wide range of uniformity conditions and average application depths. Decreasing the spacings from 30 by 30 inches to 12 by 12 inches caused a 6-fold increase in the average application depths for all four patterns.

If the line and lateral spacings of a network of nozzles were unequal, cross-sections of the application pattern in directions parallel and perpendicular to the lines would be entirely different. Unless the uniformity of the application pattern was relatively high, the response of the laboratory catchments to such an asymmetrical input would depend upon their orientation with respect to the nozzle network. In their preliminary work with a prediction analysis prototype, J. Amorocho and G. T. Orlob (1961) investigated the effect of an asymmetrical input on the response of a test basin for the basic two- dimensional case. Their rainfall simulator, described in section 2.5, provided inputs whose Christiansen uniformity coefficients were in the region of 0.70. The catchment, which consisted of a smooth, aluminium sheet 36 in square, was placed at a fixed position under the spray. Run-off responses were measured with the outflow end of the sheet orientated in two mutually- perpendicular directions.

The outflow hydrographs obtained (loc. cit., figure 18, p.45) were found to differ according to the direction of the drainage. The authors considered that the differences were significant, and proceeded to carry out the bulk of their test programme with a narrow rectangular catchment carefully positioned parallel to the isohyets of the spray to ensure a 166. TABLE 5.4.5: Summary of overlapped pattern analysis of the results from nozzle type A/D, showing values of the equivalent average application rate (1) and the Christiansen uniformity coefficient (Uc)

lateral spacing (in) line test spacing 12 18 24 30 no. (in) _ i .Uc U , U I U r_ c a. c c 30 12 20.904 0.964,13.936 0.866 10.452 0.836 8.362 0.892 3o 18 13.936 0.868 9.291 0.833 6.968 0.804 5.574 0.857 30 24 10.452 0.788 6.968 0.748 5.226 0.735 4.181 0.739 3o 3o 8.362 0.810 5.574 0.791 4.181 0.754 3.345 0.738 32 12 26.857 0.965 17.905 0.978 13.429 0.913 10.743 0.737 32 18 17.905 0.963 11.937 0.952 3.952 0.901 7.162 0.73? 32 24 13.429 0.894 8.952 0.899 6.714 0.852 5.371 0.716 32 30 10.743 0.690 7.162 0.690 5.371 0.682 4.297 0.611 34 12 31.96o 0.921 21.307 0.758 15.908 0.521 12.784 0.342 34 18 21.307 0.757 14.205 0.629 10.653 0.476 8.523 0.335 34 24 15.980 0.522 10.653 0.477 7.990 0.369 6.392 0.276 34 3o 12.784 0.343 8.523 0.343 6.392 0.276 5.114 0.178 36 12 35.160 0.970 23.440 0.779 17.580 0.587 14.064 0.435 36 18 23.44o 0.792 15.627 0.666 11.720 0.540 9.376 0.423 36 24 17.580 0.595 11.720 0.540 8.790 0.447 7.032 0.367 36 30 14.064 0.441 9.376 0.435 7.032 0.370 5.626 0.297 167. higher uniformity of input. The uniformity of the input used in their tests on the 36-in square catchment was low, and a more carefully designed rainfall simulator should provide application patterns with a greatly improved distribution. The question of whether equally significant differences would be obtained with an improved input pattern is, as yet, open to speculation, but in any case obviously asymmetrical patterns, such as those associated with rectangular networks of nozzles are best avoided. Consequently, only the networks for which the line and lateral spacings were equal, and which ideally should exhibit symmetrical application patterns parallel to and perpendicular to the lines, were considered for the present purposes.

The rectangular spacing results have been included in table 5.4.5 and do serve to show the consistency of the analysis. In every case, the average application depths for spacings of IT-A11 by "Y" equal the corresponding values for "Y" by "X". For any one of the spacings considered the computer used each of the 64 individual depths in the single-nozzle pattern array once in forming the overlapped pattern. The product of the number of readings in the overlapped pattern and its mean application rate should therefore be a constant for each of the single-nozzle patterns. Reference to table 5.4.5 will show that, subject to rounding errors in the third place of decimals, this statement is correct. Although each depth reading from the single-nozzle array was used only once, the individual depths within overlapped patterns of "X" by_ "Y" and "Y" by "X" are not necessarily equal,. and so the values of their associated uniformity coefficients may, and in some cases do, differ considerably.

Of the sixteen different arrangements of nozzles considered in table 5.4.5, only four had equal spacings parallel to and perpendicular to the lines. For clarity, the results for 168. these spacings of 12 by 12, 18 by 18, 24 by 24 and 30 by 30 in have been summarised in graphical form in figure 5.4.28. In this figure, variations of the Christiansen uniformity coefficient of the pattern and its equivalent application rate with working head are shown. The curves drawn through each group of points are based on only four sets of results, and should therefore be regarded as trend lines rather than direct relationships.

The variation of equivalent application rate with working head for each arrangement of nozzles plotted as a smooth curve whose gradient tended to decrease with increasing head. The range of depths covered by the 4-fold increase in head was roughly 1.70:1. The application depths for the 12-in spacing were obviously far too high to suit the present studies. Unfortunately, the values of the uniformity coefficients obtained for the same spacing were very good, apparently never falling below 0.92 over the whole test range. Previous investigators have also found that close spacings of units tend to give high uniformity coefficients because of the multiple overlapping of patterns (see also section 4.2; figure 4.2.4). As far as the present writer is aware, no author has yet commented upon the disagreeably high application rates which may result from such multiple overlapping.

For the 18 and 24-in spacings, the Christiansen uniformity coefficients clearly increased in value between 5.0 and 10.0 ft of head, decreased between 10.0 and 15.0 and then recovered fractionally between 15.0 and 20.0 ft. The coefficients for the 30-in spacing decreased between 5.0 and 10.0, and between 10.0 and 15.0 ft of head, reaching a value of 0.178. The patterns for the latter spacing were obviously extremely variable, and need not have been considered. Of the two remaining --"'-*"`"--- IN x 12 IN 1 ,9 U U. u-tu 0.8

04 0.6 18IN x 18IN 0 w 0.4 \\4...... 2 IN x 24 IN z • cl 0.2 U 30 IN x 30 IN

18.0 z

- :I 12.0

-4w 6.0 4En D a

5 10 15 20 HEAD AT NOZZLES , FT OF WATER . NOME 5, 4.28 Overlapped pattern analysis results for nozzle type A / D at square spacings. 170. arrangements, the 18-in offered the more uniform conditions, whereas the 24-in provided the lower rates of application. The former advantage was thought to outweigh the latter, and so a spacing of 18-in centres was finally selected.

Mathematical overlapping has a number of disadvantages, one of which is the implied assumption that all nozzles within the assumed network possess identical properties of behaviour. Any single-nozzle pattern is subject to some source of error such as the misalignment of the apparatus, and mathematical overlapping of such a pattern must inevitably perpetuate the error. The magnitude and position of asymmetrical features in the application patterns from a misaligned nozzle vary according to the conditions under which the experiments are performed. These features do not reflect any properties of the nozzle itself and the distributions of application depths resulting from the overlapping of such patterns at different spacings could lead to considerable error.

Any asymmetry in the single--nozzle patterns may be removed by averaging measurements at corresponding points in each quadrant of the sampling grid. A subroutine was added to the computer program developed for the overlapping of single- nozzle patterns which calculated a symmetrical 64-ordinate application pattern from the original depth measurements in this manner (see Appendix E). This modified program produced a second set of overlapped patterns having equivalent average application rates identical with those given in table 5.4.5, but having different values of the Christiansen uniformity coefficients. The overlappihg at equal line and lateral spacings produced the Uc values shown in table 5.4.6. For convenience, the Uc- values from table 5.4.5 have also been reproduced in table 5.4.6. 171. Table 5.4.6 shows that, in regard to the selection of the 18-in spacing, the differences between the two sets of figures are minimal*.

TABLE 5.4.6: Summary of Christiansen uniformity coefficients for overlapped patterns at equal line and lateral spacings formed from symmetrical single-nozzle patterns derived from the original depth measurements (compared with U0-values from table 5.4.5)

U -values for asymmetrical (a) and c no. symmetrical (b) single-nozzle patterns spacing mmts ... (in) in test no. 30 test no. 32 test no. 34 test no. 36 pattern a b a b a b a b

12 x 12 4 0.964 1.000 0.96511.000 0.921 1.000 0.970 1.00o 18 x 18 9 0.833 0.866 0.962 0.963 0.629 0.629 0.666 0.666 24 x 24 16 0.735 0.838 0.852 0.884 0.369 0.369 0.447 0.447 3o x 3o 25 0.738 0.836 0.611 0.634 0.178 0.209 0.297 0.308

As the whole of the above analysis was based upon only four arrays of single-nozzle data, the information contained in figure 5.4.28 can only be regarded as a first approximation to the design of the required apparatus. This first phase of the experiments may therefore be summarised as follows:

The U values of unity for all tests at the 12-in spacing c occur through having only four points within the overlapped patterns, each of which is formed by the addition of the same combination of readings from the symmetrical single-nozzle pattern. 172.

1. the preliminary testing of five different types of nozzles led to nozzle type A/D being adopted as worthy of further study,

2. theoretical overlapping of the patterns obtained from nozzle type A/D at spacings equal to multiples of the sampling grid interval showed that the most suitable spacing of the nozzle in regard to average application rates and uniformity of application was 18 by 18 inches, and

3. further examination of the performance of nozzle type A/D in multiple at the adopted spacing .1mqias necessary before finally confirming 18 inches as the design spacing of the rainfall simulator.

The second phase of experiments arising from (3) above is discussed in Chapter 6. 173. CHAPTER SIX

Experimental Work - Phase II

6.1 The geometrical arrangement of nozzle networks When sprinklers or nozzles are grouped to form multiple arrays, three simple geometrical arrangements of the units are possible, namely, square, rectangular and triangular spacings. For simplicity, only square and rectangular geometries were considered in section 4.2 when discussing methods of assessing the uniformity of distribution from a group of nozzles. As measurements of application depths are Generally taken over a square mesh of sampling points, the superposition of single-nozzle patterns in an equilateral-triangle geometry is difficult. Two of the patterns are easily integrated, but the third cannot be added without forming a new set of depth measurements by interpolating between points on the original mesh.

J. E. Christiansen (1937) performed a trial and error analysis to determine the shapes of single-sprinkler patterns which would give the highest uniformity coefficients obtainable in both square and triangular arrangements at spacings greater than the wetted radius. From this analysis, Christiansen was able to compare the optimum performance obtainable with both geometrical arrangements as the spacing of units was increased. The results were plotted using the net area covered by the group expressed as a percentage of the area covered by a single sprinkler as a basis for comparison. The net area taken for each geometrical arrangement is defined in figure 6.1.1.

The results presented by Christiansen have been reproduced in figure 6.1.2. This figure shows that the equilateral- triangle arrangement is superior to the square geometry at 174.

spacings larger than approximately 1.2 times the wetted radius. For spacings less than or equal to the wetted radius, both arrangements give almost perfect uniformity. These conclusions of •• /

„, //./ ' / / / // / / / „/ •/ -.' , yz.40.....z. _ :....-T_____.. 7...04 F /j c 14 --1 74 ic--- LIB ! L -41

a) SQUARE ARRANGEMENT b) EQUILATERAL TRIANGLE ARRANGEMENT KEY: •/ denotes the net area (43 denotes the position of a ////of the arrangement nozzle L denotes an arbitrary unit of spacing FIGURE 6.1.1 The definition of geometrical arrangements used by J. E. Christiansen (1937)

should be treated with some caution however, as the patterns and spacings of units are those giving the optimum uniformity conditions in each case.

Apart from the above work, the present writer has been unable to find other evidence in the literature that the relative merits of different geometrical arrangements have been studied in any detail. As indicated in Chapter 5, the single-nozzle patterns obtained during the present investigation were thought to be insufficiently detailed to use as the basis for the design of a rainfall simulator to the specification outlined in Chapter 3. u. 95- EQUILATERAL- TRIANGLE w o SPACING 0 - Xtv, 80'N u.

z 85, SQUARE SPACING z

U) tr 80- x

75 I 1 1 i 1 I I 20 30 1.0 50 60 70 80 90 100 NET AREA- T OF SINGLE SPRINKLER PATTERN COVERED. FIGURE. 6. 1. 2 Comparison between the highest uniformity coefficients available with square and triangular geometries of sprinklers ( after J. E. Christiansen , 1937; P. 91) 176.

The subsequent procedure indicated of examining the application patterns from a group of nozzles required the assembly of new apparatus. When designing this new apparatus, the opportunity was taken to provide facilities for the examination of both a square and an equilateral-triangle arrangement of nozzles. The information that could be acquired from increasing the flexibility of the apparatus in this manner was felt to be sufficiently valuable to justify the additional labour involved.

6.2 The apparatus At the beginning of April 1964, the Hawksley Hydraulic Engineering Laboratory was finally closed, and work was transferred to the Hydraulic Engineering Laboratory in the new Civil Engineering building. An artificial catchment area was incorporated into the design of the new laboratory specifically to accommodate the microcatchment studies already outlined in section 1.4. Situated at the eastern end of the laboratory, the catchment area consists of a 5 ft deep reinforced concrete tank, measuring 36 ft by 23 ft internally (see figure 6.2.1). The top of the tank stands 8 ft 6 in above the level of the main floor of the laboratory.

The tank is bounded by a "splash tray", 20 in wide, into which is set a channel, 6 in deep and 12 in wide, protected by open grid steel covers. The outer edge of the tank is raised 12 in above the level of the splash tray on three sides and carries li-in diameter 'Kee Klamp" railings. On the fourth (eastern) side of the tank, the raised edge and railings are omitted to accommodate a travelling bridge. Mild steel rails, running the length of the longer dimension and 5 ft beyond the eastern end of the tank, have been laid along the splash tray for this purpose. Ma. wandmarnmon•VAINPVENYA•rm. SECTION AA.

immodhea•Mv-lue,"lod a.1.0.1•Mal

.r.**.rmionionetaxemwomag...... S.MIKIRoMmaleaw.t.1, 1111.1.011101. 0 5 10 15 SCALE (ft ) -t-

//:77A )p:<7/7721,7 Thz. artificial catchment area. SECTION B B . 178. A mesh of ninety-six 7-in diameter drainage plugs have been cast into the floor of the tank at 3 ft by 3 ft centres. In addition, provision has been made for water supply to the tank through sixteen 6-in diameter pipes cast into the tank walls at various points as shown in figure 6.2.1. Three large measuring tanks are situated under the catchment area. There is approximately 7 ft of headroom at the level of the splash tray.

The apparatus for the testing of groups of nozzles was erected inside the artificial catchment area. As described in Chapter 5, a spacing of nozzles of 18-in centres was adopted for this apparatus. For convenience, the same spacing was employed for both the square and the equilateral-triangle arrangements of nozzles. The necessity to cater for both resulted in the design of apparatus shown in plate 6.2.1.

The apparatus may be considered in two parts, namely, (a) the feeders and control system, and (b) the supply pipes and nozzle fittings. Apart from two short lengths of 3-in diameter feeder immediately downstream of the tapping into the laboratory nag mains, all pipework was made up from 2-in diameter "Durapipe K" normal weight thermoplastic pipe and fittings.

The feeders and supply pipes were carried on cross beams consisting of 6-ft lengths of 12 x 11-in angle iron. The cross beams were supported by ties made from diameter bar, the upper ends of which were attached to cleats of 122- x 1-;15--in angle bolted into "Unistrut" channels cast into the beams above the tank. Both ends of the ties were cut with a B.S.W. thread, and lock-nutted to the cross beams and cleats. The cross beams were spaced at roughly 6--ft centres. Where no Unistruts were available, the cleats were rag-bolted to the beams. The centre line of the supply system was maintained approximately 6 inches PLATE 6.2.1.

GENERAL VIEW CF APPARATUS FOR THE TESTING OF GROUPS OF 3 AND 4 NOZZLES. 180. below the ceiling level above the tank.

The apparatus was connected into the laboratory water circulation system via a 6-in diameter main running along the eastern wall of the laboratory at a point roughly half-way across the width of the tank. A blank flange on the 6-in diameter main was drilled out to take a 3-in diameter feeder for the apparatus.

The feeders and control system are illustrated in plate 6.2.2. The arrangement is self-explanatory. The valves were 2-in diameter "Wiseal" butterfly valves, which served to isolate the supply lines to the nozzles rather than to control their discharge. Working conditions were set up using gas-cocks fitted into bypasses to the 2-in valves. These gas-cocks were modified as described in Chapter 5. The valves and bypasses were located directly above the eastern edge of the tank, and could be reached in comfort by an operator standing on the splash tray.

The arrangements of the nozzles in both square and equilateral-triangle geometries are shown in plates 6.2.3 and 6.2.4 respectively. The supply lines running from the feeders were erected at 9-in centres so that the nozzles attached to the outer pair could be used both as the baseline of the equilateral- triangle arrangement and as one side of the square. For the former, the position of the two nozzles on the middle line was adjusted so that each lay at exactly 18-in centres from the pair on the outer lines. The facility for changing to a square arrangement was provided by dividing up the middle line so that both nozzles were attached to separate lengths of pipework. The length of each pipe section was measured off carefully so that the middle line could be dismantled, and the nozzles re-erected on the outer lines to form the square arrangement.

The nozzles were attached to 3 to 2-in reducing sockets. PLATE 6.2.2.

FEED RS AND CONTROL SYSTEM OF 3/4 NO,GLE Ali-AREFUS. 182.

The larger end of each socket was closed up with an internally- fitting blank flange. A one-inch diameter hole bored through the centre of this blank matched up with the nozzle body. The nozzles were held in place on three lengths of studding screwed into the blank. As the headroom on the floor of the tank was nearly 12 feet, the level of the nozzles was lowered by inserting 3-ft long vertical extensions between the junctions with the supply pipes and the reducing sockets carrying the nozzles. The arrangement was stiffened by inserting ,1-in diameter spacer bars immediately above the nozzles.

The length of the supply pipes between the Wiseal valves and the nozzles on the outer lines was approximately 12 feet. This distance was sufficient to leave a clear working space at least 8 feet in diameter around the nozzles. This space was provided to minimise, if not eliminate, the effects of air turbulence generated within the tank from the air entrained by the nozzle system.

Static pressure heads were measured at each of the three nozzles in the triangular, and each of the four in the square arrangement of nozzles. Differential mercury monometers consisting of U-tubes with limbs 60 inches in length were used. Each U-tube was backed by a scale engraved in 0.10-in intervals. Five such manometers (one of which was a spare) were mounted on a sheet of white-painted board clamped to a laboratory stand (see plate 6.2.1).

In the light of experience obtained with the single-- nozzle experiments, the sampling grid was modified. The area over which application depths were sampled was considerably reduced by considering only the cell into which all three (or four) nozzles discharged. This sampling area corresponded to the net area as defined by Christiansen, and for the four-nozzle grouping measured 183.

PLATE 6.2.3. ARRANGEMENT OF 4 NOZZLES IN A SQUARE GEOMETRY AT 18-INCH CENTRES. PLATE 6.2.4. ARRANGEMENT OF 3 NOZZLES IN AN EQUILATERAL-TRIANGLE GEOMETRY AT 18-INCH CENTRES. 185. exactly 18 inches by 18 inches. The spacing of gauges was reduced to 3 inches by 3 inches. By locating one gauge directly below each nozzle, a sampling grid of 49 gauges was obtained.

The net area sampled in the case of the three-nozzle grouping was approximately 57 per cent less than that for the four-nozzle arrangement. The reduced sampling grid was oriented so that gauges were located directly below the nozzles on the outer lines, and at all other points on the grid falling within the net area of the group. There were 22 gauges in this reduced grid.

At the closer spacing of 3 inches by 3 inches, the previous method of locating the gauges by 2 in Lewis springs attached to a frame of Handy Angle could not be used as there was insufficient clearance between rows to accommodate the springs. An alternative arrangement was used in which the gauges were located at the correct spacing in a wooden tray. This tray consisted of a 2-ft square frame of 2 by 1-in timber with a hardboard base and top. 49 holes were drilled in the top at correct centres to take the 14-in diameter gauges. The gauges were supported in position by the base in which a number of 1-in diameter holes were drilled to provide for drainage. All joints in the frame were screwed, and glued with "Evostick" adhesive. The whole tray was given one barrier coat, two undercoats and one finishing coat of "Evodyne" chlorinated rubber paint. A frame of Handy Angle, the height of which was adjusted to give the required clearance of 72 inches between nozzles and sampling level, was used to support the tray.

Some initial difficulty was experienced with the four- nozzle arrangement owing to entrapped air inside the supply lines: and the vertical pipes carrying the nozzles. The effect was characterised by a marked drop in pressure between the two nozzles on each supply line. The difficulty was overcome by drilling and 186. tapping gas-cocks into the blank flanges closing off the lines, to allow the bleeding-off of the air before each test.

The exposure of the sampling grid was again controlled by the manipulation of a cover of polythene sheet attached to a frame of Handy Angle running on castors. -Owing to the increased discharge obtained with groups of nozzles, the frame was built up at an. angle to the horizontal to facilitate the drainage of excess water from the cover.

6,3 Procedure The application patterns within the net area of each arrangement of nozzles were measured using a similar procedure to that employed in the phase I experiments described in section 5.3. The procedure adopted for the phase II experiments may be summarised as follows:

1. The sampling frame was located in its correct position under the nozzles using plumb lines dropped from the pipe network. The appropriate number of spray gauges was placed in position on the frame, and the cover rolled into place over the gauges.

2. The required test condition was set up using the bypass valves on each line, making frequent reference to the heads recorded at each nozzle on the mercury manometers. When the manometer readings were sensibly constant, and the differences between the head measurements at each nozzle were sufficiently small, the cover was rolled away from the sampling frame and the gauges exposed to the spray.

3. After an exposure of ten minutes (timed with a stopwatch) the cover was replaced from the opposite side of the sampling frame from which it was removed. The final manometer readings were recorded and the valves closed down. The gauges were then removed from the sampling frame, wiped dry and weighed on the electric balance.

As in the phase I experiments, the total weight of each gauge, its number and position on the sampling frame were recorded -187. immediately after each test run. The array of catch weights from each test was analysed to provide values of mean application rate and the Christiansen uniformity coefficient. As before, catch weights in grammes were converted to depths in inches by dividing by a factor of 39.42.

Because of the arrangement of spray gauges used to sample the application patterns, the arithmetic mean of the depth measurements obtained from the tests did not equal the average application depth within the net area of each group of nozzles. Taking the simpler case first, consider the square arrangement of nozzles. With the nozzle spacing of 18-in centres and a gauge spacing of 3-in centres, the corner gauges of the sampling grid stood directly below the nozzles. Denoting the depths recorded at each gauge by dn, where the suffix n = 1,2, ... 48,49 numbering from top left to bottom right over the grid, let each gauge (excepting those at the corners and sides of the grid) represent an elemental area A of the total net area of the grouping. Then, the total discharge into the area from the nozzles in any test may be written as a volume V, where

A V = (d1 + d7 + + d49) + (d2 + d3 + all other side members of the grid)

+ A (all other members of the grid) Eq. 6.3.1.

The average application depth d may therefore be written as

V 1 d 67 - 30 (one quarter the sum of the corner members 3- + one half the sum of the side members + all other members of the grid) Eq. 6.3.2. 188.

If the above weighting factors were not taken into account, the arithmetic mean of the depth measurements would represent the average application depth over an area 21 in by 21 in. Similarly the arithmetic means of the measurements taken during the three-nozzle tests would represent an average depth over an area larger than the net area. For the latter tests, one complete row of 7 gauges was placed between the two nozzles on the outer lines of the apparatus with the end gauges directly below the nozzles. The other 15 gauges were arranged in two lines of 5, one of 3 and two of one gauge. Weighting factors for those gauges near the boundaries of the net area were derived from the geometry of the nozzle arrangement and the sampling frame. These factors are listed in table 6.3.1, with the position numbers running from left to right and from apex to baseline of the sampling grid.

Values of the mean application depth within the net area of either arrangement of nozzles may also be estimated from the total discharge-head relationship of the nozzles on the basis of certain simplifying assumptions. Suppose that the total discharge from any one nozzle at a head of H feet of water is Q cubic feet per minute. Then, if the nozzle is correctly aligned, its pattern will be symmetrical about the vertical through the nozzle. If all nozzles are assumed to possess identical Q-H relationships, the contribution from each that is discharged into the net area of either arrangement of nozzles will be proportional to the angle subtended at the nozzle within the area.

For any triangular arrangement of nozzles, the total dis- r charge into the net area from all nozzles is 180 . or 0.54 irrespective of the dimensions of the arrangement. Therefore, •an expression for the average depth of application, Tt, within the 189.

TABLE 6.3.1 Weighting factors for the sampling grid used in the three-nozzle experiments

Position Weight Position Weight Position Weight Position Weight

1 0.2796 7 1.0000 13 1.0000 18 0.5000 2 1.3812 8 1.0000 14 1.0000 19 0,5000 3 0.7680 9 1.0000 15 0.9227 20 0.5000 4 1.0000 10 0.3453 16 0.1778 21 0.5000 5 0.7680 11 0.9227 17 0.5000 22 0.1778 6 0.3453 12 1.0000'

net area of any triangular arrangement of nozzles over a period of T minutes may be written as

_ 0.5Q.T222_ t 0.513.11 B.h Eq. 6.3.3 where B is equal to the baselength of any triangle of height h. For the particular case of an equilateral triangle, equation 6.3.3 becomes

2.T dt Eq. 6.3.4 ,(5 B2 A further assumption necessary to ensure the validity of equations 6.3.3 and 6.3.4 is that the radius of influence of each nozzle should lie completely within the net area of the grouping. For example, the radius of each single-nozzle pattern would have to be less than or equal to (,/5/2)B to satisfy this assumption for an equilateral-triangle arrangement of nozzles.

For the general case of a rectangular arrangement of nozzles, the total discharge from the four nozzles into the net area is 4 . 4--3o0 . Q, or Q, again irrespective of the dimensions 190.

of the arrangement. The average application depth, CTIs, within the net area of any rectangular arrangement may therefore be written as

0.T r - 1.w Eq. 6.3.5

where 1 is equal to the length of any rectangular of width w. For the particular case of a square grouping of side 1, _ Q.T d 2 s 1 Eq. 6.3.6

Again, equation 6.3.6 is only valid when the radius of a single-nozzle pattern is less than or equal to 1.

For the phase II experiments, the dimensions B and 1 are both equal to 18 inches, so that

dt = 1.154 cj Eq. 6.3.7

or, to obtain equal depths of application from both arrangements,

B = 1.074 1 Eq. 6.3.8

As discussed in Chapter 5, the Q-H relationship of the nozzles may be considered to follow an equation of the form

Q = K (H)a Eq. 6.3.9

Equation 6.3.9 may be substituted in equations 6.3.4 and 6.3.6 to give relationships between the average application depth from each arrangement of nozzles and the working head.

Unlike the phase I experiments, total discharges were not recorded as part of the general test procedure with the three and four-nozzle arrangements, but a separate series of measurements was carried out before any application patterns were evaluated. Total discharges from individual nozzles were measured by the method already outlined in section 5.2 at a number of working pressures 191.

between 3.0 and 20.0 feet of water. For the nozzles used in the equilateral-triangle arrangement tests, 5 readings were taken for the first, 6 for the second and 5 for the third nozzle. These 16 readings were found to lie close to a common locus when plotted, and were accordingly subjected to regression analysis to determine a general Q-H relationship for the grouping. For convenience, the results were transformed on to logarithmic scales, giving

log Q= log K+ a log H Eq. 6.3.10

which we may write as

Y = aX + b Eq. 6.3.11 where X and Y denote log H and log Q respectively, and b denotes log K. Regression analyses of X on Y and Y on X both yield values of a and b. In the latter, the assumption is made that all experimental errors are concentrated in the measurements of Y (discharge) and that the X (head) readings are free from error. The converse assumption is made in the former case. The line which best fits the data is generally taken to be that which bisects the acute angle between the regression lines (see J. Topping, 1962; p.105).

For the three nozzles used in the equilateral-triangle tests, the regression of Y on X produced the equation

Y = 0.42995X - 1.85301 Eq. 6.3.12 and the regression of X on Y the equation

Y = 0.43041X - 1.85349 Eq. 6.3.13

These equations were thought to be sufficiently close for the regression of Y on X to be assumed to define the Q-H relationship without further calculation. Equation 6.3.12 is plotted in figure 6.3.1 along with the data from which it was derived.

A similar analysis was carried out for the square arrangement of nozzles. An additional 6 measurements were included for 0.06 J NOZZLE 1 : NOZZLE 2 : 0.05 NOZZLE 3 : . • sr /

do ,/ / . F

11. / ofl 0.03 ,t / / ./ ix /

0.02 REGRESSION LINE : 1 95% CONFIDENCE /

0.016 2 5 5.0 10 0 150 20.0 HEAD AT NOZZLE ( FT WATER ) FIGURE. 6.3. 1: Head - discharge retationship for triangutar arrangement of t102ZieS

193.

the fourth nozzle. The regression of Y on X was found to be

Y = 0.43382X- 1.86361 Eq. 6.3.14

and the regression of X on Y

Y = 0.43835X - 1.86827 Eq. 6.3.15

The differences between the coefficients of equations 6.3.14 and 6.3.15 are larger than those between the coefficients of equations 6.3.12 and 6.3.13. The data for all four nozzles has been plotted in figure 6.3.2. The measurements for the fourth nozzle clearly lie below those from the other three. This difference between the Q-H relationships of the nozzles can be attributed to small differences in the manufacturing process, and for present purposes, the regression of Y on X was again assumed to define the Q-H relationship of the group. Equation 6.3.14 has also been plotted in figure 6.3.2.

Having calculated values of the coefficients a and b, some measure of their accuracy is desirable. The extent to which their values are affected by experimental error may be assessed by plotting confidence limits for equations 6.3.12 and 6.3.14. It is customary to plot the 95 per cent confidence limits. The probability that an experimental result will lie outside the band defined by the 95 per cent confidence limits is one in twenty. The method used to calculate these limits was as follows.

According to Topping (loc.cit.; pp.105-6) the standard errors in the values of the coefficients obtained from a regression analysis may be written according to the formulae:

oc2 0b2 2 Eq. 6.3.16 1\1 -(x2) N3T(x2)-(Ex)2

0 where 0 2:(Y-y)2 Eq. 6.3.17 - N-2 1 0L, •

0. 10 en NOZZLE 1 : NOZZLE 2 : x / 4/ 0, NOZZLE 3 : 0 U / , NOZZLE 4 : + /

)4 / r %/ / / /

/ / 3 oz.- / / + r , / / / / / / S. / / / / — -/— 0. )2 REGRESSION LINE : / Lilt/95% CONFIDENCE iffs i

0.0 2.5 5.0 10.0 15.0 200 25.0 HEAD AT NOZZLE FT WATER )

FIGURE , S. 3. a Head -discharge retationship for square orrangernent of nozzles.

195. c4 are the standard errors associated with the values of a a'b and b respectively, and x, y are the measured values of log H and log Q respectively. Y denotes the value of log Q calculated from the regression equation, and442 the mean square error of the N pairs of observations. Equations 6.3.16 and 6.3.17 simplify to 4a4, 9 Eq. 6.3.18 a cr b N (ix 4/>:(x2)

where Crx denotes the standard deviation of the measurements of log H.

As there are two coefficients it is unlikely that both will be subject to large errors on the same occasion. According to C. E. P. Brooks and N. Carruthers (1953; p.305) an approximation to the range within which the curve might be expected to lie is obtained by finding the 90 per cent confidence limits of a and .13 separately, and calculating the two pairs of values of a and b which give extreme positions.

Given a level of probability of 0.90 and the number of degrees of freedom (number of observations minus the number of empirical constants), the departure from a computed value may be calculated from the standard error using Student's t-distribution. This distribution has been tabulated by D. V. Lindley and J. C. P. Millar (1961; p.6). The confidence limits are therefore given by the expression

log Q = (a ± t.cka) log H + (b Eq. 6.3.19

where t denotes the appropriate value of Student's distribution. From equation 6.3.19, the loci of the extremes may be obtained by adding or subtracting the values t. 0( and t.6, from the a b determined values of a and b respectively. 196.

For the three-nozzle tests, the value of the mean square error was found to be 2.2357 x 10-5, which provided values for c4 andTK of 0.0043 and 0.00517 respectively. With 14 degrees a b of freedom and a 90 per cent confidence level, Student's t is equal to 1.76, so that the confidence limits were given by the equation log Q = (0.42995 ± 0.00345) log H - (1.85301 ± 0.00910) Eq. 6.3.20

Writing the average application depth in terms of the total discharge according to equation 6.3.4

at = 61.59Q Eq. 6.3.21 with at in inches and Q in cubic feet per minute for a ten minXte test run, so that the relationship between average application depth and head is given by

log 71 = 0.42995 log H - 0.0635 Eq. 6.3.22 and the upper and lower confidence limits by the equations

log at = 0.4334 log H 0.0544 Eq. 6.3.23

log dt = 0.4215 log H - 0.0726 Eq. 6.3.24

For the four-nozzle tests, the mean square error was found 4 makingc and 0(13 0.0103 and 0.0109 to be 1.4375 x 10 , a respectively. From equation 6.3.6 the relationship between average application depth and total discharge was calculated to be

as = 53.33Q Eq. 6.3.25 with units as before. Substituting this expression into equation 6.3.14 gave

log CI = 0.43382 log H 0.1367 Eq. 6.3.26 197. The upper and lower confidence limits corresponding to the equation log Q = (0.43382±0.01782)log H (1.86361t0.01886) Eq. 6.3.27 were found to be

log Is = 0.4516 log H - 0.1178 Eq. 6.3.28

log Is = 0.4160 log H 0.1555 Eq. 6.3.29

The confidence limits corresponding to equations 6.3.20 and 6.3.27 have been plotted in figures 6.3.1 and 6.3.2 respectively- for comparison purposes. Equations 6.3.22 and 6.3.26, which define the ideal performance of both arrangements of nozzles, provide a valuable contrast to the direct measurements of application depths discussed in the following sections. The confidence limits given by equations 6.3.23 and 6.3.24, and equations 6.3.28 and 6.3.29 provide a measure of the accuracy of these relationships.

6.4 Discussion of results from the three-nozzle tests The average application rates calculated from the measurements taken during each test run with the grid of spray gauges are plotted in figure 6.4.1 along with the intensity-head relationship based upon equation 6.3.22. The 95 per cent confidence limits associated with the latter are also shown. In addition, the Christiansen uniformity coefficient of the application pattern obtained from each test run is also plotted in figure 6.4.1. As the test runs were carre out at intervals of approximately one foot of head, the connection of points by a smooth curve was thought to be justifiable. 19 3.

HEAD AT NOZZLES ( FT WATER) 2 6 8 10 12 14 16 18 20 l A TE

A APPLICATION RATE / HEAD RELATIONSHIP : R 95 CONFIDENCE LIMITS: TION

CA EXPERIMENTAL MMTS: APPLI

4 6 8 10 12 14 16 18 20 HEAD AT NOZZLES ( FT WATER ) FIGURE. 6. 4. 1. Analysis of patterns of application depths from 3 — nozzle tos 199. The intensity-head relationship and the locus of the experimental measurements of average application rate show a marked dissimilarity, although the latter curve appears to be consistent within itself. At the lowest head considered (2.89 feet of water) the experimental measurement of application depth, equivalent to 7.704 in/h lies directly below the lower 95 per cent confidence limit. At the next four head for which measurements were taken, the depth decreased reaching a minimum at a head of 6.89 ft with an equivalent rate of 5.694 in/h. At this head, the experimental measurement was only 43 per cent of the value indicated by the intensity-head relationship.

The next four test runs gave steadily increasing average application depths up to a head of 11.00 ft at which the application rate of 14.796 in/h lay directly between the upper confidence limit and the intensity-head curve. Further increases in head carried the experimental measurements above the upper 95 per cent confidence limit. As the intensity-head relationship represented by equation 6.3.22 is based upon thY total discharge of all nozzles operating within the grouping, it may also be considered to indicate a maximum application depth for any operating pressure. In these terms, the greater experimental measurements of depth over the range from 11.0 to approximately 18.0 ft of head are something of a paradox, although a rational physical explanation may be found for this behaviour as will be shown below.

At heads of 13.0 ft and above, the increase in application rate per foot increase in working pressure decreased rapidly. A marked scattering of points about the experimental curve can be observed over this portion of the working range. The experimental measurements remained between 18.0 and 18.5 in/h at heads of 15.0 feet and above, so that the final three test runs all gave values lying within the confidence limits of the intensity-head curve. 200.

The variation in the Christiansen uniformity coefficient with increasing operating pressure also shows a well-defined pattern of behaviour. Beginning with a value of 0.866 at the to lowest head of 2.89 feet, a falls)? 0.844 was obtained at 3.96 ft, and then a recovery to 0.871 at 4.97 ft. Coefficients of between 0.93 and 0.96 were recorded at the next three heads, followed by a reduction to 0.882 at 8.97 ft and 0.870 at 10.04 ft. Two further coefficients above the 0.92-mark were obtained at heads of 11.00 and 11.91 ft, after which the values decreased smoothly to 0.770 at 15.83 ft and then recovered to 0.871 at 19.97 ft. Again, a scattering of points was obtained over the higher heads of the working range.

The above results pose two important questions. Firstly, is the systematic departure of the locus of experimental measurements from the intensity-head curve significant? And secondly, if so, what is the explanation of this variability? Two factors would appear to indicate an affirmative answer to the former question. Apart from the upper third of the working range examined, no purely random scatter of points is discernible. The scatter shown at heads of 13.0 ft and above may in part be attributed to the finer spray obtained under these higher heads. With the smaller drop sizes encountered at heads of 15.0 ft and above, a temperature differential between the spray and the spray- gauges would probably be sufficient to set up convective effects which would interfere with the sampling process. The effect of small air movements in the laboratory is inevitably more critical with sprays composed entirely of small drops.

A second reason indicating that the departure of the experimental locus from the intensity-head curve is significant may be found in the order in which the test runs were carried out. The first experimental result was obtained at a head of 10.04 ft 201. of water (test number 75). Test runs were then made at successively decreasing heads down to 3.96 ft (test number 81). The measurements at 11.00 ft (test number 90) were taken after those at the next highest head of 11.91 ft (test number 84). The three highest heads were carried out successively in increasing order of magnitude (test numbers 93-5). In the opinion of the present writer, the well-defined curve resulting from this deliberately random programme of experiments indicates that the performance of the apparatus was independent of the previous test conditions. Hysteresis and random scatter were absent, pointing to the validity of the locus of experimental measurements.

An answer to the second question may be obtained in part by a re-examination of the simplifying assumptions upon which the intensity-head curve given by equation 6.3.22 was based. As previously stated in connection with the latter equation for triangular and equation 6.3.26 for square arrangements of nozzles, the relationships between depth of application and total discharge from the nozzles only remain valid if the radii of their single-nozzle patterns are less than 0.867 times and 1.0 times the nozzle spacing respectively. If the cone of influence of each nozzle extends beyond these limits, part of the total discharge is "lost" from the not area of the grouping. In the tests at present under discussion, any deficiency caused lo,r such a loss would not be made up by equal losses from adjacent nozzles laid out at the same spacings. With only three nozzles operating therefore, an increase in the wetted radius beyond approximately 15.6 inches must result in a reduction in average application depth. 202.

The reduced values of application depths obtained from the test runs at the lower head shown in figure 6.4.1 must be partly attributed to such behaviour. However, the same reasoning cannot account,for the increase in measured values over those indicated by the intensity-head curve. As the locus of the latter may also be considered as the maximum application depth obtainable under the ideal experimental conditions represented by the simplifying assumptions, the difference between these and the actual operating conditions must now be examined.

Basically, the two most important assumptions are those of identical nozzles obeying the same Q-H relationships, and correctly-aligned apparatus. The effects of minor differences in nozzle geometry on their Q-H curve has already been illustrated in section 6.3 above. To repeat the conclusion made, the differences in discharge from nozzles operating under the same head are relatively small, and certainly not large enough to account for the difference of 13 per cent in average application depth obtained at a head of 13.00 ft of water.

The problem of alignment was discussed in Chapter 5 in connection with the single-nozzle patterns, and attention was drawn to the critical effect of any misalignment on pattern shape. To repeat the example used to illustrate this point, if the nozzle is set up one degree from the true vertical, the centre of the application pattern will have moved 1.25 inches away from the vertical at sampling level. If then, the three nozzles are inclined towards the centre of the net area of the grouping, a larger proportion of each single nozzle pattern will lie inside the area. The total discharge will consequently be greater, and the resultant average application depth will be larger. The maximum increase of 13 per cent recorded could easily be built up in this manner. 203. The patterns of behaviour outlined above explain the occurrence of deficiences and excesses of the experimental measurements of average application depth with respect to the intensity-head curve. A full account of the variations recorded in figure 6.4.1 may now be compiled from these and the results from the single-nozzle tests described in Chapter 5.

At a head of 5.0 ft a single nozzle of type AAD was shown to provide an application pattern in which the highest depths were recorded on an annulus at a radius of approximately 12 to 18 inches from the nozzle (see figure 5.4.7). At a head of 10.0 ft, the pattern shape had entirely changed to one in which the highest depths occurred directly below the nozzle, and decreased with increasing radius from the nozzle (see figure 5.4.8). The change in pattern shape was found to be accompanied by a decrease in areal coverage.

Beginning at the lower end of the locus of experimental measurements in figure 6.4.1, the decrease in average application depth obtained between heads of 2.89 ft and 6.89 ft, and the increase between 6.89 ft and 11.00 ft may be considered to be caused by a parallel increase and decrease in areal coverage from individual nozzles. As noted in Chapter 5, for the single- nozzle patterns to develop from an annular to a conical shape, a pattern with a uniform depth over most of its cross-section must be obtained at some intermediate head. Reference to the curve of Christiansen 41iformity coefficient in figure 6.4.1 shows that at heads of 5.97, 6.89 and 8.09 ft exceptionally high values of 0.944, 0.954 and 0.934 were recorded. This peak in the uniformity of distribution occurs over the same range of heads within which single nozzles might be expected to provide their most uniform patterns.

Another peak in the uniformity of distribution occurs a*. between heads of 11.0 and 12.0 ft of water. At these same heads, the experimental measurements rise above the values indicated by the intensity-head curve, and the increment in the rate of application per foot increase in head begins to decrease. The single-nozzle patterns remained conical in shape at heads of 10.0 ft and above, although there was a tendency for areal coverage to increase fractionally. This second peak of uniformity must therefore be associated with the optimum combination of the single- nozzle patterns for the particular spacing and arrangement of nozzles in use. Further increase in head alters the shape of the single-nozzle patterns in both cross-section and plan, resulting in a decrease in uniformity coefficient of from 0.927 at a head of 11.91 ft to 0.770 at a head of 15.33 ft.

At heads greater than 15.0 ft, the areal coverage of a single-nozzle pattern was shown to increase at the expense of the maximum application depth within the pattern. Again, this behaviour is reflected in figure 6.4.1 by the trend towards a constant value of average application depth over this range. At heads of 16.89 ft and above the curve of Christiansen uniformity coefficient increases from 0.790 to reach a value of 0.871 at a head of 19.97 ft. This tendency towards a third peak of uniformity may be associated with the general changes in pattern shape from individual nozzles, which no doubt would reach a fresh optimum condition for the spacing and arrangement of nozzles at some higher head.

On examination, the triangular grouping of nozzles used in the present series of experiments was found to be incorrectly aligned. The dimensions of the pipe network were fractionally larger than required, so that the spacer bars inserted directly above the reducing sockets carrying the nozzles had the effect of drawing the nozzles together and inclining their axes towards the centre of the cell. 205.

The effect of such a misalignment has already been described above. As the shape of the single-nozzle patterns over heads less than 6.0 to 7.0 ft was basically annular, the "loss" from the net area was relatively larger than that with conical patterns subject to the sane misalignment. The tendency was therefore to increase the magnitude of the deficiency recorded in application depths. With the conical patterns obtained at heads greater than 7.0 ft, the increase in discharge caused by the misalignment far exceeded any "loss" from the net area, resulting in increased average application depths. The reduction in depths brought about by the increase in areal coverage at heads above 16.0 to 17.0 ft balanced this effect to some extent, giving rise to the tendency towards a constant depth shown in figure 6.4.1. To summarise, the effect of the misalignment in the setting-up of the nozzles was to increase the deficiency in average application depth over the lower half of the working range examined, and to cause an excess over the upper half.

6.5 Discussion of results from the four-nozzle tests The average application rates obtained from depth measurements at a grid of points under the square arrangement of nozzles are plotted in figure 6.5.1, along with the intensity- head curve based upon equation 6.3.26. The 95 per cent confidence limits to the latter equation have also been drawn in the figure. The curve of Christiansen uniformity 6oefficient is also shown.

The variation of the locus of experimental measurements about the intensity-head curve is essentially similar to that recorded with the triangular arrangement of nozzles discussed above. The deficiency in the experimental measurements over the lower half of the range of heads examined is not as marked as that iS z X APPLICATION COEFFICIENT 1.00 0.7 - 0.8 - 0.9 La- 2.0 - o - 2

2 FIGURE. 6. 5.1 Analysis ofpatterns of application depths from4- nozzle tests.

46 4 i

HEAD ATNOZZLES(FTWATER) HEAD AT NOZZLES(FTWATER) 6 ,

RELATIONSHIP: APPLICATION RATEIHEAD EXPERIMENTAL MMTS: 95 %CONFIDENCEUMITS: 8 8 ,

10 10 ,

12 •14 12 ,

14 i

16 16

18 18 - i

20 2 06. I 20 t 207.

for the three-nozzle tests, but the excess over the upper half is proportionally larger. Again, there are two distinct peaks in the curve of Christiansen uniformity coefficient, although the magnitude of the second is 10 per cent larger than the first.

At the lowest head recorded of 3.00 ft of water, an equivalent application rate of 6.354 in/h was obtained. An increase in head to 3.75 ft gave an increased rate of 7.35 in/h which lay just inside the 95 per cent confidence limits to the intensity-head curve. At the next largest heads of 4.93, 6.21 and 7.04 ft, application depths of 1.283, 1.289 and 1.298 in were recorded for each ten-minute exposure, causing a divergence of the experimental measurements and the intensity-head curve. However, further increases in head brought sensibly constant increases in apulication rate per foot increment in working head, so that the values at 9.99 and 11.07 ft lay within the 95 per cent confidence limits.

At heads of 11.07 ft and above, the experimental measurements were larger than the values indicated by the intensity-head curve. The average application rate of 15.378 in/h recorded at a head of 12.95 ft lay above the confidence limits. As in the three- nozzle tests, the gradient of the experimental curve was much reduced over this portion of the test range. A peak rate of 17.598 in/h was recorded at a head of 16.98 ft above which slight reductions in depth were recorded at 18.05, 19.14 and 20.18 ft.

The level of uniformity at the 3.00 ft head was greater with the square array (0.901) than with the triangular (0.866). An increase to 3.75 ft and then 4.93 ft brought a reduction in coefficients to 0.811 and then to 0.760. The coefficients recovered to 0.804 at 6.21 ft, reaching the first peak value of 0.846 at 7.04 ft. Further increase in head saw a slight fall to 0.817 at 9.01 ft, after which the value of the coefficients 208. climbed to a second peak of 0.951 at 11.07 ft. At larger heads, the level of uniformity again decreased significantly, reaching a coefficient slightly greater than 0.7 between 16.0 and 17.0 ft of head. At the highest head of 20.13 ft, the uniformity coefficient had returned to the 0.79-mark.

The curves shown in figure 6.5.1 exhibit identical features to those for the three-nozzle tests already discussed above. The limit for the radius of the single-nozzle patterns within which the assumptions connected with the intensity-head curve remain valid was 18 inches for the four-nozzle tests, compared with 15.6 inches for the three-nozzle tests. The uniform single-nozzle pattern occurring at about 7.0 feet of head had a lesser effect on the level of uniformity. Also because of the increased limit on single-nozzle pattern radius, the areal variations were less significant in causing deficiences in the experimental measurements. The slight scatter of results under the higher heads at which test runs were made is noticeable.

The misalignment of the apparatus appears to have been more marked, resulting in a maximum excess of experimental measurements over the intensity-head curve of 19 per cent. Again the effect of the misalignment, coupled with the contradiction of the basic simplifying assumptions connected with the intensity- head curve, served to increase the variations in the locus of experimental measurements.

6.6 Comparison between the performance of the three and four- nozzle arrangements The principal disadvantage of an equilateral-triangle arrangement of nozzles lies in their location at correct centres. If the distance between the nozzles on any line is S (say), then 209. the distance between lines must be set at .S/2 to complete the geometry of the arrangement. Alternatively, the lines nay be erected at centres of S/2, and the nozzles on adjacent lines staggered to give the triangular groupings. If the latter system were adopted, the distance between nozzles on any line would be -,V3.S. For a situation in which the location of nozzles is critical to the overlapping of patterns, the adoption of centres involving a factor of ,v/5 can only create problems in the erection of the apparatus. In the present case, a comparison between figures 6.4.1 and 6.5.1 shows that neither the square nor the equilateral-triangle arrangement of nozzles can claim any outstanding advantage over the other. When regarded in the light of the analysis made by Christiansen quoted in section 6,1, the conclusion must be drawn that the variations in the single- nozzle patterns are such that neither geometrical arrangement is clearly favourable over the complete test range..

Both sets of results showed that the areal variations associated with the single-nozzle patterns were greater than the phase I experiments had indicated. Over specific portions of their working range, both arrangements of nozzles provided additional contributions into area outside the net area of their grouping. The deficiences created by these "losses" were not made up from contributions into the cell from adjacent nozzles as would be the case with a large network of nozzles. Neither the group of three nor the group of four may be considered to define fully the behaviour within an elemental area of a large network. 210.

These results indicated the need to carry out further tests with networks of at least 12 nozzles. As the equilateral- triangle arrangement offered no advantages in performance over the square arrangement and its installation would create unnecessary difficulties in the location of nozzles, the square geometry was adopted for further study. A third phase of experiments involving the use of 16 nozzles at 18-inch centres was undertaken, the results of which are discussed in Chapter 7. 211.

CHAPTER SEVEN

Experimental Work - Phase III

7.1 The apparatus In order to carry out experiments with a network of 16 nozzles, further rebuilding of apparatus was necessary. The inner line of the three/four-nozzle apparatus was dismantled, and the 2-in Wiseal valve replaced by a blank flange. The length of 3-in diameter pipe immediately downstream of the tapping into the laboratory mains was extended by a further length carrying two more 2-in diameter feeders at 18-in centres. 2-in Wiseal valves were inserted in the lines in parallel with the two already in place in the existing lines, and the pipes extended over the tank as far as the third supporting crossbeam. The extra lines conveniently fitted into the existing supporting system, and no new crossbeams were necessary at the feeder end of the apparatus.

In contrast, at the nozzle end of the apparatus the existing arrangement had to be replaced by an entirely new system. As 12 additional nozzles were required, the opportunity was taken to make detail modifications to the prototype nozzle design. The production design of nozzle is illustrated in figures 7.1.1(a) and (b). The principal differences between this design and the prototype nozzle design shown in figures 5.1.1(a) and (b) lie in the shape of the nozzle body and the method of attaching the nozzles to the pipe network. The flat-plate arrangement of the prototypes was replaced by i in of 1-in B.S.P. thread. The thickness of the body wall was increased so that an "0" ring could be fitted into the shoulder below the 1-in B.S.P. thread. The sandwich of plates was modified so that the unit could be manufactured in two parts instead of three. The orifice 212.

PIPE BOSS

3" 4.

j<<:,X /

4. \

—

15" 16 16

16 GENERAL ARRANGEMENT ( HALF SECTION) SCALE: 2 x FULL SIZE .

PART. NO. NAME OF PART. MATERIAL NO. OFF.

NOZZLE BODY. BRASS 1

0 COLLAR . BRASS 1

[ .:0 SWIRL PLAAcTE,E/ MORBILFYICE PLATE BRASS 1

FIGURE. 7. 1.1( a) Production nozzle assembly - general arrangement . 0.0625' +°'®1" 0.000"

1\(((Mf SECTION AA

i SWIRL PLATE • f0425":676°1° -0.000"

0.2501 iink. maw" T 0.375"

ORIFICE PLATE

•••••••••M1W•10

0.125" DiAM. REAM ORIFICE 1.120' 0/D

FIGURE. 7.1.1(b) Production nozzle assembly detail of/ swirl plate and orifice plate assembly to a scale of 2 x full size. 214. plate, spacer and outer ring of the swirl plate were made in one part, and the inner portion of the swirl plate carrying the diagonal plots fitted into this unit. Another "0" ring was inserted between the recess carrying the sandwich of plates and the thread for the collar. An order for 550 nozzles to the design of figures 7.1.1(a) and (b) was placed with J. Electronic Supplies Ltd., S.W.11, on 26th November 1964 and delivery was taken of the first 16 early in January 1965.

The 16 nozzles were mounted in four lines of four in the new apparatus. The nozzles screwed into internally- threaded pipe bosses set at 18-in centres on lengths of Durapipe "K" light weight pipework. In order to maintain the sampling level at a convenient working height, the nozzles had to be supported some 36 inches below the level of the 2-in feeders. A new supporting system of 1i by 1;2--in angle iron and 11-in diameter bars was assembled for this purpose..

A fifth crossbeam, supported as before by;z-in1 diameter bars attached to cleats bolted on to unistrut fittings was erected 5 ft 6 in beyond the fourth crossbeam. Both the latter beams were slotted at 18-in centres to carry four further 6-ft lengths of 'GI- by angle iron running parallel to the pipe network. Each of these lengths was drilled at points 12 inches from each end and at mid-span to take three 1-in diameter rods. The nozzle network was carried on 2-in diameter pipe rings screwed on to the bottom ends of these rods. The whole supporting system is shown in detail in plate 7.1.1. In addition to the above, the line centres were maintained at 18 inches by -in diameter spacer bars running between pipe rings attached to each line.

The existing system of pipework for the three/four- nozzle apparatus was dismantled, and the length of the feeders P.1_,TE 7.1.1.

SUPPORTING SYSTEM FOR 16-NOZZLE APPARATUS. 216. cut back to the third crossbeam. 90° elbows, each of which carried a short, vertical section of 2-in diameter pipe were cemented on to the lines. The feeders and the nozzle network were then joined by lengths of ail-in internal diameter reinforced hose which were greased and clamped to the pipes by jubilee clips. As before, gas cocks were drilled and tapped into the blank flanges at the extreme ends of each line.

Pressures in the lines carrying the nozzles were measured by mercury manometers attached to two nozzles of the four on each line. The outer pair of nozzles on the first and fourth, and the inner pair on the second and third lines were suitably modified for this purpose. The pressure tappings were inserted at corresponding positions to those in the prototype nozzles. A further four 48-in U-tubes were assembled for the purpose of providing the additional measurements.

The sampling grid was now aligned directly below the inner four nozzles of the network. Exposure was controlled by the movement of the polythene canopy as in the phase II experiments. A general view of the apparatus, as set up before each test run, is shown in plate 7.1.2.

With having four nozzles on each line, the bypass arrangement previously used was found to be inadequate for pressures above 12.0 feet of water. Four additional bypasses were therefore connected up, one to each line from the redundant middle line of the original system of feeders. A gas cock was tapped into each of the lines downstream of the 2-in valves and connected to the spare feeder by polythene tubing. These secondary bypasses catered adequately for the additional flow required. The necessary fine control was obtained on the original connections. The modified control system is illustrated in plate 7.1.3. PLATE 7.1.2.

GENERAL VIEW OF APPARATUS FOR THE TESTING OF GROUPS OF 16 NOZZLES. 218.

PLATE 7.1.3. MODIFIED CONTROL SYSTEM FOR 16-NOZZLE APPARATUS. 219.

Before beginning a series of test runs to determine the new application patterns with the 16-nozzle network, total discharge measurements were taken at a number of different heads for each of the four inner nozzles of the network. Seven readings were taken for two of the nozzles, eight for the third and five for the other, making a total of 2? pairs of measurements. When plotted, these readings were found to lie about an essentially common locus (see figure 7.1.2), and so a regression analysis was performed to find a general Q-H relationship for the group of X four nozzles. The regression of Y (log Q) on) (log H) gave the equation

Y = o.4o892x - 1.86474 Eq. 7.1.1 and the regression of X on Y

Y = 0.41077X - 1.86635 Eq. 7.1.2

For convenience, the regression of Y on X was assumed to give the required relationship as in the phase II experiments. Substituting equation 6.3.25 into equation 7.1.1 to give the depth-head relationship yielded the expression

log a = 0.4089 log H - 0.4387 Eq. 7.1.3 Where d is in inches o1 depth per 5-minute exposure. The 95 per cent confidence limits to equations 7.1.1 and 7.1.3 were calculated as outlined in section 6.3. The mean square error of the 27 pairs of observations was found to be -4 1.0652 x 10 leading to values of the standard errors associated with the coefficients in equation 7.1.1 of 0.00525 and 0.00495 for andd respectively. Applying the appropriate value of a b Student's t to these figures produced the following expression for the 95 per cent confidence limits:

log Q = (0.40892 ±0.00898) log H - (1.86474 ± o.00846) Eq. 7.1.4 220.

0.05 // NOZZLE 6 : a r" NOZZLE 7 : x / U) / 0-04 NOZZLE 10 : 0 / e NOZZLE 11 : ," 4' . "'' P.4 / - z 0.03 / /...-pe` oe ,... ." le # / 401

if 002 ./ / #1° ...-.....-...... -...... -...... -.- Is. . / 4, / REGRESSION LINE : / 95°4 CONFIDENCE / / LIM/TS : /

0.011 08 2.5 5.0 10.0 15-0 20.0 25-0 HEAD AT NOZZLE (FT WATER)

FIGURE 7.1.2. Head discharge relationship for innermost four nozzles of the IS — nozzle apparatus. 221.

From this expression and equation 6.3.25, the equations for the upper and lower confidence limits to the depth-head curve were found to be

log d = 0.4179 log H - 0.4303 Eq. 7.1.5

log a = 0.3999 log H - 0.4472 Eq. 7.1.6 Equations 7.1.5 and 7.1.6, written in terms of total discharge instead of average application depth, have been plotted in figure 7.1.2 for comparison with the original observations.

An identical experimental procedure to that described in section 6.3 was used in the phase III experiments.

7.2 Discussion of results from the 16-nozzle tests The experimental measurements of average application rate within the net area of the inner four nozzles of the network are shown in figure 7.2.1, along with the intensity-head curve based upon equation 7.1.3 and the Christiansen uniformity coefficients for the application patterns obtained at each head. A range of heads of from 3.0 to 13.0 feet of water was examined. Higher heads were omitted because the excessive application rates produced were relatively unimportant to the purpose of the tests.

The conclusion that can be drawn immediately from figure 7.2.1 is that the variations of the experimental measurements about the intensity-head relationship were si4nificantly smaller. As in the four-nozzle tests shown in figure 6.5.1, the curve of Christiansen Uniformity coefficient had two peaks at heads of approximately 7.0 and11.0 feet.

At a head of 3.05 ft, the equivalent application rate of 7,092 in/h lay directly on the upper 95 per cent confidence limit of the intensit7-head curve. Increments in head up to 4.02 and 222. 2 4 10 12 >.•

1 LL

U..1 f--- (f) 1 LI

Ju- 6:?. w 7:1- 0 00

1.1.1 Lit

C.) z Z:1 IL

(.0

CL LI APPLICATION RATE / HEAD RELATIONSHIP, 95 7. CONFIDENCE LIMITS. EXPERIMENTAL MMTS. 0 a.. a.

LU 2 8 10 12 HEAD AT NOZZLES ( FT WATER ) FIGURE 72. Analysis of patiei ns of application depths from 1 nozzle tests. Test numtnrs 124 -134 ) 223.

5.06 ft gave application rates of 8.28 and 9.036 in/h, some 6 to 7 per cent above the values indicated by the curve. A further increase to 6.02 ft gave a reading of 9.312 in/h, lying within the 95 per cent confidence band, but another up to 7.10 ft saw a decrease in application rate to 9.168 in/h, a value 6 per cent less than that obtained from the intensity-head curve. At the next highest head of 8.00 ft, the rate of 9.60 in/h was also below the lower 95 per cent confidence limit. At 9.05 ft the experimental measurement of 10.74 in/h lay exactly on the intbnsity-head curve. For each of the remaining four heads at which test runs were carried out, the curve of experimental results again rose above the 95 per cent confidence band.

The highest values of the Christiansen Uniformity coefficient were obtained at heads of 7.10 ft (0.905) and 11.02 ft (0.915). Beginning with a value of 0.882 at a head of 3.05 ft, comparatively low coefficients of 0.799 and 0.798 were recorded 5 at heads of 4.02 and ‘.06 ft before the readings increased through 0.844 at 6.02 ft to reach the first peak. Between the two peaks, coefficients of 0.854, 0.847 and 0.890 showed that a high level of uniformity was maintained over this portion of the test range. Beyond the second peak, values were again reduced, falling to 0.810 at a head of 13.04 ft.

With all 16 nozzles operating, the effect of areal variations in the single-nozzle patterns observed in the phase II tests was totally eliminated. The variations in the experimental measurements of average application rate, again consistent among themselves, can only be attributed tocbfects in the apparatus. In terms of absolute values, the maximum departure of the measurements from the intensity-head curve was approximately half that recorded from the corresponding test runs with four nozzles only. 224. At the lower heads, slight misalignments in the outer lines of nozzles could result in an excess contribution into the net area of the inner four nozzles. As the greater application depths in the single-nozzle patterns would occur at a radius of from 12 to 24 inches from the nozzle under these heads, this excess could easily account for the 6 per cent variation shown in figure 7.2.1. The association of low uniformity coefficients with the larger departures from the intensity-head curve at the lower heads may be noted.

The reduction in areal coverage of the single-nozzle patterns at heads of from 5.0 to 10.0 feet may account in part for the reduction in application depth observed at a head of 7.10 feet. The change in single-nozzle pattern shape from annular to conical, coupled with this reduction in areal coverage, would remove the excess application from the net area. Any misalignment of the inner four nozzles could increase the deficiency to the extent recorded in these tests. The recurrence of excessive application rates at heads of 9.99 feet and above may again be attributed to surplus contributions from the outer 12 nozzles of the network.

The alignment of all nozzles in the network was subsequently re-examined, and an attempt was made to put right any obvious defects in the apparatus. The test programme was then repeated over a range of heads of from 2.98 to 14.0 feet of water. The results from these tests are plotted in figure 7.2.2.

These results show a much closer agreement between the locus of experimental measurements and the intensity-head curve. All readings of average application rate lay within the 95 per cent confidence band of the intensity-head relationship. The maximum departure of any measurement from the intensity-head curve, which occurred at a head of 13.03 ft was less than 4 per .0 AT 'fljS f 'VAT 5I?) 2 4 8 10 12 14

1.00 ...•4.••••••-•st TY ORMI IF

UN 09 z Z - LU cri ILLL

I C) 00

14 z 12 -

APPLICATION RATE HEAD RELATIONSHIP c5 4 ee 95% CONFIDENCE LIMITS EXPERIMENTAL WITS, 0

0 I --., , 6 6 10 12 14 HEAD Al NOZZLES (FT WATER FIGURE. 7.22. Analysts of po.ttcrns of opptirotion depths from 16 nozzte tests ( Test numbers 135— 11.6) 226.

cent. The variations were generally small enough to be accounted for by differences in the properties of individual nozzles.

In contrast, the curve of Christiansen uniformity Coefficient was considerably altered with the new setting of the nozzle network. Two peaks of uniformity were still obtained, but with the second occurring at a head of 9.90 feet, approximately one foot of head lower than previously recorded. At the lowest heads of 2.98, 4012 and 5.03 ft, the uniformity coefficients remained sensibly constant between 0.84,and 0.85, rising through 0.890 at 6.11 ft to the first peak of 0.934 at 7.01 ft. Between the two peak values, the coefficients fell slightly to 0.908 at 7.97 ft and 0.895 at 8.95 ft. The second peak of 0.911 at 9.90 ft was followed by a sharp decrease in values at higher heads. At a head of 12.05 ft, the uniformity had fallen below the 0.85-mark to 0.811. At 13.03 ft, a coefficient of 0.739 was obtained.

When the variations in the uniformity coefficients recorded for the application patterns from the 16-nozzle network are compared with those obtained with only four nozzles operating, the most noticeable difference is the smaller range in values for the former. If the range from 3.0 to 12.0 feet of head is considered, the coefficients for the four-nozzle grouping are found to vary from 0.760 to 0.951, whereas the comparable figures for the 16-nozzle network run from 0.811 to 0.934. Between heads of 3.0 and 11.0 feet of water, the level of uniformity with the 16 nozzles never fell below 0.84. The principal effect of the additional 12 nozzles appears to have been to reduce the peak uniformity coefficients and to increase the lower values over this portion of the test range.

A number of investigators have attempted to attach a quantitative value to the uniformity of application of natural 227.

rainfall. In replying to discussion of his paper, W. C. Strong (1961) stated that the uniformity "... depends upon the kind of rainfall". He quoted Christiansen uniformity coefficients of 96-7 per cent for slow drizzle and a value of 92 per cent "... under the most adverse rainfall", without stating by what method the figures were obtained. A. Shachori and I. Seginer (1962) reported another attempt to assess the uniformity of application of natural rainfall in which 25 cans were spread evenly over a plot 50 metres long and 6 metres wide. The average U for an entire winter season was given as 95 per cent, with c values of 90 per cent for individual storms not being uncommon.

Owing to the paucity of experimental detail provided in support of the above figures, their significance cannot readily be assessed. The area covered by the most localised of storm cells is generally much too large to cover with a network of regularly-spaced measuring cans. For example, C. O. Wisler and E. F. Brater (1959; p.70) state that when a thunderstorm first develops, it covers an area of not more than 3 or 4 square miles. The plot dimensions quoted by Shachori and Seginer are sufficiently small for variations in rainfall intensity perpendicular to the direction of storm movement to be insignificant. The amount of catch in each measuring can over the plot should therefore be equal. Uc values of 90 per cent and above are relatively high, and the differences between individual measurements characterised by such figures are sufficiently small to occur through splash or similar experimental errors.

Some confirmation of the above effect has been provided by L. H. Watkins (1955) who reported on the variation between rainfall measurements made with a grid of 9 standard Meteorlogical Office non-recording raingauges. The gauges were installed at 30-ft centres (in three rows of three) in the grounds of the 228.

Road Research Laboratory, Harmondsworth. The experiment ran from December 1952 to August 1954. The conclusion drawn from the results was that the small variations recorded were not true variations in rainfall over the area but arose through local wind eddies round the gauges. The Meteorological Office subsequently began a further investigation into the areal distribution of rainfall installing two grids of open-scale recordimgraingauges at Winchcombe in Gloucestershire and at Cardington in Bedfordshire (see D. J. Holland, 1964; p.28). At the time of writing, the results of the latter work have still to be published.

As outlined in section 4.2, a number of different values of the Christiansen uniformity coefficient, varying between 0.80 and 0.86, have been taken to define criteria of acceptable uniformity of distribution by previous investigators. These criteria represent a considerable depth of experience with application patterns from both nozzles and irrigation sprinklers, and may conveniently be adopted for use in the present investigation.

The results from test numbers 135 to 146 conform to and exceed these standards. The possibility remains that further improvements in performance might have been obtained with the nozzles spaced at different centres. The present writer is doubtful whether the additional experimental work involved would be repaid by a significant improvement in the level of uniformity over that recorded with the 18-inch spacing of nozzles. The requirements laid down in the specification for the rainfall simulator to produce application patterns which are uniform in time and in space can therefore be considered to have been met by using nozzle type A/D in a network at 18-inch centres. 229.

W. C. Strong (1961) has expressed the opinion that the Christiansen uniformity coefficient is not a sufficiently sensitive measure of uniformity. His reasons have already been outlined in Chapter 4. During the present investigation, enough data was obtained to permit a detailed examination of this criticism, and to illustrate further the use of the different forms of uniformity coefficient.

7.3 A comparison between the different statistical measures of uniformity W. E. Hart (1961) showed that, if observations of application depths within the overlapped patterns from a group of nozzles or irrigation sprinklers is assumed to follow the normal distribution law, inter-relationships can be demonstrated between the various forms of uniformity coefficient described in section 4.2. If, therefore, a proportionality can be shown to exist between the Christiansen uniformity coefficient and another based upon the standard deviation of the distribution of application depths (such as the H.S.P.A. uniformity coefficient) then the choice of a specific form of coefficient becomes immaterial, and the argument put forward by Strong may be entirely rejected.

Additional subroutines were incorporated into the computer program written for the overlapping of single-nozzle patterns. The Christiansen uniformity coefficient (Uc), the coefficient of variation (V), the H.S.P.A. uniformity coefficient (U )' the U.S.D.A. pattern efficiency (P ) and the ratio of the h e maximum to the minimum application depth (R) were calculated for each overlapped pattern. Full details of these subroutines are given in Appendix E. The calculations were carried out on both the measured single-nozzle patterns and the symmetrical single- 230. nozzle patterns formed from the original measurements, yielding against U a total of 128 sets of coefficients. Graphs of Uc h (figure 7.3.1), Pe against V (figure 7.3.3) and Ue against.R (figure 7.3.5) were prepared from these data. For clarity, the results from the patterns having lie-values less than 0.5 have been omitted from figure 7.3.1, Pe-values less than 0.5 from figure 7.3.3, and Ue-values less than 0.6 from figure 7.3.5. The results plotted in figure 7.3.1 show a general tendency for Uh-values to be fractionally larger than the corresponding values of Ue. This tendency becomes less marked as the coefficients .dtcrease. Christiansen uniformity coefficients between 0.5 and 0.55 correspond to coefficients of aproximately 0.6. A comparison between the figures derived from the overlapping of the symmetrical and the measured single-nozzle patterns shows that the trends exhibited by the former are more pronounced than the latter. A line of best fit at a slope less than 45 degrees could be drawn through the symmetrical-pattern results, whereas the figures for the patterns formed from the original measurements show a distinct break from the line of equal values at the 0.75-mark.

The tendency for the plotted points to depart from the line of equal values was investigated further by computing Ue and U h for each of the measured patterns from the four and sixteen-nozzle tests. These results, which were also processed by computer (see Appendix E), consisted of 13 patterns from the four-nozzle case, and two groups of 11 and 12 patterns respectively from the sixteen-nozzle network, differing only in the alignment of the apparatus. These fiures have been plotted in figure 7.3.2. In general, the scatter of points about the line of equal values is less than that shown in figure 7.3.1, although the same J OVFPJ APP:N3 WITH SYMMc:TMCAL SINGLE NOZZLE PATTERNS, 0.9 ASYMMEOAL SINGLE NCIZZLE PATTERNS.

•

Si 17 / jfe

9 * x 9 / •

114V., UNE OF EQUAL VALUES. • x / .07 1 a

0.6 , 4"•*T"""r T -1***9 • T."' 0.5 0.8 0.7 0.6 0.9 FIGURE 7.3.1_ CHRSTIANSEN UNIFORMITY COEFFICIENT. Pct of thz Christio.risim 1..!;;;.f ,-7rriltv coefficient cAgo.nst the H.S.A. unforrnity coeffici:mt for ope d pat t.'_ ,.• !",5 . 232.

1.0 -I TEST NUMBERS 97-115 " TEST NUMBERS 12L-134 TEST NUMBERS 135-146

sa z Lii 0 ft. IL 6 ILI 0

171 LINE OF EQUAL VALUES. IL

0.6 -

0.7 07 0-0 0.9 CHRISTIANSEN UNIFORMITY COEFFICIENT.

Flo.u.R.E. Plot of the Christiansen uniformity coefficient against the H .S.P. A. uniformity coefficient for the four nozzle and sixteen-nozzle tests. 233. tendency for Uh-values to be fractionally larger than the corresponding values of Uc is evident. The four-nozzle results show a well-defined trend to lie about a line whose gradient is less than 45 degrees. In contrast, the results from the correctly-aligned sixteen-nozzle network all lie close to the line of equal values. As Christiansen uniformity coefficients less than 0.7 were not recorded in any of the four or sixteen- nozzle tests, the continuation of these trends remains a matter of speculation.

The plot of P against V for the overlapped patterns e (figure 7.3.3) shows a marked scattering of points. There appears to be no significant difference between the results obtained from either group of single-nozzle patterns. Despite the scatter, the equation connecting the coefficients based upon considerations of the normal distribution given by Hart (equation 4.2.9) is close to a line of best fit. Hart stated that the point corresponding to the average of the lower quartile of observations was equivalent to an ordinate of the normal error curve having 10 per cent of the distribution on its left-hand side. Hart did not give the reasoning by which he arrived at this figure, but the choice may well have been made from consideration of a least squares fit to data plotted in the manner of figure 7.3,3. The agreement with the normal distribution relationships shown by the data plotted in figure 7.3.3 is better than that shown by the plot of Uc against Uh (figure 7.3.1) despite the scatter. The equality between Uc and Uh is based upon the well- known relationship between the mean and standard deviations of a normally-distributed population (equation 4.2.7), and therefore provides a stricter test of Hart's proposals. The trends exhibited in both figures 7.3.1 and 7.3.2 are for the normal distribution relationship to give good agreement to the calculated OVEP.! APPiNG WITH E SPRNKLFR PAT TERS ASYNNE-.-TRICAL SPRNKL;:-R PATFRN5.

o NORMAL D:STRIBUT:ON RELATIONSHIP (EQUATION. 3.23 5 LL N c.”)

1 5 34' .A. 1_ Lu 0 -4

0.0 r 0 5 V-u 0.7 0.8 0.9 RGURE. U,S.D.A. PATTERN EFFICIENCY Pe Pot of U.S.D.A. patt;?rri ccficn cf vc4ric.0:',ort for overlapped patterns. 235. figures down to Uc-values of 0.75. W. E. Hart and W. N. Reynolds (1965) stated that further investigation by the Hawaiian Sugar Planters' Association has shown that Hart's approach is applicable for patterns with Uc-values above 0.65. The choice of a lower limit is, of course, dependent upon the accuracy to which the final results are required.

The above figures do show that, for the range of uniformity coefficients encountered in the present experiments, the choice of one particular form 9f coefficient for the comparison of application patterns did not affect the results in any way. Further inter-plotting of the different uniformity coefficients presented in recent papers by R. Culver and R. F. Sinker (1966) and J. G. Beale and D. T. Howell (1966) has confirmed this tendency in other data.

The agreement shown between the normal distribution relationships and the plotted points in figures 7.3.1 and 7.3.2 does not imply that the measured and calculated patterns show distributions of observed application depths which follow the Gaussian law. There is no more evidence to support this argument than there is to suppose that they should conform to some other statistical distribution. However, the data do# permit the conclusion (also reached by Beale and Howell) that the regression lines relating pairs of different coefficients are approximated quite well within certain limits by eauations based upon the assumption that the observations of application depths are normally-distributed.

The generally-accepted methods by which frequency distributions are fitted to sampled data depend upon the higher moments of the distributions (see W. P. Elderton, 1953). As an aid to curve fitting, Pearson (1914) presented a diagram in which skewness, a parameter based upon the third moment of a 236. distribution, was plotted against kurtosis, another parameter based upon the fourth moment. The skewness, pi, is defined by the equation

Eq. 7.3.1 where 2-, (xi x) Eq. 7.3.2 and 4_ (xi - H)2 Eq. 7.3.3 and the kurtosis, p2, by the expression

Eq. 7.3.4 P2 = u 2 1 2 where P4 = 1:(X i - 7)4 Eq. 7.3.5 using the notation employed in section 4.2

The type of frequency curve providing the best approximation to the sampled data can be read from Pearson's diagram by plotting corresponding pairs of values of pi and p20 The normal distribution, which has a zero value of skewness and a kurtosis of 3.0, appears on the diagram as a single point, referred to by Pearson as the "Gaussian point".

The data from the four and sixteen-nozzle tests were analysed to give values of pi andp2, and plotted in the manner recommended by Pearson. The results are shown in figure 7.3.4. The grouping of points in this figure was found to be entirely independent of both the degree of misalignment in the apparatus and the number of nozzles in the network.

The majority of the plotted points are seen to lie to the left of the Gaussian point in a region bounded by the lines 60: TEST NUMBERS 97-115 TEST NUMBERS 124-134 2.0 - TEST NUMBERS 135-146

'.0 a

°T SSiAN T.

2.0 3.0 4.0 5.0 19CIUR, 7.4. • Plot of Skewness (131) against Kurtosis (13) for the application patterns from the four-nozzle and sixteen - nozzle tests. 238.

)31 = 0, )B1 = 1.0, P2 = 2.0 and p2 = 3. These values of skewness and kur4sis indicate that the distributions are mildly skewed and "platykurtic", i.e. having a flatter peak than the normal distribution (see A. C. Aitken, 1962, pp.36-7). The frequency of readings showing large departures from the mean are of the same order as those showing only small departures.

In contrast, a number of points lie to the right of the Gaussian point, having values of pi between 1.0 and 2.5, and values of p2 between 3.0 and 5.5. These points correspond to distributions which exhibit a more pronounced degree of skewness and are "leptokurtic", i.e. are taller and slimmer than the normal distribution. These patterns contain only a very small number of readings substantially larger or smaller than the mean. Further details of each are summarised in table 7.3.1.

TABLE 7.3.1: Further details of leptokurtic distributions of application depths recorded in the four and sixteen-nozzle tests

Test No. of Head U Number Nozzles (ft) P1 P2 c r 104 4 11.07 1.553 3.661 0.951 114 4 11.97 1.072 3.462 0.909 132 16 11.02 2.561 5.553 0.f9%15 133 16 12.03 1.389 3.906 0.873 138 16 11.12 1.510 4.155 0.878 139 16 9.90 1.882 4.327 0.911

Table 7.3.1 reveals that these leptokurtic distributions all occurred at approximately the same working pressures. Their occurrence at heads of approximately 10.0 and 11.0 feet of water during the second set of sixteen-nozzle tests instead of at 11.0 239.

and 12.0 feet as recorded in the other tests can probably be attributed to misalignment of the apparatus during the latter. Each result was obtained from a pattern exhibiting a high value of the Christiansen uniformity coefficient. Reference to figures 6.5.1, 7.2.1 and 7.2.2 also shows that the second peak of uniformity occurs at approximately the same working pressures as the leptokurtic patterns. This coincidence would appear to be reasonable, as a narrowing of the frequency distribution of application depths is only to be expected as the pattern becomes less disturbed.

The high uniformity coefficients recorded at these heads occurred as the shape of the single-nozzle patterns attained a conical profile which was the optimum at the chosen geometry and spacing for producing uniform application patterns from the network. The present writer has been unable to find an account of any other work in which P112 plots have been made for application patterns obtained from either nozzles or irrigation sprinklers. Without further evidence to confirm the above findings, the conclusion that leptokurtic distributions of application depths are characteristic of the optimum combination of conical single- nozzle patterns can only be made tentatively. The present data does not suggest that a similar criterion could be offered for the first peak of uniformity observed with the four and sixteen- nozzle tests to characterize the optimum combination of the annular type of single-nozzle pattern.

In contrast to the closer study of the higher statistical moments, Culver and Sinker (loc.cit.) have recently suggested that the ratio of the maximum to the minimum application depth within a pattern might form a suitable easily-computed measure of nozzle or sprinkler performance. Values of this ratio (R) were calculated for the overlapped patterns from both the symmetrical 24o. and the measured single-nozzle patterns, and plotted against corresponding values of Uc as shown in figure 7.3.5. The same diagram, reproduced from figure 15 (p.16) of the paper by Culver and Sinker has been included as an insert on figure 7.3.5 for comparison purposes.

Both the results presented by the latter authors and those from the present investigation are grouped about a similar shape of locus. However, the scatter of the latter is more pronounced than that of the former, giving extremely poor definition in the region corresponding to Christiansen uniformity coefficients less than approximately 0.75. In addition, the break in the curve at roughly the same point in the results presented by Culver and Sinker is entirely absent from the data from the present investigation. These differences tend to indicate that R is perhaps too coarse an index of uniformity.

A basic fault of all statistical measures of uniformity is their inability to describe an application pattern in terms of space co-ordinates. The description of input distributions of artificial rainfall in terms of position over a laboratory catchment forms an important requirement for future work. J. Amorocho and A. Brandstetter (1966) have proposed a method by which distributions of natural rainfall over a catchment area can be described by a system of non-orthogonal polynomials. A similar technique has also been applied by R. A. Pullen, J. F. A. Wiederhold and D. C. Midgley (1966) as an aid to depth-area- duration analysis of large-area storms in South Africa. These methods would be equally applicable for use in laboratory catchment studies. The present writer has investigated the possibility of using double harmonic series for the same purpose, and details of the latter approach are included in Appendix D. e_ •

AS III Ira 111

20 4-0 6.0 8.0 10.0 VAUJES OF "RI WSERT- THE SANE RELATIONSHIP AS SHOWN BY R. CULVER AND R. F. SINXER regr36 ; FIG. 15. PIS.) OVERLAPPING WITH SYMME1RICAL SINGLE NOZZLE PATTERNS . ASYMMETRICAL SINGLE x 0 NOZZLE PATTERNS. X 0 •

0 0

1.0 24 3.0 4.0 5.0 6.0 7.0 MAXIMUM PER MINIMUM APPLICATION DEPTH ,

The variation of the Christiansen uniformity . coefficient with the ratio of the fraXiMUM to the rrgrOmurn apptication depth. 242. CHAPTER EIGHT

The Measurement and Analysis of Drop Size Distributions

8.1. Methods of Measuring Drop Size Distributions

During the last 75 years, a variety of methods has been used to estimate drop size distributions in both liquid sprays and natural rainfall. Without exception, these methods involve some system of sampling the volume of liquid dispersed. As with all such techniques, the sample must be representative of the distribution under study, and the investigator must assess the accuracy of his results accordingly.

The methods used to evaluate the drop size distributions of liquid sprays have been discussed by E. G. Richardson and H. L. Green, writing in J. J. Hermans (ed; 1953). Green (in Chapter VII, p.318) reviewed the techniques applicable to atomized sprays containing droplets less than 100 microns (0.1 mm) in diameter. An arbitrary dis- tinction was made between methods involving direct measurements of droplet size, and indirect methods in which impressions made by the droplets are assessed. Richardson (in Chapter VI, p.277) considered the measurement of distributions involving droplets larger than 100 microns on the basis of the size of the volume sampled.

In extending the present discussion to include the methods used to estimate drop size distributions in natural rainfall, neither of the above criteria proves adequate to distinguish between the various techniques. Measurements in natural rainfall, or in liquid sprays containing a comparable range of drop sizes, have generally been made by indirect methods depending upon either physical or chemical linkages. There have been exceptions to thi8 statement, however. H. Lnndsberg and H. Neuberger (1938) were able to measure the size distribution of frozen raindrops collected during a sleet shower directly before significant melting took place. R. L. Green 243. (1952) has described a photographic method for directly evaluating the size and velocity of drops from an irrigation sprinkler by double exposure photographs, obtained using both direct lighting and syncro- nized flash.

In general, physical limitations within each technique of measurement restrict its application to a particular range of drop sizes. In the absence of more specific criteria, the available methods are considered below on the basis of their working range.

Where the size of drops within the distribution investigated is less than approximately 200 microns in diameter, samples may be caught on slides and examined under a microscope, or through photo- micrographs. A comprehensive account of size analysis techniques using a microscope has been given by G. L. Fairs (1943). According to K. R. May (1945), there are three principal methods of preparing slides for sampling.

When the liquid sprayed has a low volatility, such as an oil, and analysis can be completed before significant evaporation takes place, the droplets may be caught on plain glass slides. Provided that the slides are clean and grease-free, the droplets will spread uniformly and take up an equilibrium position in the form of plano- convex lenses. Using a microscope, the focal length of this "lens" may be measured along with its diameter. If the angle of contact of the liquid and its refractive index are known, the diameter of the original spherical drop may be calculated. In a later paper, K. R. May (1950) gave a working range for this "plain-glass" or "focal-length method" of from 5 to 80 microns.

Direct measurements of droplets in their original spherical form without correction for apparent sizes is possible where the slides are coated with a high-viscosity matrix of similar density, but of different refractive index to the liquid (the "absolute method"). 21+1+.

A further obvious requirement is that the liquid must be insoluble in the coating. For water droplets, May (1945) recommended a mixture of three parts light mineral oil to one part of vaseline. N. Fuchs and J. Petrjanoff (1937) used slides prepared in this manner to sample natural fog. If the samples are subject to evaporation, photomicro- graphs may be taken soon after exposure and used for size analysis. Alternatively, May (1945) described another procedure by which a further coating of the matrix was applied to the slide after exposure.

Evaporation errors may be eliminated by using an indirect sampling method. The slides are coated with a detector in which the droplets leave impressions proportional to their sizes on impact. Both D. W. Lee (1932), in studying the atomization of high-grade diesel fuel, and 0. C. French (1934), who worked on the development of insecticide sprayers, used slides coated with soot. Such layers are opaque and cannot be used with transmitted light, and magnesium oxide has been found to be more generally useful as a detector. Slides are prepared by passing them to and fro immediately above a flame from burning magnesium ribbon (the "magnesium oxide method"). May (1945) recommended that the coating should be thicker than the largest droplet size expected. Stable layers of oxide thicker than 200 microns are difficult to obtain, and this figure is generally accepted as the upper size limit for the method.

If impact velocities are sufficiently high, droplets down to 5 microns in diameter may be detected using slides coated with magnesium oxide. The method has been used to advantage by workers of the Meteorological Research Flight for the sampling of cloud droplets from aircraft. Accounts of their research have been given by R. Frith (1951), W. G. Durbin (1959) and F. Singleton and D. J. Smith (1960). The sampling devices used have been illustrated in a paper by W. G. Durbin (1958). In addition to its application in cloud 245. physics research, the magnesium oxide method has been used successfully to sample fogs (see R. C. Srivastava and R. K. Kapoor, 1960) and sea mists (see M. A. Mahrous, 1954).

In all indirect methods, the relationship between the size of drop and the size of the impression that it makes must be evaluated. May (1950) performed a calibration for the magnesium oxide method over a size range of from 10 to 200 microns and for a wide range of liquids and impact velocities. Samples of a uniform spray taken by the magnesium oxide method were compared with simultaneous measurements made by the absolute method. The latter were taken to represent the true drop size. For droplets greater than 20 microns in diameter of any liquid, the ratio of true drop size to impression size was found to be constant at 0.86. The velocity of impact was found to have no appreciable effect upon the results provided that the slides were held horizontally, and the droplets fell vertically. For droplets less than 20 microns in diameter, the ratio was found to decrease appreciably.

Other methods of preparing slides have been tried. F. Y. Rovinsky (1959) experimented with slides covered with a thin layer of gelatin containing small crystals of silver bichromate and sodium iodide. Water drops impinging on this surface began a chemical reaction which resulted in the formation of a precipitate of silver iodide. White circles appeared on the reddish-brown background of silver bichromate. According to Rovinsky, droplets of any size down to 3 microns could be detected under the microscope using slides treated in this manner.

Another indirect method of measurement, applicable to atomized sprays has been described by E. A. Watson (1948). This technique, attributed to J. R. Joyce as its originator, has been generally applied in investigations of fuel sprays. Paraffin wax, heated to a temperature at which its viscosity corresponds to that of the fuel, is sprayed 246. into the air at normal temperature, and the droplets collected in water. The size distribution is subsequently obtained by sieving and weighing the hardened droplets.

H. L. Green (loc. cit., 1953) suggested that the above type of analysis could also be applied to droplets frozen in a medium at a suitable temperature. H. Neuberger (1942) reported on a number of trial experiments in which an attempt was made to assess the size distribution of natural rainfall by artificially freezing the drops. A cylinder, containing an unspecified liquid of low freezing point, was immersed in an ice bath, and used as a collector. The drops froze instantly in the liquid, but the method was found to be unsuc- cessful owing to splitting of the frozen droplets through rapid cooling. The setting-up of a temperature gradient in the liquid in an attempt to eliminate this effect led to crystalline growth on the drops.

The "flour method", devised by W. A. Bentley (1904) for size distribution measurements in natural rainfall, is based upon similar principles to the freezing technique. Bentley allowed raindrops to fall into smooth, one-inch thick layers of fine uncompacted flour contained in shallow, four-inch diameter tins. The duration of exposure was varied according to the rainfall intensity. The raindrops collected in the layer of flour formed pellets of dough, which were allowed to dry before being removed for analysis. J. 0. Laws and D. A. Parsons (1943) adopted the flour method for their measurements of drop size distributions in natural rainfall, adding a number of refinements to the procedure. The conditions under which the pellets were dried were standardised by redrying the air-dry pellets in an oven for one hour at 110°C. The separation of the dry pellets into size groupings was carried out using a nest of sieves. The dimensions of the sieve openings did not give the size limits for 247.

the distribution however, because the larger drops were found to flatten on impact, giving rise to non-spherical pellets. The average weight of pellet on each sieve, obtained by dividing the total weight of catch by the number of pellets, was used to characterise the size groupings. The results from the sieve analysis were converted into a drop size distribution by applying the "mass ratio". This figure, the ratio of the mass of a drop to the mass of the pellet that it forms, was determined from prior calibration experiments using drops of known size.

G. Chapman (1948) applied the same procedure in studying drop size distributions under a forest canopy. D. C. Blanchard (1949a) also used the same technique, making two further modifications. A colouring agent was mixed with the flour to identify the pellets more easily; and a thicker layer of flour, having an irregular surface, was used to reduce splash effects associated with the larger drop sizes.

The same method was adopted by N. W. Hudson (1963) for a study of the drop size distributions in sub-tropical rainfall. Hudson emphasised the care needed to ensure accuracy in the calibration of drop size and pellet size. Additional precautions taken by him included the removal of the satellite drops which are obtained when large drops break away from a drop-former, and the drying of pellets to constant weight before weighing. In addition, the pellets were formed by drops striking the flour at approximately terminal velocity. A detailed account of the calibration procedure has been given in a later paper (see N. W. Hudson, 1964a).

The same investigation was also notable for the use of an automatic sampling device. A modified rainfall intensity recorder was used to trigger the apparatus when the rainfall reached a predetermined rate. Ten samples were taken at 4-second intervals in pans placed on a table rotating under an aperture designed to minimise 21+8. splashing. A full description of this device has been given in an unpublished thesis by the same author (see N. W. Hudson, 1965).

Although Bentley appears to have been the first American investigator to measure drop size distributions in rainfall, European scientists had been actively concerned with such observations for over a decade previous to the publication of his paper. E. J. Lowe (1892) attempted to measure the size of raindrops from splash marks formed on sheets of slate. German meteorologists, contemporary with Lowe, preferred to use absorbent paper surfaces as a sampling medium. The development of their sampling procedure, which has remained basically unchanged since its conception, has been summarised by Neuberger (1942).

The introduction of the method is attributed to J. Wiesner (1895). Wiesner collected raindrops on sheets of blotting paper or filter paper, and estimated their size by comparing the spots formed with those produced by drops of known size. The paper had to be the same thickness as that used for calibration purposes, and completely dry prior to exposure. P. Lenard (1904) improved on the method by dusting the spots on the paper with eosin so that permanent records were obtained. Because of its simplicity, this "stain method" was adopted for use in the present investigation, and is considered in greater detail in Section 8.2.

In addition to its simplicity, a stain method requires a minimum of materials, and is cheap to use. In contrast, the analysis of results is tedious and time-absorbing, and the method is incapable of giving continuous records unless a large number of observers is available, or an automatic device is used. A contributor to the discussion of Lowers paper proposed that records of drop sizes should be taken on a continuous tape of chemically-treated paper driven by clockwork. Some 50 years later, a number of automatic recorders were developed which successfully utilised this principle. 249.

E. G. Bowen and K. A. Davidson (1951) used a device in which drops were allowed to fall through an orifice one square inch in area into a low-velocity wind tunnel. The current of air within this wind tunnel deflected the drops horizontally through distances inversely proportional to the cube of their diameters onto a moving strip of dyed filter paper. The samples collected with this apparatus were graded into their size groupings automatically, but its use was restricted to vertically-falling drops between 0.3 and 1.5 mm in diameter.

A. T. Spencer and D. C. Blanchard (1958) developed a portable instrument for measurements in orographic rain in Hawaii. The raindrops were collected on dye-impregnated tape which was automatically exposed for three seconds at two-minute intervals by the operation of a sliding shutter. During the interval between exposures, the previous sample was dried by a heating coil, and the tape advanced in preparation for the next exposure. The area of each sample was approximately five square inches, and was found to be adequate for the type of rain under study which seldom contained drops larger than 2.0 mm in diameter. The shutter and paper transport mechanisms were driven by a 12-volt d.c. motor powered by a car battery. The instrument was capable of operating unattended for over 24 hours, and appears to have been an improved version of another device previously described by D. C. Blanchard (1953a).

M. V. Sivaramakrishnan (1961) used a basically similar instrument in a study of tropical rainfall characteristics at Poona. This apparatus differed from the Hawaiian recorder in having a continuously moving tape and no shutter mechanism. A timer, operated every 15 seconds by a microswitch, was incorporated. The tape was exposed at 2 a rate of three cm /s. The instrument was claimed to be successful in sampling rains containing drops up to 3.0 mm in diameter.

A disadvantage of the strain method is the tendency for larger drops to shatter on impact, forming distorted impressions which are 250. difficult to analyse. D. C. Blanchard (1949b) found that drops striking fine wire gauze did not splash on impact, but broke up after passing through the mesh. When the gauze was coated with a thin layer of soot, drops passing through the mesh produced clear circular impressions, proportional to their size, by removing a small quantity of the coating. M. P. Garrod (1957) has noted that the clarity of records can be improved if the screen is coated with magnesium oxide before the layer of soot is applied. Drops striking the gauze remove the black soot, leaving the white oxide exposed in clear contrast to the rest of the sample area. Nylon screens treated with benzine- lanolin solution and covered with powdered sugar have also been tried (see B. J. Mason, 1957; p.428). According to Garrod (loc. cit.), the Meteorological Research Flight adopted the sooted screen technique for the measurement of precipitation elements larger than 100 microns in diameter from aircraft. Subsequent experiments showed that aluminium foil, 0.001 - inch thick, gave cleaner and more permanent records. Drops striking the foil at normal airspeeds produced imprints proportional to their size. A continuous recording device was developed in which a continuous band of foil is fed across a sampling slot exposed to the airstream. This instrument has since become part of the standard measuring equipment used by the Meteorological Research Flight (see Durbin, 1958; also R. J. Murgatroyd and M. P. Garrod, 1960).

Particularly during the last fifteen years, considerable attention has been devoted to the development of measurement techniques which do not entail laborious analysis. As a result of these efforts, a number of instruments have been produced which detect drops acoustically or optically, giving a response in the form of electrical signals.

Neuberger (1942) described an apparatus based on these principles, which was used by F. Schindelhauer (1925) to obtain the average drop size 251. of a given rainfall. The sound produced when drops impinged on a membrane was amplified electrically and the signal used to operate a recording apparatus, giving a measure of the total number of drops per unit area per unit time. The average drop size was obtained by dividing this number into the total rainfall catch recorded during the same period. All drops were assumed to be spherical in shape, and the drops recorded had to be large enough to vibrate the membrane. The simultaneous arrival of more than one drop could not be detected. Both sources of error tended to reduce the total count, giving too large a value for the apparent average drop size.

J. Maulard (1951) developed a similar instrument capable of recording drops larger than 0.5 mm in diameter. The recording head of this apparatus consisted of a copper disc*, 4 cm- in diameter, connected by a steel rod to the diaphragm of a telephone receiver. The impulse received on the diaphragm was converted into a voltage signal, amplified and used to activate an electromagnetic counter. The minimum interval required for successive drops falling or o the receiver to produce separate signals was claimed to be 0.2 seconds.

The Division of Radiophysics of the C.S.I.R.O. have produced a more elaborate version of the same type of instrument which, in addition to counting the number of drops, also provided a measure of the size distribution. The apparatus was designed to telemeter continuous measurements of drop size distribution during balloon-bourne ascent through rain and cloud (see B. F. Cooper, 1951). A condenser- type microphone, forming one of the tuning capacitors of a 60 Mc/s radio transmitter, acted as the recording head. Drops impinging on the microphone modulated the transmitter frequency by an amount proportional to their size. A ground-level receiver converted the

* B. J. Mason (1957; p.428) is apparently incorrect in stating that the disc was leather and not copper. 252. transmission into voltage pulses which were sorted into six amplitude groups, the running total in each being registered on relay-activated counters. The original apparatus described by Cooper was incapable of discriminating drops larger than 3.0 mm in diameter.

The amount of frequency modulation caused by the impact of a given size of drop was dependent upon its momentum relative to the microphone. The rate of ascent of the transmitter was therefore an important factor in calibrating the instrument, and a standard radio- sonde baroswitch, which interrupted the signal briefly every 2,500 feet, was fitted to the apparatus.

The design of the sensing unit in such momentum devices as the above is inevitably based upon a compromise. The diaphragm must be small enough to respond to the impact of small drops, but must be large enough for edge effects to be minimised. The diaphragm decreases in sensitivity from the centre towards the edges, so that a drop of diameter d falling at the edge can give an identical record to that of a drop diameter oCd falling at the centre, where o< is less than unity. E. E. Adderley (1953; pp.387-8) worked out a correction equation for the results obtained from the C.S.I.R.O. apparatus, allowing for non-uniform response over the microphone diaphragm.

Despite the inherent difficulties of acoustic measurement, the apparatus required is simple and easily adapted for automatic recording. An aircraft-mounted momentum device was tried by I. Katz (1952). More recently, the theory of measuring raindrop sizes by an acoustic method has been discussed in detail by V. V. Mikhaylovskaya (1964). The bibliography attached to the latter contribution appears to indicate that considerable interest exists among Russian meteorologists con- cerning its application.

In all momentum devices, the field of observation is defined by a physical obstruction. The same comment is applicable to the 253. flour method and to the filter paper method, and, in each of these techniques, errors occur through the shattering of drops on impact, and their incidence at angles less than the vertical. In photoelectric methods of measurement, in which the sampling field is defined optically, these disadvantages are eliminated.

The operation of the "photoelectric raindrop spectrometer" described by B. J. Mason and R. Ramanadham (1953) was based on the ability of individual raindrops to scatter light flux into a given solid angle in proportion to their size. The two principal components of this apparatus consisted of a light source and a detector unit.

The light source was a high-pressure mercury arc lamp. Light from this lamp was passed through a carefully-corrected lens system and a rectangular slit to produce a parallel rectangular beam of uniform intensity, 50 mm wide and 5 mm deep. The detector unit consisted of a telescope system at the focus of which was positioned the cathode of a sensitive photomultiplier cell. The detector was placed in front of the light source, but to one side of the parallel, rectangular beam, so that the angle between the axis of the telescope and the beam was 20 degrees. The field of observation was therefore defined optically by the intersection of the "beams" from source and 2 detector unit. The field was 72 cm in area, and remote from both units of the instrument, thereby avoiding splash errors.

The light scattered forward at an angle of 20 degrees by drops falling within this field was focused onto the cathode of the photomultiplier cell, producing voltages pulses of amplitude proportional to their area of cross section. The voltage pulses representing different drop sizes were sorted electronically into eight predetermined size intervals, and a continuous record of the number in each read out onto telephone message registers. 254.

The apparatus was calibrated using drops of known size falling at different points through the sample area. The size of this area was chosen to be large enough to give representative samples of drop size distributions but not large enough for coincident counts to become a significant source of error. Edge errors, caused by drops falling through the edge of the beam where the intensity of illumination was diminished, could be corrected by careful calibration within the sensitive region.

Owing to variation in background illumination, the spectrometer could not be used during daylight hours. In darkness, when extraneous light was reduced to a minimum, drops down to 100 microns in diameter ..would be detected easily. Further reduction in this figure was possible by minimising the "noise" of the photocell.

J. B. Andrews (1961) made a number of improvements to the basic apparatus described by Mason and Ramanadham. By using a photomultiplier cell sensitive only to the wavelengths of near ultra-violet light absent from sunlight, Andrews was able to build a more versatile instrument capable of reliable operation during the daytime. In addition, an improved pulse height analyser was incorporated which provided four extra counting channela.-

A. N. Dingle and H. F. Schulte (1962) also developed an apparatus using the same basic principles as those employed by Mason and Ramanadham, and Andrews. The principal difference between this instrument and that described above lay in the geometry of the optical system. Dingle and Schulte preferred to use a forward-scattering angle of 30 degrees, and the rectangular beam from the light source was orientated with its longer dimension vertical instead of horizontal. The sensitive field, defined as above by the intersection of "beams" from source and detector unit, was made to scan a continuous path by rotating the whole assembly about a vertical axis. Rotating at 255. approximately 106 rev/min, the instrument was able to scan a volume of 9330 cm3/s.

The effect of turbulence caused by the scanning movement was reduced by placing the sensitive field above the level of the rotating components by tilting the axes of light source and detector unit at a small angle to the horizontal. The whole apparatus was enclosed in a specially-designed light trap to provide a uniform background of minimum illumination against which the photocell could view the sampling field.

In addition to the scattering-type of photoelectric device, another variety has been tried in which the change in intensity of a light beam momentarily obscured by a falling drop was used as a measure of its size. An aircraft-borne version of this type of instrument was tested by R. E. Katz and G. A. Wilson (1948) and found to be largely in error when drop sizes exceeded 1.0 mm in diameter. Andrews (loc. cit; p.40) noted that the fractional changes in intensity obtained with a light-obscuring device cannot be very much larger than the inherent "noise" of most photocells. Development of the obscuring-type of instrument now appears to have been abandoned in favour of the more reliable light-scattering type. A light-scattering device has been successfully adapted for airborne measurements (see A. E. Mikirov, 1957).

Acoustic and optical devices have proved to be invaluable for long-term research programmes involving numerous routine measurements. In the present series of experiments, the measurements of drop size distributions were supplementary to the main purpose of the investigation, and occupied a relatively small amount of laboratory time. Such a short series of measurements did not justify the use of the photoelectric raindrop spectrometer developed by Andrews, which was available at the time, and therefore the stain method was adopted. This method is considered in greater detail below. 256. 8.2. The Stain Method

To recapitulate, the stain method of estimating drop size distributions depends upon the assumption that a drop falling upon a uniform, absorbent paper surface produces a stain, the diameter of which is proportional to the diameter of the drop. A permanent record of the stains is easily obtained by treating the paper surface with a soluble dye. In certain experiments, in which the properties of liquid sprays have been investigated, the addition of dye to the liquid and the use of untreated paper has been found more convenient. A. G. M. Bean and D. A. Wells (1953) recommended this procedure for the evaluation of the drop size characteristics of irrigation sprinklers, and the "sprayograph" described by G. L. Shanks and J. J. Paterson (1948; 1952) also worked on the same principle.

A large number of investigations into the drop size distribution of rainfall have been carried out using the stain method, and a variety of absorbent papers and dye treatments have been tried. A number of examples of these detail variations are given in Table 8.2.1. Consistent results are only obtained with the stain method when the paper used has a standard thickness and a uniform texture. Whatman number 1 filter paper has proved to be popular in this respect, as shown by Table 8.2.1. Different types of paper have been tried by other investigators, as shown in Table 8.2.2., but none of these appears to have been used other than by their originators. None of the authors listed in Table 8.2.2. gave the relationship between drop diameter and strain diameter which applied to their particular treatment.

This relationship must be determined by prior calibration experiments. Drops of a constant size can be produced from lengths of drawn glass or hypodermic tubing under a small head of water. The size of stain obtained on a sample of the absorbent paper may be measured directly. An equivalent spherical drop diameter may be CALIBRATION i SOURCE ABSORBENT SURFACE TREATMENT CONSTANTS_ K M

BEST (1947) Whatman No. 1 filter paper dusted with Rhodamine G dye, or 4.53 1.31 soaked in a suspension of the same dye in carbon tetrachloride

MARSHALL, LANGILLE AND PALMER Whatman No. 1 filter paper dusted with powdered Gentian-violet 3.29* 1.50 (1947) dye

ANDERSON (1948) blotting paper dusted with powdered Potassium 2.97* 1.50* permanganate

FOURNIER D'ALBE AND unspecified grade of .none: samples processed immediately 3.10 1.50 HIDAYETULLA (1955) filter paper

MAGARVEY (1957); d> 1.50 mm Whatman No. 2 filter paper dusted with powdered blue analine 4.33 1.33 d<, 1.50 mm dye 3.26 1.08 '

KITKAR (1945; 1959) • glazed paper coated with ink and allowed to dry, 3.48 1.43 i or with an unspecified soluble dye

ANDREWS (1961) Whatman No. 1 filter paper soaked in an alcoholic solution of 5.11 1.23 Bromo-cresol green dye, or dusted with Rhodamine G dye

Israel Meteorological Service Whatman No. 1 filter paper sprayed with a suspension of 3.38 1.50 (as quoted by SHACHORI and Methylene blue dye in carbon SEGINER, 1962; SEGINER,1963) tetrachloride

* Calibration constants estimated from curve given by author(s).

TABLE 8.2.1. Some detail variations on the Stain Method of measuring drop size distributions. 258.

TABLE 8.2.2. Further Detail Variations on the Stain Method for Measuring Drop Size Distributions

SOURCE ABSORBENT SURFACE TREATMENT

GUNN (1949a) blueprint paper developed in strong light

LEVINE (1952) paper towelling photographed immediately after exposure

KOBAYASHI (1955) photographic paper coated with cobalt chloride

SPENCER and adding machine dusted with powdered BLANCHARD (1958) tape methylene blue dye

estimated from the weight of a predetermined number of drops formed under the same conditions. For drops less than. 2.0 mm in diameter, the construction and use of drawn glass or hypodermic tubing drop- formers becomes impracticable because of the fine bores required to produce such drop sizes. These difficulties may be overcome by the use of apparatus such as the "microburette" described by W. R. Lane (1947).

In Lane's apparatus, the drops were formed at the tip of a hypodermic needle around which flowed a concentric stream of air. This airstream assisted gravity in overcoming the surface tension forces causing the drop to adhere to the tip. The drops therefore broke away before obtaining their normal size. A range of drop sizes could be produced by varying the velocity of the airstream. 259. Using similar apparatus, Andrews (1961) was able to form drops 600 microns in diameter. A. C. Rayner and H. Hurtig (1954) were able to produce even smaller drops in the range 70-400 microns with another device in which the drops formed on the tip of a capillary tube were prematurely detached by a vibrating blade.

Difficulties are also encountered with the larger drop sizes owing to their tendency to splash on impact, forming imperfect impressions. According to Neuberger (1942), E. Neiderdorfer (1932) showed that the size of a stain is also a function of the velocity of fall for drops larger than approximately 1.1 mm in diameter. In view of these findings, care must be taken in calibrating to ensure that such sizes of drops fall a sufficient distance to reach their terminal velocity before striking the paper.

The production of stains on filter paper by drops of known dimensions has been discussed at length by T. Gillespie (1958). For liquids of low vapour pressure, the spreading of a drop into a circular stain was described by the equation 6 2 6Et eq. 8.2.1, ( ) a h where D = diameter of stain produced by a drop of diameter d, C saturation concentration of liquid in the paper, s h = thickness of paper, a constant, and t = time after collection.

The constant B is a measure of the spreading of liquid from the large pores at the centre of a stain into the finer pores at the edge under the action of capillary forces. Gillespie noted that, for low vapour pressure liquids, there is no "final stain size", and that the evaluation of results is time-dependent. A direct

26o. proportionality is obtained between stain diameter and drop diameter if 2 t >> eq. 8.2.2. 6B.0

For liquids which readily evaporate, there is a final stain size. Spreading does not proceed very far, making the second term on the right-hand side of equation 8.2.1. less significant. In this case, D is proportional to d to the power 3/2.

The so-called "simple" theory, in which the volume of a drop is equated directly with the volume of the resultant stain in the paper, gives the result

D 3 2 D (-d-) = v-a---1-1 eq. 8.2.3.

These equations only apply for drops which are large enough to penetrate from one side of the paper to the other, and have the same diameter when measured from both sides. Gillespie concluded that, in general, depending upon the significance of the spreading

D = K (d)m ; 1.0 .4:,m 40.5 eq. 8,2.4.

The values of K and m can only be held constant under strictly controlled experimental conditions. These conditions are generally achieved by the storage of unexposed papers over a suitable desiccant, and their rapid replacement after exposure. Values of K and m obtained from a number of independent calibrations are given in Table 8.2.1. In comparing these data, the following points may be noted.

In four of the examples given, the value of m is exactly 1.5, consistent with equation 8.2.3. Marshall et al stated that a curve corresponding to a three-halves power law had been deliberately drawn 261. through their plotted data. Apparently, no statistical confirmation of this power was obtained. The authors also stated that for the calibration of the larger drop sizes, stains were formed by standing the drops on a plain glass surface, and placing the filter papers directly onto the drops. This method would not take into account the effect of velocities of impact pointed out by Neiderdorfer, and must be regarded as a major error in procedure.

E. M. Fournier D'Albe and M. S. Hidayetulla (1955) also assumed an exponent of 1.5 in their calibration equation, and stated that this figure was "... expected from geometry", i.e., the "simple" theory of equation 8.2.3. K was stated to depend upon the type of absorbent surface used.

The constant and exponent for the data presented by Anderson were obtained by the present writer by regression analysis on the scaled-off ordinates of his calibration curve. In view of the paucity of the number of points through which his curve was drawn, it is possible that Anderson chose to fit a power law to conform with equation 8.2.3. No information is available on the Israeli Meteoro- logical Service's calibration other than a simple statement of the equation, but their value of m may also have been a deliberate choice.

The apparent inconsistency of the calibration constants obtained from the data given by Best and those from the data given by Andrews may be noted. Although the absorbent paper and dye used were the same, the constant of Best's equation is less than that of Andrews', but the exponent of Andrews' is larger than that of Best's. If Andrews' figures for smaller drop sizes, formed with a blown-air apparatus, are omitted and a further regression analysis performed, values of K = 4.39 and m = 1.33 are obtained. These figures are closer to those derived from Best's data. 262.

The difficulties of producing streams of small, uniform droplets have already been referred to above. Because of these difficulties, the lower limit of the range of drop sizes used in calibration experiments rarely corresponds to, and is generally higher than that found in the distributions subsequently sampled. Fournier D'Albe and Hidayetulla used drops whose equivalent spherical diameters ranged from 2.3 to 6.5 mm, but extrapolated over a range of from 1.0 to 10.0 mm.

Stimulated by the statement made by the latter authors that the exponent of the calibration equation was a constant following from geometry, R. T. Jarman (1956) investigated the drop size/stain size relationship of Whatman number 1 filter paper for five different liquids. His results gave an exponent* equivalent to a value of m equal to 1.19 :I: 0.03 using drops ranging from 0.13 to 2.0 mm in diameter. The agreement between this result and the exponent calculated from Andrews' full data may be noted.

A further detailed study of the stain method was carried out by R. H. Magarvey (1957). His results, which were obtained for Whatman number 2 filter paper using a range of drop sizes from 0.5 to 10.5 mm in diameter, showed that the value of the exponent was not constant over the entire range of the calibration. Two equations were presented, one of which applied to drops larger than 1.5 mm in diameter, and the other to drops less than the same dimension (see table 8.2.1.). Another interesting conclusion reached by the same

*Fournier D'Albe and Hidayetulla (1955), Jarman (1956) and Margarvey (1957) all presented results in the form of equations expressing drop diameter as a power of stain diameter. For consistency, their figures have been transformed into terms of equation 8.2.4. (i.e., the values of m quoted above are the reciprocals of the values stated in the original papers). 263. author was that, for Whatman number 2 filter paper, the calibration constants were insensitive to changes in impact velocity of from 15 to 25 per cent. Both Jarman and Magarvey noted the dependence of stain diameter on drying time referred to by Gillespie.

In general, the above discussion suggests that additional care is needed when determining drop size/stain size relationships to ensure that the range of drop sizes used is sufficiently large to permit confident extrapolation. The precautions taken must depend essentially upon the accuracy to which results are required. A. C. Merrington and E. G. Richardson (1947), for example, assumed a linear drop size/stain size relationship for a study of the break- up of liquid jets.

A considerable saving in laboratory time was effected in the present investigation by using the calibration data obtained by Andrews, and adopting the same materials and procedures as those employed in his study. These data are therefore quoted in full in table 8.2.3.

TABLE 8.2.3. Calibration data for the measurement of drop sizes by the stain method using Whatman number 1 filter paper (after J. B. Andrews, 1961; p.51).

using blown air apparatus using glass tips d 0.62 0.97 1.25 1.6o 2.14 2.67 2.95 3.46 3.88 4.45 5.4o 6.19

D 3.10 4.10 6.83 10.90 13.05 15.80 19.00 22.00 27.30 31.70 44.00 46.2o

NB) d = drop diameter (mm); D = stain diameter (mm). 261+.

8.3. Sampling Procedure

120 sheets of Whatman number 1 filter paper were dusted with powdered Bromo-cresol green Ph indicator using a squirrel hair artist's brush. (A Windsor and Newton number 8 was found to be adequate for this purpose.) One gramme of dye was found to be sufficient to dust approximately 70 sheets of filter paper. Each paper was numbered when treated, and then stored in an eight-inch glass desiccator over self- indicating Silica Gel.

Owing to the high spatial concentrations of drops investigated, clear, readable samples could only be obtained when the filter papers were exposed to the spray for extremely short time intervals. The technique of rapidly removing and replacing a cover held in one hand over a frame containing a filter paper held in the other was found to be too slow. A number of alternative methods were tried, resulting in the construction of the sampling device illustrated in plate 8.3.1.

The sampling device operated on a similar basis to a focal- plane shutter. The hardboard cover was constrained to slide across the lower frame containing the filter paper. In doing so, a centrally- placed, one-inch wide slot, extending the width of the cover, was moved completely across the paper. The speed with which the cover was moved was varied as far as possible to give a sample convenient for analysis, yet representative of the distribution under study. The internal measurements of the lower frame, 72 by 72 inches, were just sufficient to hold an 18.5 cm-diameter filter paper. The device was made up from i-inch square stripwood, and hardboard, which were subsequently varnished and polished.

Contact between the filter paper and the sampling frame was limited to an annulus approximately 0.6-inch wide around the extreme edge of each paper. As the following analysis was carried out over an area less than that corresponding to the full diameter of the papers, 265.

PLATE 8.3.1.

SAMPLING DEVICE AND ANCILLARY EQUIPMENT FOR THE MEASUREMENT OF DROP SIZE DISTRIBUTIONS. 266. the possibility of erroneous readings through the collection of moisture from the sampling frame within this area was avoided. In addition, the cover and the interior of the lower frame were carefully wiped dry between exposures. Both exposed and unexposed papers were handled with tweezers, and exposed papers were replaced immediately in the desiccator.

The sampling procedure adopted required two observers; one to operate the sampling device, and the other to reload the filter papers. The positioning of the sampler under the cone of the sprays was easily arranged by running a string-line at the appropriate height along the required diameter under the nozzle. The sampling points were marked out along this string-line. The sampling level was six feet below the nozzle (as in test numbers 14-63). Papers were exposed directly below and at one-foot radius from the nozzle. If the cone of spray was sufficiently wide at the sampling level, additional readings were taken at a radius of two feet from the nozzle.

The variations in the drop size distributions from two types of nozzle, A/D and B/B, were investigated at each of four different working pressures, comparable with those at which isohyetal patterns were already available. Three exposures were made at each sampling point under each test condition.

For convenience in abstracting data from the filter papers, a scale was constructed. Using the calibration equation 8.2.4. with K = 5.11 and m = 1.23, the stain diameters corresponding to drop diameters of from 0.25 to 3.75 mm were computed for increments in drop diameter of 0.25 mm. These values are quoted in table 8.3.1. Circles of diameter equal to each of these values of stain diameter were scribed onto a sheet of thin perspex. The impressions were made more distinct by rubbing a dilute solution of black indian ink into the scribe-marks. 267e

TABLE 8.3.1. Values of stain diameter, D, corresponding to drop diameters, d, of from 0.25 to 3.75 mm at 0.25 mm intervals calculated from the adopted calibration equation.

--, a d D a d D a d , D

1 0.25 0.93 6 1.50 8.4o 11 2.75 17.68

2 0.50 2.18 7 1.75 10.15 12 3.00 19.67 --, 3 0.75 3.59 8 2.00 11.96 13 3.25 21.71

4 1.00 5.11 9 2.25 13.82 14 3.5o 23.78 1 4 5 1.25 6.71 10 2.5o 15.72 15 3.75 25.87

N.B.) a interval number.

Although Bromo-cresol green is not one of the stronger soluble dyes, care is necessary in handling the coated filter papers to preveqt the fine powder from spreading unnecessarily. For this reason, all samples were placed inside polythene bags when analysed. In addition, a mask on which areas of 201.0 and 100.3 cm2 were marked was placed over the sample. This mask consisted of another sheet of perspex, 18.5 cm square, marked out radially in 45 degree sectors. Concentric circles, 5.65 and 16.0 cm in diameter, corresponding to the above areas, were also scribed onto the mask.

Only stains lying inside the 16.0 cm-diameter circle were measured and counted, thereby avoiding the edge-errors mentioned above. Each "sector" of the sample was examined in turn, moving in a clockwise direction round the mask. A "five-bar-gate" tally was kept of the 268. number of stains within each interval of drop diameter. If stains were found to fall only partly within a sector, the following rules were observed:

1) Where stains were found to lie across the radial boundaries of a sector, only those lying across the lower boundary on the right-hand side of the mask, and the upper boundary on the left were counted for that sector. 2) Where stains were found to lie across the circumferential boundary of a sector, only those on the right-hand side of the mask were counted. Those lying across the left-hand boundary were not counted.

If the areal density of stains on the sample was very large, the same counting procedure was carried out over the 5.65 cm - diameter area only.

8.4. The Estimation of Drop Size Distribution Parameters from Sampled Data The following theory is based upon that quoted by Andrews (1961; pp. 54-8). Let the number of drops whose dimensions lie within an inter- 2 val from diameter d to d Ad be nd. If the sample area A(mm ) is exposed to the spray for a time t (seconds), nd drops will be collected from a column of space of cross-section area A and height (V.)d.t (mm), is a representative terminal velocity for the interval in where (V)d mm/s. The spatial concentration of drops, Nd, (i.e., the number of drops per unit volume of space per sampling interval Ad) is given by nd N . Ad eq. 8.4.1. d A.t.(V)d

The spatial water content of the distribution, W, (i.e., the total amount of liquid per unit volume of space) may be considered as 269. a summation of the total water content in each sampling interval. The total water content in each sampling interval may, in turn, be written as a product of the spatial concentration of drops and the average volume of the drops within the interval, leading to the expression

W = Ewd.Ad =ENd.Ad. 2 . IF (d3 Adr) eq. 8.4.2.

The above equation is dimensionless. If the cumulative water content Elid.Ad is plotted against d, the drop diameter, d mv at which half the total water content of the distribution is com- posted of drops whose diameter is less than dmv may be read directly from the graph. The parameter dmv, the median volume drop diameter, has been widely used in describing drop size distributions in natural rainfall. The rate of precipitation, P (mm/s), may also be written in similar terms to equation 8.4.2. if it is considered as a summation of the volume of liquid within each size interval falling upon the sample area per unit time:

(d3 + Ed + Adi3) P = d„Ad = d. 2 eq. 8.4.3. The handling of equations 8.4.1., 8.4.2. and 8.4.3. is greatly simplified if a number of the terms are grouped into single factors. In equation 8.4.1., the reciprocal of A.(V)d is a constant for each interval for any distribution, and may be written as a single term K1, giving K d. eq. Nd.Adn 8.4.4. In using equations 8.4.2. and 8.4.3., it is convenient to write

d + (d +Ad)3 = Ad3 [(a - 1)3 + a3] = eq. 8.4.5. 270. where a is the interval number, and Ad is equal to 0.25 mm leading to

W = Wd. L1 d = ZN Ad eq. 8.4.6, d• • K3 where K is equal to 768/TT. 3 If the units of P are converted into mm/h, another factor, K41 equal to 3600/A, may be separated out from equation 8.4.3. to give K4 7, P = EPd.,6d = 7-7 z. eq. 8.4.7.

Two sources of difficulty were encountered in using the above equations, the first of which was the choice of a suitable "representative terminal velocity" for each size interval. Since the beginning of this century, a number of investigators have obtained measurements of the constant, terminal velocity of water drops falling in still air. Among the first recorded results were those of P. Lenard (1904). Contemporary with Lenard, W. Schmidt (1909) made a series of measurements of the velocities of fall of raindrops which gave comparable values. A further laboratory study by W. D. flower (1928) also gave results which agreed with those of Lenard. The results obtained by all three investigators have been plotted for comparison in figure 8.4.1. Measurements of terminal velocities were also carried out as part of the U. S. Soil Conservation Service experiments already described in section 2.2. A detailed study was made of the velocity of fall of water drops of from 1.0 to 6.0 mm in diameter falling through distances of from 0.5 to 20 metres. The figures resulting from this study, reported by J. 0. Laws (1941), were approximately 15 per cent higher than those obtained by previous investigators. Unable to find any appreciable source of error in his own data, Laws concluded that their results were in error by large amounts.

271.

x 9 0 9

V x + 1.° got/ + 0 Pi X + 0

S9( 'SP LHAUS (194B)

TERMINAL VELOCITY OF WATER DROPS IN STAGNANT AIR. SYMEIOL 4 A!;IIIORITY IC HARD, 1904. SCI-IM!DT , 1909. FLOWER, 1923. 3- LAWS 1941. x GIJNN AND K1NZER , 1949. e, BEST (AFTER DAVIES) 1950b.

0 11 1 2 3 4 6

DROP DIAMETER MM tGtJRE. 4.1. The variation ot terminal vetocity with drop diameter - measurefrr.nts and empirical rel.alionships. 272. Lenard, Schmidt, Flower and Laws all used different experimental techniques for the measurement of both velocity and drop size. This factor, coupled with the notable disagreement in values recorded by Laws, prompted further work by R. Gunn and G. D. Kinzer (1949). The latter investigators devised an electronic method of measurement, the overall accuracy of which was claimed to be less than 0.7 per cent (see also R. Gunn, 1949). The range of drop sizes covered by their studies was much wider than any attempted by their predecessors. The results obtained confirmed the conclusions made by Laws, although differences up to 13 per cent were recorded for larger diameter drops (see figure 8.4.1.). The values of terminal velocity quoted by Gunn and Kinzer are generally regarded as the most accurate data available (see B. J. Mason, 1957; N. H. Fletcher, 1962), and their figures have been adopted for use in the present investigation. A number of empirical expressions have been proposed relating terminal velocity to drop size. For drops less than 4.0 mm in diameter, A. F. Spilhaus (1948) suggested

V2 = 20.1d eq. 8.4.8. where V is the terminal velocity in m/s and d is the drop diameter in mm. The value of the constant was determined graphically from Law's data. Reference to figure 8.4.1. shows that this expression grossly- overestimates the measurements for drops less than 1.5 mm in diameter, but provides values to within 5 per cent over the range 1.5 to 4.0 mm. Another, more complex, equation, based upon previously unpublished measurements made by C. N. Davies, has been proposed by A. C. Best (1950b):

din V = exp b z (1 - CLT1 1.) eq. 8.4.9. where z is the height (km) at which the values of terminal velocity is required, and E , b, c and n are empirical constants which vary 273. according to the range of drop sizes considered and the characteristics of the atmosphere. Best quoted values of these constants for two standard atmospheres, and for drops ranging from 0.05 to 0.3, and 0.3 to 6.0 mm in diameter. Using the constants for the I.C.A.N. atmosphere and the larger range of drop sizes, values of terminal velocity at ground level are given by the equation 1.147 [ --]d V = 9.32 (1 - exp- 1.7 7 eq. 8.4.10. On comparing values obtained from this expression with the measurements of Gunn and Kinzer, the equation is seen to provide estimates to within 6 per cent for all drop sizes, and to within 3 per cent for all drops larger than 1.5 mm in diameter. In computing the "representative terminal velocity" for each interval, Andrews used the following approximation:

1 1 1 + 1 eq. 8.4.11. t 75-d 2 Va "d+Adi However, the value of (V)d obtained from this equation does not strictly correspond to the value of the terminal velocity of the drop whose volume is the mean volume for the interval as the logic of equation 8.4.2. demands. The diameter of the drop whose volume is the mean volume of the ath.. interval, as is given by the expression

d 3/r) d3 + d)3 Ad. - 3)/ K2 eq. 8 4 12 a 2 Tf8 In table 8.4.2., the terminal velocities for each interval computed from equation 8.4.11. are compared with the values corresponding to drops of diameter aa. This comparison shows that for drops larger than 1.5 mm in diameter, the error introduced by using equation 8.4.11. is negligible. For the measurement of drop size distributions

International Commission for Air Navigation atmosphere. According to Fletcher (1962; pp. 192-3), the characteristics of this atmosphere are typical of those found in temperate regions. 274.

TABLE 8.4.2. A comparison between the values of representative terminal velocities calculated from equation 8.4.11., (V)d, and those corresponding to the mean volume diameters for each interval, V.

* error a K d V- (V) 2 a d d V-d - (V)d remarks , 1 1 0.159 0.54 , 0.54 zero lower limit of 0.125 mm. 2 9 0.431 1.68 1.30 +0.38 23% below Va 3 35 0.649 2.67 L 2.47 +0.20 8% below Vd 4 91 0.892 3.64 3.51 +0.13 4% below Va 5 189 1.139 4.45 4.40 +0.05 1% belowV-d 6 341 1.386 5.13 5.08 +0.05 1% below Va 7 559 1.635 5.73 5.68 +0.05 less than 1% below Va 8 855 1.883 6.26 6.28 -0.02 ditto 9 1244 2.132 6.76 6.79 -0.03 ditto 10 1729 2.381 7.24 7.19 +0.05 ditto 11 2331 2.630 7.61 7.58 +0.03 ditto 12 3059 2.880 7.92 7.98 -0.06 ditto 13 3925 , 3.130 8.19 8.22 -0.03 ditto 14 4941 3.380 8.42 8.4o +0.02 ditto 15 6119 3.630 8.62 8.61 +0.01 ditto

* The values of terminal velocity (m/s) were taken from the data of Gunn and Kinzer (1949). A linear interpolation was assumed between successive tabulated values. The figures were rounded off to the nearest second decimal place as in the data.

in natural rainfall, the approximation provided by the equation over a to 5 does not introduce signiFicant errom.The total water content of these intervals intervalstends to be a relatively low proportion of that for the whole distribution in moderate to heavy rainfall. Swirl-type nozzles are known to produce sprays containing large proportions of small drops 275. however, and the same approximation cannot strictly be justified. The values of terminal velocity corresponding to the mean volume diameters of each interval, Va, have therefore been used in place of (V)d in equation 8.4.4. A further point to note in connection with table 8.4.2. is the occurrence of equal values of V- and (V) d for the first interval of drop size. Unless a finite lower limit is chosen for this interval, equation 8.4.11. becomes indeterminate. An arbitrary value of 0.125 mm was chosen as the lower limit solely to illustrate the procedure. The agreement between the two values of terminal velocity V therefore fortuitous. The second difficulty encountered in using equations 8.4.4., 8.4.6. and 8.4.7. arises in determining the magnitude of the exposure time, t. The necessity for brief exposures has already been discussed in section 8.3. However, the action of the sampling device could not be timed accurately with a stopwatch, and the following method of estimating t was adopted.

As the filter paper samples were taken under test conditions corresponding to those at which patterns of application depths had been previously obtained, estimates of the mean intensity of application at each sampling point could be read directly from the appropriate patterns. These intensities of application, Pis were then substituted into equation 8.4.7. to give the required values of t: 4 K .1" eq. 8.4.13. 3 The value of P' attached to each sample depended upon the relative positions of the sampling points and the grid of points at which depth measurements were taken during the phase I experiments. The sampling points either coincided with a gauge position, or lay 276. directly between four gauges. In the former case, P' was taken from the single depth measurement, whereas in the latter, the average of all four readings was used. At a radius of 24 inches from the nozzle, the sampling point lay immediately outside the boundary of the grid of spray- gauges, and only two of the four measurements were available. The value of PI attached to samples at this radius was therefore estimated by extrapolation from these readings. The drop size distribution measurements obtained during the present investigation may be considered in two aspects. Firstly, the results may be used to compare the distribution of drop sizes in the artificial rainfall with those previously recorded in natural rainfall. Secondly, the variation of the drop size distribution, both with head at fixed points within the cone of influence of a single nozzle, and with radius from the nozzle at constant working pressure may be examined and related to the work already discussed in Chapter 5. Before discussing either aspect of the results, a suitable method for characterising the drop size distributions must be chosen. For convenience, the choice has been restricted to methods which have been applied to measurements of drop size distributions in natural rainfall. Equations such as that proposed by P. Rosin and E. Rammler (1933), which have been applied to size distributions of droplets in liquid sprays, have been reviewed elsewhere (see J. M. Dalla Valle, 1943; H. L. Green, 1953) and have therefore been omitted from the following critique.

8.5. Methods of characterising drop size distributions in natural rainfall The measurement of drop size distributions in natural rainfall made by P. Lenard (1904) and his contemporaries have already been referred to in discussing methods of measurement in section 8.1. The 277. value of their work and that of other investigators as recent as V. N. Kelkar (1945) is lessened considerably by the absence of measurements of rainfall intensity concurrent with the sampling. The division of results into general categories such as "drizzle" or "heavy showers" as attempted by Kelkar can provide nothing more than a qualitative description of variations in size distribution.

An urgent need for quantitative information on drop size distributions in rainfall arose from the work on soil erosion problems during the period 1930 to 1940. As described in section 2.2., drop size distribution measurements were included within the scope of the Soil Conservation Service experiments which began in 1936. The results of this work, which were subsequently reported by J. 0. Laws and D. A. Parsons (1943), therefore form one of the first comprehensive studies of the problem. Laws and Parsons chose to characterise the measured distributions by their median volume drop diameter, dmv (see section 8.4.). A plot of this parameter against rainfall intensity, P, showed considerable scatter which the authors attributed to "... momentary and localized variations in the composition of the rain". However, they considered that, if drop sizes were averaged over longer time intervals and larger areas than those used for their samples, dmv could be expressed as a fairly strict function of P according to the equation 0.182 dmv = 2.23 p eq. 8.5.1. with dmv in mm and P in in/h. Further impetus was given to the study of drop size distributions by post-war interest in the location of rainfall by radar. The intensity of the radar echo returned by rain is proportional to the sixth power of the diameter of the drops contributing to the response. The investigation reported by J. S. Marshall, R. C. Langille

278.

and W. McK. Palmer (1947) was one of a number undertaken at that time with the purpose of evaluating this relationship. Their measurements of drop size distributions were analysed in a later paper by . J. S. Marshall and W. McK. Palmer (1948), who showed that, except for small diameter drops, the distributions could be adequately represented by the equation

N = N exp (-B.d) d o eq. 8.5.2. where Nd..Ad denotes the number of drops per »n-it volume of space having a diameter between d and d + Ad mm. N is equal to 8000 m-3 mm-1, and o the constant B is related to the rainfall intensity by the expression

B = 4.1 P-0.21 eq. 8.5.3. Equation 8.5.2. was also shown to give good agreement when applied to the data of Laws and Parsons. A more comprehensive expression for drop size distributions has been proposed by A. C. Best (1950a). Best's formula was based on measurements made by Meteorological Office staff at Shoeburyness, East Hill and Ynyslas using the filter paper method. In addition, Best also converted most of the previously-published results into a common form of presentation. The proposed formula gives the fraction of liquid water in the air, F, composed of drops with diameter less than d: F = 1 - exp (40)r eq. 8.5.4. where K is related to rainfall intensity by the equation K = s Pq eq. 8.5.5. s and s, q and r are constant(independent of P. Average values of these constants based upon the Meteorological Office's data and the work of Lenard, Laws and Parsons, and Marshall and Palmer were quoted as 1.30, 0.232 and 2.25 respectively. 279. Equations 8.5.1., 8.5.2. and 8.5.4. may only be taken to represent average size distributions taken over a urge number of samples, or rainfall characteristics averaged over long time intervals. Isolated samples showing considerable departures from the formulae, such as those recorded by B. J. Mason and R. Ramanadham (1953), are inevitable. Those authors also commented upon appreciable minute-to-minute fluctuations in the composition of drop size distributions. Changes in drop size distribution with time were also found in a sequence of measurements taken during the passage of a shower by D. Atlas and V. G. Plank (1953). Similar variations were noted by V. N. Kelkar (1962).

Measurements in warm-frontal rain reported by B. J. Mason and J. B. Andrews (1960) gave distributions at low rainfall rates which could be approximated fairly well by equation 8.5.2., interspersed with others at higher intensities with fewer small drops and a greater number of larger drops than predicted. The latter were attributed to localised areas of heavier precipitation within the frontal system. Sequential samples taken during the passage of showers by the same authors showed similar characteristics to those recorded by Atlas and Plank, and distributions completely different in form from the Marshall- Palmer equation. Distributions noted during thunderstorms were found to exhibit larger numbers of both the smaller drops less than 0.25 mm, and the larger drops up to 6.0 mm in diameter than predicted by equation 8.5.2. Sequential measurements of drop size distributions in thunderstorms and showers, which showed essentially similar features to those recorded by Mason and Andrews have also been presented by A. N. Dingle and K. R. Hardy (1962).

Other investigators have attempted to characterise the distributions obtained from different types of rain by varying the values of the constants in equations 8.5.1. and 8.5.4. Measurements taken in 280. orographic rain on the slopes of the volcanoes Mauna Kea and Mauna Loa by D. C. Blanchard (1953b) were found to yield values of the constants in equation 8.5.1. which differed significantly from those obtained from the measurements at ground level made by Laws and Parsons at Washington. R. C. Srivastava and R. K. Kapoor (1961) and M. V. Sivaramakrishnan (1961) also attempted to attach different values to the constants according to the synoptic situation. An implicit assumption made in using equation 8.5.1. is that the value of dmy will continue to increase with increase in P. To date, few investigations have been carried out in other than temperate climates in which rainfall intensities in excess of 100 mm/h (4.0 in/h) are rarely recorded. The measurements taken during sub-tropical thunderstorms in Southern Rhodesia, reported by N. W. Hudson (1963), are exceptional. The data obtained by Hudson included samples taken in rainfall intensities up to 9.0 in/h. His results revealed a trend for the median volume drop diameter to increase up to 3.0 to 4.0 in/h, and then to decrease with increasing rainfall intensity. Whether this trend is characteristic of sub-tropical storms, or is a general feature which has remained undetected through the deficiency of data at high intensities in temperate climates is open to speculation. In discussing methods of characterising drop size distributions, B. J. Mason (1957; p.431) wrote critically of "... an unfortunate tendency to smooth the data so that they may be fitted to simple empirical formulae, thus suppressing features which may be of physical significance." Although the truth in this statement must be acknow- ledged, such formulae do provide a valuable criterion for the comparison of distribution measurements taken in different intensities of rain, or in different climatic or synoptic situations. Of the two expressions contained in equations 8.5.2. and 8.5.4., the Marshall-Palmer distribution appears to have been the more popular. The latter is the 281. simpler of the two equations, and plots as a straight line on a semi- logarithmic plot of N d against d. Best's equation reduces to the form

In log (1-1-p) = r (log d - log K) - 0.36 eq. 8.5.6. which only gives a straight line when the term on the left-hand side of the equation is plotted against log d.

V. N. Kelkar (1961) attempted to fit equation 8.5.6. to drop size distribution samples taken at Poona (see also V. N. Kelkar, 1959) and found that predicted values of F were too large for drop sizes less than 1.0 mm in diameter. The disagreement was attributed to climatic differences between Poona and the temperate latitudes at which the distributions upon which Best's formula was based were obtained. Kelkar also recorded (without comment) large differences in the value of the constant r for different ranges of rainfall intensities.

The general opinion of most meteorologists on the use of the Marshall-Palmer distribution has been adequately summarised by Dingle and Hardy (1962; p.311) who wrote

"There appears very little physical reason to expect that nature should observe the Marshall-Palmer formulation, hence departures of particular observed drop-size spectra from the M-P semi-logarithmic relation should not necessarily be regarded as anomalous. Nonetheless, the M - P formula provides a reasonably good approximation to the average spectrum for a given rainfall intensity. It is therefore convenient as a standard of comparison in studies of raindrop-size spectra."

The Marshall-Palmer distribution was consequently adopted as a suitable criterion of comparison for the present investigation.

8.6. Discussion of Results The following discussion is confined to the measurements of drop size distribution taken from nozzle type A/D. Those from nozzle 282. type B/B are considered separately in Appendix C along with the application patterns obtained from the same nozzle during the phase I experiments.

The wetted diameter of nozzle type A/D was sufficiently Jnrge at the sampling level to permit measurements directly below, and at points 12 and 24 inches away from the nozzle at each of the four chosen working pressures. Three filter papers were exposed at each position, making a total of 36 separate samples. These samples were analysed as described in section 8.3. to give values of nd for successive intervals in drop diameter of 0.25 mm. Spatial densities and cumulative water contents were then calculated for each sample according to the procedure outlined in section 8.4. The labour involved in these calculations was considerably reduced by processing the results on the Imperial College I.B.M. 7090/1401 computer. Details of the program* written for this work are included in Appendix E. Cumulative water content ogives were plotted for each sample. A typical set of curves, corresponding to the samples taken directly below the nozzle at a head of 10.03 feet of water, are reproduced in figure 8.6.1. The median volume drop diameter of each sample, corresponding to the 50 per cent ordinate of cumulative water content, was read from each ogive. The three figures from each group of samples were then averaged to give the characteristic values shown in table 8.6.1. Some indication of the comparison between the measured distributions and those for the same intensities of natural rainfall may be obtained by plotting the figures for dmv shown in table 8.6.1. against the intensities of application previously recorded at each sampling point. D. Atlas (1953) showed that the Marshall-Palmer - P relationship of the form distribution reduces to a dmv ) ) •

SAMPLE MED. VOL, NUMBE:R DROP DIAM. 10 0,70 11 0.62 12 0.67

0 0.5 1.0 1.5 2.0 2.5 3.0 DROP DIAMETER (MM) FIGURE 6.6.1. Typical cumulative water content curves from the distributions sampled from nozzle type Al D 284. 0.21 d mv = 0.92 P eq. 8.6.1. with dmv in mm and P in mm/h, and this equation has been plotted in figure 8.6.2. along with the figures from table 8.6.1.

TABLE 8.6.1. Median volume drop diameters (mm) obtained from sampled distributions at three points within the cone of influence of nozzle type A/D under four different working pressures.

head radius from nozzle (ins) (ft) zero 12 24

4.71 0.62 1.10 0.74 10.03 0.66 0.94 0.64 15.25 0.41 0.35 0.41 20.50 0.31 0.25 0,23

The scatter of the experimental points in figure 8.6.2. is random, and no significance can be attached to their position with respect to either working pressure or radius. All points lie below the line corresponding to the Marshall-Palmer equation, but there are wide variations in the values of d given by the line and the experi- mv mental results. The only significant conclusion which may be drawn from figure 8.6.2. is that the measured drop size spectra are much narrower than those found to occur on average in natural rainfall. The figure does serve to underline the limitations of characterising a distribution by a single parameter. Further information may be obtained by comparing the experimental results with the Marshall-Palmer distribution itself. For 6.0

EXPERIMENTAL POINTS 0 4.0

ds. R

E 2.0

ET 0.21 my- 0.91 P P DIAM 0 1.0 0 DRO

UME 0 L 0 0

AN VO 0.5

MEDI O 0

0.2 1.0 10.0 100.0 160.0 INTENSITY OF APPLICATION , MM H

FIGURE 8.6. 2. Plot of median volume drop diameter, dmv , against intensity of application, P, from filter paper samples compared with the empirical equation obtained by D. Atlas (1953) from the data of J. S. Marshall and W. McK• Paltrier (1948) . 286. this purpose, the samples whose median volume drop diameters most closely corresponded to the average values given in table 8.6.1. were selected as representative of each group of three. The spatial densities of drops, Nd.2Sd, in the representative samples were then plotted along with the Marshall-Palmer distributions for the corresponding rates of natural rainfall as shown in figures 8.6.3. and 8.6.4. For clarity, the Marshall-Palmer lines have not been extended beyond the number of intervals of drop diameter recorded in the measured distributions. Each of the theoretical distributions meets the drop diameter axis at some point well to the right of the measured distributions. As deduced from figure 8.6.2., the drop size distributions in the artificial rainfall were much narrower than those expected on the average in natural rainfall of comparable intensities. Without exception, the measured distributions contained greater numbers of smaller drops and showed marked deficiencies in the number of larger drops. As the sampling of drop size distributions was of minor importance to the main theme of the present investigation, attention was confined to the behaviour of single nozzles, and no separate measurements were taken for the three, four and sixteen-nozzle networks. Even if the superposition of drop size distributions from a single nozzle to form the distributions from a network were a valid process, and there is no evidence to suggest whether it is or not, the information contained in the present results would be insufficient for the purpose. However, unless appreciable coalescence

The extrapolation of the Marshall-Palmer distribution to rainfall rates of 450 mm/h cannot be justified other than to draw attention to features of the measured distributions.

TS O PL WER O L (

24 IN RADIUS c"' 6) ;,„. 10.03 FT HEAD ZERO RADIUS 10.03 FT HEAD. 12 IN RADIUS 10.03 FT HEAD

104 - L or)

LU LL

102 -2. Ui C.1

•

0 I -11"--"" DROP DIAMETER IN 0.25 MM, INTERVALS FIGURE. 6.6.3. Drop size distribution measurements for nozzle type AID compared with the Kimball - Palmer distribution for natural rainfall 2U.

112 IN RADIUS 20.50 FT HEAD.

L 104

ZERO RADIUS 20.50 FT HEAD 0 102

24 IN RADIUS 0 20.50 FT HEAD

ILgrJ io2- (7) r_z1 D ZERO RADIUS 15.25 FT, HEAD, 12 IN RADIUS 15.25 FT HEAD. 24 IN RADIUS 15.25 FT HEAD. a.

0 DROP DIAMETER IN 0:25 MM INTERVALS . FIGURE._8, Drop size distribution measurements for nozzle type A/D compared with the Marshall -Palmer distribution for natural rainf all. 289.

and accretion of small and large drops takes place where the cones of spray from adjacent nozzles intersect, the drop size spectra at all points will remain narrower than those indicated by the Marshall- Palmer equation. The excess of small-diameter drops must also increase appreciably.

The break-up of liquid jets from swirl-type nozzles such as those used in the present investigation is an extremely complex phenomenon (see Appendix B). Although the distributions of drop sizes at various points within the cone of influence of a nozzle under various working pressures are almost entirely dependent upon the dispersion properties of the nozzle, there is insufficient detail in the results to make an exhaustive study of this particular aspect of nozzle behaviour. However, table 8.6.1. and figures 8.6.3. and 8.6.4. do provide enough indication of variations in the drop size distributions to give further insight into the formation of the single- nozzle application patterns discussed in Chapter 5. If the fractional increase of 0.04 mm in the median volume drop diameter directly below the nozzle on increasing the head from 4.71 to 10.03 feet of water is ignored, there is a general trend for dmv to decrease with increasing head at all radii. The decrease is large, particularly at the 12-inch radius on increasing the head from 10.03 to 15.25 feet of water. There also appears to be a tendency towards a constant d mv at all radii at the higher heads. At the two lower heads, the largest value of dmir occurred at a radius of 12 inches from the nozzle. At the lowest head, the position of this maximum coincides with the annulus of high application depth. This coincidence tends to indicate a dispersion mechanism which throws larger drops up to 3.0 mm in diameter into a trajectory inter- secting the sampling level in this region. With an increase in head up to 10.0 feet of water, the dispersion mechanism must change to one 290. in which large numbers of smaller drops are ejected into the area immediately below the nozzle. Their numbers are sufficiently large for the volume of water at the centre of the pattern to increase more rapidly than that at a radius from the nozzle, resulting in the observed change to a conical shape of application pattern.

The differences in values of dmv at each sampling point at the two higher heads indicate little change in the properties of the drop size distributions with radius from the nozzle. Whether this agreement is significant or arises from having an inadequate number of samples is clearly a point for further study. The shape of the jet immediately below the nozzle at these heads (see Appendix B) shows that the break-up is approaching the atomization stage at which more sophisticated methods of measurement, such as those described at the beginning of section 8.1., are necessary to evaluate drop spectra to any degree of accuracy. The sampling interval of 0.25 mm is probably too coarse to show up variations in the narrow drop size distributions obtained at these heads.

The general trends indicated by the results are sufficiently clear, however, for the assumption of previously measured values of P to have had little or no effect. Some investigators (Hudson, 1963, for example) hold the opinion that rainfall rates calculated directly from samples may be considerably in error. With the drop size distributions encountered in natural rainfall, the occurrence of small numbers of large drops can substantially increase the total water content of the sample, and thereby alter the calculated value of P considerably.

Because the distributions measured in the present investigation contained such large numbers of small drops, the inclusion of small numbers of larger drops in any sample could not produce very pronounced increases in total water content. Values of the median 291. volume drop diameter were therefore less sensitive in this respect than figures for distributions in natural rainfall. The cumulative water content ogives shown in figure 8.6.1. provide some evidence of this effect. Sample number 10 extends up to a drop diameter of 2.5 mm, whereas sample number 12 does not rise beyond 1.75 mm. Both curves yield almost the same median volume drop diameter. For distributions containing large numbers of small drops, counting errors over the first few intervals of drop diameter also become proportionally less significant. The measured distributions shown in figures 8.6.3. and 8.6.4. are probably a more accurate representation of nozzle behaviour than the Marshall-Palmer distribution is of average drop size spectra in natural rainfall. 292. CHAPTER NINE

Summary,_ conclusions and recommendations for further study

Natural rainfall is highly variable in its occurrence, intensity and duration. The progress of field investigations in which these phenomena are significant can be greatly impeded by such variability, and the rainfall simulator has developed logically from the need to provide a greater degree of control over experimental conditions. The only property of natural rainfall reproduced by the first rainfall simulators was the intensity of water applied to the test area. A complete lack of fundamental data on the distributions of drop sizes in different intensities of rain, and on the velocities of fall of different sizes of drops prevented the adoption of more comprehensive criteria. The work of the U. S. Department of Agri- culture Soil Conservation Service did much to improve the current state of knowledge, and their published results have provided the basis for the more detailed studies undertaken in recent years.

The type of investigation in which rainfall simulators have been employed has had a predominantly agricultural bias, with particular emphasis being placed on problems connected with soil erosion. Apart from the "sprinkling infiltrometers" used to determine the infiltration properties of soils, the concept of applying the technique to the study of more general hydrological problems has been slow to gain acceptance. Since the Soil Conservation Service experiments, a number of investigations have been made into the hydraulics of run-off from impervious and semi-impervious surfaces subjected to constant rates of artificial rainfall, but an explicit mathematical treatment of the problem has been•developed only recently. 293.

The use of rainfall simulators and scaled laboratory models has been combined in an attempt to evaluate the rainfall/run-off relationships of selected catchment areas by applying the principles of dynamic similarity. This work has met with little apparent success. Other investigators have used laboratory catchments to test the assumptions of both linear and non-linear conceptual models of catchment behaviour. The latter type of laboratory catchment has been used specifically to generate run-off hydrographs from controlled applications of artificial rainfall. In effect, this apparatus has been considered as a "black box" whose "input and "output" have taken the form of flowing water. The conceptual models tested have been mathematical functions capable of reproducing the recorded hydrographs from given artificial storms.

These conceptual models can and do provide solutions to the problem of predicting run-off from rainfall both quickly and econo- mically. However, once the model for a particular catchment has been tested and proved, that model may only be used to provide run- off data for predetermined storm inputs. The method contributes little to our understanding of the time-distribution of the hydrological processes involved in transforming the rainfall into run-off. More complex mathematical models, consisting of several components, each representing a different element of the hydrological cycle, have been evolved in an attempt to gain further insight into catchment behaviour. To date, this work has not been extended into laboratory studies, and yet this also is a field in which artifical catchment investigations could make a useful contribution.

A study of any catastrophic flood shows that the geometrical and topographic features of the affected catchment are a major influence in determining the distribution in time of the volume of run-off. With a rainfall simulator to provide storms whose variations in time 294.

and space are controlled, and a laboratory catchment, whose size, shape and slopes may be varied as required, such effects become amenable to examination. Problems of scale do not arise as this type of laboratory catchment, which the present writer proposes to call a "microcatchment", is a miniature catchment possessing essentially the same features in operation as a natural drainage basin.

Microcatchment studies present a number of problems in experimentation, not the least of which is the generation of storms of artificial rainfall. A review of the extensive literature on methods of simulating rainfall revealed that reproducible applications of artificial rainfall containing a range of drop sizes could only be produced from systems of nozzles or irrigation sprinklers. As the discharge from a nozzle increases as the pressure at the nozzle increases, but the range of drop sizes produced decreases, some method of providing an intermittent application is necessary if the drop size distribution is to approximate that measured in natural rainfall at the required intensity of application. However, if the discharge from a nozzle system is interrupted at regular intervals, or the nozzles are rotated or oscillated in some way, roughly equal depths of water may be applied at all points within the test area during a complete cycle, but instantaneous rates of application will not be uniform throughout the test. Clearly, both total depths and rates of application must be uniform for the purposes of microcatchment experiments. Only a system of nozzles, exhibiting conical dispersion and spraying vertically downwards, similar to that installed at the Unit of Soil Physics laboratory in Cambridge, can provide these properties over a large test area.

The rates of application from rainfall simulators are generally restricted to one specific figure, which can only be altered either by changing the nozzles, or by providing additional systems of 295. nozzles whose patterns are superimposed to provide different intensities. The configuration of the patter4 of application depths from a nozzle is known to change with its working pressure, but the present writer has been unable to find quantitative evidence that the changes are sufficiently marked to prevent one system of nozzles being used over at least a small range of heads. With this possibility in mind, the following specification for a rainfall simulator for use in the proposed microcatchment studies was compiled:

(a) the application should be continuous over the test area, i.e., depths should be uniform in space, and application rates should be uniform in time, (b) depths of application should be reproducible under identical experimental conditions, (c) rates of application should be continuously variable, if possible, over a range of 10:1 or larger, subject to conditions (a) and (b) above, (d) the maximum application rate provided should be at least 10 in/h, and (e) provision should be made for the construction of moving storm or distributed parameter patterns, subject to the condition that depths should be reproducible according to (b) above.

The provision of moving storms is primarily a function of the type of control system adopted rather than of the basic design of equipment, but the requirement is sufficiently important to be listed in the specification. The maximum of 10 in/h mentioned in (d) above is not based upon any particular recorded figures, but reference to published tables shows that the occurrence of such a rate over time intervals less than one hour is not a physical impossibility.

The absence of any reference to drop size distribution criteria from the specification is apparent, and requires justification: The question which must be asked in this connection is "What effect 296. have individual drop sizes on the working of the proposed experiments?". As stated above, rainfall simulators have been employed largely in the investigation of problems connected with the behaviour of soils. In such studies, the emphasis is placed on the disturbance of the soil surface (erosion) caused by the impact of drops and not on that of sheet flow (turbulence) as would be the case with a microcatchment. Existing literature on the disturbance of sheet flow by rainfall indicates that the impact of drops hastens the change from conditions of laminar to turbulent flow, and that an allowance for this effect may be made by an adjustment in the value of the resistance coefficient. If the variation of the latter with Reynolds number and rainfall intensity can be determined by prior experiments, then the rainfall/run-off relationship becomes largely independent of variations in drop size distributions and the velocities of fall of the drops. As a first approximation therefore, such considerations have been omitted from the specification.

The possibility of adapting commercially-available nozzles to meet the above requirements was examined tentatively, but this approach was abandoned in favour of developing a simple design of nozzle, based upon the principle of the swirl-type atomizer. This nozzle was capable of indefinite variations in its internal geometry, and could be assembled without difficulty in the College workshops. The nozzle consisted essentially of a chamber into which fluid entered in a substantially tangential direction, and left through an axial orifice. The performance of five such nozzles, each having a circular orifice and varying in the geometry of the entry into the chamber, were compared at heads of 5.0, 10.0, 15.0 and 20.0 feet of water. The comparison was based upon the patterns of application depths obtained 72 inches below the nozzle on a plane at right angles to its axis. Each test was repeated once to obtain some measure of the reproductivity of depths. 297. The overlapping of single-nozzle patterns to form uniform distributions of depths over large areas depends upon the variation of application depths with radius from the nozzle, the wetted diameter and the maximum application depths recorded within each pattern. The measured patterns were compared on this basis, and the nozzle with the most suitable characteristics chosen for further study. This nozzle, referred to as nozzle type A/D, also exhibited the best reproductivity figures of the five tested.

A similar series of tests was carried out on a nozzle fitted with an equilateral-triangle profile orifice. This nozzle (type B/B) produced patterns of application depths whose properties were inferior to those of the patterns produced by any of the nozzles fitted with a circular orifice. In consequence, this line of investigation was not pursued beyond the testing of single nozzles.

The four patterns obtained from nozzle type A/D were subsequently analysed to determine a suitable spacing of nozzles for the rainfall simulator. These patterns were overlapped at spacings of 12, 18, 24 and 30-in centres in two mutually perpendicular directions. The comparison between the different spacings was based upon the equivalent mean application rate and a coefficient which provided an index to the uniformity of distribution of each overlapped pattern. This analysis showed that the 18 by 18-in arrangement of nozzles was the most suitable. However, because of the limited amount of data available, a more detailed study of the performance of at least four nozzles at this spacing was considered to be necessary before the figures cauld be confirmed for the final design of the rainfall simulator. Although the mathematical overlapping analysis was carried out for equal line and lateral spacings, a symmetrical network may also be obtained with the nozzles set up in an equilateral-triangle geometry. 298. In the second phase of experiments therefore, the application patterns from groups of both three nozzles in an equilateral-triangle and four in a square geometry were measured and compared. The patterns were recorded at approximately 1 - ft intervals in head from 3.0 to 20.0 ft of water.

Both sets of results showed that the changes in areal coverage from each nozzle over the chosen range of working pressures were more pronounced than had been indicated by the measured single-nozzle patterns. Increases in the wetted radius of the nozzles above the network spacing caused "losses" from the area within which the overlapped patterns were measured. These losses were not made up by other nozzles, which would have formed adjacent elements of a larger network, discharging back into the test area. The variations in wetted radius with changes in working pressure therefore caused deficiencies in the equivalent mean application rate of the overlapped patterns, which were accentuated further by misalignments in the apparatus.

Neither the square nor the equilateral-triangle arrangement of nozzles could claim any outstanding advantages over the other. The location of nozzles was critical to the correct overlapping of•the single-nozzle patterns, and the adoption of centres involving a factor of /3, as with an equilateral-triangle arrangement of nozzles, could only create problems in the erection of apparatus. Conse- quently, a square arrangement of nozzles was adopted for the rainfall simulator.

The results from the second phase of experiments showed that

1+-nozzle tests could not be taken to define fully the behaviour within an element of a larger network of nozzles. A third phase of experiments was therefore undertaken with a network of 16 nozzles. Application patterns were measured within the net area of the innermost 299. four nozzles at 1-ft intervals in head between approximately 3.0 and 13.0 ft of water.

Misalignment of the apparatus again resulted in small variations in the recorded equivalent mean application rates about the figures obtained from simple theory based upon the total discharge from the nozzles. A further series of tests, carried out after adjustments had been made to the apparatus, showed greatly improved agreement, with all experimental measurements lying within the 95 per cent confidence limits to the theoretical relationship between intensity of application and working pressure. The values of the uniformity coefficients obtained between heads of approximately 3.0 and 12.0 feet of water indicated that the variations in the uniformity of distribution with changes in working pressure were very small. In absolute terms, the coefficients exceeded standards of acceptable uniformity of distribution contained in the existing literature.

There are a number of different forms of uniformity coefficient, each of which is regarded by its advocates as possessing superior qualities of sensitivity to its rivals. The coefficients based upon the mean of the absolute deviations of measurements of application depths within a pattern from their average may be related to others, based upon the standard deviation, if the Gaussian distribution is assumed to apply to the data. This assumption was tested with data from the present investigation. Inter-plotting of the different coefficients for both measured and mathematically overlapped patterns showed that the normal distribution relationships provided a good approximation to the calculated figures for all patterns having a Christiansen uniformity coefficient greater than 0.75.

This agreement must not be taken to imply that the distributions of observed application depths within the measured, and calculated depths within the mathematically overlapped patterns, follow 300. the Gaussian law. There is no more evidence to support this conclusion than there is to suppose that they should conform to a Pearson- type distribution (say). The conclusion which can be drawn is that the regression lines relating pairs of different coefficients are approximated quite well (within certain limits) by equations based upon the assumption that the observations of application depths are normally-distributed.

This analysis also indicated that, for the purposes of the present work, the comparison of patterns of application depths was not influenced in any way by the choice of a specific uniformity coefficient. However, the results did not indicate whether any or none of the coefficients is an adequate measure of uniformity. In an attempt to clarify this point, the third and fourth statistical moments were computed for the distributions of sampled depths within both the 4-nozzle and 16-nozzle application patterns. These calculations revealed that the distributions of observations in the patterns obtained at heads of between approximately 9.0 and 12.0 ft of water in each series of tests were consistently leptokurtic.

At these particular heads, the patterns of application depths from the single nozzles were roughly conical in outline, and approaching a shape at which overlapping produces optimum conditions of uniformity. Whether or not the occurrence of leptokurtic distributions of application depths forms a characteristic of overlapped patterns obtained from the superposition of conical single-nozzle patterns at their ideal spacing would be an interesting topic for further investigation. The data did not appear to indicate similar criteria for the overlapping of different shapes of single-nozzle pattern. However, it is possible that a series of criteria, based upon progressively higher moments of the distribution of observations within an overlapped pattern, could be devised to form a more rigorous method of assessing uniformity. 301. Although considerations of drop size distributions did not enter into the adopted specification, a limited series of measurements were taken using the filter paper method. These measurements were confined to samples at various radii from a single-nozzle of type A/D under four different working pressures. At all four heads, the distributions sampled at any radius from the nozzle contained an excess of small drops, and were deficient in the numbers of drops larger than 1.0 to 2.0 mm in diameter compared with the distributions found to occur on the average in natural rainfall at the saiintensities of application. The results tended to indicate that the distributions obtained from networks of nozzles would also be too narrow, unless coalescence and accretion of small and large drops at the intersections of the cones of influence of adjacent nozzles results in the formation of a substantial number of larger drops. In general, the drop size distributions at any particular radius from the nozzle were found to narrow with increasing working pressure, and contain increasing numbers of drops less than 0.5 mm in diameter.

The results obtained from the testing of nozzle type A/D may now be compared with the original specification. The adopted method of simulating rainfall ensures that the application of water to the test area is continuous, so that depths are uniform in space and rates uniform in time. Tests of reproductivity carried out with a single nozzle of the chosen design showed that half the measurements were reproduced to within 4 per cent, and nearly all to within 9 per cent, a result which compares favourably with those from previous designs of apparatus. The experimental work proved that variations in working pressure can be used to provide satisfactory control of the rates of application from a network of nozzles. The final series of tests showed that the intensity of application could be varied continuously from 6.0 to 12.0 in/h without causing an appreciable change in the uniformity of 302. distribution. These figures represent a range of 2;1 compared with that of 10;1 specified.

No tests were performed at heads less than 3.0 feet of water, but qualitative examination of the behaviour of the nozzles at these small working pressures has tended to indicate that the range could at least be doubled. The uniformity coefficients would undoubtedly fall below the level recorded at the higher heads, but the extent to which more disturbed application patterns may be tolerated depends upon the ability of the microcatchments to "damp" the variability in the artificial rainfall. The extension of the range over which the intensities of application may be continuously varied is therefore a matter for further experimentation once the apparatus has been erected.

With nozzles spaced at 18-in centres along parallel manifolds also spaced at 18-in centres, individual controls for each line of nozzles would ensure that intensities of application could be varied with time along the direction perpendicular to the lines. Rotation of the microcatchment with respect to the rainfall simulator would enable the observer to select storm paths at any angle to the catchment. For the purposes of analysis, it is convenient to describe such distributed parameter systems in terms of a mathematical expression, and an approach using double harmonic series is suggested for further consideration. 303.

Appendix A Bibliography

ADAMS, J. E. (1957), A rainfall simulator and the erodibility of some Iowa soils (abstract of unpublished Ph.D. thesis), Iowa State Coll. J. Sci., Vol.31, pp. 347-8.

ADAMS, J. E., D. KIRKHAM and D. R. NIELSEN (1957), A portable rainfall-simulator infiltrometer and physical measurements of soil in place, Proc. Soil Sci. Soc. Amer., Vol.21, pp. 473-7. ADDERLEY, E. E. (1953), The growth of raindrops in cloud, Quart. J. Roy. Met. Soc., Vol.79, pp. 380-8. AITKEN, A. C. (1962), Statistical mathematics, Oliver and Boyd, 8th edn. reprinted, 153 pp. AKESSON, N. B. and W. A, HARVEY (1948), Equipment for the application of herbicides, Agr. Engng., Vol.291 pp. 384-9. ALLRED, E. R, and R. E. MACHMEIER (1962), Effect of wind resistance on rotational speed of boom sprinklers (a theoretical analysis), Trans. Amer. Soc. Agr. Engns., Vol. 5, pp. 218/19/25. AMERICAN SOCIETY OF CIVIL ENGINEERS (1949), Hydrology handbook A.S.C.E. Manual of Engng. Practice no.28, 184 pp. AMOROCHO, J. (1963), Measures of the linearity of hydrologic systems, J. Geoph. Res., Vol.68, pp. 2237-49.

AMOROCHO, J. and A. BRANDSTETTER (1966), Characterization of gauge level precipitation patterns, paper presented at the Southwest Regional Meeting of the American Geo- physical Union, San Jose, February, 1966. Abstract in Trans. Amer. Geoph. Union Vol.47 (1966), p.428. 304.

AMOROCHO, J. and W. E. HAW (1964), A critique of current methods in hydrologic systems investigation, Trans. Amer. Geoph. Union, Vol.45, pp. 307-21. idem (1965) The use of laboratory catchments in the study of hydrologic systems, J. Hydrology, Vol. 3, pp. 106-23. AMOROCHO, J. and G. T. ORLOB (1961), Nonlinear analysis of hydrologic systems, Water Resources Centre, Univ. of California, contribution no.401 147 pp. ANDERSON, L. J. (1948), Drop size distribution measurements in orographic rain, Bull. Amer. Met. Soc., Vol.29, pp. 362 -6. ANDREWS, J. B. (1961), Size distribution of precipitation elements, unpublished Ph.D. thesis, Imperial College of Science and Technology, Univ. of London, 210 pp. ATLAS, D. (1953), Optical extinction by rainfall, J. Met., Vol.10, pp. 486 -8. ATLAS, D. and V. G. PLANK (1953), Drop size history during a shower, J. Met., Vol.10, pp. 291-5. BARGER, E. L., E. V. COLLINS, R. A. NORTON and J. B. LILJEDAHL (1948), Problems in the design of chemical weed control equipment, Agr. Engng., Vol.29, pp. 381 -3/9.

BASU, J. K. and N. B. PURANIK (1954), Erodibility studies by a rainfall simulator - section 4: engineering part I, J. Soil and Water Conserv. in India, Vol. 2, pp. 177-85.

BAYER, L. D. (1938), Ewald Wollny - a pioneer in soil and water conservation research, Proc. Soil Sci. Soc. Amer., Vol. 3, pp. 330-3. 305.

BEALE, J. G. and D. T. HOWELL (1966), Relationships among sprinkler uniformity measures, J. Irrigation and Drainage Div., Proc. Amer. Soc. Civil Engns., Vol.92, IR1, pp. 41-8. BEAN, A. G. M. and D. A. WFifiLS (1953), Soil capping by water drops, National Institute of Agricultural Engineering report no.23, 11 pp., BEAN, A. G. M., E. J. WINTER and D. A. WELLS (undated), Design of a precision plot irrigator, National Institute of Agricultural Engineering report no.30, 11 pp. BENTLEY, W. A. (1904), Studies of rain drops and rain drop phenomena, Monthly Weather Revue, Vol.32, pp. 1+50 -6. RF,RTRAND, A. R. and J. F. PARR (1960), Development of a portable sprinkling infiltrometer, 7th International Congress of Soil Science, Madison, Wisc., Transactions, Vol. 1, pp. 433-40. BEST, A. C. (1947), The size distribution of raindrops, Meteorological Research Paper 352, 15 pp. plus 7 pp. figures. idem (1950a), The size distribution of raindrops, Quart. J. Roy. Met. Soc., Vol.76, pp. 16-36. idem (1950b), Empirical formulae for the terminal velocity of water drops falling through the atmosphere, ibid, Vol.76, pp. 302-11. BEUTNER, E. L., R. L. GAEBE and R. E. HORTON (1940), Sprinkled- plat run-off and infiltration experiments on Arizona desert soils, Trans. Amer. Geoph. Union, Vol.21, pp. 550-8. 306.

BILANSKI, W. K. and E. H. KIDDER (1958), Factors which affect distribution of water from a medium-pressure rotary irrigation sprinkler, Trans. Amer. Soc. Agr. Engns., Vol. 1, pp. 19-23/8. BITTINGER, M. W. and R. A. LONGENBAUGH (1962), Theoretical distribution of water from moving irrigation sprinkler, ibid, Vol. 5, pp. 26-30. BLANCHARD, D. C. (1949a), The distribution of raindrops in natural rain, Occasional Report 15, Project Cirrus, General Electric Res. Lab., Schenectady, N.Y. idem (1949b), The use of sooted screens for determining raindrop size and distribution, Occasional Report 16, Project Cirrus, General Electric Res. Lab., Schenectady, N.Y. idem (1953a), A simple recording technique for determining raindrop size and time of occurrence of rain showers, Trans. Amer. Geoph. Union, Vol.34, pp. 534-8. idem (1953b), Raindrop size distribution in Hawaiian rains, J. Met., V01.10, pp. 457-73. BOWEN, E. G. and K. A. DAVIDSON (1951), A raindrop spectrograph, Quart. J. Roy. Met. Soc. Vol.77, pp. 445-9. BROOKS, C. E. P. and N. CARRUTHERS (1953), Handbook of statistical methods in meteorology, H.M.S.O., 412 pp.

BUBENZER, G. D. and L. D. MEYER (1965), Simulation of rainfall and soils for laboratory research, Trans. Amer. Soc, Agr. Engns., Vol. 8, pp. 73/5. CHAPMAN, G. (1948), Size of raindrops and their striking force at the soil surface in a Red Pine plantation, Trans. Amer. Geoph. Union, Vol.29, pp. 664 - 70. 307.

CHERY, D. L. (1966), Design and tests of a physical watershed model, J. Hydrology, Vol. 4, pp. 224-35. CHILDS, E. C. (1943), The water table, equipotentials and streamlines in drained land, Soil Sci., Vol.56, pp. 317-30. idem (1953), A new laboratory for the study of the flow of fluids in porous beds, Proc. Inst. Civil Engns., Vol. 2, part 3, pp. 134-41. CHOW, VEN TE (1959), Open-channel hydraulics, McGraw-Hill, 680 pp.

CHOW, VEN TE and T. E. HARBAUGH (1965), Raindrop production for laboratory watershed experimentation, J. Geoph. Res., Vol.70, pp. 6111 9. CHRISTIANSEN, J. E. (1937), Irrigation by sprinkling, Agr. Engng., Vol.18, pp. 533-8. idem (1941), The uniformity of application of water by sprinkler system, ibid, Vol.22, pp. 89-92. idem (1942), Hydraulics of sprinkler systems for irrigation, Trans. Amer. Soc. Civil Engns., Vol.107, pp. 221 -50. idem (1965), discussion to paper by D. T. Howell (1964a), J. Irrigation and Drainage Div., Proc. Amer. Soc. Civil Engns., Vol.91, IR1, pp. 224-6.

COOPER, B. F. (1951), A balloon-borne instrument for telemetering raindrop-size distribution and rainwater content of cloud, Australian J. App. Sci., Vol. 2, pp. 43-55.

CRIDDLE, W. D., S. DAVIS, C. H. PAIR and D. G. SHOCKTRY (1956), Methods for evaluating irrigation systems, U. S. Dept. Agr., Soil Conserv. Service, Agriculture Handbook no.82, 24 pp. 308.

CULVER, R. and R. F. SINKER (1966), Rapid assessment of sprinkler performance, J. Irrigation and Drainage Div., Proc. Amer. Soc. Civil Engns., Vol.92, IR1, pp. 1-17. DABBOUS, B. J. (1962), A study of sprinkler uniformity evaluation methods, unpublished M.S. thesis, Utah State Univ., Logan, Utah. DALLAVALLE, J. M. (1948), Micromeritics. The technology of fine particles, Pitman Publishing Co., N.Y., 2nd edn., 555 pp. DAWDY, D. R. and T. O'DONNELL (1965), Mathematical models of catchment behaviour, J. Hydraulics Div., Proc. Amer. Soc. Civil Engns., Vol.911 HY4, pp. 123-37. DINGLE, A. N. and K. R. HARDY (1962), Description of rain by means of sequential raindrop-size distributions, Quart. J. Roy. Met. Soc., Vol.88, pp. 501-14. DINGLE, A. N. and H. F. SCHULTE (1962), A research instrument for the study of raindrop-size spectra, J. App. Met., Vol. 1, pp. 48-59. DOBBIE, C. H. and P. 0. WOLF (1953), The Lynmouth flood of August 1952, Proc. Inst. Civil.Engns., Vol. 2, part 3, pp. 522-88. DOBOS, A. and P. SALAMIN (1960), Investigations into the nozzles of sprinkling equipment, Vizugyi Kozlemenyek (Hydraulic Engng.), Budapest, pp. 207-51. DOOGE, J. C. I. (1959), A general theory of the unit hydrograph, J. Geoph. Res., Vol.64, pp. 241 -56. DULEY, F. L. and O. E. HAYS (1932), The effect of degree of slope on run-off and erosion, J. Agr. Res., Vol.45, pp. 349-60. 309.

DURBIN, W. G. (1958), Recent aircraft research into cloud physics, Weather, Vol.13, pp. 143-51. idem (1959), Droplet sampling in cumulus clouds, Tellus, Vol.11, pp. 202-15.

EKERN, P. C. (1950), Raindrop impact as the force initiating soil erosion, Proc. Soil Sci. Soc. Amer., Vol.15, PP. 7-10. idem (1953), Problems of raindrop impact erosion, Agr. Engng., Vol.34, pp. 23-5/8. EKERN, P. C. and R. J. MUCKENHIRN (1947), Water-drop impact as a force in transporting sand, Proc. Soil Sci. Soc. Amer., Vol.12, pp. 441-4. ELDERTON, W. P. (1953), Frequency curves and correlation, Cambridge Univ. Press, 4th edn., 272 pp.

ELHANANI, S. (1961), Sprinkler irrigation (fundamentals), Ministry of Agriculture Extension Authority, Tel Aviv. ELHANANI, S. and J. KRAUS (1956), Sprinkler uniformity application tests A. Naan sprinklers, Ministry of Agriculture, Water Authority, Field &tension Service and the Jewish Agency for Palestine, Agricultural Colonisation Department, Irrigation Division, Tel Aviv, 31 pp.

ELLISON, W. D. (1945), Some effects of raindrops and surface-flow on soil erosion and infiltration, Trans. Amer. Geoph. Union, Vol.26, pp. 415-29. Ki,LISON, W. D. and W. H. POMERENE (1944), A rainfall applicator, Agr. Engng., Vol.25, p. 220. FAIRS, G. L. (1943), The use of the microscope in particle size analysis, Chemistry and Industry, Vol.62, pp. 374-8. 310.

FLETCHER, N. H. (1962), The physics of rainclouds, Cambridge Univ. Press, 386 pp. FLOWER, W. D. (1928), The terminal velocity of drops, Proc. Phys. Soc., London, Vol.40, pp. 167-76. FOURNIER D'ALBE, E. M. and M. S. HIDAYETULLA (1955), The break-up of large water drops falling at terminal velocity in free air, Quart. J. Roy. Met. Soc., Vol.81, pp. 610-3. FREE, G. R. (1960), Erosion characteristics of rainfall, Agr. Engng., Vol.41, pp. 447-9/55. FRENCH, O. C. (1934), Machinery for applying atomized oil spray, ibid, Vol.15, pp. 324-6. FRITH, R. (1951), The size of cloud particles in stratocumulus cloud, Quart. J. Roy. Met. Soc., Vol.77, pp. 441-4,

FUCHS, N. and J. PETRJANOFF (1937), Microscopic examination of fog, cloud and rain droplets, Nature, Vol.139, p. 111. GARROD, M. P. (1957), Recent developments in the measurement of precipitation elements from aircraft, Meteorological Research Paper 1050, 8 pp. plus 11 pp. figures.. GILLESPIE, T. (1958), The spreading of low vapour pressure liquids in paper, J. Colloid Sci., Vol.13, pp. 32-50. GOODMAN, L. J. (1952), Erosion control in engineering works, Agr. Engng., Vol.33, pp. 155-7. GREEN, H. L. (1953), Atomization of liquids, Chapter VII of J. J. HERMANS (ed; 1953) pp. 299-322. GRFEN, R. L. (1952), A photographic technique for measuring the sizes and velocities of water drops from irrigation sprinkler, Agr. Engng., Vol.331 pp. 563/4/6/8. 311. GUNN, R. (1949a), Electronic apparatus for the determination of the physical properties of freely falling rain drops, Rev. Sci. Instrum., Vol.20, pp. 291-6. idem (1949b), Mechanical resonance of freely falling raindrops, J. Geoph. Res., Vol.54, pp. 383-5. GUNN, R. and G. D. KINZER (1949), The terminal velocity of fall for water droplets in stagnant air, J. Met., Vol. 6, pp. 243-8. HALL, W. A. and P. A. BOVING (1956), Non-circular orifices for sprinkler irrigation, Agr. Engng., Vol.37, pp. 27-9. HANSEN, V. E. (1960), New concepts in irrigation efficiency, Trans. Amer. Soc. Agr. Engns., Vol. 3, pp. 55-7/61/4. HART, W. E. (1961), Overhead irrigation pattern parameters, Agr. Engng., Vol.42, pp. 354-5. idem (1963), Sprinkler distribution analysis with a digital computer, Trans. Amer. Soc. Agr. Engns., Vol. 6, pp. 206-8. HART, W. E. and W. N. REYNOLDS (1965), discussion to paper by D. T. HOWELL (1964a), J. Irrigation and Drainage Div., Proc. Amer. Soc. Civil Engns., Vol.91, IR2, pp. 80-2. HENDERSON, F. M. and R. A. WOODING (1964), Overland flow and ground- water flow from a steady rainfall of finite duration, J. Geoph. Res., Vol.69, pp. 1531-40. HENDRICKSON, B. H. (1934), The choking of pore space in the soil and its relation to run-off and erosion, Trans. Amer. Geoph. Union, Vol.14, pp. 500-5. HERMANS, J. J. (ed. 1953), Flow properties of disperse systems, North-Holland Publishing Company, 445 pp. 312. HERMSMEIER, L. F., L. D. MEYER, A. P. BARNETT and R. A. YOUNG (1963), Construction and operation of a 16-unit Rainulator, U. S. Dept. Agr., Agr. Res. Service, 136 pp.

HICKS, W. I. (1944), discussion to paper by C. F. IZZARD and M. T. AUGUSTINE (1943), Trans. Amer. Geoph. Union, Vol.25, pp. 1039-41. HOLLAND, D. J. (1964), Rain intensity frequency relationships in Britain, Meteorological Office Hydrological Memoranda no.33, 28 pp. HORTON, R. E. (1938), The interpretation and application of run- off plot experiments with reference to soil erosion problems, Proc. Soil Sci. Soc. Amer., Vol. 3, pp. 34o - 9. HOWELL, D. T. (1964a), Non-uniformity and sprinkler application efficiency, J. Irrigation and Drainage Div., Proc. Amer. Soc. Civil Engns., Vol.90, IR3, pp. 41 -5.3. idem (1964b), Sprinkler non-uniformity characteristics and yield, ibid, Vol.90, IR3, pp. 55-67. HUDSON, N. W. (1963), Raindrop size distribution in high intensity storms, Rhodesian J. Agr. Res., Vol. 1, pp. 6-11. idem (1964a), The flour pellet method for measuring the size of raindrops, Res. Bull. no. 4, Dept. of Conserv. and EXtension, Federal Ministry of Agriculture, Southern Rhodesia, 26 pp. idem (1964b), A review of artificial rainfall simulators, Res. Bull. no. 7, Dept. of Conserv. and Extension, Federal Ministry of Agriculture, Southern Rhodesia, 15 pp. 313. idem (1965), The influence of rainfall on the mechanics of soil erosion with particular reference to Southern Rhodesia, unpublished M.Sc. thesis, Univ. of Cape Town, 316 pp. ISLER, D. A. (1963), Methods for evaluating coverage and drop size in forest spraying, Trans. Amer. Soc. Agr. Engns., Vol. 6, pp. 231-3. ISRAELSEN, O. W. and V. E. HANSEN (1962), Irrigation principles and practices, Wiley, 3rd edn., 447 pp.

IZZARD, C. F. (1942), Run-off from flight strips, Proc. Highway Res. Board, Vol.22, pp. 94-9. idem (1944), The surface profile of overland flow, Trans. Amer. Geoph. Union, Vol.251 pp. 959-68. idem (1946), Hydraulics of run-off from developed surfaces, Proc. Highway Res. Board, Vol.26, pp. 129-50. IZZARD, C. F. and M. T. AUGUSTINE (1943), Preliminary report on analysis of run-off resulting from simulated rainfall on a paved plot, Trans. Amer. Geoph. Union, Vol.24, pp. 500-9,

JARMAN, R. T. (1956), Stains produced by drops on filter papers, Quart. J. Roy. Met. Soc., Vol.821 p. 352. JENNINGS, A. H. (1950), World's greatest observed point rainfalls, Monthly Weather Revue, Vol.78, pp. 1+-5. JOHNSTONE, D. and W. P. CROSS (1949), Elements of applied hydrology, Ronald Press, N.Y.,. 276 pp.

KATZ, I. (1952), A momentum disdrometer for measuring raindrop size from aircraft, Bull. Amer. Met. Soc., Vol.33, pp. 365 - 8. 314. KATZ, R. E. and G. A. WILSON (1948), The disdrometer, an instrument for measuring the distribution of raindrop sizes encountered in flight (abstract only), Bull. Amer. Met. Soc., Vol.29, pp. 523 - 4.

KELKAR, V. N. (1945), Size of raindrops, Proc. Indian Acad. Sci., Vol.22A, pp. 394-9. idem (1959), Size distribution of raindrops - part I, Indian J. Met. and Geoph., Vol.10, pp. 125-36. idem (1961), Size distribution of raindrops - part III, ibid, Vol.121 pp. 553 -9. idem (1962), Size distribution of raindrops - part IV, ibid, Vol.13, pp. 173 - 82. KEULEGAN, G. H. (1944), Spatially variable discharge over a sloping plane, Trans. Amer. Geoph. Union, Vol.25, pp. 956 - 9. KOBAYASHI, T. (1955), Measurement of raindrop size by means of photographic paper treated with CoC12, J. Met. Soc. Japan, series II, Vol.33, pp. 217 - 9. KRUMBEIN, W. C. (1959), Trend surface analysis of contour maps with irregular control-point spacing, J. Geoph. Res., Vol.64, pp. 823-34. KRUM:WIN, W. C. and F. A. GRAYBILL (1965), An introduction to statistical models in geology, McGraw Hill, 475 pp.

LANCZOS, C. (1956), Applied analysis, Prentice-Hall, 539 pp. LANDSRFRG, H. and H. NEUBERGER (1938), On the frequency distribution of sleet-drop sizes, Bull. Amer. Met. Soc., Vol.19, pp. 354 -5. LANE, W. R. (1947)1 A microburette for producing small liquid drops of known size, J. Sci. Instrum., Vol.24, pp. 98-101. 315.

LAWS, J. O. (1940), Recent studies in raindrops and erosion, Agr. Engrg. , Vol.21, PP. 431-3. idem (1941), Measurements of the fall-velocity of water drops and rain drops, Trans. Amer. Geoph. Union, Vol.22, pp. 709-21.

LAWS, J. O. and D. A. PARSONS (1943), The relation of raindrop size to intensity, ibid, Vol.24, pp. 452-60. LEE, D. W. (1932), Fuel-spray formation, Trans. Amer. Soc. Mech. Engns., Vol.54, Oil and Gas Power, pp. 63-73. LENARD, P. (1904), Uber Regen, Meteorologische Zeitschrift, Vol.21, pp. 248-62. (For translation by R. H. SCOTT, see Quart. J. Roy. Met. Soc., Vol.31 (1905), pp. 62-73).

LEVINE, G. (1952), Effects of irrigation droplet size on infiltration and aggregate breakdown, Agr. Engng., Vol.33, PP. 559-60. LINDLEY, D. V. and J. C. P. MILLER (1961), Cambridge elementary statistical tables, Cambridge Univ. Press, 35 pp. LINSLEY, R. K., M. A. KOHTJR and J. L. H. PAULHUS (1949), Applied hydrology, McGraw Hill, 689 pp. idem (1958), Hydrology for engineers, McGraw Hill, 340 pp. LIPTAK, F. (1962), The spray distribution with different nozzle patterns in sprinkler irrigation, Vizugyi Kozlemenyek (Hydraulic Engng.), Budapest, pp. 369-403. LOWDERMILK, W. C. (1930), Influence of forest litter on run-off, percolation and erosion, J. Forestry, Vol.28, pp. 474-91. 316.

LOWE, E. J. (1892), Rain drops, Quart. J. Roy. Met. Soo:, Vol.18, pp. 242-5.

MACHMEIER, R. E. and E. R. ALLRED (1962), Operating performance of a boom sprinkler - a field study, Trans. Amer. Soc. Agr. Engns., Vol. 5, pp. 220-5. MAGARVEY, R. H. (1957), Stain method of drop-size determination, J. Met., Vol.14, pp. 182-4. MAHROUS, M. A. (1954), Drop sizes in sea mists, Quart. J. Roy. Met. Soc., Vol.80, pp. 99-101. MAMISAO, J. P. (1952), Notes on development of an agricultural watershed by similitude, unpublished M.S. thesis, Iowa State Coll., Ames, Iowa, 113 pp. MARSHALL, J. S., R. C. LANGILTE and W. McK. PALMER (1947), Met Measurements of rainfall by radar, /ihid, Vol. 4, pp. 186-92. MARSHALL, J. S. and W. McK. PALMER (1948), Distribution of raindrops with size, J. Met., Vol. 5, pp. 165-6. MASON, B. J. (1957), The physics of clouds, Oxford (Clarendon Press), 481 pp. MASON, B. J. and J. B. ANDREWS (1960), Drop size distributions from various types of rain, Quart. J. Roy. Met. Soc., Vol.86, pp. 346-53.

MASON, B. J. and R. RAMANADHAM (1953), A photoelectric raindrop spectrometer, ibid, Vol.79, pp. 490-5. idem (1954), Modifications of the size distribution of falling raindrops by coalescence, ibid, Vol.80, pp. 388-94.

MAULARD, J. (1951), Mesure du nombre de gouttes de pluie, Journal Scientifique de la Meteorologie, Vol. 3, pp. 69 - 73. 317.

MAY, K. R. (1945), The cascade impactor. An instrument for sampling coarse aerosols, J. Sci. Instrum., Vol.22, pp. 187 - 95. idem (1950), The measurement of airborne droplets by the magnesium oxide method, ibid, Vol.27, pp. 128-30. MERRINGTON, A. C. and E. G. RICHARDSON (1947), The break-up of liquid jets, Proc. Phys. Soc. London, Vol.59, pp. 1-13. MEYER, L. D. (1960), Use of the rainulator for runoff plot research, Proc. Soil Sci. Soc. Amer., Vol.24, pp. 319-22. idem (1965), Simulation of rainfall for soil erosion research, Trans. Amer. Soc. Agr. Engns., Vol. 8, pp. 63-5. MEYER, L. D. and J. V. MANNERING (1960), Soil and water conservation research with the rainulator, 7th International Congress of Soil Science, Madison, Wisc., Transactions, Vol. 1, pp. 457-63. MEYER, L. D. and D. L. McCUNE (1958), Rainfall simulator for run-off plots, Agr. Engng., Vol.39, pp. 664 - 8. MIKHAYLOVSKAYA, V. V. (1964), The theory of measuring the size of raindrops by the acoustic method, Soviet Hydrology: selected papers no.1, pp. 85-90. MIKIROV, A. E. (1957), A photoelectric method of investigating the distribution of particle size of precipitation, Bull (Izv.) U.S.S.R. Acad. Sci. (Geoph.Ser.) no.1, pp. 120-5. MINSHALL, N. E. (1960), Predicting storm run-off on small experimental watersheds, J. Hydraulics Div., Proc. Amer. Soc. Civil Magna., Vol.86, HY8 pp. 17-38. 318. MORGAN, P. E. and S. M. JOHNSON (1962), Analysis of synthetic unit-graph methods, ibid, Vol-88, HY5, pp. 199-220. MURGATROYD, R. J. and M. P. GARROD (1960), Observations of precipitation elements in cumulus clouds, Quart. J. Roy. Met. Soc., Vol.86, pp. 167-75. MUTCHLER, C. K. (1965), Using the drift of waterdrops during fall for rainfall simulator design, J. Geoph. Res., Vol.70, pp. 3899-3902.

MUTCHLER, C. K. and L. F. HERMSMEIER (1965), A review of rainfall simulators, Trans. Amer. Soc. Agr. Engns., Vol. 8, pp. 67 - 8. MUTCHLER, C. K. and W. C. MOLDENHAU1 (1963), Applicator for laboratory rainfall simulator, ibid, Vol. 6, pp. 220-2. NASH, J. E. (undated), A unit hydrograph experiment, unpublished report, Hydraulics Research Station, Wallingford, 15 pp. plus 7 figures. idem (1958), Determining run-off from rainfall, Proc. Inst. Civil Engns., Vol.10, pp. 163 - 84. idem (1959), Systematic determination of unit hydrograph parameters, J. Geoph. Res., Vo1.64, pp. 111-5. idem (1960), A unit hydrograph study, with particular reference to British catchments, Proc. Inst. Civil Engns., Vol.17, pp. 249-82. NEAL, J. H. (1938), The effect of the degree of slope and rainfall characteristics on run-off and soil erosion, Missouri Agr. Exp. Sta. Res. Bull. no.280, 47 pp. 319. NEAL, J. H. and L. D. BAVER (1937), Measuring the impact of raindrops, J. Amer. Soc. Agronomy, Vol.29, pp. 708-9. NEIDERDORIER, E. (1932), Messungen der Grosse der Regentropfen, Meteorologische Zeitschrift, Vol.49, pp. 1-14.

NEUBERGER, H. (1942), Notes on measurements of raindrop sizes, Bull. Amer. Met. Soc., Vol.23, pp. 274-6. NICHOLS, M. L. and H. D. SEXTON (1932), A method of studying soil erosion, Agr. Engng., Vol.13, pp. 101-3. O'DONNELL, T. (1960), Instantaneous unit hydrograph derivation by harmonic analysis, International Assoc. Sci. Hydrology, General Assembly, Helsinki, Commission of Surface Waters, publication no.51, pp. 546-37.

PARSONS, D. A. (1943), discussion to paper by H. G. WILM (1943), Trans. Amer. Geoph. Union, Vol.24, pp. 485-7. PEARSON, K. (1914), Tables for statisticians and biometricians, Cambridge Univ. Press, 143 pp. PEELE, T. C . and O. W. BEALE (1955), Laboratory determination of infiltration rates of disturbed soil samples, Proc. Soil Sci. Soc. Amer., Vol.19, pp. 429-32. PULLEN, R. A., J. F. A. WIEDERHOLD and D. C. MIDGLEY (1966), Storm studies in South Africa: large-area storms: depth-area-duration analysis by digital computer, The Civil Engnr. in South Africa, Vol. 8, pp. 173-87. RAYNER, A. C. and H. HURTIG (1954), Apparatus for producing drops of uniform size, Science, Vol.120, pp. 672-3. RICHARDSON, E. G. (1953), Liquid sprays, Chapter VI of J. J. HERMANS (ed; 1953) pp. 266-98. 320.

RILEY, H: W. (1909), A sprayograph, Trans. Amer. Soc. Agr. Engns., Vol. 3, pp. 78-82. ROSIN, P. and E. RAMMLER (1933), The laws governing the fineness of powdered coal, J. Inst. Fuel, Vol. 7, pp. 29-36. ROVINSKY, F. Y. (1959), New methods for recording water droplets, Bull. (1zv.) U.S.S.R. Acad. Sci. (Geoph. Ser.) pp. 768-70. SCHINDELHAUE R, F. (1925), Versuch einer Registrierung der Tropfenzahl bei Regenfallen, Meteorologische Zeitschrift, Vol.421 PP. 25 - 7. SCHLEUSENER, P. E. and E. H. KIDDER (1960), Energy of falling drops from medium-pressure irrigation sprinkler, Agr. Engng., Vol.411 pp. 100-3.

SCHMIDr, W. (1909), Eine unmittelbare Bestimmung der Fallgesch- windigkeit von Regentropfen, Ber. Akad. Wiss Wien, Vol.118, pp. 71 -84. SCHOENLEBER, L. H. (1944), Performance of irrigation sprinkler units, Agr. Engng. Vol.251 pp. 49 51. SEGINER, I. (1963), Water distribution from medium pressure sprinklers, J. Irrigation and Drainage Div., Proc. Amer. Soc. Civil Engns., Vol.89, IR2, pp. 13-29. idem (1965), Tangential velocity of sprinkler drops, Trans. Amer. Soc. Agr. Engns., Vol. 8, pp. 90-3, SHACHORI, A. and I. SEGINER (1962), Sprinkler assembly for simulation of design storms as a means for erosion and run-off studies, Bull. International Assoc. Sci. Hydrology, Vol. 7, pp. 57-72. SHANKS. G. L. and J. J. PATTERSON (1948), Technique for spray- nozzle testing, Agr. Engng., Vol.29, pp. 539-40., 321. idem (1952), The Riley sprayograph, ibid, Vol.33, p. 428. SHERMAN, L. K. (1932), Streamflow from rainfall by unit-graph method, Engng. News-Record, Vol.108, pp. 501-5. SINGLETON, F. and D. J. SMITH (1960), Some observations of drop size distributions in low layer clouds, Quart. J. Roy. Met. Soc., Vol.86, pp. 454-67. SIVARAMAKRISHNAN, M. V. (1961), Studies of raindrop size characteristics in different types of tropical rain using a simple raindrop recorder, Indian J. Met. and Geoph., Vol.121 pp. 189 -216. SPARROW, G. N., R. L. CARTER and J. R. STANSELL (1958), Irrigator for research plots, Trans. Amer. Soc. Agr. Engns., Vol. 1, pp. 43-4/7. SPENCER, A. T. and D. C. BLANCHARD (1958), A portable raindrop recorder for semi-continuous determination of size distributions, Trans. Amer. Geoph. Union, Vol.39, pp. 853 - 7. SPILHAUS, A. F. (1948), Drop size intensity radar echo, J. Met., Vol. 5, pp. 161-4. SREENIVAS, L. J. R. JOHNSTON and H. O. HILL (1947), Some relationships of vegetation and soil detachment in the erosion process, Proc. Soil Sci. Soc. Amer., Vol.12, pp. 471-4. SRIVASTAVA, R. C. and R. K. KAPOOR (1960), Drop size distribution and liquid water in a winter fog at Delhi, Indian J. Met. and Geoph., Vol.11, pp. 157 - 62. idem (1961), Thunderstorm rain versus steady precipitation from layer type clouds, as judged by study of raindrop sizes, ibid, Vol.12, pp. 93 -102. 322. STAEBNER, F. E. (1931), Tests on spray irrigation equipment, U.S. Dept. Agr. circular 195, 29 pp. STAMMERS, W. N. and H. D. AYERS (1957), The effect of slope and microtopography on depression storage and surface detention, International Assoc. Sci. Hydrology, General Assembly, Toronto, Proceedings, Vol. 3, pp. 89-94.

STRONG, W. C. (1961), The absolute necessity of obtaining maximum overall irrigation efficiency, "Africa and Irrigation", an international symposium sponsored by Wright Rain Ltd., Salisbury, Southern Rhodesia, August 21-29, 1961; Proc., pp. 192-8. SUTTON, O. G. (1960), Understanding weather, Penguin Books, 215 pp.

SWANSON, N. P. (1965), Rotating-boom rainfall simulator, Trans. Amer. Soc. Agr. Engns., Vol. 8, pp. 71-2. THOM, H. C. S. (1958), A note on the gamma distribution, Monthly Weather Revue, Vol.86, pp. 117-22.

TOPPING, J. (1962), Errors of observation and their treatment, Chapman and Hall, 3rd edn., 119 pp. WATKINS, L. H. (1955), Variation between measurements of rainfall made with a grid of gauges, Met. Mag., Vol.84, pp. 350-4. idem (1963), An investigation of the hydraulics of run-off from road surfaces: first report, unpublished laboratory note no. LN/418/LHW, Road Research Laboratory, 10 pp. plus 3 diagrams and 11 plates.

WATSON, E. A. (1948), Fuel systems for the aero-gas turbine, Proc. Inst. Mech. Engns., Vol.158, pp. 187-208. 323.

WIESNER, J. (1895), Beitrage zur Kenntnis des tropischen Regens, Ber. Akad, Wiss Wien, Vol.104, pp. 1397-1431+. WILCOX, J. C. and G. E. SWAITRS (1947), Uniformity of water distribution by some undertree orchard sprinklers, Scientific Agriculture, Vol.27, pp. 565-83. WILM, H. G. (1941), Methods for the measurement of infiltration, Trans. Amer. Geoph. Union, Vol.22, pp. 678 - 86. idem (1943), The application and measurement of artificial rainfall on types FA and F infiltrometers, ibid, Vol.24, pp. 480 4. WISCHMEIER, W. H. and D. D. SMITH (1958), Rainfall energy and its relationship to soil loss, ibid, Vol.39, pp. 285-91. WISLER, C. O. and E. F. BRATER (1959), Hydrology, Wiley, 2nd. edn., 408 pp. WOLF, P. O. (1957), The influence on flood peak discharges of some meteorological, topographical and hydraulic factors, International Assoc. Sci. Hydrology, General Assembly, Toronto, Proc., Vol. 3, pp. 26-39. WOO, DAH..CHENG and - H. F. BRATER (1962), Spatially varied flow from controlled rainfall, J. Hydraulics Div., Proc. Amer. Soc. Civil Engns., Vol.88, HY6, pp. 31-56. WOODRUJV, C. M. (1947), Erosion in relation to rainfall, crop cover and slope on a greenhouse plot. Proc. Soil Sci. Soc. Amer., Vol.12, pp. 475-8. WOODWARD, G. O. (ed. 1959), Sprinkler irrigation, Sprinkler Irrigation Assoc., 2nd edn., 377 pp. YU, Y. S. and J. S. McNOWN (1964), Run-off from impervious surfaces, J. Hydraulic Res., Vol. 2, pp. 3-24. 324.

Appendix B

The configuration of spray from swirl-type nozzles

Swirl-type nozzles consist essentially of a chamber into which fluid enters in a substantially tangential direction and leaves through an axial orifice. A vortex with an air core is established inside the chamber, and the resultant discharge from the orifice takes the form of a hollow cone of spray which subsequently breaks up into droplets. The design of nozzle adopted for the present investigation (see figures 5.1.1 and 7.1.1) is similar to that of the swirl-type atomizers whose behaviour has been discussed at length by E, A. Watson (1948) and H. L. Green (1953). Watson (loc.cit., p.196) described the formation of the hollow cone of spray as follows:

"The paths of the particles issuing from the orifice at points on a given radius R will form a surface , which except for a small negligible portion near the orifice may be regarded as the surface of a cone. The apex angle of this cone will depend on the relative axial and tangential velocities at the point of emergence and, as the tangential velocity is inversely proportional to the radius, the apex angle of particles issuing at a small value of R will be greater than those at a larger angle (sic.). In other words the particle issuing on the inside of the spray will try to tierce the path of other particles and get to the outside. At low flows, where the kinetic energy of the liquid is small, this tendency is resisted by the combined effects of surface tension and viscosity and the liquid issues as a continuous coherent film." Unbroken f ilm Unbroken film. Atornizktic-n Cone angle forming usrfnences very of spray. bubbte. close to orfi Ragged dg •,1;, Coarse breaking down to In air In vacua spray atomization finer maintains conical Atomization. ent r e gig fri \‘. tt-an in (a) but r ained ,P,1a • I kk1\ form. still coarse. contract tf spraY-

(a) "BUBBLE" STAGE OF (WTULIPISTAGE OF {c) FULLY DEVELOPED SPRAY IN NORWI

ATOMIZATION. ATOMIZATION. STAGE OF ATOMIZATION

FIGURE. B.I. Three stages in the configuration of spray from a swirt -type nozzle (after E. A. Watson P 197). The same diagrams are reproduced by H. I,.,. Green (1953 P 300). 326.

The shape of this liquid film depends upon the rate of flow of the nozzle. Watson illustrated the changes obtained as the discharge increases by the three diagrams reproduced in figure B.1.

At very low flows, the film forms into a hollow "bubble" as shown in figure B.1(a). As the rate of flow is increased, the hollow bubble changes into the "tulip" form of figure B.1(b). Further increases in the flow rate cause the film to break-up into droplets nearer to the orifice until the stage shown in figure B.1(c) is reached at which the film virtually ceases to exist.

A comparison between figure B.1 and the series of photographs reproduced in plate B.1 shows the similarity between the behaviour of nozzle type A/D and that described by Watson. At a head of 3.89 feet of water, (plate B.1(a)), the shape of film corresponds to the hollow bubble of figure B.1(a). Plate B.1(b), taken at a head of 7.30 feet, shows an intermediate stage between the ububble" and the "tulip". Plate B.1(c) and B.1(d) corresponding to heads of 11.93 and 15.86 feet of water, both exhibit the tulip form of figure D.1(b). In plate B.1(e), (21.24 feet of water), the length of unbroken film has shortened. The fully-developed form of break up shown in figure B.1(c) was not attained within the range of working pressures considered in the present investigation.

Evidence of the progressively larger numbers of smaller droplets obtained with increasing pressure at the nozzle, as implied by Watson in figure B.1, is contained in Chapter 8.

a ( b

PLATE . B.1. Configuration of spray from nozzle type A/D at five different working pressures.

(e) 328.

Appendix C

The behaviour of swirl-type nozzles fitted with triangular orifices

W. A. Hall and P. A. Boving (1956) carried out a series of experiments with sharp-edged triangular orifices with the object of determining their suitability for use on irrigation sprinklers. Their results showed that the pattern of application depth7obtained from a sprinkler fitted with a triangular orifice having a 1:1 base- to-height ratio approached the ;ideal" distribution for conditions of 100 per cent overlap presented by J. E. Christiansen (1941), previously referred to in section 6.1. Further work by W. K. Bilanski and E. H. Kidder (1958) and I. Seginer (1963) has confirmed that sprinklers fitted with triangular orifices produce more desirable patterns of application depth than those fitted with circular orifices. In addition, triangular orifices are stated to produce more uniform drop sizes.

The above conclusions apply to rotating irrigation sprinklers having the axis of their nozzles inclined at an angle of approximately 30 degrees to the horizontal. These conditions are completely different from those under which the prototype nozzles used in the present investigation were employed. However, the possibility that triangular orifices produce improved drop size distributions was considered to be worth further investigation. Consequently, a limited number of tests was carried out using a nozzle fitted with a type B swirl plate (see table 5.1.1) and a sharp-edged equilateral triangle-profile (type B) orifice plate. Patterns of application depth were obtained for nozzle type B/B at four different working pressures using the standard test procedure described in section 5.3. 329.

Hall and Boving noted that jets issuing from triangular orifices exhibit three separate "fins" of liquid. These fins lie opposite each corner of the orifice, and roughly in the plane of the bisector of the angle forming the corner. For isosceles triangle-profile nozzles, the fin opposite the most remote corner was stated to contain a greater proportion of the discharge and produce larger droplets than the other two. An equilateral triangle-profile orifice might therefore be expected to produce fins containing an approximately equal proportion of the discharge. The distribution of drop sizes from the jet should also show greater uniformity.

The behaviour of nozzle type B/B was complicated further by reliance on the presence of a vortex within the nozzle to cause dispersion of the jet. The formation of hollow bubbles and tulip- shaped films, as described for nozzle type A/1D in Appendix B, bined with the fins to produce a complex dispersion mechanism which resulted in the application patterns shown in figures C.1-C.4. The contours of application depth in these figures are expressed as before in units of inches of depth per 10-minute test time.

A common feature which can be seen immediately on examining figures C.1-C.4 is the tendency for the contours of equal application depth at the edges of all four patterns to assume a roughly triangular shape. This tendency is less marked in the patterns obtained at the two lowest heads The innermost contours of the latter, corresponding to the highest application depths, are more elliptical than triangular in shape.

Another notable feature of the same two patterns is their low areal coverage at sampling level. The 0.25-in contour encloses an area of only 2.06 ft2 at a head of 4.98 feet of water, "'"'u.

121N 6 0 2FT J~~i~i~i~i ~i~i~i~~i~i~~------~------'I SCALE

NOZZLE POSITION +

FIGURE C.l FIGURE C.2

Application pattern for nozzle type B / B Application pattern for nozzle type B / B under head of 4·98 ft water (test number 55) under a head of 10·35 ft · water (test number 57) ,

0·25

FIGURE C. 3 FIGURE C.L.

Application pattern for nozzle type B / B Application pattern for nozzle type B / B under a head of 1L. · 53 ft water (test number 59) under a head of 20·05 ft water (test number 61)

------_. 331. 2 and 2.56 ft at 10.35 feet. At both heads, the angle of the cone of dispersion was visibly narrower than that obtained with any of the nozzles fitted with circular orifices.

Increasing the working pressure from 10.35 to 14.53 feet of water brought about a pronounced change in the general shape of the pattern. Areal coverage increased by almost 50 per cent, with the area enclosed by the 0.25-in contour rising to 3.77 ft2. This increase in pressure was also accompanied by a widening of the angle of the cone of dispersion. The three fins therefore intersected the sampling level at a wider radius than at the two lowest heads, resulting in the formation of three separate "peaks" in the pattern of application depth. Figure C.3 shows that one of the recorded peaks was much larger than the other two. Their positions are still clearly defined however, and if lines are drawn between them, the angles of the triangle so formed are roughly 60 degrees. This symmetry, coupled with the relative positions of the peaks with respect to the nozzle, tends to indicate that the accumulation of water on one side of the pattern was caused by the misalignment in the apparatus already discussed in section 5.4.

These trends were maintained as the working pressure was increased to 20.05 feet of water. The pattern obtained at the latter head (figure C.4) shows that areal coverage increased, the 2 area bounded by the 0.25-in contour rising to 4.28 ft . The three peaks of application depth were clearly evident, although again one peak was proportionally larger than the other two. All three peaks were located at a greater radius from the nozzle.

In general, the changes in shape of the application patterns with increasing head were more pronounced than the changes in areal coverage. Plots of application depth against the area receiving amounts greater than or equal to the recorded 332. depth were therefore less successful than those used to compare the properties of the nozzles fitted with type A orifices. The depth-area curves for nozzle type B/B are shown in figure C.5. Apart from the increase in total areal coverage obtained with increasing head, these curves do not reflect any of the significant changes in behaviour evident from figures C.1-C.4.

As each test was repeated once in accordance with the standard test procedure adopted for single nozzles, a limited assessment of reproductivity can be made. The wide spacing of sampling points and small areal coverages obtained with nozzle type B/B led to the use of relatively small numbers of spray- gauges in test numbers 55-62. The number of pairs of readings which could be used for a reproductivity analysis (57) was correspondingly much smaller than those taken from the tests of the nozzles with circular orifices (see table 5.4.2). The analysis is summarised in table C . 1 .

Table C.1 shows that the uncorrected reproductivity figures from nozzle type B/B are similar to those based upon the results of all tests made with nozzles fitted with circular orifices, but are higher than those from nozzle type A/D1 only. When the irregular nature of the patterns and the sharp gradients in application depth between adjacent gauges, which were obtained with nozzle type B/B, are taken into account, this result must at least be regarded as adequate. Because of the small number of pairs of readings available, no corrections such as those described in section 5.4f were made to the figures from test numbers 55-62.

An interesting feature of the dispersion mechanism of nozzle type B/B was the angle at which the three fins of liquid were thrown out from the orifice. As pressure at the nozzle increased, the cone angle of the dispersion also increased. 333 .

1.1.;

1.0 2.0 3.0 AREA RECialK; DEPTH ,/ REcoRpEo (SQ. FT

ELGURE. 5 Depth rea curves for nozzlenozz type 13 . 334.

TABLE C.1: Reproductivity analysis (uncorrected figures)

maximum difference (%) between proportion of corresponding measurements for that pro- total number of portion of the total number of readings pairs used in analysis (%) all nozzles with nozzle type nozzle type type A orifice A/D B/B

25 2.5 2.5 2.0 50 5.0 4.5 5.5 75 8.5 7.o 11.5 95 20.0 10.0 18.0

Increases in the tangential velocities of droplets led to changes in the position of the region in which the fins intersected the sampling level. The position of the three peaks of application depth relative to the nozzle* was therefore found to alter as the working pressure was varied.

This property of nozzle type B/B was thought to be sufficient to form a major source of error in any overlapping exercise that might be carried out with the patterns in figures C.1-C.4. Furthermore., unless care was taken to match the orientation of the orifices, the same changes in the position of these peaks of application depth could cause extreme variations in the performance of a network of such nozzles.

The manner in which the shape of the application patterns altered with increases in working pressure also introduced a further source of error into the interpretation of measurements

As the orifice and swirl plates were removed for examination between tests at different heads, no significance can be attached to the relative positions of the peaks in figures C.3 and C.4. 335.

of drop size distributions from filter paper samples. Owing to the lack of data, the application rates used in calculating the exposure time of each sample (see section 8.4) were read directly from the points corresponding to the sampling positions on each measured application pattern. Although care was taken to orientate the triangular orifice in the same sense for each test, even minor differences in position could cause changes in pattern shape, and this procedure can only be regarded as an approximation.

Samples were taken directly below the nozzle at each of four heads, and at 12 inches radius from the nozzle at all but the lowest head. The variation of median volume drop diameter with both working pressure and radius is shown in table C.2. Typical drop size distributions from the three replications taken at each point under each head are given in figure C.6.

Table C.2 shows that at the sampling point directly below the nozzle, the median volume drop diameter decreases with increasing working pressure. At the 12-in radius, an increase was recorded as the head was increased from 10.35 to 14.53 feet of water. At the two highest heads, the median volume drop diameter was found to be larger at the 12-inch than at the zero

TABLE C.2: Median volume drop diameters (mm) obtained from sampled distributions at two points within the cone of influence of nozzle type B/B under four different working pressures

working pressure (ft of water) radius (in) 4.95 9.66 14.94 19.84

zero 1.23 0.81 0.43 0.30 12 0.50 0.58 0.57 336. radius. Both the latter variations may be attributed to the fins thrown out from the orifice, which tend to deposit larger sizes of drops at a radius rather than directly below the nozzle.

The sampled distributions shown in figure C.6 confirm the trends shown by the data presented in table C.2. These size distributions are wider than those obtained from nozzle type A/D (figures 8.6.3 and 8.6.4). Comparing the two sets of results, the size distributions from nozzle type B/B do not appear to be more uniform than those from type A/D.

The results of the above tests on a swirl-type nozzle fitted with a triangular orifice may be summarised as follows:

1. the properties of the application patterns from nozzle type B/B were inferior to those from type A/D;

2. the reproductivity of the application patterns compared favourably with the average performance of the nozzles with circular orifices previously tested, but again was less successful than that of type A/D;

3. the drop spectra from nozzle type B/B were wider than those from type A/D, but did not exhibit any superior features in regard to uniformity in drop sizes as previously suggested in the literature. 12 IN RAD:US I 12 iN RADUS 19-8e.r. FT HEAD. 1 12 N 1."-W.-YUS 1-1 14-9(.. FT HEAD. L 9.66 FT HEAD.

ZERO RADIUS ZERO RADIUS ZERO R_-\DIUS ZERO PADIUS TY 4-95 FT HEAD. 9.56 FT HEAD. 1L9 F HEAD. 19.84 FT HEAD, NSI 0 -I DE ATIAL P -1ra, t,1—"T-7771—

S r""1.1tb14 DROP DIAMETER 0-2S MM INTERVALS. FIGURE C.6. Drop size distribution measurements for nozzle type E.) B. 338. Appendix D

The parametric representation of rainfall patterns. a. Natural rainfall events

A method of expressing instantaneous measurements of rainfall intensity over a catchment area in terms of time and space co-ordinates has recently been proposed by J. Amorocho and A. Brandstetter (1966). In this method, measurements from a network of raingauges are considered separately in terms of variations with time at each gauge, and variations in space at any instant of time. Records of the former, as shown by the trace from a raingauge, always exhibit high frequency, low amplitude fluctuations caused by a combination of factors ranging from the turbulent motion of the air during a storm to the mechanical defects of the raingauge itself. These fluctuations are generally strongly damped by the catchment, so that their effect on the run-off history from a storm is negligible. On the basis of this assumption the authors fitted a two-parameter gamma distribution to the record from each raingauge according to the method outlined by H. C. S. Thom (1958). This procedure yielded a relationship between the "filtered" rainfall intensity, P', and the time, t, at any point (x, y, z):

(P')xyz = vi (t; [ a1, ... , ak, •.,. 1 aqJ xy ) Eq. D.1

The values of the q parameters ak depend upon the co- ordinates of each station. A polynomial relationship of the form:

2 2 2 + b + b y + bkz + b x + b6y + b z + b8xy ak = (b1 2 3 5 7

+ b yz + b10xz + b11x3 + ...) Eq. D.2 9 339.

, b etc. was assumed, and the values of the coefficients b1 2 obtained by the statistical methods for irregular sampling station arrays previously used by W. C. Krumbein (1959). A comprehensive account of the same procedure has recently been provided by W. C. Krumbein and F. A. Graybill (1965; chapter 13). This treatment yielded the expression

531 Eq. D.3 (P')xyz (x $y z t.$ bi ) where Wk represents each array of coefficients b.

The procedure outlined by Amorocho and Brandstetter would no doubt bn equally applicable in describing distributions of artificial rainfall. However, the present writer has considered an alternative approach using double harmonic analysis.

When a function, f(x), is defined only by a set of observations at equidistant points over a limited range of x between x = 0 and x = 1 (say), the method of trigonometric interpolation may be employed to give an analytical expression for the observations (see C. Lanczos, 1956; chapter IV). Although f(x) may not be periodic in itself nor return to the same value at the beginning and end of the range of observations, the interval x = 0 to x = I may be chosen as the half-period of an even function such that f(-x) = f(x), thereby avoiding the discontinuity at -11.. If f(x) is assumed to be even, the function may be expanded as a half-period cosine series.

A similar procedure may be adopted when measurements are taken over a grid of equally-spaced points. In this case, each row and column of observations is assumed to define the half- period of an even function. In general, the intensities of application, P, measured at any co-ordinate (x,y) of the rainfall surface may be expressed as a trigonometric expansion of the form: 34o.

oo P = f(x,y) = :2J . cos inx cos ----ja y Z. Ai L L Eq. D.4 i=0 j=0 3 1 2 where 1 04y‘L2. If, however, f(x,y) is defined only at discrete points over a sampling grid containing N rows of N observations, L 12 Xu = 11,7-7 U . = 11,11.4.,14; Y IT. v = 1,...,N Eq. D.5 and M N cos v (la) P uv = ifo rj=b 3_A.3. cos u Eq. D.6

The harmonic coefficients are then given by the following equations: M N 1 A00 = cim f(x,y) ,y ) Eq. D.7 MN u=0 v=0 u v

M N A. L f(x ) cos u -()17 Eq. D.8 2.0 = MN u=0 v=0 u lyv

M N AOj - MN f(x y ) cos v (11 ) Eq. D.9 u=0 v=0 u l v M N A. = f(x y ) cos u (IF) cos viT Eq. D.10 iN MN 4U=0---;,/ v=0I s U/ V

M N AM,. = N. f(xu,yv) cos ulT cos v (AFT11) Eq. D.11 u=0 v=0 and 4 M N (ITT A. = I f(x y v) cos u cos v j Eq. D.12 1j MN z--u=01 " v=0 341.

If the original observations represent unequal elements of the sampling grid, then appropriate weighting factors, W , must be uv applied to each value of f(xu,yv), giving rise to equations of the form

h A. = T ' W f(x ly ) cos u 7(-) cos v TTirr) Eq. D.13 MN A om uv u v ( ij u=v v=u

Note that although weighting factors are applied to the observations to calculate the harmonic coefficients, the ordinates reconstituted by substituting the harmonic coefficients into equation D.6 are the unweighted figures. b. Artificial storms The application patterns from the 16-nozzle network discussed in Chapter 7 may be represented schematically as a space distribution of instantaneous rates of application, P, as shown in figure D.1, in a similar manner to any natural rainfall event. As the sampling area used in those experiments may also be considered to be the smallest representative element of any larger size of rainfall simulator, the measured patterns can be used to characterise the behaviour of that rainfall simulator over the particular range of working pressures for which the patterns were obtained.

Provided that the application patterns are reproducible to close limits, there will always be a specific distribution of P in space associated with every value of average application rate, T. If, therefore, the rainfall simulator were to be used to generate an artificial storm in which the variation of P with time, t, over an area was as shown in figure D.2 (say), the required space distribution of P at discrete value of t could be formed from the measured patterns. The parametric representation AP

FIGURE D.I. TypiCat space -variation of intensity of apptiCCAU011 at any tirnq C.

FIGURE:0.2 iypicu, tims-voriation of QvrQ pptiCQhOi depth over on 31+3. of artificial storms as fldistributed-parameter" inputs therefore reduces to the problem of expressing instantaneous values of P as some function of the space co-ordinates (x,y):

P = (x,y; [ C1,..., C Eq. D.14 1 nr1) such that each of the parameters Cn takes discrete values for each pattern representing a different value of T. If there are with r value of Cn for each pattern, then the variation of P time (figure D.2) may be transformed into a variation of each of the r parameters with t:

C = (t. dm' ...,ds1) Eq. D.15 n 2 ' L 1'"" which includes another set of parameters d equal in number s to m the number of values of t considered. An expression of the form

Eq. D.16 P = (x'Y' 9f21 1 "fii gC2in" "1/2-1 r would give the desired distributed parameter input of artificial rainfall..

Both stages in the setting-up of equation D.16 may be carried out using harmonic analysis. Equation D.14 may be expressed in terms of a double harmonic series (as equation D.6 above), and equation D.15 in terms of a single expansion (see Lanczos, loc.cit., 1956). In order to illustrate the procedure, double cosine series were fitted to the measured patterns from test numbers 135-146.

Each of the measured patterns was found to contain minor asymmetrical variations in distribution, attributable to small differences in the properties of the individual nozzles forming the network. A measure of this effect was obtained by finding the co-ordinates of the centroid of each pattern with respect to the centre of the net area as origin. The calculations 344. were carried out on the Imperial College IBM 7090/1401 computer, and details of the appropriate program are included in Appendix E. Values of the "radius of gyration" obtained for each pattern are presented in Table D.1.

TABLE D.1: Distance (inches) between the centre of the sampling area and the centroid of the application patterns from test numbers 135-146

test distance test distance test distance

135 0.565 139 0:174 143 0.390 136 0.448 1 14o 0.384 144 0.435 137 0.246 141 0.327 145 0.258 138 0.214 142 0.131 146 0.455

This parameter is not a strict function of the symmetry of the patterns as near-zero values may occur for asymmetrical distributions of application depths. An example of such a distribution would be one in which the first moments of high application depths occurring near to and on one side of the pattern centre were cancelled out by those of low application depths on the extreme edge of the opposite side of the pattern. Inspection of the data from test numbers 135-146 showed that where the patterns exhibited this type of feature, the differences in depths were too small to prevent the radius of gyration being used as an index to symmetry for the purposes of the present work.

Table D.1 shows that the maximum distance between the centre of the sampling area and the centroid of any application pattern was fractionally over 9/16-inch, indicating that the effect of the differences in the properties of the individual 345. nozzles was negligible. By taking into account the minor variations associated with these nozzles, harmonic analysis of the full mesh of 7 rows of 7 observations would therefore lead to the fitting of unwanted "noise" as well as the "signal". The asymmetry of the patterns was partly eliminated by forming an average quadrant of 16 observations from the original 49. A computer program was written to calculate the double cosine series fitting each of the 12 sets of 16 ordinates (see Appendix E). A typical result, corresponding to the form of equations D.6 and D.14, taken from the data of test number 146 is quoted below:

uri 21.01 P = 6.9143 + 0.0376 cos --- 0.0216 cos — 0.0133 cos uTt uv 3

v-TY U TT 2uTr vTr - 0.132 cos — - 0.3095 cos — cos — + 0.0211 cos --- cos 3 3 3 3 3 vri uTT cos 2vTT - 0.0134 cos urrcos — 0.0927 cos 2viT - 0.0034 cos 7 - 3

+ 0.0769 cos EITcos LT + 0.0303 cos uTIcos ?viT 3 3 3 2uTT + 0.0249 cos vii- 0.0185 cos IllYcos vir+ 0.0139 cos —3 cos viT 3

+ 0.0037 cos urrcos vii Eq. D.17

Apart from A00, which is the mean height of the surface, the values of the harmonic coefficients have no physical significance.

The use of a 16-term as opposed to a 49-term harmonic series does not completely eliminate the "noise" resulting from asymmetry in the measured patterns. In addition to their symmetry about two mutually-perpendicular axes through the centre of the sampling grid, the patterns should also have been symmetrical 346. about another set of axes at 45 degrees to the first set. "Folding" the pattern about the first pair of axes produces the 16-ordinate case considered above. Further folding about the second pair reduces the number of observations, and therefore the number of terms in the harmonic series, to 10.

The development of the 10-term double cosine series is now under investigation. Work is also continuing on procedures for formulating the distributed parameter inputs corresponding to equation D.16. Note that the number of harmonic coefficients always equals the number of ordinates used in the analysis. Consequently, the advantage of expressing the application patterns in terms of a double harmonic series lies purely in operational convenience. 347.

Appendix E

Computer Programs

The computer programs written in Fortran IV language in connection with the present investigation may be considered under four separate headings, namely:

1. The overlapping of single-nozzle patterns to form application patterns from various spacings of nozzle networks (see Chapter 5),

2. The calculation of drop size distribution parameters (see Chapter 8),

7 • The calculation of statistical parameters for the four-nozzle and sixteen-nozzle application patterns (see Chapter 7), and

4. The fitting of double harmonic series to the sixteen-nozzle application patterns (see Appendix D).

All programs except (2) above consisted of a main deck and up to four subroutines. The former contained the instructions for "reading-in" the data to be processed, and for "writing-out" the results from the calculations. All calculations were carried out by the subroutines which were "called" in order from the main deck. The reading-in and writing-out of data, and the calling of subroutines are standard procedures to be found in any programming manual, and need not be repeated here. However, the subroutines written specifically for the present work are described in outline below. 348

1. "Sprinkler patterns" program (a) Subroutine PATERN: The single-nozzle patterns obtained during the phase I experiments were defined by measurements of application depths over a sampling grid containing an equal number of rowso-f columns. In subroutine PATERN, overlapped patterns from groups of nozzles whose spacings were multiples of the sampling grid interval were built up from these data, The single-nozzle patterns were stored as a one-dimensional array of data, As, where the subscript s denotes the position of the ordinate numbering from top left to bottom right of the grid. The overlapped patterns were formed as two-dimensional arrays of data, Bij, where the subscripts i, j denote the number of the column and row of the array respectively, numbering from the top left-hand position of the overlapped pattern grid.

The method by which the ordinates B.. . were formed from the original data may be conveniently illustrated by means of a simple example. The single-nozzle patterns obtained during the phase I experiments were wholly defined by eight rows of eight sampling points. Consider therefore, the formation of the overlapped pattern within a cell of 4 nozzles located at a spacing of four times the distance between sampling points in a square geometry. The overlapping of single-nozzle patterns has already been considered at length in Chapter 4, and the discussion need not be repeated here. However, as the spacing is greater than or equal to the radii of influence of the single-nozzle patterns, one quadrant of the pattern from each nozzle lies completely within the cell.

The overlapping of the patterns is represented schematically in figure E.1. For clarity, the sampling grids for only two of the four nozzles are shown. If the single-nozzle patterns are always orientated with the ordinate A in the top left-hand corner of the l sampling grid, then the bottom left-hand quadrant of the pattern from SINGLE-NOZZLE PAT FERNS

1 i i •'Pt ,

i ! jA37 I

i i

•Schematic representation C the overtupping on 8 x sngle-nozzie pattern gi sd to form Q x overtopped pattern. 350. the nozzle at Q and the bottom right-hand quadrant of the pattern from the nozzle at P will lie within the cell PQRS. Similarly, the nozzles located at P and S will provide the top left-hand and top right-hand quadrants respectively of the same single-nozzle pattern, The ordinates B.. of the overlapped ij pattern are therefore formed by the superposition of measurements at coincident points within the quadrants of the sampling grid. The ordinate for example, is given by the summation of A B„.,1'1 l (from the nozzle at 10, (fro„1 S), A33 (from Q) and A37 (from P) as shown in figure E.1(a). In general, therefore,

B. . = /,A ij Eq. E.1

and the problem of calculating the overlapped-pattern ordinates reduces to the computabion of subscripts s for given i and j.

The mo',:hod of calcuJ ation adopted was based upon that used in a computer-program for analysing patterns of application depths from irrigation sprinklers, previously described by W. E. Hart (198). Hart proposed the following formula for the subscripts s of the depth measurements that go to form the ordinate in the ith column a-ad jAi the overlapped pattern:

n , + h(p-1) + Hv (q-1) + H (j-1) Eq. E.2

where H represents the -n-,].ner of columns of observations in the single-sprinkler pattern, and h, v denote the number of columns and r'.L.ws respectively in the overlapped patterns p, q are dummy variables, Note that

i h (-1) Eq. E.3

S HV Eq. E.1

where V represents the number of rows of data in the single- sprinkler pattern,

351.

A listing of the subroutine based upon the above equations is given in figure E.2. H, V, h, v, i, j, s, p and q appear as

r-±-i-csuBjaCKELN- Rytri:b.IG E = 0 \LEILA PRED-P A T T ERN DA_TAARRA-Y SUBROUTINE PATERN ( A • B •ORCOL • ORROW •PACOL •PAROW ) rNT_EGE-VI;QC(:)L -ORROW • PACOL PA ROW D-1--NlENS-1-CklA_(_6_4_)_e_fal 5 , 5 ) --- P-1 1-3_1=1

_B _( I •J)=0

40 K= I+PACOL.x- ( M-1) L-K+ORCOL-X-PAROW* (N=1-) +DROOL-X. ( J- 1 ) IF ( K•GT•ORCOL ) GO TO 50 I E-1_10RCOL4FORRO_WI_GO . TO 60_ _ 8( I•W=B( I•J)+A(L) - M N14-_ 1 _ GO TO 40 L=•:GrTiii-ORCOL*ORROW ) GO TO 60 N=N+1 G0=--f2r-0-3-(7 60 IF ( I •ED•PACOL) GO TO 70 I-- 1 GO TO 20 70-=I PAROW )—GO -TO 80 J= J+1 G 0 - 80 CONTINUE RL=T-URN _ _ _ END

FIGURE E.2: Subroutine PATERN

ORCOL, ORROW, PACOL, PAROW, I, J, L, M and N respectively. The computation begins with I, J, M and N set at unity for given ORCOL, ORROW, PACOL and PAROW, and proceeds by calculating valid subscripts L. The depths corresponding to these values of L are successively added into the register B(I,J). When the value of L exceeds the product ORCOL times ORROW, the value of I is increased by one, and the procedure repeated until all points in the first

352.

row of the overlapped pattern have been obtained. The value of J is then increased by ono. Successive rows are covered in the same manner. and control is transferred to the main deck only when and J reach their respective vnlues of PACOL and PAROW. The maximum spacing of nozzles considered in the calculations was five times the sampling grid interval,

(b) S'?hroutine UNIFC0: In this subroutine, the average application depth, XffiR, the mean deviation, XDEV, the standard deviation, XSTA, the Christiansen uniformity coefficient, UUC, the coefficient of variation, UVA, and the H,S.P.A. coefficient, UUH, for the overlapped pattern data array, B, are calculated. Details of the subroutine are presented in Figure E.5. The uniformity coefficients a2e defined in Chapter 4, and the calculations are ---C-SOBROLLT-UN O LAS' I NG UN -I F ORALLY COE-FF-1-C I FN-TC -E01:2- 1 =OVFRLAPPF-D--DATA- SUBROUTINE UNIFC0(B,PACOLtPAROW•RARRAY,XBAR,XDEVoXSTA•UUC,UVAIUUH) I NTEGE-f- Ws- PA RRA Y Da_MENS I ON B ( 5 • 5 ) • C ( 5 • 5 ) St../MA-=-00 SUMB=0. 0 SO DO 200 Kl=loPACOL ---CVAR04,1 210 SUMA=SUMA+B(K1,1.1) -- _2 OD E XBAR=SUMA/FLOAT(PARRAY) - DO 230 L2=1 • PA ROW EMEI rre03 •••••11Pas 13AR ) SUMB=SUMB+C(K2eL2) 230=SOM-C-=SUMC=VCTK241:2T*Cr(K2eL2) 220 CONTINUE -XBAR-=67•-0-404RAP XDEV=6 • 0*SUMB/FLOAT ( PARRAY) xs-71-A 6 041-S-OrZ_TUMC/FLO A171 P A RRA Y ) UUC= 1 • 0- ( XDEV/XBAR UVA-_XST-A/XBAR UUH=1,0-0•798*UVA - RN END FIGURE E.3: Subroutine UNIFCO 353.

self-explanatory. Note, however, that the overlapped pattern data are expressed in inches of depth per 10 minute test exposure, and the pattern parameters (where appropriate) are read out in units of inches per hour.

(c) Subroutine EFFCO: In the first part of this subroutine (see figure E.4), the overlapped pattern data array, B, is written into a one-dimensional array, D, in descending order of magnitude. The magnitude of each ordinate in the array B is compared in turn with the contents of a register COMP. If COMP is found to contain a number less than or equal to any ordinate, then that ordinate is written into COMP, and a note made of its position in the overlapped pattern data array. (Initially, COMP contains zero, so that B(1,1) is immediately written into it.) When COMP has been compared with all ordinates of the array B, its contents are written into the array D, and the particular ordinate B from which it was taken is overwritten with a zero. When the array D has been filled with an equal number of ordinates to that in the array B, control is transferred to the second part of the subroutine, where the U.S.D.A. pattern efficiency, Elill, and the maximum per minimum application depth, R, (as defined in Chapter 4) are calculated.

(d) Subroutine AVARA: This subroutine calculates a symmetrical single-nozzle application pattern from the original depth measurements by averaging corresponding ordinates from each quadrant of the sampling grid. A series of dummy variables (J1, 12, 13, 14 and 15) are computed which form the addresses of the corresponding grid points in the one-dimensional array, DATA, containing the original depth measurements. The symmetrical application pattern is read into the array A (see figure E.5).

354.

C50EIROUTINEEOR WIRlT7TNTOVERLAPPED:=OATA ARRAY=LN=DES(..=ENDTNGROF'-- CMAGNITUDE AND CALCULATING EFFICIENCY FACTORS AND MAX/MIN RATIO __SUBRO-U-T99c1E—EFFIC:3* P ARRAY • PACOL sPAROW sEFU DIMENSION B(5,5),D(25) PA(.01..-_,ERAROIN *PARR AY I A= I aaaaomp,..o o DO 310 JA=1,PACOL

IF(COMPoLE,B(JA.JB)) GO TO 320 Go—T:)-3 1 0 - 320 COMP=B(JA14B) L-A=JA LB=JF3 ----3107CONTINUE D(IA)=COMP -7B(LAoLB)=0- IA=IA+1 IFIIALF-D_PARRAYGO-T0-300 SUM1=0.0 _MAF-_PARRAY/4- DO 330 NA=leMA 307SUKL=SUMI+D-CNA1r:-- SUM1=SUM1/FLOAT(MA) sumai;a4o--- DO 340 IB=1,PARRAY -1-184==— SUM3=SUM3/FLOAT(PARRAY) FUUM1/SUM3______-- -- R=D(1)/D(PARRAY) RETURN END

FIGURE E.4: Subroutine El!FC0 355.

ilING—.A--sAMIME_TR I CAL IDATA- ARRAy—Ea(7M-0-RIG-INAL7 CMEASUREMENTS SUBFZ0U-T-11 PD_ AnTA-, A) DIMENSION DATA ( 64 ) ,A (64) DO 100- Ji1==-14-4 — J2= ( J1-1 ) *8

12=11+J2 41711EIZAAP I 4=56-J2+11 L J - A( I2 ) =0. 25* ( DATA ( 12) +DATA ( I ) +DATA ( 14 )-+•DATA( 15) )

A( I4)=A( I2)

100 CONTINUE

END

FIGURE E.5: Subroutine AVARA

2. "Drop size distributions" program This program (figure E.6) is based directly upon the equations and procedures quoted in section 8.4. The areal densities of drops, DROPNO, on each filter paper are combined with the measured intensities of applications, PPTN, to produce estimates of the duration of exposure, TIME. These figures are used in turn to compute spatial densities, SPADEN, and cumulative water contents, CUWACO, for each interval of drop diameter, K. In addition to these parameters, the ordinates of the Marshall- Palmer distribution, THEORY, (see section 8.5) are calculated for each intensity of application.

356.

INTFGER=—DAT-SE=T-4F-1 - READ ( 54 500 ) DATSET • AREA C;i1 MENSIONS1=1. 23-9-T ER VE L( 12 ) • SP ADEN ( 12-) ••W A TCON(-1- 2) • URO-PNQ 1HEORY ( 12 ) • PLOT A ( 12 ) • PLOTB ( 12 ) - ODATA-CONal-E1=4ECONS12/1 • .9. 435* 4 91 • • 1 3 9 Aw3414-9-559• 18b57s ifl.-2-471 • • 1729.-f2'71. 1331•.13059•9244•4/9 TERVEL/0•54,1•3•204703•51,4•40,5•08•5•68,6•28,6e -2:79±T,T_t-J9m-561alt7w98/ - DO 10 KOUNT= I tDATSET PVVEr I 1--TNO4PRTN D ROPNO - C ONS 3 = 3600 e /( AREA *PP T N*C ONS T2 ) -CONST4=4-4FAUPPT***0•21) TIME=0•0 DO ao- 1=1-4,1? 20 T I ME = T I ME+DROPNO ( I )*CONST1 ( I ) __Timr_TI-ME*(,,ONSF3 WRITE( 6,520) FILTNO,TIME,PPTN CUWAC0=0Ar 0 - DO 30 K=1.12 I-F ( DROP-INO_(..K1_,Eas •0 ) GO TO 30 D I AM=0 • 25*FLOAT ( K ) SPADENtKrY=-1-000000•*DROPNO-(K)/(TERVELkKz):*AREA*TIME PLOT A ( K ) =ALOG10 ( SPADEN ( K ) ) THEORY--(-KA=2-0-00•-/E--XP(-CONST4*D I AM ) PLOTB ( K ) =ALOGIO ( THEORY (K ) ) WAA:CDNT-K45PADENIK)*CONSTS(K)- CUWACO=CUWACO+WATCON(K)/CONST2 K ) PLO TA K 3-•11-1EOR (1)T, P14)713-POict. 30 CONTINUE -- SO CONTI NUL- - 500 FORMAT ( I 3 • F8 • 1 )

5200FORMAT ( 21H FILTER PAPER NUMBER 113,15H EXPOSURE TIME • F6 • 4 • 20H PR /A GI I K=SPADEN=PLOTT-A—T-)_; 2CUWACO) 530 FORMAT (A=H-91-20-1- 1-9•1 t2X-9F6* 4 s 2X IP F6 • 12) OVFO• 4•S2X•F-7-•-1 ) STOP ND

FIGURE E.6: Drop size distributions program 357.

3. "Distribution parameters" program (a) Subroutine XYMOM: The co-ordinates of the centroid of the 49-ordinate application patterns from the four-nozzle and sixteen-nozzle tests are calculated in this subroutine (figure E.7). The total volume of water contained in each pattern, VOL, is obtained by the addition of the ordinates weighted with respect to the area that they represent. Moments are then taken about the centre of the sampling grid in both the x and the y directions to yield TMOMX and TMOMY. The co-ordinates, XARM and YARM, and the square root of the sum of their squares, GYRAD, is formed from TMOMX, TMOMY and VOL in the usual way.

(b) Subroutine COEFS: This subroutine calculates the mean application depth, ABAR, the standard deviation, USD, the skewness, USK, the kurtosis, UKT, the Christiansen uniformity coefficient, UUC, the coefficient of variation, TJVA, and the H.S.P.A. uniformity coefficient, UUH, for a 49-ordinate application pattern (see. figure E.8). Note that weighting factors, W, are applied to the ordinates, A, in computing ABAR (see section 6.3).

4. "Double harmonic" program (a) Subroutine COSXY: The cosine terms needed for the double harmonic analysis are calculated in this subroutine, and stored in arrays COSX and COSY (see figure E.9). Note that only the cosines of angles between zero and 360 degrees need to be stored (see subroutine HARIVICO). If there are n rows of m ordinates in the pattern, the number of cosine terms needed, M2, N2, are given by the expressions

M2 = 2 (m-1) Eq. E.5

N2 = 2 (n-1) Eq. E.6

SUaROUTTMEIffXYMGMTA/X A PM o YARM • G YR AU ) DIMENSION A(49) .XMOM(6).YMOM(6 ) V • ZS* ( A-(-1-)=+-A-(---7--)-+ A ( 43 ) -+ Az( 49 ) ) DO 100 1=2,6 .=--==r1JDO=VOL= VOL-+0•5*TA171r) + A ( 1+42 ) ) DO 110 J=8.36.7 ----=1-TOVOL=-VOL+0451ECAJATJ+6 ) ) _D0_1_20 K=10_5 KK=K— DO 130 L=9013 LL1+KK* 130 VOL=VOL+A (LL ) 120 CONTA NUS DO 140 I A=1.3

I AB=50- I A 174-0XMOMTIrA ( 1 A-A-) -A-( IA )+A( IAB)-A ( IA +42 ) DO 150 KA =8010 --=XMOMTKA -4 ) 0 - - DO 160 JA=1.29.7 JAA=z2- J A -KA J AB= jA +K A-1 160-XMOMTKA-4 )==_XMOMTKA -4 ) +A ( JA A) -AT-JAB ) 150 CONTINUE OTMONIX=MOM- 6-87-5+ X MOM (:2)L-f_xmom 3) * 0 5+-XMOMT4 IT*-375-+XMOMT5/1*24.- 1+ XMOM ( 6 ) 8-0 - - DO 170 H3=101507 15A=--13--JB*6 I BB=44- I (5 I-BC X50=18 YMOM( IBA)=A( IB)-A( IBB)+A( IB+6)-A( IBC)

DO 180 KB =103 _ YMOM ( KBA+4 ) =0.0

LBA=LB+KBA*7

190 YMOM(KBA+4)=YMOM(KBA+4)+A(LBA1-A(LBb ) I 80±CIONTTNUE OTMOMY=YMOM ( 1 )*0.6875+YMOM ( 2 ) +YMOM ( 3 )*0 o5+YMOM (4 )*1.375+YMOM (5 ) *200

XARM=(TMOMX/VOL)*3.0 LT-M_OW14W03- -.-0 GYRAD= SORT ( RM*XA RM ARM*Y A RM ) - - RETURN - - - - END

FIGURE E.7: Subroutine XYMOM

SUBROUTIMF=r0EFStA•_WAABARsUSD,USK_ILIKT4UUCSUVA/-UUM- DIMENSION A(49),W(49) WSUMA DO 200 IC=1.49 200 WSUM,A=_WSMA +A (-I-C-)*W ( 1C ) ABAR=WSUMA/36•0 = usum2=0.0 USUM3 0.0 USUM4=0.0 DO=210__,3C=149 DEV=A(JC)-ABAR -1- 13E-V--41-CT-•_0-6-0) —GO Tel 230 DEV=ABS(DEV) V 11.1.' ir USUM2=USUM2+DEV**260 USUM3=USUM3=-DEV*-*3•0' USUM4=USUM4+DEV**4•0 230 USUM1=USUM1+ABS(DEV) USUW2 UM2 DEV**2 fv0 - USUM3=USUM3+DEV**3• 0 -_,IUSUM4=USUM44-DEV**44-0-r- 210 CONTINUE sumT=usum_1v494-0=,--- USUM2=USUM2/4900

USUM4=USUM4/49•0 USQ-SORTUSQM2Y USUM3=ABS(USUM3) USKVJSUM3**2-A•04YAUSUM2**3s0) UKT=USUM4/(USD**4.0) tiLt_ StiAlAEkR _ UVA=USD/ABAR - ABAR=IABAR*1200)139442 17/394142- - - RETURN ENr

FIGURE E.8:Subroutine Can S

36o. -_--CGENERAL ROUTANE=Fal ---CAL_CULAT-I NG COSINES NEEDED____‘C)R-:=N4_QMON1 Imo- SUBROUTINE COSXY ( M21 NI2 COSX COSY ) IXFMEN -511:3N--- 14-2 C--0S-Y(- N2 ) P I =3 • 1415927 S-P 1-/FLOAT-CM272I ARGX=0 • 0 --- DO -?00A=1:=-1:11M2---- COSX ( I 1 ) =COS ( ARGX ) --2O 0A R G3C=A£ZG7S IF(M2•NE•N2 ) GO TO 205 -DO -715- K-1-1-• 215 COSY(K1)=COSX(K1)

205 S1=PI/FLOAT(N2/2)

DO 210 J1=1*N2 C-OSYTJYT=TCOS( ARGY) 210 ARGY=ARGY+S1 ----7-20WRITE6560Y_M2InNa_t_cOSX•COSY 560 FORMAT (1H1,216/6F10•6/6F10•6) RETURN END FIGURE E.9: Subroutine COSXY SUBROUTINE AVQUAD(A•CoLeM1uN1 ) DTMENSTON_I=t- DO 300 I2=1.3

DO 310 J2=1.3

J4=8+7*I3-J2 ittleMIP=klia• J6=50-J3 310 Ci I?:J2i=.3•01FCA(J3)+A(J4 )+A( J5 )+A(J6 )-)/39.42 300 CONTINUE - DO 320 14=4,18.7 IS O 14 I 6=14+ ( 4-K ) *6 17=50=1_6 C(K•4)=6•0*(A( 14 )+A( 15) )/39•42 CAAI K.31=6*--0*-z(=A=C161.) +A ( 17) ) /39.42 - 320 K=K+1 (-4-c-41-1-=-12 • 0*_A5-3-1-39 • 42 - DO 330 KK1=1 •Ml __ KK - 330 C(KK1,1\11)=0•5*C(KK1 •N1 ) DO-a40-11=1-= lAtta - - C ( 1 •LL1 )=0•5*C( 191-L1 ) ) - RETURN END FIGURE E.10: Subroutine AVOUAD

361„

(b) Subroutine AVQUAD: Given a 49-ordinate application pattern, this subroutine averages the measurements at corresponding points in each quadrant to form a 16-ordinate quarter-pattern. The 16 data are then weighted in preparation for the harmonic analysis by multiplying the first and last columns, and the top and bottom rows by a factor of one-half (see Appendix•D). Note that the original measurements contained in the array, A, (Figure E.10) are in units of grammes of catch per 5-minute test exposure, and the "average" ordinates, C, are expressed in inches per hour.

CGENFRAT-- ROUT-1-NEOR=_C-ALCULATA NG_ HARMON I C COEFFAC I_EN_T_S-1-VENI±ORaLNATES— SUBROUT I NE HARMCO ( AA • M39N39COSX t COSY • COEF e M24 N2 ) 07-I-MENS-11ON=-AA-A-MatiN3 Lt.COEF( M3,-N3-)-4C0 SX-(-M2)-e CO SYJ Na) _ — DO 400 IA=191,43 D07-4TO JA=7--_1_9N3- - -- K A=1

DO 420 JB=1*N3 LTA =-1 DO 430 IB=19M3 COSUM=TGOSUM_+AA ( I B9JB ) *COSX ( LA )*COSY ( KA-) _ LA=LA+ I A-1 CM2.-- LA__.)__GO__T 0 430 LA=LA-M2 43-CoNTINT-TE KA=KA+JA-1 -I F ( N2 ...GEK)_ GO._= - 420 KA=KA-N2 ----420C_GNIZI NUE 410 COEF ( I A JA ) =4•0*COSUM/FLOAT ( ( M3-1 )* ( N3-1) ) =--- 400=_ICONTI-NU DO 440 IA1=1 0,13 COEF ( I Al t N3 ) =0_9,_*COEF CI A1 t N3 ) 440 COEF ( I A191 ) =0 •5*COEF ( IA1 tl ) C10=445-1A2 aN3 -- COEF ( M3. I A2 ) =0 •5*COEF ( M3 e I A2 ) 445 COEF (-I-9 I A-a) =05*COEF I-A2 ) - RETURN END FIGURE E.11: Subroutine HARMCO

362.

calculated in this subroutine (figure E.11). Each coefficient COW is formed from M3 by N3 terms consisting of the product of an ordinate of the data array AA and two cosine terms, COSX and COSY. (M2 and N2, the numbers of terms stored in the arrays COSX and COSY are, of course, related to Y3 and N3, the numbers of columns and rows in the data array, by equations E.5 and E.6.) Note that when the size of the angles, KA and LA, exceed 360 degrees, origin-shifts are applied by means of "logical-IF" statements, minimising the numbers of cosines that need to be stored (see subroutine CCSXY). The multiplying factors on each coefficient are subsequently applied by halving the first and last columns, and top and bottom rows of the array COEF.

(d) Subroutine ORDCAL: This subroutine (figure E.12) reconstitutes ordinates BB•given the corresponding array of harmonic coefficients COEY, and is identical in logic to subroutine HARMCO. Subroutine ORDCAL was included in the harmonic analysis programme solely for the purpose of checking the calculations. SUBROUTINE ORDC AL ( COEF e M3 • N3 COSX • COSY • BB • M2•N2 ) DTMENSON-C-OEF-(M3•N3 ) e CO SX ( M2 ) COSY ( N2 Ye BB ( MaviN13) DO 450 IC1-21 eM3 no 4-6 =•1 BSUM=O .0 KB= -I DO 470 JE= 1•N3 LB I DO 480 IE=1 eM3 BSUM=BSUK-ECOEFr(zI E JE ) *COSX ( LB) *CUSP ( KB ) LB=LB+ IC-1 L F -(44 00=-48 0 L B =LB -M2 - 480-FONT-INUE K B=KB4-JC- I IF ( N2*GE•KB ) GO TO 4-70 KB=KB-N2 _ 470 CONT LNUE 460 BB ( I C•JC ) =B SUM

RETURN END FIG Subroutine .),..1)6AL