Optimization of water resources for irrigation in Dinajpur and Rangpur, East Pakistan.
Item Type Thesis-Reproduction (electronic); text
Authors Karim, Muhammad Abdul,1940-
Publisher The University of Arizona.
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Link to Item http://hdl.handle.net/10150/191493 OFTIMIATION OF WATER RESOURCES
FOR IRRIGATION IN DINAJPUR AND RANGPUR, EAST PAKISTAN
by
Muhammad A. Karim
A Thesis Submitted to the Faculty of the
CONNITTEE ON HYDROLOGY AND WATER RESOURCES In Partial Fulfillment of the Requirements For the Degree of
MASTER OF SCIENCE
In the Graduate College
THE UNIVERSITY OF ARIZONA
1968 STATEMEN'r BY AUTHOR
This thesis has been submitted in partial fulfill- ment of requirements for an advanced degree at The Univer- sity of Arizona and is deposited in the University Library to be made available to borrowers under rules of the Library. Brief quotations from this thesis are allowable without special permission, provided that accurate acknowledgment of source is made. Requests for permis- sion for extended quotation from or reproduction of this manuscript in whole or in part may be granted by the head of the major department or the Dean of the Graduate Col- lege when in his judgment the proposed use of thematerial is in the interests of scholarship. In all other instances, however, permission must be obtained from the author.
SIGD 4n
APPROVAL BY THESIS DIRECTOR
This thesis has been approved on the date shown below:
EUGEHE S. SIIVIIPSON Professor of Hydrology AC KNO WI FUDGMENIS
The author is greatly indebted to Dr. Eugene S.
Simpson, thesis director, for his valuable suggestions and guidance in accomplishing this task.
Special thanks are due to the Personnel of the
International Engineering Company, Inc., and the Direc- torate of Hydrology, East Pakistan Water and Power
Development Authority, Dacca, East Pakistan, for com- pilation of hydrologic data as needed for this study.
The author is grateful to Dr. Daniel D. Evans,
Chairman of the Committee on Hydrology and Water
Resources, and to Dr. Jerome J. Wright for their guidance and encouragement. The author is indebted to East Pakistan Water and Power Development Authority, and the United Nations
Food and Agriculture Organization for providing the opportunity and facilities for training the author in hydrology.
111 TABLE OF CONTEN'IS
Page
LIST OF TABLES vi
LIST OF ILLUSTRATIONS viii
ABSTRACT ix
CHABTER
I IWDRODUCTION 1
II GENTRAL DESCRIPTION OF THE AREA 4
Location 4 Topography and Drainage 4 Soils 6 Geology 6 Climate and Hydrology 7 Available Surface Water for Irrigation 11
Available Ground Water Storage . 13
III AQUIFER CHARACTERISTICS AND PERFORMANCE OF TUE WELL 16
Kozeny Method 17 Hantush Method 20 Kraijenhoff Method 22 Performance of Wells 26
Ill FUTURE CROP AND IRRIGATION NEEDS 32
Need for Irrigation 32 Irrigation Water Requirements 32
iv V
Page V T EFFECT OF A WELL ON THE FLOW OF A ]NEAREY STREAM 44
VI ECONOMIC SPACING OF WELLS 51 VII ECONOMY OF DEEP WELLS
VIII SUMMARY AND CONCLUSIONS 60
REFERENCES 63 LIST OF TABLES
Table Page
1 General Characteristics of the Material Penetrated in the Drillings 8
2 Mean Monthly Rainfall for Dinajpur, East Pakistan,1900-1962 9
3 Mean Monthly Rainfall for Rangpur, East Pakistan,1900-1960 10 Summary Results of Computing Evapotranspira- tion and Water Balance - after Thornthwaite and Mather(1957) 15
5 Transmissivity by Kozeny Method 20 6 Transmissivity by Hantush Method(196)4) 23
7 Transmissivity by Kraijenhoff Method(1958) 26 8 Summary Results of Transmissivity and Stor- age Coefficient of Aquifer 27
9 Suggested Future Cropping Patterns in Dinajpur and Rangpur Districts, East Pakistan 33
10 Monthly Consumptive Use Dinajpur and Rangpur Districts, East Pakistan 36
11 Consumptive Use of Water for the Suggested Future Crops after Blaney-Criddle(1966) for 100 Acres of Farm Land in Dinajpur and Rangpur, East Pakistan 37 12 Consumptive Use Based on Thornthwaite(19)48) in Dinajpur and Rangpur Districts, East Pakistan 38
vi vii
Table Page
13 Future Agriculture Production in the Project Area 42 Expected Annual Income and Benefits in the Project Area (per 100 Acres) )43
15 Estimated Annual Cost per Acre in Ground 5)4 Water Irrigation Project Dinajpur .
16 Estimated Annual Cost of Items for380 Tubewells in Dinajpur Districts 55 LIST OF ILLUSTRATIONS
Figure Page
1 Location Map of East Pakistan 2 2 Location Map of Groundwater Projects, Dinajpur and Rangpur Districts S 3 A. Hydrograph of Karatoa(1963-196)4) B. Hydrograph of Tangon(1962-1963). . . 12 Ease Discharge of Tangon River versus Time 25
5 Graph for Determining Potential Evapotrans- piration after Thornthwaite(19)48) . . . . 39 6 Rainfall and Irrigation Demand (based on 90%dry year and land use) after Blaney- Criddle(1966)
7 Graph for Determining the Portion of Well- Discharge Furnished by a Nearby River after Glover and Balmer(195)4) 8 Graph for Determining the Portion of Well- Discharge Furnished by a Nearby River after Hantush(196)4) )49
viii ABSTRACT
An area of about 300,000 acres in Dinajpur and
Rangpur districts will be irrigated by the combination of pumpage from the Tangon and Karatoa rivers and from about
1000 wells located between the rivers. It was calculated that the lowering of the water table 12-15 feet, as needed for irrigation, due to pumpage from the underground will stop or severely limit the accretion to the stream flow from underground. The Tangon will, in absence of accretion to the stream from the underground, cease to
flow during the irrigation season. Likewise the flow of Karatoa, in absence of accretion to the stream from the underground will be reduced to about 153 cfs which can be
used to irrigate 15,000 acres along the banks of rivers
only. The average discharge of 2.5 cfs over a 150-day interval of wells located 3000 feet apart will not exceed the average annual recharge of 2.8 feet to the aquifer from
precipitation. This particular arrangement was examined from the relationship of aquifer characteristics - trans-
missivity 120,000 gpd/ft and the storage coefficient0.20. The resulting calculated benefit-cost ratio of thebenefit
ix x of crops produced from assured irrigation to the cost of construction of wells275feet deep is2:1. If the average aquifer properties remain constant at depths greater than275feet, better economy will result by drilling wells deeper than275feet. CHAPTER I
INR0DUCTI0N
Iring between2005!arid 26°)Q!north latitude and88° 03 and92°)40' east longitude, East Pakistan is a major part of the Ganges-Bhramaputra-Megna delta which is roughly twice the size of. the Mississippi delta, Fig.
1. With about 1,000 people per square mile, the area has one of the densest rural populations in the world. The climate is characterized by a wet season from
June to October when average precipitation totals about
70 inches, and a dry season from November to February when precipitation totals about3inches. The months of March through May have a total rainfall of about 10 0 0 inches but temperature averages90F to95F; conse- quently these months have the greatest moisture deficiency. Until recent years, little or no attempt was made to irrigate during the dry months and the fields remained barren. A program is now underway to provide irrigation water from wells and streams wherever possible. Since many streams go dry from March toMay, the main dependence for irrigation water is on wells. Even for the perennial streams, only run-of--the-river water is available, since
1 2
GENERAL MAP
INTERNATIONAL BOUNDARY '- ' ---- DISTRICT BOUNDARY RIVERS AND STREAMS IMPORTANT CITIES STUDY AREA
SCALE .0 20 50
MILES
BOGRA SYLHET MYMENSINGH
R A.J S H AH I
MEGIIN
FAR I D PUR
GA RA I
S JESSORE
KHULNA
THE GA OF COX'S BAZAR BEN F BA'?
Figure 1.Location Map of East Pakistan 3 the country is too fiat to construct dams. On the other hand, the reserve of subsurface water is very large since the alluvium is thousands of feet thick (maximum thick- ness unknown). The development of the ground water basin constitutes the most important means to attain optimum utilization of the available water resources. It is anticipated that up to 300,000 acres of land will be irri- gated in this area by a combination of pumpage from the
Tangon and Karatoa rivers and from about 1,000 wells
situated between the rivers. Since stream discharge is supported by effluent seepage, there undoubtedly will be
a lessening of stream flow when the wells are pumped. This effect on stream flow will be most severe near the
end of the irrigation period when stream flow is lowest
and the demand is highest. This creates a unique prob-
lem: how best to supply a sufficient quantity of water at all points of the system, at the time of the greatest
demand. This, in turn, demands full knowledge of the operational characteristics and capabilities of the under-
ground reservoir and its relationship with the surface
storage. CHAPTER II
GENIRAL DESCRIPTION OF THE AREA
Location
The area to be irrigated by the pumpage from the underground reservoir and possibly pumpage from the
stream is shown in Fig. 2. This area is relatively high and most of it is
denied irrigation water from streams because of its loca-
tion beyond the reach of the surface diversion.
Topography and Drainage The area consists largely of the piedmont plain
built up by alluvial fan deposits originating in the foothills of the Himalayas, and carried by the rivers
Teesta, Karatoa and their tributaries. The land gradi- ent varies from three feet per mile to one foot per mile
in the north. Flatter slopes are found further south. Two large rivers flow through this area. Karatoa,
which has its source in India, is the larger. Midway between Panchgarh and Debigonj, it is joined by the Karam
River as shown in Fig. 2. Below Kansama where the river becomes known as Atrai, a portion of its flow MAHANANDA RIVER // TITALYA - 1 TALMA RIVER INDIA BHAJAN - PUR TEESTA RIVER / 4-GANGES PADM r- RIVER (BRANMAPUTRA- JAMUNA RIVER EAST KARATO RIVER K ARRIVER AM (J BURl TEESTA RIVER - CALCU \ 'j .' \ K A RATOA RIVER BAY OF BENGAL ( BLOCK C BLOC C) KHAN S AMA O 50 100 i '. (\c BLOC F BLOC K-. D BLOCK NIL PI-IAMARI SCALE IN MILES - - - PROJECT LOCATION BLOCK E TANGON RIVER B A MU M ESA RI RIVER -. INTERNATIONAL BOUNDARY LEGEND GAGINGWELLSLOWPROPOSED LIFT INSTALLED-BLOCKSTATION PUMPS NEW PROJECT LIMIT Figure 2. Location Map of Ground water Projects, Dinajpur and Rangpur Districts SCALE O 3 MR ES 6 9 2 6 branches southeast to Depa. The minimum recorded flow at
Khansama Station l42 is 273 cfs. The second river is
Tarigon, which rises just above the Pakistan border and
flows southward past Thakurgaon, where its recorded mini- mum dry weather discharge was60cfs on3May1963.
Soils
Soils in the area consist of comparatively young
stratified sediments ranging in texture from fine sand
to clay, but predominantly sandy loam. With the excep- tion of the coarse textured soils in some areas, all
are well adapted to a wide variety of crops.
Geology The area is underlain by alluvial sediments laid
down by the Karatoa River and its tributaries and adjacent streams, all of which drain the foothills and
the mountainous areas to the north. These streams carry
a heavy sediment load ranging from gravel and coarse
sands to silts and clay. Because of its position near the mountains where there are abrupt changes in grade,
sands and gravels tend to be deposited and the fine tex-
tured sediments are carried through. The total depth of the sediment deposit has not yet been determined. A
bore-hole 2150 feet deep did not encounter the bed rock. 7 Titalya area being near the foothills is underlain by relatively coarser sediments. Geologically, Thakurgaon and Rangpur areas of the project are of the same type; therefore, the underlain strata of the two areas are also alike.
Table 1, based on l2-I- logs of wells, located in four different segment areas (Fig. 2) around Thakurgaon, shows the general characteristics of the material pene- trated in the drillings.
Climate and Hydrology
Temperature. The cool weather within the proj- ect area begins in November and continuesto the end of
February. During this period, temperatures may vary from a minimum of 39°F. to a maximum of9°F. About
March the warmer weather arrives andtemperatures continue to rise about the middle of June. This is the hottest period in the year with temperaturesreaching 111°F.
From the middle of June to themiddle of October the mon-
soon or the rainy season occursduring which temperatures 0 0 vary from 5)-I- F. to107F. Rainfall. The rainfall from 1900-1962 in the area is given in Tables 2 and3. The average annual rainfall is70inches in
Dinajpur and87inches in Rangpur, but in90percent of 8
TABLE 1
GENERAL CHARACTERISTICS OF THE MATERIAL
PENETRATED IN THE DRILLINGS
Thickness of Ranges in Depth Sand or Block Number of Wells Gravel (Dinaj- of Well pur) Logs Maximum Minimum Maximum Minimum (Feet) (Feet) (Feet) (Feet)
A 16 286 238 280 208 B 6i 326 250 310 216
C la-I- 300 256 290 201
F )l3 318 256 315 233 9
TABT 2
MEAN MONTHLY RAINFALL FOR DINAJPUR,
EAST PAKISTAN,1900-1962
(INcHEs)
Month Maximum Minimum Mean 90%dryyra January 3.69 0.00 0.38 0.00 February 2.22 0.00 0.59 0.00 March 3.86 0.00 0.62 0.00 April 7.01 0.00 2.00 0.00 May 17.89 0.00 6.70 2.50 June 30.31 3.Ll l3J6 6.00 July 28.1)- )4.)49 15.20 8.00
August Li0.69 2.-I-2 13.09 5.25
September 35.12 3.85 11.76 5.25 October 22.97 0.0 5.33 0.55 November )4.62 0.0 .33 0.00 December 0.31 0.0 .03 0.00
Total Annual 69.!4
a. Rainfall equaled or exceeded that shown90percent of time. 10
TABLE3
MEAN MONTHLY RAINFALL FOR RANGPUR, EAST PAKISTAN,1900-1960
(INCHES)
Month Maximum Minimum Mean 9O dryyra
January 3.91 0.00 O.L!0 0.00 February 3.19 0.00 0.65 0.00 March 4.91 0.00 1.02 0.00 April 11.92 0.00 3.36 0.05 May 31.58 3.62 11.56 0.50 June 45.73 6.4 20.41 10.00 July 33.96 4.11 16.36 7.00 August 27.83 3.28 13.39 4.80 September 28.7)4 1.43 12.98 4.60 October 26.29 0.00 6.70 0.60 November 4.28 0.00 0.30 0.00 December 0.96 0.00 0.00 0.00
Total Annual87.19 a. Rainfall equaled or exceeded that shown90percent of time. 11 the time, the rainfall equaled or exceeded 22 and 27 inches
in ]Dinajpur and Rangpur, respectively.
Evaporation. The mean pan evaporation rate is53 inches per year. The computed potential evaporation rate
based on Thornthwajte (1914-8) is about66inches (see
Table 21-).
Humidity. The relative humidity of the area ranges
from30to 97 percent. It is minimum February through
April and maximum August through December.
Available Surface Water for Irrigation The rainfall in the area June through October
which is the monsoon or rainy season is generally suffi- cient in normal years to meet the irrigation needs. The stream runoff during this period is maximum but at the
end of the rainy season the stream flow gradually becomes
very low and the streams are fed byeffluent ground water (see Fig.3). The increase of stream runoff downstream in each stream in the absence of rainfall undoubtedly proves that the stream is fed by groundwater.
The gain of60of s during the dry period in the
reach of about 18 miles indicates that more than3cfs
of ground water seepage enters the streams permile
length. The drawdown caused by pumpage of all wellswill
probably stop the effluent seepage to the streambecause 12
850
750 NOTE: STATION 142Is 20 MILES DOWNSTREAM OF 141 650
0U- z 450 STATION 142 Lu A a: STATION 141 0r350 (I) 0 250 NOTE :STATION 286 Is 18 MILES DOWNSTREAM OF 284
ISO
STATION 286 B 5 STATION 284 DEC. JAN. FEB. MAR. APR.
Figure 3.A.Hydrograph of Karatoa (1963-1964)
B. Hydrograph of Tangon (1962-1963). 13 the ground water level atirrigation season will fall below the stream channel bottom.
In the years of normal rainfall, the minimum dis- charge of Tangon is on the order of 90 cfs of which 72 cfs is from ground water seepage in i8 mile reach of the river. Since planned well production will divert the ground water it is justified to conclude that there will not be a sufficient amount of water available for pumpage from the Tangon.
The minimum discharge of the Atrai-Karatoa is 273 cfs as recorded at Station 1)42 on 13 March 1959 to 30
March 1959. The reach of the river and its tributaries above
Station 1)42, which will be affected by the pumpage, totals about )40 miles.
Assuming that the river system in this area received about 3 cfs effluent seepage per mile of channel, the base discharge would be reduced by 120 cfs if all the ground water seepage is diverted to pumping wells. Hence, during low flow, only about 153 cfs would be available for runoff river pumpage.
Available Ground Water Storage
Ground water storage. The total area of the proj- ect is 300,000 acres. An average value of 0.20 was obtained for the coefficient of storage by Mawla (1968). l4
Exclusive of infiltration, lowering the water level would
release about60,000acre-feet of water per vertical foot of the aquifer.
Flow of ground water. The contour maps of high and minimum water level for1965-66 (FAO-l966)indicate the average seasonal rise of water in the area to be
about10-12feet. The water table contours show that throughout the year, except during the high flood period,
the ground water discharges to the streams. The average discharge of the ground water to the streams is about
)-l- cfs per mile length of channel.
Ground water recharge. Based on the daily water balance after Thornthwaite and Mather(1957),the yearly recharge to the water table by vertical percolation of rainfall was estimated to be about2.75feet, for the water year1965-66which was a year of nearly normal
rainfall. Chemical quality of water. Water samples were obtained at the conclusion of drilling some of the400
wells in the area and analyzing in the laboratory. Dis-
solved solids range from 140 to1,065F.F.M. of twenty-
one samples. Total hardness ranges from 40 P.P.M. to80 P.P.M. and chloride and sulphates content ranges from 4F.F.M. to12 P.P.M.,the average being less than8P.
P.M. The carbonate and bicarbonate content ranges from 15 nil to500 P.P.M.while calcium content ranges from3 P.P.M.to13 P.P.M.
TABLE L
SUMMARY RESULTS OF COMPUTING
EVAPOTRANSFIRATION AND WATER BALANCE - AFTER TRORNIEIWAITE AND MATRER(1957)
Station: Thakurgaon Amount Dinajpur in 1965-1966 Inches
Rainfall 83 Potential evapotranspiration 66
Actual evapotranspiration 35
Surface runoff 15 Recharge to ground water table 33 CHAPTER III
AQUIFER CHARACTERISTICS AND PERFORMANCE
OF THE WELL
The worth of an aquifer as a source of water supply depends largely on two inherent characteristics: its ability to transmit water, and its ability to store water. Furthermore, quantitative knowledge of these characteristics facilitates calculation of hydrologic entities such as recharge, leakage, and evapotranspira- tion. It is recognized that the two characteristics
referred to as the coefficients of storage andtransmis- sivity, generally provide the very foundation on which
quantitative studies are constructed. Within the science
of ground-water hydrology, ground-water hydraulicsmethods
are applied to determine theseconstants from field data. Field data refer to bore-hole logs,pumping test
data and geophysical investigation data. The selection of equations or procedures to be used foranalysis of the
data is governed largely by the physicalconditions of the
aquifer, in so far as they establish hydraulicboundaries
of the system. The variability in the coefficientsof
16 17 storage and transmissivity combined with the irregulari- ties in the shape of the flow system encountered in many ground water studies precludes uninhibited support of calculated coefficients on vague or meager data. The number of equations available has grown rapidly and steadily during the past few years but the applicability of those equations for solutions of the problem requires idealization of the physical phenomena associated with ground water movement (above discussion modified from
Ferris, and others, 1962). Judging from the boundary conditions of the aqui- fer and the nature of the pump test conducted in the project area, ]Dinajpur and Rangpur, it seems that the following methods of analysis can be applied.
Kozeny method (Muskat 1937, p.27)4)
= T(sw-C2)K (3.1) 1/2 2ct[1 + 7(w() ) cos irc. where K = 2.30 Log 10 r /r e w
= discharge of wells,cfs
T = transmissivity,ft2/sec
= drawdown in the well,ft
C = screen loss constant, sec25/ft
a = percent penetration(equals screen length
divided by average thickness ofaquifer) i8 b = average saturated thickness of aquifer, ft
r radius of well, ft re = radius of the cone of influence (distance
from the pumped well to the locus of zero
drawdown)
The average well depth is 275 feet of which the upper80feet (from surface to a depth of80feet) is blind pipe. The remaining part of the well consists of well screen of total length 130 ft placed against coarser permeable materials and about 65 ft of blind pipe placed against layers of silt and clay found in between the perme- able zones. The upper 25 ft of the aquifer consists mostly of clay and silt and it has not been considered in the satur- ated thickness of aquifer. Hence the total effective thickness of aquifer is 250 ft. Water levels drop to 20 to 30 feet below ground surface after a few hours of pumping. Pump tests were conducted for about 12 hours duration each. Near the end of each of the pump tests there was almost no change in water level. Hence Kozeny's formula can be used to analyze the pump test data to find transmissivity of the aquifer after assuming the aquifer is homogeneous, isotropic and of infinite areal extent, and the pumping system reached steady state. The average rate of pumping can be considered to be constant and the 19 flow is radial. The radius of the cone of influence has been taken as 1000 ft. The well is gravel-packed. The
radius of well r equals the radius of the bore holes.
The well loss for each well was determined by a step
drawdown test analysis.
According to assumptions, the value of K in equa-
tion (3.1) is calculated as follows:
1/2 130 (0.92 ) x [1 x cos 2x250'xl30 2xl30) 1000 2.30 Ig 100.92
= 0.55
Hence the equation (3.1) is reduced to
T = ft2sec 0.55(s-c2) w
or 1.17 x106Q T= gpd/ft (3.2) (s -C) w Seven pump tests (one in each block) were analyzed and the results are given in Table5. In computing percent penetration a. in the formula
(3.1), 130 feet of screen length was considered to be one
continuous length at the top of the aquifer. Since the well has screen and blind pipe placed against the layers
of more permeable and less permeable zones, respectively,
the convergence loss will be less than provided for in
the formula. The computed transmissivity, therefore, 20
TABLE 5
TRANSMISSIVITY BY KOZENY METHOD
(MTJSKAT 1937, p. 27k)
Location Block Well No. Transmissivity in (gpd/ft)
Dinajpur A 98 1.50 x 10
Dinajpur B 170 1.00 x 10
Dinajpur C k6 1.22 x 1O
Dinajpur D 327 1.37 x 10
Dinajpur E 2k0 1.25 x 1O
Dinajpur F 205 i.k5 x lO
Dinajpur G 33k 1.22 x 1O
Average 1.30 x 10
probably will be a little high. The average transmissivity
of seven tests is 130,000 gpd/ft.
Hantush method. The drawdown "s" at the face of apumping well
partially penetrating the aquifer accordingto Hantush
(196k):
(3.3) S 4r'N (rw2/krt, al/ru) 21
The equation is valid when
t Sb (1-l/2b)2/5K where Q, = discharge of well in cfs
Kr horizontal hydraulic conductivity ft/sec = vertical hydraulic conductivityft/sec
1 = length of screen
b = thickness of aquifer
t time since pumping started in sec
T/S
S storage coefficient of aquifer
a = (K/K)
rw radius of well
The depth of basement rock in Dinajpurwell field has not yet been determined. It is generally believed that the aquifer is very deep and may be morethan 1000 feet, hence the depth of basement rock istaken to be
1000 feet (arbitrarily). The total depth of a typical well is 280 feet of which the upper80 feet consist mostly of clay, silt, and fine sand and arecased off with blind pipe. Most of the remaining 200 feet depth of the well is screened against mediumto coarse sand.
Pccording to Walton (1962),tUnconfined Stratified sediments often react to pumping for a short timeafter
pumping begins as would an artesian aquifer. Gravity 22 drainage is not immediate but water is released instantan- eously from storage by compaction of the aquifer andits associated beds and by expansion of wateritself."
The pump test in Dinajpur well field wasperformed
in steps. Firstly, with low rate of pumping, therate was increased in steps. During the low rate of pumpingat the
very beginning of the test,well loss was negligible and
the aquifer could be considered as aconfined one overlain
by a semi-pervious layer80feet thick as described above. Making the above assumptions andboundary condi-
tions, the equation (3.3) was appliedto analyze the
seven sets of pump testdata by trial and error procedure
and the results are given inTable6. Kraijenhoff method According to Kraijenhoff(1958),the "tail reces-
sion," of the base flow of a stream maybe approximated
by the following equation = constant -t/j (3.)
or,
2.303 A log 10 where t = time since beginningof wet season(approximately) (2a)2 S j = reservoir coefficient
a = distance from groundwater divide to stream S = coefficient of storage of aquifer
T coefficient of transmissivity of aquifer 23
TABLE6
TRANSMISSIVITY BY HANTUSH METHOD (196)-i-)
Location Block Well Conductivity Transmissivity No. K ft/sec gpd/ft when B = 1000
1 2 3 4 5 Dinajpur A 98 4.5 xl0 2.9 xl0 Dinajpur B 221 5 xl0 3.2 x10
Dinajpur C 46 5.6 xl0 3.6 xl0 Dinajpur B 327 5 x10 3.2 xl0
Dinajpur E 240 6.5 x10 4.2 xl0
Dinajpur F 250 7 xl0 4.5 x10 Dinajpur G 334 5 xl0 3.2 x10 Average 5.5x l0 3.5x 10
Equation (3.4) is a simplified formof a more gen-
eral equation which involves the sum of aninfinite series
of terms. After the end of the wet season,and after a sufficient time has elapsed, all terms ofthe series
except the first may be neglected andequation (3.4)
results. Applying the Kraijenhoff criterionthat eqn. (3.4) may be used when the second termof the series is
less than one percent of the firstterm, it is calculated
that in the present instance this occurswhen t= 700days 21
(approximately). To make this calculation it is necessary to use estimates of S and T obtained previously. To a less exact, but still useful approximation, equation (3.2-i-) may be applied when t= 330days, or about 210 days after the end of the wet season. In other words, equation (3.!1) applies when the log of the discharge plotted against
time results in a straight line. This is seen to occur
(Fig.Li-) toward the end of the dry season. Using the slope of this portion of the curve, it is calculated that j = 2.86 x l0. Assuming S = 0.20 and for various values
of a, we may then calculate T. These calculations are given in Table7. The results of analysis for transTrnissivity coef-
ficient of the aquifer by Kozeny's andKraijerthoffts methods (Tables5 and 7)are consistent, which mayindi- cate that most of the base flow is derived from the upper
200 or300feet of aquifer. The Hantush method gives a better estimate of the true transmissivityonly, if the aquifer properties remain constant with depthand the
assumed depth of 1000 ft is approximatelycorrected. The
value of specific capacity was estimated byMawla (1968)
to be 0.20 based on lithologic analysis of75bore holes
in the region. He also estimated the transmissivity of the aquifer range from 80,000 to 12,000gpd/ft on litho-
logic analysis as well as on analysis of pumptest data 0U-Cf.) 200 z (00 LOG 80 70 I (40 mUU) SLOPE LOG (40 JO !Q 70 3.5 x I (0 30 Figure 4. 50TIME IN DAYS STARTING FROM DECEMBER I, 1963Base Discharge of Tangon River70 versus Time 90 (10 (30 5O 26
TABLE 7
TRANSMISSIVITY BY KRAIJENHOFF METHOD (1958)
2 Distance a a Slope T in gpd/ft in whenS=0.2O 2 ft ft
15,000 9 x l0 3.5 x 10 1.05 x 10 i6,000 1.03 x 1.23 x 10
17,000 1.13 108 1.37 x l0 i8,000 1.23 i.8 x 10
on the Theim formula. The results of analysis fortransmis- sivity and storage coefficient aresummarized in Table 8.
Performance of Wells The discharge of wells used forirrigation should be such that each well cansupply water as needed but it does not cause permanentundesirable effects. Continuous over-draft of ground water in excess ofrecharge will cause permanent undesirable effects, butover-draft during
severe draught, which canbe replenished duringwet cycles
of climate, may not causeundesirable effects. In
Dinajpur and Rangpur districts therainall is 70-80 27
TABTE 8
SUMMARY RESULTS OF TRANSMISSIVITY
ANID STORAGE COEFFICIENT OF AQUIFER
Method Transmissivity Storage Remarks Analysis in gpd/ft in Co e f f ic i e nt (after) thousands
Mu s kat 100- 150 Average (1937) T = 1.3 x 10 gpd/ft
Hantush (l96Ll) 300-LISO 0.01 - 05 Earlier pump test data analysis depth of basement b - 1000 ft (arbitrarily)
Kraijenhoff 100-150 T = 1.23 x lO (1968) 10 gpd/ft when a = 1600
Mawla (1968 70-108 For 250 ft (Litho logic depth of aquifer
Mawla (1968) 80-120
(pump test) 28 inches/year in normalyears and the minimum rainfall recorded in 60 years of record is about 15 inches in
Dinajpur and 18 inches in Rangpur. Recharge to ground water is favored by two factors: (1) small dikes which surround the segmental plots can hold3to LIinches of water for a long time allowing extra time for rain water to percolate into the soil, and (2) the soil is mostly sand and sandy loam which have high infiltration capaci- ties. In normal years of rainfall, irrigation is required mainly from November through April in an amount estimated to be about 2.5 feet and the recharge was estimated 2.75 feet (Table LI-). The development of a well field will probably cause induced recharge to the underground which otherwise would be lost by discharge to the river. Hence
it is probable that there will be recharge to the ground water in normal years in excess of irrigation withdrawal.
As a rough check on the 2.75 feet of recharge estimated by Thornthwaite method, we see that the rise in the water- table during the wet season is about 12 feet. If S = 0.20, this rise represents a minimum of 2.4 feet of recharge.
The latter figure does not represent total recharge because ground water is continuously being discharged to the streams and lost by evapotranspiration during the recharge period. The two estimates are in accord with one another. Therefore, an average of 2.75 feet of 29 recharge can be taken as available forpunipage from the aquifer in order to maintain the source indefinitely.
The duration of pumping will vary with climatic variations. During wet years it may be less than 100 days/year but in draught it may be equivalent to 200 days/year. The average duration of continuous pumping is 150 days/year. The radius of influence due to pumping continuously for 100, 150 and 200 days will extend about
)-l-700, 5700 and 6000 feet, respectively, as estimated according to 0.3Tt 2 0 r = e S
(Ferris and others, 1962, p. 100). The values of T and S
(1.20 x 10 gpd/ft and 0.2, respectively) were taken from the previous calculations. Hence there will be over- lapping of the area of influence of wells if they are located 3000 ft apart in a rectangular grid. The draw- down at any point in the area of influence caused by the discharge of several wells is equal to the sun of the drawdown caused by each well individually. According to
Theis (19)40), the interference of eight wells located
3000 feet apart in rectangular grid the drawdowns at the center-well after continuous pumping for 100, 150 and 200 days at a rate of 1100 gpm are calculated as follows: 30
Drawdown after 100 days of continuous pumping: ul6 s {w(u1) + w(u2) + w(u3)} (3.6) where w(u1), w(1J2) and w(U3) are the well functions ofU for the pumping well and for wells at 3000 and)4250 feet, respectively, away from it; other symbols arepreviously
defined. 1.87Xrx S 1.87 x .81 x .2 U1 - 2.52 = Tt 1.20 x 10x 100
Therefore, (Ferris and others,1962, pp. 96-97),
= 16.90
1.87 x r22x S 1.87 x(3000)2x 0.2 l0_l U2 - 2.8 x = Tt 1.20 x 10 x 100
= 0.96 hence w(U2) = .96 x = 3.8k
= 0 since area of influence in100 days is less than L250 feet.
Therefore,
ll.6 x 1100[16.90 + 3.8k] = 21.8 feet 5w= 1.20 x 105 Drawdown after 150 days of continuouspumping:
1.87 r2xS w 1.87 x .81 x 0.2 x108 U1- Tt 1.20x10x1507
= 17.3
1.87Xr2X (3000)2 1.87 x X0.2= 1.9 x i0 Tt l.20xl05x150
= 1.26 hence )4w(u2) = 31
1.87Xr3x S 1.87 x(4250)2x 0.2 U3 4.1 x Tt 1.20 x 10 x 150 w(u3) = 0.69 4w(u3) = 2.76
Substituting the values of W(TJ1), w(u2) and W(U3) into
equation (3.6), the drawdown "s at the center well is
26.1 feet and the drawdown after 200 days of continuous
pumping is found by similar calculations to be28.8 feet. Similarly, assuming the drawdown curve is a seg-
ment of parabola, the drawdown of 26.1 feet ateach well
face after 150 days of continuous pumpingwill result in
the dewatering of approximately14 feet of aquifer aver-
aged over the entire aquifer. CHAPTER IV
FUTURE CROP AND IRRIGATION N}EDS
Need for Irrigation
The project area is suitable for plant growth the year round. However, rainfall does not satisfy the moisture requirements except in the wet season. Based on the90percent dry year data of precipitation given in Tables2and3,the project area has no effective pre- cipitation from October through April. During the rest of the year the rainfall is also not sufficient for all crops. With irrigation water assured, the land of the project area can be placed in full production and can raise two or even three crops in a year (Table9).
Irrigation Water Reauirements Consumptive use includes all transpiration
and evaporation losses from the land on which thereis
growth of vegetation of any kind plus evaporation from bare land and from the water surfaces. It is the best
index of irrigation requirements. The irrigation
requirement is the amount of water exclusive ofprecipi-
tation that is needed for production of crops. It
32 33
TkBLE9
SUGGESTED FUTURE CROPPING PATTERNS IN
DINAJPUR AND RANGPUR DISTRICTS, EAST PAKISTAN
CROPPING CALENDAR
Jan Feb March April May June July Aug Sept Oct Nov Dec
a b Pulse Aus Tr Ibnan
Pu is e
Pulse and oil seeds Tr Arnan
Pu is e and AusC Oil Seed Wheat, veg, Wheat, veg, tobacco tobacco and and maize Aus or jute maize Ground nuts and Ground Aus or jute spices Fruit
Sugar cane
a Pulse = the edible seeds of variouslegumiflous crops
b Tr Aman = Transplanted rice
c Aus = a kind of rice
d Ground nuts = seed with a separablerind or shell and interior kernel (onions, garlic,etc.) includes plant transpiration, evaporation, deep percola- tion and other economically unavoidable wastes. Many factors operate singly or in combination to influence the amount of water consumed by plants; these include: climate, water supply, soil and topography. Of the climatic factors affecting the plant growth, the temper- ature and precipitation undoubtedly have the greatest influence. Pmong the various methods for calculating consump- tive use, the Blaney-Criddle formula(1966)and a pro- cedure outlined by Thornthwaite(19)-I-8)for determining the potential evaporation are most commonly used. The
Blaney-Criddle formula is expressed mathematically U in which U is the consumptive use of crops in inches for any period, F is the sum of themonthly consumptive use factor for that period (sum of the products of mean monthly temperature and monthly percentage ofdaytime hours of the year), and K is an empiricalcoefficient (for growing season) determined for a particular cropin
some locality. The values of the coefficient K for dif- ferent crops were used from experimental farmirrigation
data of East Pakistan and other countries ofthe world.
Based on the90percentage dry year data of precipitation (Tables 2 and3),Blaney-Criddle and Thornthwaite formulae have been used to calculate the 35 water requirement of the suggested future cropping pattern of the area of project (Tables 10, 11, and 12). Thorn- thwaite1s method can be expressed mathematically in simpler form:
I=(t/s) - 1
e=1.6 (10 t/3)a where I=heat index
e=potential evapotranspiration (1)2 a=0.000000675 (i) - 0.000077 + 0.01792 I 0.L9239
t mean monthly temperature In Blaney-Criddle method, the waterrequirements
for plant growth is given by
Wr =U-R and by Thornthwaite method
Wr =e-R where Wr=water required for irrigation R=effective rainfall By Blaney-Criddle method, totalrequirement of water for irrigation, based on the 90 percent dry yearof precipita-
tion and 65% efficiency of the pumpingsystem, was found
to be 5.1 acre-ft/acre/yr. By the Thornthwaitemethod (Table 12 and Fig. 5), irrigation demand wasestimated to
be 5 acre-ft/acre/yr. Hence, five feet of water peryear 36
TASLE 10
MONTHLY CONSUMPTIVE USE DINAJPUR AND RANGPUR
DISTRICTS, EAST PAKISTAN
Hour Percent Mean F Consump-Monthly per of temp. tive Irriga- day Annual Us e t ion °F Factor(K) (inches..)
January 10.8 7.39 64.1 4.80 0.50 2.40 February 11.3 7.76 66.8 4.76 .60 2.86 March 12.0 8.23 76.3 6.41 .70 4.50 April 12.7 8.74 83.4 7.21 .70 5.05 May l3.-!- 9.16 85.3 8.00 10 8.00 June 13.7 9.38 83.7 7.79 10 8.00 July 13.5 9.28 83.8 7.95 1.20 9.55 August 13 8.92 83.4 7.59 1.20 9.1 September12.4 8.49 83.1 6.96 1.40 9.80 October 11.4 7.83 80.0 6.45 1.0 6.45 November10.9 7.50 72.2 5.31 1.0 5.31 December io.6 7.32 66.3 4.87 .50 2.43 CONSUNPTIVTE USE OF WATER FOR THE SUGGESTED FUTURE CROPS AFTER BLNEY-GRIDDTR TABLE 11 Crops and Land Use (1966) FOR 100 ACRES OF FARM LAND IN DINAJPUR AND RANGPUR, EAST PAKISTAN % krea SeasonGrowingLength of F(Sea- cientCoeffi- K U =(inches) rainfallEffective farmrequiredTotal head- Water at 65 12sonal) (Sea- 5 ona 1) inchesin gate100(acre-ft) per acres TobaccoVegetablesPulseWheat oil (winter) seed 354 10/1-3/3110/1-12/1-3/15 3/31 21.2 .70.60 1)4.8 7.2 86.0011.50 6.809.00 MaizeJuteAusGround (rice) Nuts & spices 10 1560 3 Lj/1)4_8/3110/1-3/314/1- 7/15 21.227.5319.60 1.0 .70 24.7317.6414.8 12.20 7.5 101.00 30.4023.00 6.80 TrAnianSugarFruits Cane (rice) 55 55 Whole7/15Whole - 12/15 yr. yr. 7024.90 1.40 .70.80 50.4044.131.32 Total 15.7515.75 8. 512.30191.00 26.8020.20 38 TABLE12
CONSUMPTIVE USE BASED ON THORNTHWAITE(19)1-8) IN DINAJPURAND RANGPUR DISTRICTS, EAST PAKISTAN
Jan. Feb. March April May June July Aug. Sept. Oct. Nov. Dec. Yearly
1. Heat Index 17.4 19.3 24.6 28.3 29.6 28.6 28.5 28.3 28.6 26.7 22.2 1.9 138.8 2. Monthly Air Temp °C 16.6 7.7 12. 13.6 14.6 14.0 13.8 13.6 12.5 8.4 7.5 3. SI. potential Ev 3.4 5.3 10.5 15.0 15.90 15.20 15.17 15.0 15.20 13.70 8.0 5.20 4. Correction Factor(26°N) .92 8.8 1.03 1.06 1.15 1.15 1.17 1.12 1.02 .99 .91 .91 5. P.E. (cm) 3.12 4.6 10.80 15.90 i8.4o 17.50 17.70 16.80 15.50 13.60 7.30 4.75 i46.00 6. P.E. (inch) 1.24 1.83 4.25 6.23 7.22 6.90 6.96 6.61 6.10 5.35 2.87 1.87 57.5 7. Rainfall (inch) .00 .00 .00 .00 2.50 6.00 8.00 5.25 5.25 .05 .00 .00 8. Effective precipitationa .00 .00 .00 .00 2.20 3.40 3.40 3.30 3.30 .05 .00 .00 9. Irrigation demandb(inches) 1.24 1.83 4.25 6.23 5.00 3.50 3.56 3.31 2.80 5.30 2.87 1.87 a Rainfall corrected mainly for surface runoff b Row6minus row8 c Total irrigation demand feet = x - = 5.0 100° -1000 TEMP °C UNADJUSTED PE. 28.5027.026.529.0027. 05 0 15.5415.17(cm)14.3713.9513.50 200300 26.5°C 305030.0029503131.0° 5° 17.0716.8016.5216.2115.89 100 100138. 32.5032.0°35.0°34.5°335033.00 18.2918.1817.9017.3117.7217.53 0 Figure 5. UNADJUSTED POTENTIAL EVAPOTRANSPIRATION20 PE. (mm)Graph(1948). for Determining Potential Evapotranspiration after Thornthwaite40 60 80 100 200 400 800 1000 240
can be taken for the estimation of the requirement of water for irrigation in the project area.
Based on the 90 percent dry year of precipitation
(Tables 2 and 3), and land use (Table 11), a monthly rain-
fall-irrigation demand was plotted (Fig. 6) after Blaney-
Criddle (1966). In computing irrigation demand, long-term
average values of monthly temperatures were used as were
rainfall values of 10 percent driest year. Strictly speak-
ing, this does violence to the Thornthwaite method, but
it is believed to give an approximate value of maximum
irrigation demand. Nonetheless, as was calculated in Chapter II on a daily basis for 1965-66, the potential
evaporation was 66 inches (Table 24). This is not far dif-
ferent than the figure of 57.5 inches obtained by average monthly temperature (line 6, Table 12). With the supply of a sufficient quantity ofwater
in dry seasons, it is possible to grow crops in theproj-
ect area throughout the year (Table 13) and thenet income
from the crop production is Rs 257 per acre(Table 124). I09 9.55' 9.55" 9.1" 8 8.0" 8.0" 8.0 V IRRIGATIONRAINFALL DEMAND LEGEND 67 6.0 A S 4.5. .4 4V 525 4 525" 45" 4.23" 4 2.86" 3.0 V .4 23 2 40 / V I 2.43" P1 // 0 Figure 6. JAN FEB afterRainfall Blaney-Criddle and Irrigation (1966) Demand (based MARon 90% dry year and land use) APR MAY / JUNE JULY AUG 0 SEP OCT NOV DEC l-2
TABLE 13
FUTURE AGRICULTURE PRODUCTION IN THE PROJECT AREA
Type of % of Yield Production Value Gross crop area Mds/ MdSa Rs/Md Value Acre in b rupee,
Tr I\nian 55 26 1,11-30 12 17,160
Aus 60 18 1,080 12 12,960
Jute 15 20 300 22 6,600
Pulse (fodder) -i-o 100 4,OOO 1 1I,OOO
Pulse (grain) 10 10 100 15 1,500
Mustard 15 6 90 32 2,800
Wheat 5 15 75 18 1,350
Vegetables 1-i- 75 300 10 3,500
Maize 3 20 60 l-1- 8)-i-o
Ground Nuts 5 12 60 31
Chilis and 5 10 50 80 4,OOO onions
Tobacco 3 15 -I-5 100
Fruit 5 170 850 10 8,500
Sugar Cane 5 800 )-!-,000 2 8,00.Q
23O Gross Value per Acre Rs 77,070
Rs 771.00
a 1 Md 82 lbs. b l = Rs )J.75 L.3
TABLElL
EXPECTED ANNUAL INCOME AND BEPEFITS IN
THE PROJECT AREA
(per 100 ACRES)
77070a Gross Income after project Table 13 Rs
Gross Present Annual Income 25642.
Gross Annual Benefit Rs 5l,)-l-28
Net Annual Income (1/2 gross) Rs 25,71!1-
Benefit per acre = Rs 257
a l = Rs )L75 CHAPTER V
THE EFFECT OF A RELL ON TIIFLOW OF A
NEARBY STREAM
The prospective well fields of Dinajpur and
Rangpur districts, Fig.2,lie along the streams - Karatoa and Tangon and their tributaries. The increase of runoff (hydrograph Fig.3)downstream of the river Karatoa and the Tangon simply represents anaccretion from effluent ground water flow, and it occursbecause the water table is higher than the streamlevel. The accretion from effluent seepage to the streamis at minimum rate of three cfs per milelength of stream
(Fig. ). Heavy and continuous pumping forthe longest dry periods in this area will lower the waterlevel below
ground surface to about25-30feet, which is certainly below the minimum water level in the stream. At that
stage, accretion from effluent groundwater to the
stream will cease completely. Furthermore, a well adja-
cent to a river takes a portion of itssupply from the
river. When pumping of a well near a riverbegins, water is at first withdrawn from the water table inthe
LL immediate neighborhood of the well. As the zone of efflu- ence widens, however, it begins to draw part ofits flow fron the river. Making a certain idealization of the actual hydraulic system in the field, two mathematicalmodels were prepared - one according toGlover and Balmer (195)4) and the other according to Hantush(196)4) to find the quantity of stream water that will be tappedby wells
pumping near the stream. According to Glover and Balmer,
the part of the total flow of thewell which comes from
the river is given by: t)l/2} q/ = 1 - P[x/ (5.1)
where q = the flow(ft3/sec) taken from a river at a dis- tance x feet from the well
flow of the well inft3sec
P(z) ={2/()1 2 exp(-v) dv (5.2) S
This is a probabilityintegral which has beenextensively tabulated in form of the upperlimit of z" (U. S.
Federal Works Agency,19)41; also Jahnke and de 19)45).
1/2 v = x/()4 t)
= KD/S (5.3)
D = saturated thicknessof the water bearing formation K = permeability of the aquiferft/sec S storage coefficient or effective porosity
t time from the beginning of the pumping in sec.
Taking KD T = 120,000 gpd/ft, the coefficient of storage 0.20 and the time 100 days and 200 days, the part of total flow of the well which will be expected to come from stream has been calculated. A distance from the strean against a part of the total flow of the well was plotted in Fig.7. A second mathematical treatment of the stream depletion was made assuming that layers of fine sand,silt and clay above well screen can be combined to asingle layer of uniform thickness b1, and K1, the hydraulic con- ductivity of this layer which is considered to be asemi- pervious layer. Then the rate q of the river depletionat the end of a continuous pumping ?Tt is given by Hantush(196)1)
q = [exp(-x0/B) erfc[U0 - (x0/2B)/U0]
+ exp(x0/B) erfc[U0+(x0/2B)/U0fl (5.14) where q = discharge of well inft3/sec
x = distance from the stream 0 B = (Kb/K1/b1) = (T/K1/b1)
T = transmissivity of the mainaquifer inft2/sec = coefficient of leakage= 5x l0 sec (assumed) 47 Uo = xo/ (4 t)l/2 a = T/S
The equation (5.4) has been solvedfor different dis- tances of the well from streams and theresults plotted (Fig.8).
Although the two methods of analysis give almost the same percentage of water that can be taken by wells from the stream, the assumptions made for idealization of the hydraulic system in order to simplify the problem to make it amenable to mathematical treatment may introduce some errors.
It can be seen in Figs.7and8that at the end of the longest period of continuous pumping in the driest year only 0.2 to 0.3 fraction of total well discharge will be taken from the stream for wells placed one mile away from the stream. During normal years of rainfall, the continuous pumping period will be shorter than that of the
driest period and the rate of pumping will be less. The areal extent of effluence of the pumping will be less and virtually no water from the stream will be taken by wells placed a mile away. However, even at this distance, a
line of pumping wells probably would intercept the seepage that otherwise would go to the stream. Without accretion from effluent ground water flow, the base flow of the
Tangon even in a year of normal rainfall is not sufficient IS ASSUMPTIONS0.20I.20x105 gpd/ft a:0 ECONOMIC SPACING OF WELLS From experience in other areas of East Pakistan it had been decided that each 2)1-0 acres would be served by one well. As per irrigation demand given in Chapter IV, it is calculated that each well would have todis- charge about 2.5 cfs in dry years to satisfythis demand. Although it seems clear that this spacing andyield of wells is in accord with aquifer capacity, itis not known whether or not it is optimum spacing in formsof minimum cost. To explore this problem, the methodof Hantush (1961)may be applied. In other words, if the well spacing were reduced there would be anincrease in the cost of power because the increasedmutual interference of wells would result in greaterlift but a decrease in cost of power transmission linesbecause the wells would be closer together. The cost of distribution fl canals would not change much and may beneglected. The equation of Hantush is asfollows: N t1 C=Ctôm3Cfl Dndt (6.1) n=l 51 52 in which C total yearly cost of operation as affected by well interference Ct= capitalized cost, in unit currency per year per unit length of pipe line, for maintenance, depreciation, original cost of pipe line, etc. C" = cost, in unit currency, to raise a unit vol- ume of water consisting largely of power charges, but also properly including some additional charges on equipment Dn = total drawdown in the nth well causedby pumping all other wells ôm = length of connecting pipe linesbetween wells and the power installation N = member of wells in operation = discharge of thenth well in unit volume per unit time = period of continuouspumping in time units m = "spacingparameter" which is the distance between any two wells; otherintervening distances are expressed interms of m o = a constant whichwhen multiplied by m, the length of connecting pipelines results In this case we do not considerthe cost of pipe line, but rather the cost ofelectrical transmission line. There are no pipe lines and thecost of distribution 53 may be neglected. The first term on the right-hand side of equation (6.1) refers to the cost of transmission lines and the second term refers to the cost of power to provide the necessary pumping lift. By differentiating this equation and evaluating it at zero, we may solve for the optimum distance m for various aquifer characteristics. The basic economics used in the analysis are given in Tables 15 and 16. The calculations which are not given in detail herein show that the optimum spacing parameter mtl is 3,270; 3,800; and 2,680 feet when "T1' is 1.2 xlOb, 1.0 x l0 and 1.5 x l0 gpd/ft, respectively. It is evident from these results that the bestestimate we have for transmissivity gives an optimumspacing very close to that decided upon (Chapterill). However, it is also evident that the optimum spacing issensitive to the errors in the estimateof transmissivity. If it should turn out that transmissivityis significantly different than 1.2 x 10 gpd/ft, the optimum spacing of wells would change accordingly. The problem should be keptin mind as the program develops. TABLE 15 ESTIMATED ANNUAL COST PER ACRE IN GROUNDWATER IRRIGATION PROJECT DINAJPUR It em Amortiza- Replace - OperationTotal in tion and ment and Main- Rupees Interest Reserve tenance Electric Tubewells 225, 000 a. 380 tube- 2,390,000 575,000 1,260,000 wells and accessor- 270,000 i,kO5,000 ieS 910,000 225,000 b. Power Plant 175,000 1,715,000 c. Transmis- 1,310,000 230,000 sion line d. Power )4,155,000 )4,l55,000 (fuel) 126 Cost per acre 55 TABLE 16 ESTIMATED ANJNTJAL COST OF ITEMS FOR 380 TUBEWELLS IN DINAJPUR DISTRICTSa It em Amount in rupees Power Plant: Amortization and interest operation Rs l,-1-05,0OO and maintenance including reserve for replacement of parts Transmission line (264.5 miles) Amortization and interest operation Rs 1,715,000 and maintenance including reserve for replacement of parts 3 Equipment: Pumps, motors, etc. Amortization and interest operation Rs 1,6)48,000 and maintenance including reserve for replacement of parts )4 Power - charge Rs 4,155,000 203,000 5. Cost of distributing canals Rs (139 miles) a Condensed from EPWAPDA (1965) b $1.00 = Rs )J.75 CHFTER VII ECONOMY OF DEEP WELLS Another aspect of the cost minimizingproblem is that of the depth of the well related to thetotal depth of aquifer. The total depth of the alluvialaquifer in the Rangpur and the Dinajpur districtsis not known except that it is much deeper than275feet. If we assume a total depthof 1,000 feet, calculations maybe made to determine the costadvantage (ordisadvantage) of installing deeper wells. A deeper well wouldhave higher initial and maintenance cost,but the power cost for pump- ing a given quantity ofwater would be less. By deepening each well, the amount ofdrawdown due to mutualinterfer- in the pre- ence would bedifferent than that discussed of vious chapter, and hencewould affect the calculation should optimum spacing. A full treatmentof optimum spacing However, such a include the effect ofwell deepening. of treatment would lead tocomplexities beyond the scope of the effect this thesis. Nevertheless, an indication considering one well of well deepening maybe obtained by only. 57 The change in pumping lift caused by a change in relative penetration may be estimated by the formula of Kozeny (Muskat 1937, p. 27)4). Assume that the total depth of formation is 1,000 feet and that the transmissivityis as calculated in Chapter III accordingto the Hantush method (Table 6) where T=3.5 x 10 gpd/ft. The Kozeny formula for partial penetration (neglectingwell loss) is as follows: 2 7(rl2ab)1/2c05 a/2] Tswa{l (7.1) Loge re/rw where a=fractional part oft1b" tapped by the pumped well. Other symbols are aspreviously noted. Using this equation(7.1) under the conditions: 275 - 0.275 for welldepth=275 feet - 1000 500 - 0.50 for welldepth=500 feet a2=1000 =1000 feet. a3= - 1 for welldepth 2.5 cfs is as The resulting drawdownin each case for Q= state follows (note that the Kozenyequation is for steady and is used for purposesof comparisononly): For a s =l8.)4 feet 1 w For a s =10.3 feet 2 w s = 5.25 feet For a3 w Assuming that each well has a life of 20 years, the power cost for the 20-year period for each case is (from the cost of power of the installed wells [EPWAFDA, 1965, AppendixL-21): For a1 Power cost = Rs 220,000 For a2 Power cost = Rs 161,000 For Power cost = Rs 125,000 Calculations given above were based onthe linear relationship of the cost of powerwith the pumping lift of the installed well which is275 feet deep. The pumping lift of the well is the sumof the drawdown and static water level which is about12 feet below the groundlevel at the beginning of irrigationseason. It is also evident savings in from the above calculationsthat there would be the cost of power of Rs59,000 and 95,000 in 20 yearsfor wells of 500 and 1000 feetdeep against thecost of power of a for a well 275 feet deep. The cost of construction transportation 275 feet deep wellis Rs 31,000, including The extra and shipping cost(EPWAPDA, 1965, Appendix1-1). of 500 and 1000 cost of deepening thewell up to the depth the total feet is Rs 31,000 and Rs93,000, respectively, if four cost of the installation isconsidered to be two and times that of wells of 275feet deep. 59 It shows from the above considerations that a deep well will give better economics in the long run. CHAPTER VIII SUIV]MARY AND CONCLUSIONS In the course of analysis, it has been found that the water table in Dinajpur and Rangpur well field will be lowered12to15feet by pumpage from underground as needed to irrigate the area. This lowering of water table will result in a depth of25to30feet below the surface which brings the level below the minimum water level of the Tangon and Karatoa rivers. Hence the accretion to stream flow from ground water will be severely limited or stopped. The Tangon will cease to flow in the absence of accretion from ground water during irrigation season. The discharge of the Karatoa will be reducedto about153 cfs which can be pumped for irrigation oflimited areas along the banks of the river. However, this analysis was based on ten years of record of discharge ofTangon and Karatoa. Longer term records of discharge maygive a dif- ferent result, although there is not a markedchange in. discharge of streams during dry periods from yearto year. The Kozeny(1937)partial penetration method of analysis and the Kraijenhoff(1958)drainage equation gave the value of transmissivity in the range of100,000 to 60 61 150,000 gpd/ft for 275 feet depth of aquifer. Hantush1s (196)1-) partial penetration method based on early pump test data and the thickness of aquifer (arbitrarily) taken to be 1000 feet, gave transmissivity 3.5 x l0gpd/ft which is about three times the average transmissivity of the upper 275 feet of the aquifer determined by the abovemeth- ods. Although there is consistency of the values of transmissivity in three methods of analysis, thethickness of the alluvium deposits being unknown, theanalysis of short pump test data, by conventional methods,leads to some uncertainty of the value oftransmissivity. However, the general value of transmissivity1.2 x 10 gpd/ft for 275 feet depth of well underanalysis is considered reason- able in computing the productivity ofwells, effect on stream flow by pumping a nearbywell and the economic spacing of wells. The specific yield, 8, ofthe aqui- fer was estimated to be 0.20. The annual recharge to the watertable from precip- itation was estimated to be2.8 feet by computing the water balance of the area. The observed annualfluctuation of water level is 10-12 feet whichis equivalent to about 2.2 feet of water assuming s = 0.20. It seems that the estimated recharge is reasonable eventhough simplifying assumptions were made in computing the waterbalance of the 62 area after Thornthwaite and Mather (1957). It was cal- culated that an average discharge of 2.5 ofSover a 150- day period will not exceed the average annualrecharge to water table from precipitation and will notresult in excessive drawdown. This average discharge of 2.5cfs can supply water as needed to irrigate 2#0 acresof land. The spacing of wells at 3000 feet intervalsin a rectangular grid was found to be economical forthe irrigation of20 acres each. This particular arrangementhas a benefit cost ratio of 2:1. The deep wells (500 feetand 1000 feet) in Dinajpur and Rangpur wellfield showed better economy return in mystudy. However, this particular type of study was notbased on a detailedcost analysis productivity of of the component parts inrelation to the aquifer was con- the deep wells. Furthermore, the deep in the sidered to be composed ofthe same materials as upper 275 feet. REF ERE NC ES BiLaney, H. F., 1955, Climate asan Index of Irrigation Needs; U. S. Department of Agriculture Year Book of 1955. Blaney and Criddle, W. D., 1966. Determination of Con- sumptive Use for Water Development. Method of Estimating of Evapotranspiration. Irrigation and Drainage Specialty Conference, Las Vegas, Nevada, Pmerican Soc. Civil Engineer, Nov. 1966. East Pakistan Water and Power Development Authority, 196)4, Ground Water in East Pakistan. Prepared by International Engineering Company, Inc., California, U. S. A. 1965, Project Report of the Ground Water and Low Lift Pump Irrigation Project in Northern Districts of East Pakistan. Prepared by International Engineering Company, Inc. Dacca, East Pakistan. FAO-1966, Republic of Pakistan, United Nations Special Fund Froject Hydrological Survey in East Pakistan Third Phase Ground Water Investigation Final Report Ferris, J. G., Knowles, D. B., Brown, R. H., Stallman, R. W., 1962. Theory of Aquifer Tests, U. S. Geological Survey Water Supply Paper l536-E. Glover, R. E., and Balmer, G. G., 195)4, River Depletion Resulting from Pumping a Well Near a River. Trans. Pmerican Geophys. Union Vol. 35, pp. 468-)170. Hantush, M. S., 1961, Economic Spacing of Interfacing Wells. In "Ground Water in Arid Zones," pp. 350- 36)4, Intern. Assoc. Sci. Hydrol. Pub.57,1961. 196)4, Hydraulics of Wells, in Advances in Hydro- science, ed. Vente Chow: Academic Press, Inc., New York, pp. 281-4)42. 63 64 Jacob, C. E., 19)47. Drawdown Test to Determine Effective Radius of Artesian Well. Trans. Amer. Soc. Civil Engineer Paper 2321,pp. 1047-1070. 1963. Correction of Drawdown Caused by a Pump Well Tapping Less Than the Full Thickness ofan Aquifer Method of Determining Permeability, Transmissibility and Drawdown. U. S. Geological Survey, Water Supply Paper 1536-1. Jahnlce, Eugene and Fritz Emde, 1945, Tables of Functions with Formulas and Curves, Dover Pub., Table I, pp. 6-8. Kraijenhoff, Van de Leur, D. A., 1958, A Study of Non- Steady Ground Flow with Special Reference to a Reservoir Coefficient. Delngenieur (The Netherlands) B. BOUW-en Water Boun Kunde 9 May 1958,pp.87-94. Mawla, G., 1968, The Relationship of Ground Water to Alluvium in Dinajpur and Rangpur, East Pakistan. N. S. Thesis in Geology, in the University of Arizona, Tucson, Arizona, U. S. A. Muskat, M. 5., 1937, The Flow of Homogeneous Fluids Through Porous Media. McGraw-Hill, pp. 270-271. Rorabaugh, N. I., Groundwater in Northeastern Louisville and Kentucky with Reference to Induced Infiltra- tion. U. S. Geological Survey Water Supply Paper 1360-B. Theis, C. V., 1940, The Source of Water from Wells Essential Factors Controlling the Response of an Aquifer to the Development. Amer. Soc. Civil Engineers Magazine, pp. 277-280, for May 1940. Thornthwaite, C. W., 19)48, An Approach Towards a Rational Classification of Climate. Geography Review, Vol. 38, No. 1, pp. 45_9)4. Thornthwaite and Mather, J. R., 1957, Instruction and Tables for Computing Potential Evapotranspiration and the Water Balance. Drexel Institute of Technology Laboratory of Climatology. Publ. Climatology, Vol. x, No. 3. 65 U. S. Federal Works Agency (19)41), Work Projects Administration for the City of New York, Tables of Probability Function U. I. Table MT8, Super- intendent of Documents, Washington, D. C., U. S. A. Walton, W. C.,1962,Selected Analytical Methods for Well and Aquifer Evaluation. Bull.)49. State Water Survey Division, State of Illinois, Department of Registration and Education.