The SI Metric SystelD of Units and SPE METRIC STANDARD

Society of Petroleum Engineers The SI Metric System of Units and SPE METRIC STANDARD

Society of Petroleum Engineers

Adopted for use as a voluntary standard by the SPE Board of Directors, June 1982.

Contents

Preface ...... ,...... 2

Part 1: SI - The International System of Units ...... 2

Introduction...... 2

SI Units and Unit Symbols...... 2

Application of the Metric System...... 3 Rules for Conversion and Rounding...... 5 Special Terms and Quantities Involving Mass and Amount of Substance...... 7 Mental Guides for Using Metric Units...... 8

Appendix A (Terminology)...... 8

Appendix B (SI Units)...... 9 Appendix C (Style Guide for Metric Usage) ...... 11

Appendix D (General Conversion Factors) ...... 14 Appendix E (Tables 1.8 and 1.9) ...... 20

Part 2: Discussion of Metric Unit Standards...... 21

Introduction...... 21

Review of Selected Units...... 22 Unit Standards Under Discussion ...... 24

Notes for Table 2.2 ...... 25 Notes for Table 2.3 ...... 25 Second Printing June 1984 Copyright 1984, Society of Petroleum Engineers of AIME. Printed in U.S.A. This publication or any parts thereof may not be reproduced by any means without the prior written permission of the publisher: Society of Petroleum Engineers, P.O. Box 833836, Richardson, TX 75083-3836. Contact the publisher for additional copies, individual or in bulk, of this publication. Preface

The SPE Board in June 1982 endorsed revisions to "SPE proposed and/or adopted by other groups involved in the Tentative Metric Standard" (Dec. 1977 lPT, Pages metrication exercise, including those agencies charged 1575-1611) and adopted it for implementation as this with the responsibility (nationally and internationally) "SPE Metric Standard." for establishing metric standards. These few exceptions, The following standard is the final product of 12 years' still to be decided, are summarized in the introduction to work by the Symbols and Metrication Committee. Part 2 of this report. Members of the current Metrication Subcommittee in These standards include most of the units used com clude John M. Campbell, chairman, John M. Campbell monly by SPE members. The subcommittee is awarethat & Co.; Robert A. Campbell, Magnum Engineering Inc.; some will find the list incomplete for their area of Robert E. Carlile, Texas Tech U.; J . Donald Clark, specialty . Additions will continue to be made but too petroleum consultant; Hank Groeneveld, Mobil Oil long a list can become cumbersome. The subcommittee Canada; Terry Pollard, retired, ex-officio member; and believes that these standards provide a basis for metric Howard B. Bradley, professional/technical training practice beyond the units listed. So long as one maintains consultant. these standards a new unit can be "coined" that should With very few exceptions, the units shown are those prove acceptable.

Part 1: SI-The International System of Units

Introduction SI Units and Unit Symbols3 Worldwide scientific, engineering, industrial, and com The short-form designations of units (such as ft for feet, mercial groups are converting to SI metric units. Many kg for kilograms, m for meters, mol for moles, etc.) in the u.s. are now active in such conversion, based on have heretofore been called unit "abbreviations" in SPE work accomplished by national I and international2 terminology to avoid confusion with the term "sym authorities. Various U. S. associations, professional bois" applied to letter symbols used in mathematical societies, and agencies are involved in this process, in equations. However, international and national standard cluding, but not limited to , American Society for Testing practice is to call these unit designations "unit sym and Materials (ASTM),3 American Petroleum Inst. bois" ; the latter usage will be followed in this report. (API), 4,5 American Nat! . Standards Inst. (ANSI),3, 6 SI Units American Society of Mechanical Engineers (AS ME) ,7 and American Nat!. Metric Council (ANMC).8 The SI is based on seven well defined "base units" that Canadian Petroleum Assn. (CPA) and other Canadian quantify seven base quantities that by convention are groups have been especially active in conversion regarded as dimensionally independent. It is a matter of work. 13 The Society of Petroleum Engineers of AIME choice how many and which quantities are considered intends to keep its worldwide membership informed on base quantities. 9 SI has chosen the seven base quantities the conversion to and use of SI metric units. and base units listed in Table 1.1 as the basis of the Inter The term "sr' is an abbreviation for Le Systeme In national System. In addition, there are two "supplemen ternational d'Unites or The International System of tary quantities" (Table 1.2). Units. Tables 1.1 and 1.2 show current practices for SI is not identical with any of the former cgs, mks, or designating the dimensions of base and supplementary mksA systems of metric units but is closely related to physical quantities, plus letter symbols for use in them and is an extension of and improvement over them. mathematical equations. SI measurement symbols are identical in all languages. SI "derived units" are a third class, formed by com As in any other language, rules of spelling, punctuation, bining, as needed, base units, supplementary units, and and pronunciation are essential to avoid errors in other derived units according to the algebraic relations numerical work and to make the system easier to use and linking the corresponding quantities. The symbols for understand on a worldwide basis. These rules, together derived units that do not have their own individual sym with decimal usage, units coherence, and a series of bols are obtained by using the mathematical signs for standard prefixes for mUltiples and submultiples of most multiplication and division, together with appropriate SI units, provide a rational system with minimum dif exponents (e.g., SI velocity, meter per second, m/s or ficulty of transition from English units or older systems m' s -I ; SI angular velocity , radian per second, rad/s or of metric units. Refs. 1 through 4 of this paper are rad·s -I). recommended to the reader wishing official information, Table 1.3 contains a number of SI derived units, in development history, or more detail on SI; material from cluding all the 19 approved units assigned special names these and other references cited has been used freely in and individual unit symbols. this report. Appendix B provides a more detailed explanation of Appendix A provides definitions for some of the terms the SI systems of units, their definitions, and used. abbreviations.

2 SI Unit Prefixes8 Style and Usage The SI unit prefixes, multiplication factors, and SI prefix Take care to use unit symbols properly ; the agreements symbols are shown in Table 1.4. Some of the prefixes in international and national standards provide uniform may seem strange at first, but there are enough familiar rules (summarized in Appendix C). It is essential that ones in the list to make it relatively easy for technical these rules be followed closely to provide maximum ease personnel to adjust to their use; kilo, mega, deci, centi, of communication and to avoid costly errors . Handling milli, and micro are known to most engineers and of unit names variessomewhat among different countries scientists. because of language differences, but using the rules in One particular warning is required about the prefixes: Appendix C should minimize most difficulties of in the SI system, k and M (kilo and mega) stand for 1000 communication. and 1 000 000, respectively, whereas M and MM or m and mm have been used previously in the oil industry for Usage for Selected Quantities designating thousands and millions of gas volumes. Note Mass, Force, and Weight. The principal departure of SI carefully, however, that there is no parallelism because from the gravimetric system of metric engineering units SI prefixes are raised to the power of the unit employed, is the use of explicitly distinct units for mass and force. while the customary M and MM prefixes were not. Ex In SI, kilogram is restricted to the unit of mass. The 3 not amples: km means cubic kilometers, thousands of newton is the only SI unit of force. defined as 1 not cubic meters; cm2 means square centimeters, one (kg ' m)/s 2 , to be used wherever force is designated, in hundredth of a square meter. The designation for 1000 cluding derived units that contain force-e.g., pressure 3 3 cubic meters is 10 m and for 1 million cubic meters is or stress (N/m2 =Pa), energy (N"m =J), and power 6 m3-not 3 3 10 km and Mm , respectively. [(N·m)/s=W]. Appendix C gi.ves examples of the vital importance of There is confusion over the use of the term weight as a following the precise use of upper-case and lower-case quantity to mean either force or mass. In science and letters for prefixes and for unit symbols. technology, the term weight of a body usually means the Application of the Metric System force that, if applied to the body, would give it an ac celeration equal to the local acceleration of free fall (g, General when referring to the earth's surface). This acceleration SI is the form of the metric system preferred for all ap varies in time and space; weight, if used to mean force, plications. It is importantthat this modernized version be varies also. The term force of gravity (mass times ac thoroughly understood and properly applied. This sec celeration of gravity) is more accurate than weight for tion, together with Appendix material, provides this meaning. guidance and recommendations concerning style and In commercial and everyday use, on the other hand, usage of the SI form of the metric system. the term weight nearly always means mass. Thus, when

TABLE 1.1 - SI BASE QUANTITIES AND UNITS· SPE Letter Symbol SI Unit Symbol for Mathematical ("Abbreviation"). Equations. Base Quantity or Use Roman Use Italic "Dimension" SI Unit (Upright) Type (Sloping) Type length meter m L mass kilogram kg m time second s t electric current ampere A I thermodynamic temperature kelvin K T amount of substance molet mol n luminous intensity candela cd

·The seven base units, two supplementary units and other terms are defined in Appendixes A and S, Part1. ""SPE heretofore has arbHrarily used charge q, the product of electric current and time, as a basic dimension. In unH symbols this would be A's; in SPE mathematical symbols, for. tWhen the mole is used, the elementaryentHies must be specified; they may be atoms, molecules, Ions, electrons, other particles,or specified groups of such particles.In petroleum work, the terms "kilogram mole," "pound mole," etc .. often are shortened erroneously to "mole."

TABLE 1.2 - SI SUPPLEMENTARY UNITS· SPE Letter Symbol SI Unit Symbol for Mathematical ("Abbreviation"). Equations. Supplementary Quantity or Use Roman Use Italic "Dimension" SI Unit (Upright) Type (Sloping) Type plane angle radian rad e solid angle steradian sr n

"The seven base units, two supplementary unHs, and other terms are defined in Appendixes A and S, Part1. "ISO specifies these two angles as dimensionless wHh respect to the seven base quantHies.

3 TABLE 1.3 - SOME COMMON SI DERIVED UNITS 51 Unit Symbol ("Abbreviation"), Formula, Quantity Unit Use Roman Type Use Roman Type absorbed dose gray Gy Jlkg acceleration meter per second squared m/s2 activity (of radionuclides) becquerel Bq 1/s angular acceleration radian per second squared rad/s2 angular velocity radian per second rad/s area square meter m2 Celsius temperature degree Celsius °C K density kilogram per cubic meter kg/m" dose equivalent sievert Sv J/kg electric capacitance farad F . A'sN (=CN) electric charge coulomb C A·s electrical conductance siemens 5 AN electric field strength volt per meter VIm electric inductance henry H V·s/A (=Wb/A) electric potential volt V W/A electric resistance ohm n VIA electromotive force volt V W/A energy joule J N'm entropy joule per kelvin J/K force newton N kg·m/s2 frequency hertz Hz 1/s illuminance lux Ix Im/m2 luminance candela per square meter cd/m2 luminous flux lumen 1m cd'sr magnetic field strength ampere per meter AIm magnetic flux weber Wb V's magnetic flux density tesla T Wb/m2 potential difference volt V W/A power watt W J/s pressure pascal Pa N/m2 quantity of electricity coulomb C A·s quantity of heat joule J N'm radiant flux watt W J/s radiant intensity watt per steradian W/sr specifiC heat joule per kilogram kelvin J(kg'K) stress pascal Pa N/m2 thermal conductivity watt per meter kelvin W/(m·K) velocity meter per second m/s viscosity, dynamic pascal second Pa·s viscosity, kinematic square meter per second m2/s voltage volt V W/A volume· cubic meter m" wavenumber 1 per meter 11m work joule J N'm 'In 1964,the General Conference on Weights and Measures adopted I�er as a special name for the cubic decimeter but discouraged the use of I�er for volume measurement of extreme precision (sse Appendix B).

TA BLE 1.4 - SI UNIT PREFIXES 51 Prefix Symbol, Meaning SI Use Roman In Other Multiplication Factor Prefix Type Pronunciation (U.S.)· Meaning (U.S.) Countries 1 000 000 000 000 000 000 = 10'8 exa·· E ex' a (a as in a bout) one quintillion timest trillion 1 000 000 000 000 000 = 10'5 peta·· P as inp etal one quadrillion timest thousand billion 1 000 000 000 000 = 10'2 tera T as in terra ce one trillion timest billion 1000 000 000 = 109 giga G jig' a (a as in a bout) one billion timest milliard 1 000 000 = 106 mega M as in mega phone one million times 1 000 = 10" kilo k as in kilo watt one thousand times 100 = 102 hecto; h heck' toe one hundred times 10 = 10 deka; da deck' a (a as in a bout) ten times 0.1 = 10- 1 deci; d as in deci mal one tenth of 0.01 = 10-2 centi; c as in senti ment one hundredth of 0.001 = 10-" milli m as in military one thousandth of 0.000 001 = 10-8 micro II. as in micro phone one millionth of 0.000 000 001 = 10-9 nano n nan' oh (an as in an t) one billionth oft milliardth 0.000 000 000 001 = 10-12 pico p peek' oh one trillionth oft billionth 0.000 000 000 000 001 = 10-15 femto f fem' toe (fem as in one quadrillionth oft thousand billionth fem inine) 0.000 000 000 000 000 001 = 10-18 atto a as in anato my one quintillionth oft trillionth

'The first syllable of every prefix is accented to assure that the prefix will retain its identity. Therefore, the preferred pronunciation of kilometer places the accent on the first syllable, not the second. "Approved by the 15th General Conference of Weights and Measures (CGPM), May-June 1975. tThesa terms should be avoided in technical writing because the denominations above 1 million are different in most other countries, as indicated in the last column. *While hecto, deka, deci, and centi are Sl prefixes, their use generally should be avoided except for the SI un� muHiples for area, volume, moment, and nontechnical use of centimeter, as for body and clothing measurement. 4 one speaks of a person's weight, the quantity referred to Energy. The SI unit of energy, the joule, together with is mass. Because of the dual use, the term weight should its multiples, is preferred for all applications. The be avoided in technical practice except under cir kilowatt-hour is used widely as a measure of electric cumstances in which its meaning is completely clear. energy, but this unit should not be introduced into any When the term is used, it is important to know whether new areas; eventually it should be replaced by the mass or force is intended and to use SI units properly as megajoule. described above by using kilograms for mass and newtons for force. Torque and Bending Moment. The vector product of Gravity is involved in determining mass with a balance force and moment arm is expressed in newton meters or scale. When a standard mass is used to balance the (N . m) by SPE as a convention when expressing torque measured mass, the effect of gravity on the two masses is energies. canceled except for the indirect effect of air or fluid buoyancy. In using a spring scale, mass is measured in Pressure and Stress. The SI unit for pressureand stress directly since the instrument responds to the force of is the pascal (newton per square meter); with proper SI gravity. Such scales may be calibrated in mass units if prefixes it is applicable to all such measurements. Use of the variation in accelerationof gravity andbuoyancy cor the old metric gravitational units-kilogram-force per rections are not significant in their use. square centimeter, kilogram-force per square millimeter, The use of the same name for units of force and mass torr, etc.-is to be discontinued. Use of the bar is causes confusion. When non-Si units are being con discouraged by the standards organizations. verted to SI units, distinction should be made between It has been recommended internationally that pressure force and mass-e.g., use lbf to denote force in units themselves should not be modified to indicate gravimetric engineering units, and use Ibm for mass. whether the pressure is "absolute" (above zero) or Use of the metric ton, also called tonne (1.0 Mg), is "gauge" (above atmospheric pressure). If the context common. leaves any doubt as to which is meant, the word "pressure" must be qualified appropriately: " ...at a Linear Dimensions. Ref. 3 provides discussions of gauge pressure of 13 kPa," or " ...at an absolute length units applied to linear dimensions and tolerances pressure of 13 kPa," etc. of materials and equipment, primarily of interest to Units and Names To Be Avoided or Abandoned engineers in that field. Tables 1.1 through 1.3 include all SI units identified by Temperature. The SI temperature unit is the kelvin (not formal names, with their individual unit symbols. Vir "degreeKe lvin"); it is the preferred unit to express ther tually all other named metric units formerly in use .(as modynamic temperature. Degrees Celsius (DC) is an SI well as nonmetric units) areto be avoided or abandoned. derived unit used to expresstemperature and temperature There is a long list of such units (e.g., dyne, stokes, intervals. The Celsius scale (formerly called centigrade) "esu," gauss, gilbert, abampere, statvolt, angstrom, is related directly to the kelvin scale as follows: the fermi, micron, mho, candle, calorie, atmosphere, mm temperature interval 1 DC =1 K, exactly. Celsius Hg, and metric horsepower) . The reasons for abandon temperature (Toe) is related to thermodynamic ing the non-Si units arediscussed in Appendix B. Two of temperature (TK) as follows: Toe =TK -To exactly, the principal reasons are the relative simplicity and where To =273.15 K by definition. Note that the SI unit coherence of the SI units. symbol for the kelvin is K without the degree mark, Rules for Conversion and Rounding3 whereas the older temperature units are known as degrees Fahrenheit, degrees Rankine, and degrees Conversion Celsius, with degree marks shown on the unit symbol Table 1.7, Appendix D, contains general conversion fac (OF, OR, DC). tors that give exact values or seven-digit accuracy for im-· plementing these rules except where the nature of the Time. The SI unit for time is the second, and this is dimension makes this impractical. preferred, but use of the minute, hour, day, and year is The conversion of quantities should be handled with permissible. careful regardto the implied correspondencebetween the accuracy of the data and the given number of digits. In Angles. The SI unit for plane angle is the radian. The use all conversions, the number of significant digits retained of the arc degree and its decimal submultiples is per should be such that accuracy is neither sacrificed nor missible when the radian is not a convenient unit. Use of exaggerated. the minute and second is discouragedexcept possibly for Proper conversion procedure is to multiply the cartography. Solid angles should be expressed in specified quantity by the conversion factor exactly as steradians. given in Table 1.7 and then round to the appropriate number of significant digits. For example, to convert Volume. The SI unit of volume is the cubic meter. This 11.4 ft to meters: 11.4xO.3048=3.474 72, which unit, or one of its regularly formed multiples, is pre rounds to 3.47 m. ferred for all applications. The special name liter has been approvedfor the cubic decimeter (see Appendix B), Accuracy and Rounding but use of the liter is restricted to the measurement of liq Do not round either the conversion factor or the quantity uids and gases. before performing the multiplication; this reduces ac-

5 curacy . Proper conversion procedure includes rounding or "maximum, " must be handled so that the stated limit the converted quantity to the proper number of signifi is not violated. For example, a specimen "at least 4 in. cant digits commensurate with its intended precision. wide" requires a width of at least 101.6 mm, or (round The practical aspects of measuring must be considered ed) at least 102 mm. when using SI equivalents. If a scale divided into six teenths of an inch was suitable for making the original Significant Digit. Any digit that is necessary to define measurements, a metric scale having divisions of 1 mm the specific value or quantity is said to be significant. is obviously suitable for measuring in SI units, and the For example, a distance measured to the nearest 1 m may equivalents should not be reportedcloser than the nearest have been recorded as 157 m; this number has three 1 mm. Similarly, a gauge or caliper graduated in divi significant digits. If the measurement had been made to sions of 0.02 mm is comparable to one graduated in divi the nearest 0.1 m, the distance may have been 157.4 sions of 0.001 in. Analogous situations exist for mass, m-four significant digits. In each case, the value of the force, and other measurements. A technique to deter right-hand digit was determined by measuring the value mine the proper number of significant digits in rounding of an additional digit and then rounding to the desired converted values is described here for general use. degree of accuracy . In other words, 157.4 was rounded to 157; in the second case, the measurement may have General Conversion. This approach depends on first been 157.36, rounded to 157.4. establishing the intended precision· or accuracy of the quantity as a necessary guide to the number of digits to Importance of Zeros. Zeros may be used either to in retain. The precision should relate to the number of dicate a specific value, as does any other digit, or to in digits in the original, but in many cases that is not a dicate the magnitude of a number. The 1970 U.S. reliable indicator. A figure of 1.1875 may be a very ac population figure rounded to thousands was curate decimalization of a noncritical 1:X6 that should 203 185 000. The six left-hand digits of this number are have been expressed as 1.19. On the other hand, the significant; each measures a value. The three right-hand value 2 may mean "about 2" or it may mean a very ac digits are zeros that merely indicate the magnitude of the curate value of 2, which should then have been written as number rounded to the nearest thousand. To illustrate 2.0000. It is therefore necessary to determine the intend further, each of the following estimates and ed precision of a quantity before converting. This measurements is of different magnitude, but each is estimate of intended precision should never be smaller specified to have only one significant digit: than the accuracy of measurement but usually should be smaller than one tenth the tolerance ifone exists. After 1000 estimating the precision of the dimension, the converted 100 dimension should be rounded to a minimum number of 10 significant digits (see section on "Significant Digits") 0.01 such that a unit of the last place is equal to or smaller 0.001 than the converted precision. 0.000 1.

Examples It is also important to note that, for the first three 1. A stirring rod 6 in. long: In this case, precision is numbers, the identification of significant digits is possi estimated to be about Yz in. (± 1,4 in.). Converted, Yz in. ble only through knowledge of the circumstances. For is 12.7 mm. The converted 6-in. dimension of 152.4 mm example, the number 1000 may have been rounded from should be rounded to the nearest 10 mm, or 150 mm. about 965, or it may have been rounded from 999.7, in 2. 50 OOO-psi tensile strength: In this case, precision is which case all three zeros are significant. estimated to be about ± 200 psi (± 1.4 MPa) based on an Data of Varying Precision. accuracy of ±0 .25 % fo r the tension tester and other fac Occasionally, data required tors. Therefore, the converted dimension, 344.7379 for an investigation must be drawn from a variety of MPa, should be rounded to the nearest whole unit, 345 sources where they have been recorded with varying MPa. degrees of refinement. Specific rules must be observed added. subtracted. multiplied. 3. Test pressure 200± 15 psi: Since one tenth of the when such data are to be or divided. tolerance is ±1.5 psi (10.34 kPa), the converted dimen answer sion should be rounded to the nearest 10 kPa. Thus, The rule for addition and subtraction is that the 1378.95 14± 103 .421 35 kPa becomes 1380± 100 kPa. shall contain no significantdigit s fartherto the rightthan occurs in the least precise number. Consider the addition Special Cases. Converted values should be rounded to of three numbers drawn from three sources, the first of the minimum number of significant digits that will main which reported data in millions, the second in thousands, tain the required accuracy . In certain cases, deviation and the third in units: from this practice to use convenient or whole numbers may be feasible. In that case, the word "approximate" 163 000 000 IDust be used following the conversion-e.g., 1 'M! 217 885 000 in. = 47 .625 mm exact, 47 .6 mm normal rounding, 47 .5 96 432 768 mm (approximate) rounded to preferred or convenient 477 317 768 half-millimeter, 48 mm (approximate) rounded to whole number. This total indicates a precision that is not valid. The A quantity stated as a limit, such as "not more than" numbers should first be rounded to one significant digit

6 farther to the right than that of the least precise number, Examples: and the sum taken as follows. 4.463 25 if rounded to three places would be 4.463. 8.376 52 if rounded to three places would be 8.377. 163 000 000 4.365 00 if rounded to two places would be 4.36. 217 900 000 4.355 00 if rounded to two places would be 4.36. 96 400 000 477 300 000 Conversion of Linear Dimensions of Interchangeable Parts Then, the total is rounded to 477 000 000 as called for Detailed discussions of this subject are provided by by the rule. Note that if the second of the figures to be ASTM, 3 API, 4 and ASME7 publications, and are added had been 217 985 000, the rounding before addi recommended to the interested reader. tion would have produced 218 000 000, in which case the zero following 218 would have been a significant Other Units digit., Temperature. General guidance for converting The rule for multiplication and division is that the tolerances fromdegrees Fahrenheit to kelvins or degrees product quotient or shall contain no more significant Celsius is given in Table 1.5. Normally, temperatures fewest digits than are contained in the number with the expressed in a whole number of degrees Fahrenheit significant digits used in the multiplication or division. should be converted to the nearest 0.5 K (or 0.5°C). As The difference between this ruleand the rule for addition with other quantities, the number of significantdigits to and subtraction should be noted; for addition and sub retain will depend on implied accuracy of the original traction, the rule merely requires rounding digits to the dimension e.g., * right of the last significant digit in the least precise number. The fo llowing illustration highlights this 100±5 °F (tolerance); implied accuracy, estimated difference. total 2°F (nearest 1°C) 37.7778±2.7778°C rounds to 38±3"C. Multiplication: 1 13.2 X 1.43 = 161.876 rounded l000±50°F (tolerance); implied accuracy, estimated to 162. tota120°F (nearest lO°C) 537. 7778±27 .7778°C Division: 113.2+ 1.43 =79.16 rounded rounds to 540±30°C. to 79.2 Addition: 113.2+1.43=114.63 rounded Pressure or Stress. Pressure or stress values may be to 114.6 converted by the same principle used for other quan Subtraction: 113.2-1.43=111.77 rounded tities. Values with an uncertainty of more than 2 % may to 111 .8. be converted without rounding by the approximate factor: The above product and quotient are limited to three significant digits since 1.43 contains only three signifi I psi =7 kPa. cant digits. In contrast, the rounded answers in the addi tion and subtraction examples contain four significant For conversion factors see Table 1.7. digits. Numbers used in the illustration are all estimates or Special Length Unit-the Vara. Table 1.8, Appendix Numbers that are exact counts (and con measurements. E, provides conversion factors and.explanatory notes on version factors that are exact) are treated as though they the problems of converting the several kinds of vara units consist of an infinite number of significant digits. Stated to meters. more simply, when a count is used in computation with a measurement, the number of significant digits in the Special Terms and Quantities Involving answer is the same as the number of significant digits in Mass and Amount of Substance the measurement. If a count of 40 is multiplied by a The International Union of Pure and Applied Chemistry, measurement of 10.2, the product is 408. However, if 40 the International Union of Pure and Applied Physics, were an estimate accurate only to the nearest 10 and, hence, contained one significantdigit , the product would TA BLE 1.5 - CONVERSION OF TEMPERATURE be 400. TOLERANCE REQUIREMENTS Rounding Values10 Tolerance Tolerance (OF) (K or °C) o When a figure is to be rounded t fewer digits than the ::!:1 ::!:O.5 total number available, the procedure should be as ::!:2 ::!:1 follows. ::!:5 ::!:3 ::!:10 ::!:5.5 ::!:15 ::!:8.5 When the First Digit The Last Digit ::!:20 ::!: 11 Discarded is Retained is ::!:25 ::!:14 less than 5 unchanged more than 5 increased by 1 'Unless a number of rounded values are to appear in a given problem, most roundings 5 fo llowed only unchanged if even, conform to the first two procedures - i.e., rounding upward when the first digit dis by zeros* increased by 1 if odd cardedis 5 or higher.

7 and the International Organization for Standardization 10. "American National Standard Practice for Inch-Millimeter Con provide clarifying usages for some of the terms involving version for Industrial Use," ANSI B48.1-1933 (RI947), ISO R370-1964, IntI. Organization for Standardization, ANSI, New the base quantities "mass" and "amount of substance." York. (A later edition has been issued: "To1eranced Dimen Two of these require modifying the terminology appear sions-Conversion From Inches to Millimeters and Vice Versa," ing previously in SPE's Symbols Standards. ISO 370-1975.) Table 1.6 shows the old and the revised usages. II. "Factors for High-Precision' Conversion," NBS LCI071 (July 1976). Mental Guides for Using Metric Units 12. "Information Processing-Representations of SI and Other Units for Use in Systems With Limited Character Sets," IntI. Standard Table 1.9, Appendix F, is offered as a "memory jog ISO 2955-1974, IntI. Organization for Standardization, ANSI, ger" or guide to help locate the "metric ballpark" New York City. (Ref. 5 reproduces the 1973 edition of this stan relativeto customary units. Table 1.9 is not a conversion dard in its entirety.) 13. "Supplementary Metric Practice Guide for the Canadian table. For accurate conversions, referto Table 1.7 or to Petroleum Industry," fourth edition, P.F. Moore (ed.), Canadian Tables 2.2 and 2.3 for petroleum-industry units, and Petroleum Assn. (Oct. (979). round off the converted values to practical precision as 14. "Letter Symbols for Units of Measurement," ANSI/IEEE Std. described earlier. 260-1978. Available from American Natl. Standards Inst., New York City. References** IS. Mechtly, E.A.: "The International System of Units-Physical Constants and Conversion Factors," NASA SP-7012, Scientific 1. "The International System of Units (SI)," NBS Special Publica and Technical Information Office, NASA, Washington, D.C. tion 330, U.S. Dept. of Commerce, Natl. Bureau of Standards, 1973 edition available from U.S. Government Printing Office, Superintendent of Documents, U.S. Government Printing Office, Washington, D.C. Washington, D.C. (1981). (Order by SD Catalog No. 16. McElwee, P.G.: The Texas Vara. Available from Commissioner, C\3.1O:330/3.) General Land Office, State of Texas, Austin (April 30, 1940). 2. "SI Units and Recommendations for the Use of Their Multiples and of Certain Other Units," second edition, 1981-02-15, IntI. 'See Appendix A and prior paragraph on "General Conversion." Standard ISO 1000, IntI. Organization for Standardization, •• For cost and address information on ordering, see paper SPE 6212, or contact SPE Headquarters. American Natl. Standards Inst. (ANSI), New York (1981). 3. "Standard for Metric Practice," E 380-82, American Soc. for Testing and Materials, Philadelphia. (Similar material published APPENDIX A3 in IEEE Std. 268-1982.) 4. Metric Practice Guide-A Guide to the Use of SI-The Interna Terminology tional System of Units, second edition. API Pub. 2563 (now being To ensure consistently reliable conversion and rounding revised), American Petroleum Institute, Washington, D.C. (Jan. 1973). (This material is derived from ASTM E 380-72.) practices, a clear understanding of the related 5. Conversion of Operational and Process Measurement Units to the nontechnical terms is prerequisite. Accordingly, certain Metric (SI) System, first edition. API Pub. 2564, Washington, terms used in this standard are defined as follows. D. C. (March 1974). 6. "A Bibliography of Metric Standards," ANSI, New York (June Accuracy (as distinguished from Precision). 1975). (Also see ANSI's annual catalog of national and interna The tional standards. ) degree of conformity of a measured or calculated value 7. ASME Orientation and Guide for Use of S] (Metric) Units, sixth to some recognized standard or specified value. This edition. Guide SI-I, American Soc. of Mechanicill Engineers concept involves the systematic error of an operation, (ASME), New York (May 1, 1975). (ASME also has published which is seldom negligible. Guides SI-2, Strength of Materials; SI-3, Dynamics; SI-5, Fluid Mechanics; SI-6, Kinematics; SI-8, Vibration; and SI-IO, Steam Charts.) Approximate. A value that is nearly but not exactly cor 8. Metric Editorial Guide, third edition, American Natl. Metric rect or accurate. Council (ANMC), Washington, D.C. (July 1981). 9. "'General Principles Concerning Quantities, Units and Symbols," Coherence. A characteristic of a coherent system of General Introduction to ISO 3], second edition, Inti. Standard ISO 31/0, IntI. Organization for Standardization, ANSI, New units, as described in Appendix B, such that the product York City (1981). or quotient of any two unit quantities is the unit of the

TA BLE 1.6 - SPECIAL TERMS AND QUANTmES INVOLVING MASS AND AMOUNT OF SUBSTANCE Old Usage Standardized Usage Dimensions (ISO Symbols, SI Unit Term See Table 1 .1 ) Term Symbol atomic weight M mass of atom kg (SPE Symbols Standard) atomic weight relative atomic mass (elsewhere) equivalent mole mol mass of molecule M molecular mass kg molar molar (means, "divided by 1/mol amount of substance") molarity concentration mol/m3 molecular weight M molar mass kg/mol (SPE Symbols Standard) molecular weight relative molecular mass (elsewhere) normal - obsolete ·Dimensionless

8 resulting quantity. The SI base units, supplementary assigned to each; in some cases, special names and unit units, and derived units form a coherent set. symbols are given-e.g., the newton (N) .

Deviation. Variation from a specified dimension or One Unit Per Quantity. The great advantage of SI is design requirement, usually defining upper and lower that there is one, and only one, unit for each physical limits (see also Tolerance). quantity-the meter for length (L), kilogram (instead of gram) for mass (m), second for time (t), etc. From these Digit. One of the 10 Arabic numerals (0 to 9). elemental units, units for all other mechanical quantities are derived. These derived units are defined by simple Dimension(s). Two meanings: (1) A group of fun equations among the quantities, such as v=dLldt damental (physical) quantities, arbitrarily selected, in (velocity), a=dvldt (acceleration), F=ma (force) , terms of which all other quantities can be measured or W=FL (work or energy), and P= WIt (power) . Some of identified. 9 Dimensions identify the physical nature of, these units have only generic names, such as meter per or the basic components making up, a physical quantity . second for velocity; others have special names and sym They are the bases for the formation of useful dimen bols, such as newton (N) for force, joule (J) for work or sionless groups and dimensionJesl> numbers and tor the energy, and watt (W) for power. The Sf units for force, powerful tool of dimensional analysis. The dimensions energy, and power are the same regardless of whether for the arbitrarily selectedbase units of the SI are length, the process is mechanical, electrical, chemical, or mass, time, electric current, thermodynamic tempera nuclear. A force of 1 N applied for a distance of 1 m can ture, amount of substance, and luminous intensity. SI produce 1 J of heat, which is identical with what 1 W of has two supplementary quantities considered dimension electric power can produce in 1 second. less-plane angle and solid angle. (2) A geometric ele ment in a design, such as length and angle, or the Unique Unit Symbols. Corresponding to the SI advan magnitude of such a quantity . tages of a unique unit for each physical quantity are the advantages resulting from the use of a unique and well Figure (numerical). An arithmetic value expressed by defined set of symbols. Such symbols eliminate the con one or more digits or a fraction. fusion that can arise from current practices in different disciplines such as the use of "b" for both the bar (a unit Nominal Value. A value assigned for the purpose of of pressure) and barn (a unit of area). convenient designation; a value existing in name only. Decimal Relation. Another advantage of SI is its reten Precision (as distinguished from Accuracy). The tion of the decimal relation between multiples and sub degree of mutual agreement between individual multiples of the base units for each physical quantity. measurements (repeatability and reproducibility). Prefixes areestablished for designating multiple and sub multi�le units from "exa" (1018) down to "atto" Quantity. A concept used for qualitative and quan (10 - 8) for convenience in writing and speaking. titative descriptions of a physical phenomenon. 9 Coherence. Another major advantage of SI is its Significant Digit. Any digit that is necessary to define a coherence. This system of units has been chosen in such value or quantity (see text discussion) . a way that the equations between numerical values, in cluding the numerical factors, have the same form as the Tolerance. The total range of variation (usually corresponding equations between the quantities: this bilateral) permitted for a size, position, or other required constitutes a "coherent" system. Equations between quantity; the upper and lower limits between which a units of a coherent unit system contain as numerical fac dimension must be held. tors only the number 1. In a coherentsystem , the product or quotient of any two unit quantities is the unit of the U.S. Customary Units. Units based on the foot and the resulting quantity . For example, in any coherent system, pound, commonly used in the U.S. and defined by the unit area results when unit length is multiplied by unit Natl . Bureau of Standards.II Some of these units have length (1 m x 1 m = 1 m 2 ), unit force when unit mass * is the same name as similar units in the U.K. (British, multiplied by unit acceleration (1 kg xl m/s 2 = 1 N) , English, or U.K. units) but are not necessarily equal to unit work when unit force is multiplied by unit length (1 them. N x 1 m = 1 J), and unit power when unit work is divided by unit time (1 J + 1 second= 1 W). Thus, in a coherent APPENDIX B3 system in which the meter is the unit of length, the SI Units squaremeter is the unit of area, but the are** and hectare Advantages of SI Units are not coherent. Much worse disparities occur in systems of " customary units" (both nonmetric and older SI is a rationalized selection of units from the metric metric) that require many numerical adjustment factors system that individually are not new. They include a unit in equations. of force (the newton) , which was introduced in place of the kilogram-force to indicate by its name that it is a unit Base Units. of force and not of mass. SI is a coherent system with Whatever the system of units, whether it be seven base units for which names, symbols, and precise coherent or noncoherent, particular samples of some

. definitions have been established. Many derived units • Note that the kilogram (not the gram) is the coherent SI unit of rt)8SS. are defin� in terms of the base units, with symbols "The are is an old metric unit. 9 physical quantities must be selected arbitrarily as units of and placed one meter apart in vacuum, would produce those quantities. The remaining units are defined by ap between these conductors a force equal to 2 x 10 -7 propriate experiments related to the theoretical interrela newton per meter of length. " (Adopted by Ninth CGPM tions of all the quantities. For convenience of analysis, 1948.) units pertainingto certain base quantities are by conven "Kelvin (K)-The kelvin, unit of thermodynamic tion regarded as dimensionally independent; these units temperature, is the fraction 11273.16 of the ther , are called base units (Table 1.1), all all others (derived modynamic temperature of the triple point of water. ' 3 units) can be expressed algebraically in terms of the base (Adopted by 13th CGPM 1967.) units. In SI, the unit of mass, the kilogram, is defined as "Mole (mol)-The mole is the amount of substance of the mass of a prototype kilogrampreserved by the Inter a system which contains as many elementary entities as national Bureau of Weights and Measures (BIPM) in there are atoms in 0.012 kilograms of carbon-12." Paris. All other base units are defined in terms of (Adopted by 14th CGPM 1971.) reproducible phenomena-e.g., the wave lengths and "Note-When the mole is used, the elementary en frequencies of specified atomic transitions. tities must be specified and may be atoms, molecules, ions, electrons, other particles, or specified groups of Non-SI Metric Units such particles." , 'Candela Various other units are associated with SI but are not a (cd)-The candela is the luminous intensity part thereof. They are related to units of the system by in a given direction of a source that emits powers of 10 and are employed in specialized branches monochromatic radiationof frequency540 (E + 12) hertz of physics. An example is the bar, a unit of pressure, ap (Hz) and that has a radiant intensity in that direction of proximately equivalent to 1 atm and exactly equal to 100 11683 watt per steradian." "Radian kPa. The bar is employed extensively by meteorologists. (rad)-The radian is the plane angle between Another such unit is the gal, equal exactly to an accelera two radii of a circle which cut off on the circumference tion of 0.01 m/s2• It is used in geodetic work. These, an arc equal in length to the radius." "Steradian however, are not coherent units-i.e., equations involv (sr)-The steradian is the solid angle ing both these units and SI units cannot be written which, having its vertex at the center of a sphere, cuts off without a factor of proportionality even though that fac an area of the surface of the sphere equal to that of a tor may be a simple power of 10. square with sides of length equal to the radius of the Originally (1795), the liter was intended to be identical sphere." tThis definition supersedes the ephemeris second as the unit of time. to the cubic decimeter. The Third General Conference Definitions of SI Derived Units on Weights and Measures (CGPM) in 1901 defined the Having Special Names3 liter as the volume occupied by the mass of 1 kilogram of pure water at its maximum density under normal at Physical Quantity Unit and Definition mospheric pressure. Careful determinations subsequent Absorbed dose The gray (Gy) is the absorbed ly established the liter so defined as equivalent to dose when the energy per unit 1.000 028 dm3 . In 1964, the CGPM withdrew this mass imparted to matter by definition of the liter and declared that "liter" was a ionizing radiation is 1 J/kg. special name for the cubic decimeter. Thus, its use is Activity The becquerel (Bq) is the activi permitted in SI but is discouraged because it creates two ty of a radionuclide decaying at units for the same quantity and its use in precision the rate of one spontaneous measurements might conflictwith measurementsrecord nuclear transition per second. ed under the old definition. Celsius temperature The degree Celsius (0C) is equal to the kelvin and is used in place SI Base Unit Definitions of the kelvin for expressing Authorized translations of the original French definitions Celsius temperature (symbol of the seven base and two supplementary units of SI Toe) defined by Toe =TK -To, fo llow3 (parenthetical items added) . where T K is the thermodynamic "Meter (m)-The meter is the length equal to 1 650 temperature and To =273.15 K 763.73 wavelengths in vacuum of the radiation cor- by definition. . responding to the transition between the levels 2 p \0 and Dose equivalent The sievert is the dose 5ds of the krypton-86 atom." (Adopted by 11th CGPM equivalent when the absorbed 1960.) dose of ionizing radiation "Kilogram (kg)-The kilogram is the unit of mass multiplied by the dimensionless (and is the coherentSI unit); it is equal to the mass of the factors Q (quality factor) and N international prototype of the kilogram." (Adopted by (product of any other multiply First and Third CGPM 1889 and 1901.) ing factors) stipulated by the "Second (s)-The second is the duration of 9 192 631 IntI . Commission on Radiolog 770 periods of the radiation corresponding to the transi ical Protection is 1 J/kg. tion between the two hyperfine levels of the ground state Electric capacitance The farad (F) is the capacitance of the cesium-133 atom. t" (Adopted by 13th CGPM of a capacitor between the plates 1967.) of which there appears a dif "Ampere (A)-The ampere is that constant current fe rence of potential of 1 V when which, if maintained in two straight parallel conductors it is charged by a quantity of of infinite length, of negligible circular cross-section, electricity equal to 1 C. 10 Electric The siemens (S) is the electric the force exerted on an element conductance conductance of a conductor in of current is equal to the vector which a current of I A is pro product of this element and the duced by an electric · potential magnetic flux density. difference of I V. Power The watt (W) is the power that Electric inductance The henry (H) is the inductance represents a rate of energy of a closed circuit in which an transfer of 1 J/s. electromotive force of I V is Pressure or stress The pascal (Pa) is the pressure produced when the electric cur or stress of 1 N/m 2 . rent in the circuit varies uniform Electric charge, Electric charge is the time in ly at a rate of I A/s. quantity of tegral of electric current; its unit, Electric potential The volt (V) is the difference of electricity the coulomb (C), is equal to 1 difference, elec electric potential between two A·s. tromotive force points of a conductor carrying a constant current of I A when the No other SI derived units havp been assigned special power dissipated between these names at this time. points is equal to I W. Electric resistance The ohm (0) is the electric APPENDIX C3,8* resistance between two points of Style Guide for Metric Usage a conductor when a constant dif Rules for Writing Metric Quantities ference of potential of I V, ap Capitals. Units-Unit names, including prefixes, are not plied between these two points, capitalized except at the beginning of a sentence or in produces in this conductor a cur titles. Note that for "degree Celsius" the word rent of I A, this conductor not "degree" is lower case; the modifier "Celsius" is being the source of any elec always capitalized. The "degree centrigrade" is now tromotive force. obsolete. Energy The joule (J) is the work done Symbols-The short forms for metric units are called when the point of application of unit symbols. They are lower case except that the first a force of I N is displaced a letter is upper case when the unit is named for a person. distance of I m in the direction (An exception to this rule in the U.S. is the symbol L for of the force. liter. ) Force The newton (N) is that force which, when applied to a body Examples: Unit Name Unit Symbol having a mass of I kg, gives it meter** m an acceleration of I m/s2 . gram g Frequency The hertz (Hz) is the frequency newton N of a periodic phenomenon of pascal Pa which the period is I second. Printed unit symbols should have Roman (upright) let lux Illuminance The (lx) is the illuminance ters, because italic (sloping or slanted) letters are re producedby a luminous fluxof I served for quantity symbols, such as m for mass and L 1m uniformly distributed over a for length. 2 surface of 1m . Prefix Symbols-All prefix names, their symbols, and lumen Luminous flux The (lm) is the luminous pronunciation are listed in Table 1.4. Notice that the top fluxemitted in a solid angle of I five are upper case and all the rest lower case. sr by a point source having a· The importance of following the precise use of upper uniform intensity of I cd. case and lower-case letters is shown by the following ex weber Magnetic flux The (Wb) is the magnetic amples of prefixes and units. flux which, linking a circuit of one tum, produces in it an elec G for giga; g for gram. tromotive force of I V as it is K for kelvin; k for kilo. reduced to zero at a uniform rate M for mega; m for milli. in I s. N for newton; n for nano. Magnetic flux The tesla (T) is the magnetic T for tera; t for tonne (metric ton) . density flux density of I Wb/m 2 . In an magnetic induction alternative approach to defining Information Processing-Limited Character Sets the magnetic field quantities the Prefixes and unit symbols retain their prescribed forms tesla may also be defined as the regardless of the surrounding typography, except for magnetic flux density that pro systems with limited character sets. ISO has provided a duces on a I-m length of wire standard 1 2 for such systems; this standard is carrying a current of I A, recommended. oriented normal to the flux den sity, a fo rce of 1 N, magnetic Plurals and Fractions. Names of SI units form their flux density being defined as an plurals in the usual manner, except for lux, hertz, and axial vector quantity such that siemens.

11 Values less than one take the singular fonn of the unit Compound Units. For a unit name (not a symbol) de name; for example, 0.5 kilogram or 'h kilogram. While rived as a quotient (e.g., for kilometers per hour) , it is , decimal notation (0.5, 0.35, 6.87) is generally preferred, preferable not to use a slash (I) as a substitute for ' 'per' the most simple fractions are acceptable, such as those except where space is limited and a symbol might not be where the denominator is 2, 3, 4, or 5. understood. Avoid other mixturesof words and symbols. Symbols of units are the same in singular and Examples: Use meter per second, not m/s. Use only one plural-e.g., 1 m and 100 m. "per" in any combination of units-e.g., meter per sec ond squared, not meter per second per second. Periods. A period is not used after a symbol, except at For a unit symbol derived as a quotient do not, for ex the end of a sentence. Examples: "A currentof 15 rnA is ample, write k. p.h. or kph for km/h because the firsttwo found ..." "The field measured 350 X 125 m." are understood only in the English language, whereas km/h is used in all languages. The symbol km/h also can - The Decimal Marker. ISO specifies the comma as the be written with a negative exponent-e.g., km · h \ . decimal marker9 ; in English-language documents a dot Never use more than one· slash (I) in any combination on the line is acceptable. In numbers less than one, a of symbols unless parenthesesare used to avoid ambigui zero should be written before the decimal sign (to pre ty ; examples are m/s2 , not m/s/s; W/(m ·K), not vent the possibility that a faint decimal sign will be W/m/K. overlooked). Example: The oral expression "point For a unit name derived as a product, a space or a seven five" is written 0.75 or 0,75. hyphen is recommended but never a "product dot" (a period raised to a centered position)-e.g., write newton Grouping of Numbers. Separate digits into groups of meter or newton-meter, not newton · meter. In the case of three, counting from the decimal marker. A comma the watt hour, the space may be omitted-watthour. should not be used between the groups of three 9 ; in For a unit symbol derived as a product, use a product stead, a space is leftto avoid confusion, since the comma dot-e.g., N· m. For computer printouts, automatic is the ISO standard for the decimal marker. typewriter work, etc., a dot on the line may be used. Do In a four-digit number, the space is not requiredunless not use the product dot as a multiplier symbol for the four-digit number is in a column with numbers of calculations-e.g., use 6.2x5, not 6.2·5. five digits or more: Do not mix nonmetric units with metric units, except those for time, plane angle, or rotation-e.g., use For 4,720,525 write 4720 525 kg/m3 , not kg/ft3 or kg/gal. For 0.52875 write 0.528 75 A quantity that constitutes a ratio of two like quantities For 6,875 write 6875 or 6 875 should be expressed as a fraction (either common or For 0.6875 write 0.6875 or decimal) or as a percentage-e.g., the slope is 11100 or 0.687 5 0.01 or 1 %, not 10 mm/m or 10 m/km . • Ref. 8 is primary source .

• ·The spellings "metre" and "litre" are preferred by ISO but "meter" and "liter" are official u.s. government spellings. SI Prefix Usage. General-SI prefixes should be used to indicate orders of magnitude, thus eliminating non Spacing. In symbols or names for units having prefixes, significant digits and leading zeros in decimal fractions no space is left between letters making up the symbol or and providing a convenient alternative to the powers the name. Examples are kA, kiloampere; and mg, of-lO notation preferred in computation. For example, milligram. 12 300 m (in computations) becomes 12.3 km (in non When a symbol follows a number to which it refers, a computation situations); 0.0123 /LA (12.3 X 10 -9 A for space must be left between the number and the symbol, computations) becomes 12.3 nA (in noncomputation except when the symbol (such as 0) appears in the situations) . supersc1Pt position. Examples: 455 kHz, 22 mg, 20 Selection-When expressing a quantity by a numerical mm, 10 N, 30 K, 20°C. value and a unit, prefixes should be chosen so that the When a quantity is used as an adjective, a hyphen numerical value lies between 0.1 and 1000 . Generally, should be used between the number and the symbol (ex prefixes representing steps of 1000 are recommended cept 0C). Examples: It is a 35-mm film; the filmwidth is (avoiding hecto, deka, deci, and centi). However, some 35 mm. I bought a 6-kg turkey; the turkey weighs 6 kg. situations may justify deviation fromthe above: Leave a space on each side of signs for multiplication, 1. In expressing units raised to powers (such as area, division, addition, and subtraction, except within a com volume and moment) the prefixes hecto, deka, deci, and pound symbol. Examples: 4 cm X 3 m (not 4 cm X 3 m); centi may be required-e.g., cubic centimeter for kg/m3 ; N·m. volume and cm4 for moment. 2. In tables of values of the same quantity, or in a Powers. For unit names, use the modifier squared or discussion of such values within a given context, it cubed after the unit name (except for area and generally is preferable to use the same unit multiple volume)-e.g., meter per second squared. For area or throughout. volume, place a modifier beforethe unit name, including 3. For certain quantities in particularapplicat ions, one in derived units:-e.g., cubic meter and watt per square certain multiple is used customarily; an example is the meter. millimeter in mechanical engineering drawings, even For unit symbols, write the symbol for the unit fol when the values lie far outside the range of 0.1 to 1000 lowed by the power superscript-e.g., 14 m2 and 26 mm. cm 3 . Powers of Units-An exponent attached to a symbol 12 containing a prefix indicates that the multiple or sub Equations. When customary units appear in equations, multiple of the unit (the unit with its prefix) is raised to the SI equivalents should be omitted. Instead of inserting the power expressed by, the exponent. For example, the latter in parentheses, as in the case of text or small tables, the equations should be restated using SI unit 1 cm3 =(1O-2 m)3 =1O-6 m3 symbols, or a sentence, paragraph, or note should be 1 ns -1 =(10-9 s) -1 =109 s-1 added stating the factor to be used to convert the 2 3 2 =1O-5 m2 /s 1 mm /s =(10 - m) /s calculated result in customary units to the preferred SI units. Double Prefixes-Double or multiple prefixes should not be used. For example, Pronunciation of Metric Terms use GW (gigawatt), not kMW; The pronunciation of most of the unit names is well use pm (picometer), not p.p.m; known and uniformly described in American dic use Gg (gigagram), not Mkg; tionaries, but four have been pronounced in various use 13.58 m, not 13 m 580 mm. ways. The following pronunciations are recommended:

Prefix Mixtures-Do not use a mixture of prefixes candela - Accent on the second syllable and unless the difference in size is extreme. For example, pronounce it like dell. use 40 mm wide and 1500 mm long, not 40 mm wide joule - Prortounce it to rhyme with pool. and 1.5 m long; however, 1500 m of 2-mm-diameter pascal - The preferred pronunciation rhymes wire is acceptable. with rascal. An acceptable second Compound Units-It is preferable that prefixes not be choice puts the accent on the second used in the denominators of complex units, except for syllable. kilogram (kg) which is a base unit. However, there are siemens - Pronounce it like seamen 's. cases where the use of such prefixes is necessary to ob tain a numerical value of convenient size. Examples of For pronunciation of unit prefixes, see Table 1.4. some of these rare exceptions are shown in the tables contained in these standards. Typewriting Recommendations Prefixes may be applied to the numerator of a com Superscripts. The question arises of how numerical pound unit; thus, megagram per cubic meter (Mg/m3 ), superscripts should be typed on a machine with a con but not kilogram per cubic decimeter (kg/dm 3 ) nor gram ventional keyboard. With an ordinary keyboard, per cubic centimeter (g/cm3 ). Values required outside numerals and the minus sign can be raised to the the range of the prefixes should be expressed by powers superscript position by rolling the platen half a space of 10 applied to the base unit. before typing the numeral, using care to avoid in Unit of Mass-Among the base units of SI, the terference with the text in the line above. kilogram is the only one whose name, for historical reasons, contains a prefix; it is also the coherent SI unit Special Characters. For technical work, it is useful to for mass (See Appendices A and B for discussions of have Greek letters available on the typewriter. If all SI coherence.) However, names of decimal multiples and symbols for units areto be typed properly , a key with the submultiples of the unit of mass are formed by attaching upright Greek lower-case p. (pronounced "mew," not prefixes to the word "gram." , 'moo' ') is necessary, since this is the symbol for micro, Prefixes Alone-Do not use a prefix without a meaning one millionth. The symbol can be approximated unit-e.g., use kilogram, not kilo. on a conventional machine by using a lower-case u and Calculations-Errors in calculations can be minimized adding the tail by hand (p.) . A third choice is to spell out if, instead of using prefixes, the base and the coherent the unit name in full. derived SI units are used, expressing numerical values in For units of electricity, the Greek upper case omega powers-of-10 notation-e. g., 1 MJ = 106 J . (0) for ohm also will be useful; when it is not available, the word "ohm" can be spelled out. Spelling of Vowel Pairs. There are three cases where It is fortunate that, except for the more extensive use the final vowel in a prefix is omitted: megohm, kilohm, of the Greek p. for micro and 0 for ohm, the change to SI and hectare. In all other cases, both vowels are retained units causes no additional difficulty in manuscript and both are pronounced. No space or hyphen should be preparation. used. The Letter for Liter. On most U.S. typewriters, there is Complicated Expressions. To avoid ambiguity in com little difference between the lower-case "el" ( " 1 " ) and plicated expressions, symbols are preferred over words. the numerical "one" (" 1 "). The European symbol for liter is a simple upright bar; the Canadians 1 3 employed Attachment. Attachment of letters to a unit symbol for an upright script f but now have adopted the upright giving information about the nature of the quantity is in capital L; ANSI now recommends the upright capital L. correct: MWe for "megawatts electrical (power)," kPag for "kilopascals gauge (pressure)," Paa for "pascals ab Typewriter Modification. Where frequently used, the solute (pressure)," and Vac for "volts ac " are not ac following symbols could be included on typewriters: ceptable. If the context is in doubt on ·any units used, superscripts 2 and 3 for squared and cubed; Greek p. for supplementary descriptive phrases should be added to micro; 0 for degree; . for a product dot (not a period) for making the meanings clear. symbols derived as a product; and Greek 0 for ohm. 13 A special type-b. II that contains all the superscripts, /L, Where less than six decimal places are shown, more n, and other characters used in technical reports is precision is not warranted. vail able for some typewriters. Some machines have The fo llowing is a fu rther example of the use of Table replaceable character keys. 1.7.

Longhand. To assure legibility of the symbols, m, n, To ConvertFrom To Multiply By /L. and it is recommended that these three symbols be pound-force per written to resemble printing. For example, write nm, not square foot Pa 4.788 026 E+Ol ...n. The symbol /L should have a long distinct tail and pound-force per should have the upright form (not sloping or italic). square inch Pa 6.894 757 E+03 inch m 2.540* E-02 Shorthand. Stenographers will find that the SI symbols generally are quicker to write than the shorthand fo rms These conversions mean fo r the unit names.

APPENDIX D I Ibf/ft2 becomes 47 . 880 26 Pa, I lbflin. 2 becomes 6.894.757 Pa or General Conversion Factors* 6.894 757 kPa, and General I inch becomes 0.0254 m (exactly). The accompanying Table 1.7 is intended to serve two purposes: The unit symbol for pound-force sometimes is written Ibf 1. To express the definitions of general units of and sometimes lb f or Ibf; the form lbf is recommended. measure as exact numerical multiples of coherent "metric" units. Relationships that are exact in terms of Organization the fu ndamental SI unit are fo llowed by an asterisk. The conversion factors generally arelisted alphabetically Relationships that are not fo llowed by an asterisk either by units having specific names and compound units are the result of physical measurements or are only derived from these specific units. A number of units approximate. starting with the. pound symbol (lb) are located in the 2. To provide mUltiplying factors for converting ex "p" section of the list. pressions of measurements given by numbers and Conversion factors classified by physical quantities are general or miscellaneous units to corresponding new listed in Refs. 3 and 4. numbers and metric units. The conversion factors for other compound units can be generated easily from numbers given in the 'Based on ASTM Pub. E380-82 (ReI. 3); values 01 conversion lactors tabulated alphabetical list by substitution of converted units. For herewith are identical with those in E380·82; generally similar material is lound in ReI. 4. Conversion values in earlier editions 01 E 380 (lor example. E 380-74) are example: based on ReI. 15. which has available some lactors with more than seven digits. I. Find the conversion factor for productivity index, (B/D)/(lbf/in. 2 ) to (m3 /d)/Pa. Convert I BID to Notation 1.589 873 (E-Ol) m 3 Id and I Ibf/in. 2 to 6.894 757 Conversion factors are presented for ready adaptation to (E+03) Pa. Then, substitute computer readout and electronic data transmission. The factors are written as a number equal to or greater than [1.589 873 (E -Ol)]/[6.894 757 (E - 03)] one and less than 10, with six or fewer decimal places =2.305 916 (E-05) (m3 /d)/Pa. (i.e.• seven or fe wer total digits). Each number is fo l lowed by the letter E (for exponent), a plus or minus 2. Find the conversion factor for tonf'mile/ft to symbol. and two digits that indicate the power of 10 by MJ/m. Convert 1 tonf to 8.896 444 (E+03) N; 1 mile to which the number must be multiplied to obtain the cor 1.609 344* (E +03) m; and 1 ft to 3.048* (E -Ol) m. rect value. For example, Then, substitute 3.523 907 (E -02) is 3.523 907 X 10-2 or [8. 896 444 (E +03)] [1.609 344 (E+03)] 0.035 239 07 . +[3.048 (E-Ol)] Similarly, =4.697 322 (E+07) (N 'm)/m or JIm 3.386 389 (E +03) is 3.386 389 X 103 =4.697 322 (E+Ol) MJ/m. or 3386.389. When conversion factors for complex compound units are being calculated from Table 1.7, numerical uncer An asterisk (*) after the numbers shown indicates that tainties may be present in the seventh (or lesser last the conversion factor is exact and . that all subsequent "significant") digit of the answer because of roundings digits (for rounding purposes) are zero. All other conver already taken for the last digit of tabulated values. sion factors have been rounded to the figures given in ac Mechtly 15 provides conversion factors of more than cordance with procedures outlined in the preceding text. seven digits for certain quantities.

14 TA BLE 1.7-ALPHABETICAL LIST OF UNITS (symbols of SI units given In parentheses) To Convert From To Multiply By" abampere ampere (A) 1 .0' E+Ol abcoulomb coulomb (C) 1.0" E+Ol abfarad farad (F) 1.0' E+09 abhenry henry (H) 1.0' E-09 abmho siemens (5) 1.0' E+09 abohm ohm (0) 1.0' E-09 abvolt volt (V) 1.0' E-08 acre·foot (U.S. survey)" ) meter3 (ma) 1.233 489 E+03 acre (U.S. survey)" ) meter2 (m2) 4.046 873 E+03 ampere hour coulomb (C) 3.6" E+03 are meter2 (m2) 1.0' E+02 angstrom meter (m) 1.0" E-l0 astronomical unit meter (m) 1.495 979 E+ll atmosphere (standard) pascal (Pa) 1.013 250' E+05 atmosphere (technical = 1 kgf/cm2) pascal (Pa) 9.806 650" E+04 bar pascal (Pa) 1.0' E+05 barn meter2 (m2) 1.0" E-28 barrel (for petroleum, 42 gal) meter3(ma) 1.589 873 E-Ol board foot meter3 (ma) 2.359 737 E-03 British thermal unit (International Table)(2) joule (J) 1.055 056 E+03 British thermal unit (mean) joule (J) 1.055 87 E+03 British thermal unit (thermochemical) joule (J) 1.054 350 E+03 British thermal unit (39°F) joule (J) 1.059 67 E+03 British thermal unit (59°F) joule (J) 1.054 80 E+03 British thermal unit (60°F) joule (J) 1.054 68 E+03 Btu (International Table)-ft/(hr-ft2-0F) (thermal conductivity) watt per meter kelvin [W/(m'K)] 1.730 735 E+OO Btu (thermochemical)-ft/(hr-ft2-OF) (thermal conductivity) watt per meter kelvin [W/(m'K)] 1.729 577 E+OO Btu (International Table)-in.l(hr-ft2-0F) (thermal conductivity) watt per meter kelvin [W/(m'K)] 1.442 279 E-Ol Btu (thermochemical)-in.l(hr-ft2-0F) (thermal conductivity) watt per meter kelvin [W/(m'K)] 1.441 314 E-Ol Btu (International Table)-in.l(s-ft2_OF) (thermal conductivity) watt per meter kelvin [W/(m'K)] 5. 192 204 E+02 Btu (thermochemical)-in.l(s-ft2_OF) (thermal conductivity) watt per meter kelvin [W/(m·K)] 5.188 732 E+02 Btu (International Table)/hr watt (W) 2.930 711 E-Ol Btu (thermochemical)/hr watt (W) 2.928 751 E-Ol Btu (thermochemical)/min watt (W) 1.757 250 E+Ol Btu (thermochemical)/s watt (W) 1.054 350 E+03 Btu (International Table)/ft2 joule per meter2 (J/m2) 1.135 653 E+04 Btu (thermochemical)/ft2 joule per meter2 (J/m2) 1.134 893 E+04 Btu (thermochemical)/(ft2-hr) watt per meter2 (W/m2) 3.182 48 1 E+OO Btu (thermochemical)/(ft2-min) watt per meter2 (W/m2) 1.891 489 E+02 Btu (thermochemical)/(ft2-s) watt per meter2 (W/m2) 1.134 893 E+04 Btu (thermochemical)/(in.2-s) watt per meter2 (W/m2) 1.634 246 E+06 Btu (International Table)/(hr-ft2-0F) (thermal conductance) wall per meter2 kelvin [W/(m2'K)] 5.678 263 E+OO Btu (thermochemical)/(hr-ft2-0F) (thermal conductance) wallper meter2 kelvin [W/(m2'K)] 5.674 466 E+OO Btu (International Table)/(s-ft2_OF) watt per meter2 kelvin [W/(m2'K)] 2.044 175 E+04 Btu (thermochemical)/(s-ft2-0F) wall per meter2 kelvin [W/(m2'K)] 2.042 808 E+04 Btu (International Table)lIbm joule per kilogram (J/kg) 2.326" E+03 Btu (thermochemical)lIbm joule per kilogram (J/kg) 2.324 444 E+03 Btu (International Table)/(lbm-OF) (heat capacity) joule per kilogram kelvin [J/(kg'K)] 4.186 8' E+03 Btu (thermochemical)/(lbm-OF) (heat capacity) joule per kilogram kelvin [J/(kg'K)] 4.184 000 E+03 ..See footnote on Page 13. ")Since 1893 the U.S. basis of length measurement has been derived from metric standards. In 1959 a small refinement was made in the definition of the yard to resolve discrepancies both in this countryand abroad. which changed its length from 360013937 m to 0.9144 m exactly. This resu"ed in the new value being shorterby two partsin a million. At the same time it was decided that any data in feet derived from and published as a result of geodetic surveys within the U.S. would remain with the old standard (1 It = 120013937 m) until furtherdecision. This foot is named the U.S. survey foot.As a result. all U.s. land measurements in U.S. customaryunits will relate to the meter by the old standard. All the conversion factors in these tables for units referenced to this footnote are based on the U.S. surveyfoot. rather than the international foot. Conversion factors for the land measure given below may be determined from the following relationships: 1 league = 3 miles (exactly) 1 rod = 16'!\! It (exactly) 1 chain = 66 It (exactly) 1 section = 1 sq mile 1 township = 36 sq miles

2 ( )This value was adopted in 1956. Some of the older Intemational Tables use the value 1.055 04 E+03. The exact conversion factor is 1.055 055 852 62' E +03.

15 TA BLE 1.7-ALPHABETICAL LIST OF UNITS (cont'd.) (symbols of SI units given In parentheses) To ConvertFrom To Ml:llti�l�B�"" bushel (U.S.) meter'l (m3) 3.523 907 E - 02 caliber (inch) meter (m) 2.54" E-02 calorie (International Table) joule (J) 4.186 8" E+oo calorie (mean) joule (J) 4.190 02 E+OO calorie (thermochemical) joule (J) 4.184" E+oo calorie (15°C) joule (J) 4.185 80 E+OO calorie (20"C) joule (J) 4.181 90 E+oo calorie (kilogram, International Table) joule (J) 4.186 8" E+03 calorie (kilogram, mean) joule (J) 4.190 02 E+03 calorie (kilogram, thermochemical) joule (J) 4.184" E+03 cal (thermochemical)/cm2 joule per meter'! (J/m2) 4.184" E+04 cal (International Table)/g joule per kilogram (J/kg) 4.186" E+03 cal (thermochemical)/g joule per kilogram (J/kg) 4.184" E+03 cal (International Table)/(g'oC) joule per kilogram kelvin [J/(kg'K)] 4.186 8" E+03 cal (thermochemical)/(g'°C) joule per kilogram kelvin [J/(kg'K)] 4.184" E+03 cal (thermochemical)/min watt (W) 6.973 333 E-02 cal (thermochemical)/s watt (W) 4.184" E+OO cal (thermochemical)/(cm�'min) wattper meter'! (W/m2) 6.973 333 E+02 cal (thermochemical)/(cm2·s) watt per meter'! (W/m2) 4.184" E+04 cal (thermochemical)/(cm's'°C) watt per meter kelvin [W/(m·K») 4.184" E+02 capture unit (c.u. = 10-3 cm -') per meter (m-') 1.0" E-Ol carat (metric) kilogram (kg) 2.0" E-04 centimeter of mercury (O°C) pascal (Pa) 1.333 22 E+03 centimeter of water (4°C) pascal (Pa) 9.806 38 E+Ol centipoise pascal second (Pa·s) 1.0" E-03 centistokes meter'!per second (m2/s) 1.0" E-06 circular mil meter'! (m2) 5.067 075 E-l0 clo kelvin meter'! per watt [(K·m2)1W) 2.003 712 E-Ol cup meter'l(m3) 2.365 882 E-04 curie becquerel (Bq) 3.7" E+l0 cycle per second hertz(Hz) 1.0" E+OO day (mean solar) second (s) 8.640 000 E+04 day (sidereal) second (s) 8.616 409 E+04 degree (angle) radian (rad) 1.745 329 E-02

degree Celsius kelvin (K) TK = Toe + 273.15 degree centigrade (see degree Celsius) degree Fahrenheit degree Celsius T.c = (T'F - 32)/1 .8 degree Fahrenheit kelvin (K) = TK (T'F + 459.67)/1. .8 degree Rankine kelvin (K) TK = T.Jl .8 °F'hr-t't2lBtu (International Table) (thermal resistance) kelvin meter'!per watt [(K·m2)1W) 1.781 102 E-Ol °F·hr-ft2/Btu (thermochemical) (thermal resistance) kelvin meter'!per watt [(K·m2)1W) 1.762 250 E-Ol denier kilogram per meter (kg/m) 1.111 111 E-07 dyne newton (N) 1.0" E-05 dyne-cm newton meter (N'm) 1.0" E-07 dyne/cm2 pascal (Pa) 1.0" E-Ol electronvolt joule (J) 1.602 19 E-19 EMU of capacitance farad (F) 1.0" E+09 EMU of current ampere (A) 1.0" E+Ol EMU of electric potential volt (V) 1.0" E-08 EMU of inductance henry (H) 1.0" E-09 EMU of resistance ohm (0) 1.0" E-09 ESU of capacitance farad (F) 1.112 650 E-12 ESU of current ampere (A) 3.335 6 E-l0 ESU of electric potential volt (V) 2.997 9 E+02 ESU of inductance henry (H) 8.987 554 E+ 11 ESU of resistance ohm (0) 8.987 554 E+ 11 erg joule (J) 1.0" E-07 erg/cm2.s watt per meter'! (W/m2) 1.0" E-03 erg/s watt (W) 1.0" E-07 faraday (based on carbon-12) coulomb (C) 9.648 70 E+04 faraday (chemical) coulomb (C) 9.649 57 E+04 faraday (physical) coulomb (C) 9.652 19 E+04 fathom meter (m) 1.828 8 E+OO fermi (femtometer) meter (m) 1.0" E-15 fluid ounce (U.S.) meter'l (m3) 2.957 353 E-05 foot meter (m) 3.048" E-Ol foot (U.S. survey)I'J meter (m) 3.048 006 E-Ol

16 TA BLE 1.7-ALPHABETICAL LIST OF UNITS (cont'd.) (symbols of SI units given In parentheses) To Convert From To Multiply By" foot of water (39.2·F) pascal (Pa) 2.988 98 E+03 sq ft meter2 (m2) 9.290 304* E - 02 ft2/hr (thermal diffusivity) meter2 per second (m2/s) 2.580 640* E - 05 ft2/s meter2 per second (m2/s) 9.290 304* E-02 cu ft (volume; section modulus) meters (m3) 2.831 685 E-02 ft3/min meters per second (m3/s) 4.719 474 E-04 ft3/s metersper second (m3/s) 2.831 685 E - 02 ft4 (moment of section)(3) meter' (m4) 8.630 975 E - 03 ftlhr meter per second (m/s) 8.466 667 E-05 ftlmin meter per second (m/s) 5.080* E-03 ftls meter per second (m/s) 3.048* E-01 ftls2 meter per second2 (m/s2) 3.048* E-01 footcandle lux (Ix) 1.076 391 E+01 footlambert candela per meter2 (cd/m2) 3.426 259 E+OO ft-Ibf joule (J) 1.355 818 E+OO ft-Ibf/hr watt (W) 3.766 161 E-04 ft-Ibf/min watt (W) 2.259 697 E - 02 ft-Ibf/s watt (W) 1.355 818 E+OO ft-poundal joule (J) 4.214011 E-02 free fall, standard (g) meter per second2 (m/s2) 9.806 650* E+OO cmls2 meter per second2 (m/s2) 1.0* E-02 gallon (Canadian liquid) meters(m3) 4.546 090 E - 03 gallon (U.K. liquid) meters (m3) 4.546 092 E - 03 gallon (U.S. dry) meters(m3) 4.404 884 E - 03 gallon (U.S. liquid) meters (m3) 3.785 412 E-03 gal (U.S. Iiquid)/day metersper second (m3/s) 4.381 264 E-08 gal (U.S. Iiquid)/min meters per second (m3/s) 6.309 020 E - 05 gal (U.S. Iiquid)/hp-hr (SFC, specific fuel consumption) meters per joule (m3/J) 1.410 089 E-09 gamma (magnetic field strength) ampere per meter (AIm) 7.957 747 E - 04 gamma (magnetic flux density) tesla (T) 1.0* E-09 gauss tesla (T) 1.0* E-04 gilbert ampere (A) 7.957 747 E - 01 gill (U.K.) meters (m3) 1.420 654 E - 04 gill (U.S.) meters (m3) 1.182 941 E-04 grad degree (angular) 9.0* E-01 grad radian (rad) 1.570 796 E-02 grain (117000 Ibm avoirdupois) kilogram (kg) 6.479 891* E-05 grain (Ibm avoirdupoisl7ooo)/gal (U.S. liquid) kilogram per meters (kg/m3) 1.71 1 806 E-02 gram kilogram (kg) 1.0* E-03 g/cm3 kilogram per meters(kg/m3) 1.0* E+03 gram-force/cm2 pascal (Pa) 9.806 650* E + 01 hectare meter2 (m2) 1.0* E+04 horsepower (550 ft-Ibf/s) watt (W) 7.456 999 E+02 horsepower (boiler) watt (W) 9.809 50 E + 03 horsepower (electric) watt (W) 7.460* E+02 horsepower (metric) watt (W) 7.354 99 E+02 horsepower (water) watt (W) 7.460 43 E + 02 horsepower (U.K.) watt (W) 7.457 0 E+02 hour (mean solar) second (s) 3.600 000 E+03 hour (sidereal) second (s) 3.590 170 E+03 hundredweight (long) kilogram (kg) 5.080 235 E + 01 hundredweight (short) kilogram (kg) 4.535 924 E + 01 inch meter (m) 2.54* E-02 inch of mercury (32·F) pascal (Pa) 3.386 38 E + 03 inch of mercury (60·F) pascal (Pa) 3.376 85 E + 03 inch of water (39.2·F) pascal (Pa) 2.490 82 E + 02 inch of water (60·F) pascal (Pa) 2.488 4 E+02 sq in. meter2 (m2) 6.451 6* E - 04 cu in. (volume; section modulus)(4) meters (m3) 1.638 706 E-05 in.3/min meters per second (m3/s) 2.731 177 E-07 in.4 (moment of section)(3) meter' (m4) 4.162 314 E-07 in.!s meter per second (m/s) 2.54* E-02 in.!s2 meter per second2 (m/s2) 2.54* E-02 kayser 1 per meter (11m) 1.0* E+02 kelvin degree Celsius T.c = TK - 273.15 (3) This sometimes is called the moment of inertiaof a plane section about a specified axis. (4) The exact conversion factor is 1.638 706 4"E-05.

17 TA BLE 1.7-ALPHABETICAL LIST OF UNITS (cont'd.) (symbols of SI units given In parentheses) To Convert From To Multi�l� B�** kilocalorie (International Table) joule (J) 4.186 8* E+03 kilocalorie (mean) joule (J) 4.190 02 E+03 kilocalorie (thermochemical) joule (J) 4.184* E+03 kilocalorie (thermochemical)/min watt (W) 6.973 333 E + 01 kilocalorie (thermochemical)/s watt (W) 4.1 84* E+03 kilogram-force (kgf) newton (N) 9.806 65* E+OO kgf·m newton meter (N'm) 9.806 65* E+OO kgf's2/m (mass) kilogram (kg) 9.806 65* E+OO kgf/cm2 pascal (Pa) 9.806 65* E+04 kgf/m2 pascal (Pa) 9.806 65* E+OO kgf/mm2 pascal (Pa) 9.806 65* E+06 km/h meter per second (m/s) 2.777 778 E-01 kilopond newton (N) 9.806 65* E+OO kilowatthour (kW-hr) joule (J) 3.6* E+06 kip (1000 Ibf) newton (N) 4.448 222 E+03 kip/in.2 (ksi) pascal (Pa) 6.894 757 E+06 knot (international) meter per second (m/s) 5.144 444 E-01 lambert candela per meterZ (cd/m2) 1hr* E+04 lambert candela per meterZ (cd/m2) 3.183 099 E+03 langley joule per meter2 (J/m2) 4.184* E+04 league meter (m) (see Footnote 1) light year meter (m) 9.460 55 E+15 Iiter5) meter3 (m3) 1.0* E-03 maxwell weber (Wb) 1.0* E-08 mho siemens (S) 1.0* E+OO microinch meter (m) 2.54* E-08 microsecond/foot (j.LSIft) microsecond/meter (foLs/m) 3.280 840 E+OO micron meter (m) 1.0* E-06 mil meter (m) 2.54* E-05 mile (international) meter (m) 1.609 344* E+03 mile (statute) meter (m) 1.609 3 E+03 mile (U.S. survey)(') meter (m) 1.609 347 E+03 mile (international nautical) meter (m) 1.852* E+03 mile (U.K. nautical) meter (m) 1.853 184* E+03 mile (U.S. nautical) meter (m) 1.852* E+03 sq mile (international) meterZ (m2) 2.589 988 E + 06 sq mile (U.S. survey)(') meterZ (m2) 2.589 998 E + 06 mile/hr (international) meter per second (m/s) 4.470 4* E-01 mile/hr (intemational) kilometer per hour (km/h) 1.609 344* E+OO mile/min (international) meter per second (m/s) 2.682 24* E+01 mile/s (international) meter per second (m/s) 1 .609 344* E + 03 millibar pascal (Pa) 1.0* E+02 millimeter of mercury (O·C) pascal (Pa) 1.333 22 E+02 minute (angle) radian (rad) 2.908 882 E-04 minute (mean solar) second (s) 6.0* E+01 minute (sidereal) second (s) 5.983 617 E+01 month (mean calendar) second (s) 2.628 000 E+06 oersted ampere per meter (AIm) 7.957 747 E+01 ohm centimeter ohm meter (n·m) 1.0* E-02 ohm circular-mil per ft ohm millimeterZ per meter [(n'mm2)mJ 1.662 426 E-03 ounce (avoirdupois) kilogram (kg) 2.834 952 E-02 ounce (troy or apothecary) kilogram (kg) 3.110348 E-02 ounce (U.K. fluid) meter3 (m3) 2.841 307 E-05 ounce (U.S. fluid) meter3 (m3) 2.957 353 E-05 ounce-force newton (N) 2.780 139 E-01 ozf·in. newton meter (N'm) 7.061 552 E-03 oz (avoirdupois)/gal (U.K. liquid) kilogram per meter3 (kg/m3) 6.236 021 E+OO oz (avoirdupois)/gal (U.S. liquid) kilogram per meter3 (kg/m3) 7.489 152 E+OO oz (avoirdupois)/in.3 kilogram per meter3 (kg/m3) 1.729 994 E+03 oz (avoirdupois)/ft2 kilogram per meterZ (kg/m2) 3.051 517 E-01 oz (avoirdupois)/yd2 kilogram per meter2 (kg/m2) 3.390 575 E-02 parsec meter (m) 3.085 678 E+16 peck (U.S.) meter3 (m3) 8.809 768 E-03 pennyweight kilogram (kg) 1.555 174 E-03 perm (·C)(6) kilogram per pascal second meterZ [kg/(Pa·s'm2)] 5.721 35 E-11

(5)ln 1964 the General Conference on Weights and Measures adopted the name liter as a special name for the cubic decimeter. Prior to this decision the liter differed Slightly (previous value. 1.000 028 dm3) and in expression of precision volume measurement this fact must be kept in mind. (S)Not the same as reservoir "perm."

18 TA BLE 1.7-ALPHABETICAL LIST OF UNITS (cont'd.) (syrnbols of SI units given in parentheses) To Convert From To Multiply By" perm (23°C)16) kilogram per pascal second meter2 [kg/(Pa·s'm2)] 5.745 25 E-11 perm·in. (O°C)!7) kilogram per pascal second meter [kg/(Pa's'm)] 1.453 22 E-12 perm·in. (23°C)(7) kilogram per pascal second meter [km/(Pa·s'm)] 1.459 29 E-12 phot lumen per meter2 (Im/m2) 1.0' E+04 pica (printer's) meter (m) 4.217518 E-03 pint (U.S. dry) metel'! (m3) 5.506 105 E-04 pint (U.S. liquid) metel'! (m3) 4.731 765 E-04 point (printer's) meter (m) . 3.514 598' E-04 poise (absolute viscosity) pascal second (Pa's) 1.0' E-01 pound (Ibm avoirdupois)IB) kilogram (kg) 4.535 924 E-01 pound (troy or apothecary) kilogram (kg) 3.732 417 E-01 Ibm-ft2 (moment of inertia) kilogram meter2 (kg·m2) 4.214011 E-02 Ibm-in.2 (moment of inertia) kilogram meter2 (kg·m2) 2.926 397 E-04 Ibm/ft-hr pascal second (Pa·s) 4.133 789 E-04 Ibmlft-s pascal second (Pa·s) 1.488 164 E+OO Ibmlft2 kilogram per meter2 (kg/m2) 4.882 428 E+OO Ibm/ft3 kilogram per metel'!(kg/m3) 1.601 846 E+01 Ibm/gal (U.K. liquid) kilogram per metel'! (kg/m3) 9.977 633 E+01 Ibm/gal (U.S. liquid) kilogram per metel'!(kg/m3) 1.198 264 E+02 Ibm/hr kilogram per second (kg/s) 1.259 979 E-04 Ibm/(hp' hr) (SFC, specific fuel consumption) kilogram per joule (kg/J) 1.689 659 E-07 Ibmlin.3 kilogram per metel'!(kg/m3) 2.767 990 E+04 Ibm/min kilogram per second (kg/s) 7.559 873 E-03 Ibmls kilogram per second (kg/s) 4.535 924 E-01 Ibm/yd3 kilogram per metel'!(kg/m3) 5.932 764 E-01 pouridal newton (N) 1.382 550 E-01 poundal/ft2 pascal (Pa) 1.488 164 E+OO poundal-slft2 pascal second (Pa·s) 1.488 164 E+OO pound-force (lbf)19) newton (N) 4.448 222 E+OO Ibf-ftl10) newton meter (N'm) 1.355 818 E+OO Ibf-ftlin.(11) newton meter per meter [(N'm)/m)] 5.337 866 E+01 Ibf-in.(11) newton meter (N·m) 1.129 848 E-01 Ibf-in.lin. (11) newton meter per meter [(N'm)/m] 4.448 222 E+oo Ibf-slft2 pascal second (Pa's) 4.788 026 E+01 Ibflft newton per meter (N/m) 1.459 390 E+01 Ibf/ft2 pascal (Pa) 4.788 026 E+01 Ibf/in. newton per meter (N/m) 1.751 268 E+02 Ibf/in.2 (psi) pascal (Pa) 6.894 757 E+03 Ibfllbm (thrust/weight[m ass] ratio) newton per kilogram (N/kg) 9.806 650 E+OO quart (U.S. dry) metel'! (m3) 1.101 221 E-03 quart(U.S. liquid) metel'! (m3) 9.463 529 E-04 rad (radiation dose absorbed) gray (Gy) 1.0' E-02 rhe 1 per pascal second [1/(Pa·s)] 1.0' E+01 rod meter (m) (see Footnote 1 ) roentgen coulomb per kilogram (C/kg) 2.58 E-04 second (angle) radian (rad) 4.848 137 E-06 second (sidereal) second (s) 9.972 696 E-01 section meter2 (m2) (see Footnote 1) shake second (s) 1 .000 000' E - 08 slug kilogram (kg) 1.459 390 E+01 slug/(ft-s) pascal second (Pa·s) 4.788 026 E+01 slug/ft3 kilogram per metel'! (kg/m3) 5.153 788 E+02 statampere ampere (A) 3.335 640 E-10 statcoulomb coulomb (C) 3.335 640 E-10 statfarad farad (F) 1.112650 E-12 stathenry henry (H) 8.987 554 E+11 statmho siemens (S) 1.112650 E-12 statohm ohm (!l) 8.987 554 E+ 11 statvolt volt (V) 2.997 925 E+02 stere metel'! (m3) 1.0' E+OO (7)Not the same dimensions as "millidarcy-foot:' (BlThe exact conversion factor is 4.535 923 7'E - 01. (9)The exact conversion factor is 4.448 221 615 260 5'E +OO. 110)Torque unit; see text discussion of "Torque and Bending Moment:' (11)Torque divided by length; see text discussion of "Torque and Bending Moment."

19 TA BLE 1.7-ALPHABETICAL LIST OF UNITS (cont'd.) (symbols of SI units given In parentheses) To Convert From To Multi�l:i B:i·· stilb candela per meter2 (cd/m2) 1.0· E+04 stokes (kinematic viscosity) meter2 per second (m2/s) 1.0· E-04 tablespoon meter" (m3) 1.478 676 E-05 teaspoon meter" (m3) 4.928 922 E-06 tex kilogram per meter (kg/m) 1.0· E-06 therm joule (J) 1.055 056 E+08 ton (assay) kilogram (kg) 2.916 667 E-02 ton (long, 2,240 Ibm) kilogram (kg) 1.016 047 E+03 ton (metric) kilogram (kg) 1.0· E+03 ton (nuclear equivalent of TNT) joule (J) 4.184 E+09,(12) ton (refrigeration) watt (W) 3.516 800 E+03 ton (register) meter" (m3) 2.831 685 E+OO ton (short,2000 Ibm) kilogram (kg) 9.071 847 E+02 ton (long)/yd3 kilogram per meter" (kg/m3) 1.328 939 E+03 ton (short)/hr kilogram per second (kg/s) 2.519 958 E-01 ton·force (2000 Ibf) newton (N) 8.896 444 E+03 tonne kilogram (kg) 1.0· E+03 torr (mm Hg, O·C) pascal (Pa) 1.333 22 E+02 township meter2 (m2) (see Footnote 1) unit pole weber (Wb) 1.256 637 E - 07 watthour (W·hr) joule (J) 3.60· E+03 W·s joule (J) 1.0· E+OO W/cm2 watt per meter2 (W/m2) 1.0· E+04 Wlin.2 watt per meter2 (W/m2) 1.550 003 E+03 yard meter (m) 9.1 44· E-01 yd2 meter2 (m2) 8.361 274 E-01 yd3 meter" (m3) 7.645 549 E-01 yd3/min meter" per second (m3/s) 1.274 258 E-02 year (calendar) second (s) 3.153 600 E+07 year (sidereal) second (s) 3.155 815 E+07 year (tropical) second (s) 3.155 693 E+07 (l2)Defined (not measured) value.

APPENDIX E TA BLE 1.8 - CONVERSION FACTORS FOR THE VA RA* Value of Conversion Factor, Location Vara in Inches Varas to Meters Source Argentina, Paraguay 34.12 8.666 E-01 Ref. 16 Cadiz, Chile, Peru 33.37 8.476 E-01 Ref. 16 California, except San Francisco 33.3720 8.476 49 E-01 Ref. 16 San Francisco 33.0 8.38 E-01 Ref. 16 Central America 33.87 8.603 E-01 Ref. 16 Colombia 31.5 8.00 E-01 Ref. 16 Honduras 33.0 8.38 E-01 Ref. 16 Mexico 8.380 E-01 Refs. 16 and 17 Portugal, Brazil 43.0 1.09 E+OO Ref. 16 Spain, Cuba, Venezuela, Philippine Islands 33.38·· 8.479 E-01 Ref. 17 Texas Jan. 26, 1801, to Jan. 27, 1838 32.8748 8.350 20 E-01 Ref. 16 Jan. 27, 1838 to June 17, 1919 , for surveys of state land made for Land Office 33-1/3 8.466 667 E-01 Ref. 16 Jan. 27, 1838 to June 17, 1919, on private surveys (unless changed to 33-1/3 in. by custom arising to dignity of law and overcoming former law) 32.8748 8.350 20 E-01 Ref. 16 June 17, 1919 , to present 33-1/3 8.466 667 E-01 Ref. 16

'It is evident from Ref. 16 that accurate defined lengths of the vara varied significantly. acccrding to historical date and locality used. For work requiring accurate conversions, the user should check closely into the date and location of the surveys involved. with due regard to what local practice may have been at that time and place. " This value quoted from Webster's New InternaOonaJ DicOonary.

20 TABLE 1.9-"MEMORY JOGGER"-METRIC UNITS "BallPark" Metric Values; (Do Not Use As Customary Unit Conversion Factors) acre 4000 square meters { 0.4 hectare barrel 0.16 cubic meter British thermal unit 1000 joules British thermal unit per pound-mass 2300 joules per kilogram { 2.3 kilojoules per kilogram calorie 4 joules centipoise 1· millipascal-second centistokes 1· square millimeter per second darcy 1 square micrometer degree Fahrenheit (temperature difference) 0.5 kelvin dyne per centimeter 1· millinewton per meter foot 30 centimeters { 0.3 meter cubic foot (cu tt) 0.03 cubic meter cubic foot per pound-mass (ft3/lbm) 0.06 cubic meter per kilogram square foot (sq tt) 0.1 square meter foot per minute 0.3 meter per minute { 5 millimeters per second foot-pound-force 1.4 joules foot-pound-force per minute 0.02 watt foot-pound-force per second 1.4 watts horsepower 750 watts (% kilowatt) horsepower, boiler 10 kilowatts inch 2.5 centimeters kilowatthour 3.6· megajoules mile 1.6 kilometers ounce (avoirdupois) 28 grams ounce (fluid) 30 cubic centimeters pound-force 4.5 newtons pound-force per square inch (pressure, psi) 7 kilopascals pound-mass 0.5 kilogram pound-mass per cubic foot 16 kilograms per cubic meter 260 hectares section 2.6 million square meters { 2.6 square kilometers ton, long (2240 pounds-mass) 1000 kilograms ton, metric (tonne) 1000· kilograms ton, short 900 kilograms ·Exact equivalents

APPENDIX F Part 2: Discussion of Metric Unit Standards

Introduction The standards and conventions shown in Part 1 are part commonly to achieve convenient unit size. Any ap of the SPE tentative standards. Table 2. 1 presents proved prefix may be used in combination with an ap nomenclature for Tables 2.2 and 2.3. Table 2.2 is a proved SI unit without violation of these standards ex� modified fonn of a table in API 2564 reflecting SPE cept where otherwise noted. recommendations. Table 2.3 shows a few units com monly used in the petroleumindustry that are not shown Other Allowable. A small, selected list of non-SI units in Table 1.7 and 2.2. The columns in these tables are that are approved temporarilyfor the convenience of the based on the following. English-metric transition. Use of the allowable units may be discouraged but is not prohibited. Any tradi Quantity and SI Unit. The quantity and the base or tional, non-SI unit not shown is prohibited under these derived SI unit that describes that quantity. standards.

Conversion Factor. For certain commonly used units, a Customary Unit. The unit most commonly used in ex conversion factor is shown. The primary purpose in pressing the quantity in English units. these tables is to show how the preferred metric unit compares in size with the traditional unit. An effort has SPE Preferred. The base or derived SI unit plus the ap been made to keep the unit sizes comparableto minimize proved prefix, if any, that probably will be used most transition difficulties. 21 A detailed summary of general conversion factors is (a). Note that (a) is used as the abbreviationfor year (an included as Table 1.7 in Part 1 of this report. num) instead of (yr) . The use of the minute as a time unit The notation for conversion factors in Tables 2.2 and is discouraged because of abbreviation problems. It 2.3 is explained in the introduction to Table 1.7. should be used only when another time unit is absolutely Fig. 2.1 shows graphically how SI units are related in inappropriate. a very coherent manner. Although it may not be readily apparent, this internal coherence is a primary reason for Date and Time Designation adoption of the metric system of units. The Subcommittee proposes to recommend a standard The SPE Metrication Subcommittee is endeavoring to date and time designation to the American Nat!. Stan provide SPE members with all information needed on the dards Inst., as shown below. This form already has been International System of Units and to provide tentative introduced in Canada. standards (compatible with SI coherence, decimal, and other principles) for the application of the SI system to 76 - 10 - 03 - 16 24 14 SPE fields of interest. The tentative SPE standards are year month day hour minute second intended to reflect reasonable input from many sources, (76-10-03-16:24: 14) and we solicit your positive input with the assurance that all ideas will receive careful consideration. The sequence is orderly and easy to remember; only Review of Selected Units needed portions of the sequence would be used - most documents would use the first three. No recommenda Certain of the quantities and units shown in Tables 2.2 tion has been made for distinguishing the century, such and 2.3 may require clarification of usage (see also the as 1976 vs. 1876 vs. 2076. notes preceding Tables 2.2 and 2.3). Time Area Although second(s) is the base time unit, any unit of time The hectare (ha) is allowable but its use should be con may be used - minute (min), hour (h), day (d), and year finedto large areasthat describe the areal extent of a por-

TABLE 2.1 -NOMENCLATURE FOR TA BLES 2.2 AND 2.3 Unit Symbol Name Quantity Type of Unit A ampere electric current base SI unit a annum (year) time allowable (not official SI) unit 8q becquerel activity (of radionuclides) derived SI unit = 1/s bar bar pressure allowable (not official SI) unit, = 105 Pa C coulomb quantity of electricity derived SI unit, = 1 A·s cd candela luminous intensity base SI unit ·C degree Celsius temperature derived SI unit = 1.0 K degree plane angle allowable (not official SI) unit d day time allowable (not official SI) unit, = 24 hours F farad electric capacitance derived SI unit, = 1 A·s/V Gy gray absorbed dose derived SI unit, = Jlkg g gram mass allowable (not official SI) unit, = 10-3 kg H henry inductance derived SI unit, = 1 V's/A h hour time allowable (not official SI) unit, = 3.6 x 1Q3 s Hz hertz frequency derived SI unit, = 1 cycle/s ha hectare area allowable (not official SI) unit, = 10' m2 J joule work, energy derived SI unit, = 1 N'm K kelvin temperature base SI unit kg kilogram mass base SI unit kn knot velocity allowable (not official SI) unit, = 5.144 444 x 10-1 m/s = 1.852 kmlh L liter volume allowable (not official SI) unit, = 1 dm3 1m lumen luminous flux derived SI unit, = 1 cd'sr Ix lux illuminance derived 81 unit, = 1 Im/m2 m meter length base SI unit min minute time allowable (not official 81) unit minute plane angle Allowable cartography (not official 81) unit N newton force derived 81 unit, = 1 kg'm/s2 naut. mile U.S. nautical mile length allowable (not official 81) unit, = 1.852 x 103 m n ohm electric resistance derived 81 unit, = 1 VIA Pa pascal pressure derived 81 unit, = 1 N/m2 rad radian plane angle supplementary SI unit S siemens electrical conductance derived SI unit, = 1 AN s second time base SI unit second plane angle allowable cartography (not official SI) unit sr steradian solid angle supplementary SI unit T tesla magnetic flux density derived SI unit, = 1 Wb/m2 t tonne mass allowable (not official SI) unit, = 1Q3 kg = 1 Mg V volt electric potential derived SI unit, = 1 W/A W watt power derived 81 unit, = 1 J/s Wb weber magnetic flux derived 81 unit, = 1 V's 22 tion of the earth's crust (nonnally replacing the acre or In the U. S., the " -er" ending for meter and liter is of section). ficial. The official symbol for the liter is "L." In other Volume countries the symbol may be written as "f" and spelled The liter is an allowable unit for small volumes only. It out with the "-re" ending (metre, litre). Since SPE is in should be used for volumes not exceeding 100 L. Above ternational, it is expected that members will use local this volume (or volume rate), cubic meters should be conventions. used. The only two prefixes allowed with the liter are Notice that "API barrel" or simply "barrel" disap "milli" and "micro:' pears as an allowable volume term.

BASE UNITS DERIVED UNITS WITH SPECIAL NAMES

kilogr.m ..._ ....

------�rIY -- - (J/k.) ,I_I ------Gy

ABSORBED DOSE PRESSURE, • STRESS

-�-"""" ------m2 - , I ...... -- L__ �:;..- r I I 1 I I

bKqu.,,1 1 f':'\It Is) h.rtz (:)It Is) 1 t , PACTIVITY (OF IONIZING FREQUENCY SKond ..._ _ " , RADIATION SOURCE) 'i'I , I s Mtt W,) �------J ------(A'S) TIME molt r::l POWER, HEAT FLOW RATE � AMOUNT OF SUBSTANCE

.mptr. ...._ _

ktlvin _-_ rd"'" C.lsius

I ° I c I clnd...... - ... ------� I CELSIUS I TEMPE RATURE I 1 I MAGNETIC I toc =TC 213.15 1 flUX 1 L __ __.J D E NSITY I SUPPLEMENTARY UNITS I I lUI I "dilnG ____ 2 J - m PLANE ANGLf ,"redi.n ...- ... LUMINOUS flUX Il lUMINANCE

SOLIO ANGLE SOLID LINES INDICATE MULTIPLICATION; BROKEN LINES, DIVISION

Rg. 2.1-Graphic Relationships of 51 Units With Names.

23 Force Unit Standards Under Discussion Any force tenn will use the newton (N). Derived units There are some quantities for which the unit standards involving force also require the newton. The expression have not been clarified to the satisfaction of all parties of force using a mass tenn (like the kilogram) is ab and some controversy remains. These primary quantities solutely forbidden under these standards. are summarized below.

Mass Permeability The kilogram is the base unit, but the gram, alone or The SPE-preferred penneability unit is the square with any approved prefix, is an acceptable SI unit. micrometer (I-Lm2). One darcy (the traditional unit) For large mass quantities the metric ton (t) may be equals 0.986 923 I-Lm2 . * used. Some call this "tonne:' However, this spelling The fundamental SI unit of penneability (in square sometimes has been used historically to denote a regular meters) is defined as follows: "a penneability of one short ton (2,000 Ibm). A metric ton is also a megagram meter squared will pennit a flow of 1 m 3 Is of fluid of (Mg). The tenns metric ton or Mg are preferred in text 1 Pa ' s viscosity through an area of 1 m 2 under a references. pressure gradient of 1 Palm." The traditional tenns of "darcy" and "millidarcy " Energy and Work have been approved as preferred units of penneability. The joule (J) is the fundamental energy unit; kilojoules Note 11 of Table 2.2 shows the relationships between (kJ) or megajoules (MJ) will be used most commonly. traditional and SI units and points out that the units of the The calorie (large or small) is no longer an acceptable darcy and the square micrometer can be considered unit under these standards. The kilowatthour is accep equivalent when high accuracy is not needed or implied. table for a transition period but eventually should be replaced by the megajoule. Standard Temperature Some reference temperature is necessary to show certain Power propertiesof materials, such as density, volume, viscosi The tenn horsepower disappears as an allowable unit. ty , energy level, etc . Historically, the petroleumindustry The kilowatt (kW) or megawatt (MW) will be the almost universally has used 60°F (15.56°C) as this multiples of . the fundamental watt unit used most reference temperature, and metric systems have used commonly . ooe, 20oe, and 25°e most commonly, depending on the data and the area of specialty. Pressure API has opted for 15°e because it is close to 60°F ASME has used 200e in some of its metric guides. The The fundamental pressure unit is the pascal (Pa) but the bulk of continental European data used for gas and oil kilopascal (kPa) is the most convenient unit. The bar correlations is at ooe, although 15°e is used sometimes. (100 kPa) is an allowable unit. The pressure tenn The SPE Subcommittee feels that the choice between kglcm 2 is not allowable under these standards. ooe and 15°e is arbitrary . Tentatively, a standard of 15°e has been adopted simply to confonn to API stan Viscosity dards. It may be desirable to have a flexible temperature standard for various applications. The tenns poise, centipoise, stokes, and centistokes are no longer used under these standards. They are replaced Standard Pressure by the metric units shown in Table 2.2. To date, some groups have opted for a pressure reference of 101.325 kPa, which is the equivalent of one standard Temperature atmosphere. The Subcommittee considers this an unac Although it is pennissible to use °e in text references, it ceptable number. Its adoption possesses some short-tenn is recommended that "K" be used in graphical and convenience advantages but condemns future genera tabular summaries of data. tions to continual odd-number conversions to reflect the change of pressure on properties. It also violates the powers-of- lO aspect of the SI system, one of its primary Density advantages. The fu ndamental SI unit for density is kglm 3 . Use of this The current SPE standard is 100 kPa and should be unit is encouraged. However, a unit like kg/L is used until further notice. It is our hope that reason will pennissible. prevail and others will adopt this standard. The traditional tenn "specific gravity" will not be used. It will be replaced by the tenn "relative density. " Gauge and Absolute Pressure API gravity disappears as a measure of relative density . There is no provision for differentiating between gauge and absolute pressure, and actions by international Relative Atomic Mass and Molecular Mass bodies prohibit showing the difference by an addendum The traditional tenns "atomic weight" and "molecular to the unit symbol. The Subcommittee recommends that weight" are replaced in the SI system of units by gauge and absolute be shown using parentheses follow "relative atomic mass" and "relative molecular mass," ing p: respectively . See Table 1.6. p=643 kPa, p(g) =543 kPa

24 [p is found · from peg) by adding actual barometric 10. See discussion of "Energy, Torque, and Bending pressure. (100 kPa is suitable for most engineering Moment," Part 1. calculations.)] 11. The permeability conversions shown in Table 2.2 In custody transfer the standard pressure will be are for the traditional definitions of darcy and specifiedby contract. Unless there is a special reason not millidarcy . to do so, the standard pressure will be 100 kPa to In SI units, the square micrometeris the preferred preserve the "multiples of ten" principle of the metric unit of permeability in fluid flow through a porous system. medium, having the dimensions of viscosity times Standard pressure normally is defined and used as an volume flow rate per unit area divided by pressure absolute pressure. So, p sc = 100 kPa is proper notation. gradient, which simplifies to dimensions of length Absolute pressure is implied if no (g) is added to denote squared. (The fundamental SI unit is the square gauge pressure specifically. meter, definedby leaving out the factor of 10 - 12 in the equation below). Standard Volumes A permeability of 1 p,m 2 will permit a flow of 3 Cubic meters at standard reference conditions must be 1 m / s of fluid of 1 Pa' s viscosity through an area 2 2 equated to a term with the standard "se" subscript. For of 1 m under a pressure gradient of 10 1 Palm example, for a gas production rate of 1 200 000 m 3 /d, (neglecting gravity effects): write 1 p,m2 = 10-12 Pa 's [m3 /(s 'm2 )](m/Pa) 6 3 3 = 10 - 12 Pa ' s(m/s)(m/Pa) qgsc =1.2X10 m /d or 1.2 (E +06) m /d read as "1.2 million cubic meters per day. " = 10-12 m2 •

If the rate is 1200 cubic meters per day, write The range of values in petroleum work is best served by units of 10 - 3 p,m2 • The traditional millidarcy (md) is an informal name for 10-3 p,m2 , qgsc =1.2X10 3 m 3 /d. which may be used where high accuracy is not For gas in place, one could write implied. For virtually all engineering purposes, the Gsc =I1.0X1012 m 3 • familiar darcy and millidarcy units may be taken equal to 1 p,m2 and 10 -3 p,m2 , respectively. Notes for Table 2.2 12. The ohm-meter is used in borehole geophysical 1. The cubem (cubic mile) is used in the measurement devices. of very large volumes, such as the content of a 13. As noted in Section 1, the mole is an amount of sedimentary basin. substance expressible in elementary entities as 2. In surveying, navigation, etc., angles no doubt will atoms, molecules, ions, electrons, and other par continue to be measured with instruments that read ticles or specified groups of such particles. Since out in degrees, minutes, and seconds and need not the expression kilogram mole is inconsistent with be converted into radians. But for calculations in other SI practices, we have used the abbreviation volving rotational energy , radians are preferred. " kmol" to designate an amount of substance which 3. The unit of a million years is used in contains as many kilograms (groups of molecules) geochronology. The mega-annum is the preferred as there are atoms in 0.012 kg of carbon 12 SI unit, but many prefer simply to use mathematical multiplied by the relative molecular mass of the notation (i.e., X 106 ). substance involved. In effect, the "k" prefix is 4. This conversion factor is for an ideal gas. merelya convenient way to identify the type of en 5. Subsurface pressures can be measured in tity and facilitate conversion from the traditional megapascals or as freshwater heads in meters. If the pound mole without violating SI conventions. latter approach is adopted, the hydrostatic gradient becomes dimensionless. Notes for Table 2.3 6. Quantities listed under "Facility Throughput, 1. The standard cubic foot (sct) and barrel (bbl) re Capacity" areto be used only for characterizing the fe rred to are measured at 60°F and 14.696 psia; the size or capacity of a plant or piece of equipment. cubic meter is measured at 15°C and 100 kPa Quantities listed under "Flow Rate" are for use in (1 bar) . design calculations. 2. The kPa is the preferred SPE unit for pressure. But 7. This conversion factor is based on a density of 1.0 many are using the bar as a pressure measurement. kg/dm3 • The bar should be considered as a nonapproved 8. Seismic velocities will be expressed in km/s. name (or equivalent) for 100 kPa. 9. The interval transit time unit is used in sonic log 3. See discussion of "Torque, and Bending Mo ging work. ment," Part 1.

25 TABLE 2.2-TABLES OF RECOMMENDED SI UNITS Conversion Factor* Metric Unit Multiply Customary Customary SPE Other Unit by Factor to Quanti� and SI Unit Unit Preferred Allowable Get Metric Unit

SPACE,.* TIME Length m naut mile km 1.852* E+OO mile km 1.609 344* E+OO chain m 2.01 1 68* E+01 link m 2.01 1 68* E-01 fathom m 1.828 8* E+OO m m 1.0* E+OO yd m 9.144* E-01 ft m 3.048* E-01 cm 3.048* E+01 in. mm 2.54* E+01 cm 2.54* E+OO cm mm 1.0* E+01 cm 1.0* E+OO mm mm 1.0* E+OO mil ILm 2.54* E+01 micron (IL) ILm 1.0* E+OO Length/length m/m ftlmi mlkm 1.893 939 E-01 Lengthlvolume m/m3 ftlU.S. gal m/m3 8.051 964 E+01 ftlft3 m/m3 1.076 391 E+01 ftlbbl m/m3 1.917 134 E+OO Length/temperature m/K see "Temperature, Pressure, Vacuum" Area m2 sq mile km2 2.589 988 E+OO section km2 2.589 988 E+OO ha 2.589 988 E+02 acre m2 4.046 856 E+03 ha 4.046 856 E-01 ha m2 1.0* E+04 sq yd m2 8.361 274 E-01 sq ft m2 9.290 304* E-02 cm2 9.290 304* E+02 sq in. mm2 6.451 6* E+02 cm2 6.451 6* E+OO cm2 mm2 1.0* E+02 cm2 1.0* E+OO mm2 mm2 1.0* E+OO Area/volume m2/m3 ft2/in.3 m2/cm3 5.699 291 E-03 Area/mass m2/kg cm2/g m2/kg 1.0* E-01 m2/g 1.0* E-04 Volume, capacity m3 cubem km3 4.168 182 E +00 Illt acre-ft m3 1 .233 489 E+03 ha·m 1.233 489 E-01 m3 m3 1.0* E+OO cu yd m3 7.645 549 E-01 bbl (42 U.S. gal) m3 1.589 873 E-01 cu ft m3 2.831 685 E-02 dm3 L 2.831 685 E+01 U.K. gal m3 4.546 092 E-03 dm3 L 4.546 092 E+OO U.S. gal m3 3.785 412 E-03 dm3 L 3.785 412 E+OO liter dm3 L 1.0* E+OO U.K. qt dm3 L 1.136 523 E+OO U.S. qt dm3 L 9.463 529 E-01 U.S. pt dm3 L 4.731 765 E-01

• An asterisk indicates that the conversion factor is exact using the numbers shown; all subsequent numbers are zeros. " Conversion factors for length. area. and volume (and related quantities) in Table 2.2 are based on the international fool. See Footnote 1 of Table 1.7. Part 1. [See Notes 1 through 13 on Page 25. 26 TABLE 2.2-TA BLES OF RECOMMENDED SI UNITS (cont'd.) Conversion Factor" Metric Unit Multiply Customary Customary SPE Other Unit by Factor to Quanti� and SI Unit Unit Preferred Allowable Get Metric Unit

SPACE," TIME Volume, capacity m3 UK fl oz cm3 2.841 308 E+01 U.S. fl oz cm3 2.957 353 E+01 cu in. cm3 1.638 706 E+01 mL cm3 1.0' E+OO Volumellength m3/m bbllin. m3/m 6.259 342 E+OO (linear displacement) bbl/ft m3/m 5.216 119 E-01 ft31ft m3/m 9.290 304" E-02 U.S. gal/ft m3/m 1.241 933 E-02 dm3/m Urn 1.241 933 E+01 Volume/mass m3/kg see "Density, Specific Volume, Concentration, Dosage" Plane angle rad rad rad 1.0' E+OO deg CO) rad 1.745 329 E-02 (2) 1.0' E+OO min e') rad 2.908 882 E-04 (2) 1.0' E+OO sec (") rad 4.848 137 E-06 (2) 1.0" E+OO Solid angle sr sr sr 1.0' E+OO Time s million years (MY) Ma 1.0' E+OO (3) yr a 1.0' E+OO wk d 7.0' E+OO d d 1.0' E+OO hr h 1.0' E+OO min 6.0' E+01 min s 6.0' E+01 h 1.666 667 E-02 min 1.0" E+OO s s 1.0" E+OO millimicrosecond ns 1.0' E+OO

MASS, AMOUNT OF SUBSTANCE Mass kg U.K. ton (long ton) Mg 1.016 047 E+OO U.S. ton (shortton) Mg 9.071 847 E-01 U.K. ton k!i! 5.080 235 E+01 U.S. cwt kg 4.535 924 E+01 kg kg 1.0' E+OO Ibm kg 4.535 924 E-01

oz (troy) 9 3.1 10348 E+01 oz (av) 9 2.834 952 E+01 9 9 1.0" E+OO grain mg 6.479 891 E+01 mg mg 1.0" E+OO 9 9 1.0" E+OO Mass/length kg/m see "Mechanics" Mass/area kg/m2 see "Mechanics" MasS/Volume kg/m3 see "Density, Specific Volume, Concentration, Dosage" Mass/mass kg/kg see "Density, Specific Vo lume, Concentration, Dosage" Amount of mol Ibm mol kmol 4.535 924 E-01 substance gmol kmol 1.0" E-03 sid m3 (O·C, 1 atm) kmol 4.461 58 E-0214,13) sid m3 (15·C, 1 atm) kmol 4.229 32 E-02 14,13) std ft3 (60·F, 1 atm) kmol 1.1953 E -03 14,13)

27 TABLE 2.2-TABLES OF RECOMMENDED SI UNITS (cont'd.) Conversion Factor* Metric Unit Multiply Customary Customary SPE Other Unit by Factor to Quanti!y and SI Unit Unit Preferred Allowable Get Metric Unit

CALORIFIC VALUE, HEAT, ENTROPY, HEAT CAPACITY Calorific value J/kg Btu/Ibm MJ/kg 2.326 E-03 (mass basis) kJ/kg J/g 2.326 E+OO (kW·h)/kg 6.461 112 E-04 cal/g kJ/kg J/g 4.184* E+OO cal/lbm J/kg 9.224 141 E+OO Calorific value J/mol kcal/g mol kJ/kmol 4.184* C+03'3 (mole basis) Btu/Ibm mol MJ/kmol 2.326 E-03'3 kJ/kmol 2.326 E+00'3 Calorific value J/m3 therm/U.K. gal MJ/m3 kJ/dm3 2.320 80 E+04 (volume basis - kJ/m3 2.320 80 E+07 solids and liquids) (kW'h)/dm3 6.446 660 E+OO Btu/U.S. gal MJ/m3 kJ/dm3 2.787 163 E-01 kJ/m3 2.787 163 E+02 (kW'h)/m3 7.742 119 E-02 Btu/U.K. gal MJ/m3 kJ/dm3 2.320 8 E-01 kJ/m3 2.320 8 E+02 (kW'h)/m3 6.446 660 E-02 Btulft3 MJ/m3 kJ/dm3 3.725 895 E-02 kJ/m3 3.725 895 E+01 (kW'h)/m3 1.034 971 E-02 kcal/m3 MJ/m3 kJ/dm3 4.184* E-03 kJ/m3 4.184* E+OO cal/mL MJ/m3 4.184* E+OO ft·lbf/U.S. gal kJ/m3 3.581 692 E-01 Calorific value J/m3 cal/mL kJ/m3 J/dm3 4.184* E+03 (volume basis - kcal/m3 kJ/m3 J/dm3 4.184* E+OO gases) Btu/ft3 kJ/m3 J/dm3 3.725 895 E+01 (kW ' h)/m3 .1 .034 971 E-02 Specific entropy J/kg'K Btu/(lbm·oR) kJ/(kg'K) J(g 'K) 4.186 8* E+OO cal/(g·oK) kJ/(kg'K) J(g ' K) 4.184* E+OO kcal/(kg·°C) kJ/(kg'K) J(g 'K) 4.184* E+OO Specific heat J/kg·K kW·hr/(kg·oC) kJ/(kg'K) J(g.K) 3.6* E+03 capacity Btu/(lbm·oF) kJ/(kg'K) J(g ' K) 4.186 8* E+OO (mass basis) kcal/(kg·°C) kJ/(kg·K) J(g ' K) 4.184* E+OO Molar heat J/mol·K Btu/(Ibm mol·oF) kJ/(kmol'K) 4.186 8* E+00'3 capacity cal/(g mol·°C) kJ/(kmol'K) 4.184* E-00'3

TEMPERATURE, PRESSURE, VACUUM

Temperature K OR K 5/9 (absolute) OK K 1.0* E+OO Temperature K OF °C (OF - 32)/1 .8 (traditional) °C °C 1.0* E+OO Temperature K OF K °C 5/9 E+OO (difference) °C K °C 1.0* E+OO Temperature/length KIm °F/100 ft mKlm 1.822 689 E+01 (geothermal gradient) Length/temperature m/K ttrF m/K 5.486 4* E-01 (geothermal step) Pressure Pa atm (760mm Hg at O°C or MPa 1.01 3 25* E-01 14.696 (lbf/in.2) kPa 1.013 25* E+02 bar 1.013 25* E+OO bar MPa 1.0* E-01 kPa 1.0* E+02 bar 1.0* E+OO at (technical atm., kgf/cm2) MPa 9.806 65* E-02 kPa 9.806 65* E+01 bar 9.806 65* E-01

28 ' TABLE 2.2-TABLES OF RECOMMENDED SI UNITS (cont'd.) Conversion Factor* Metric Unit Multiply Customary Customary SPE Other Unit by Factor to Quantity and SI Unit Unit Preferred Allowable Get Metric Unit

TEMPERATURE, PRESSURE, VACUUM Pressure Pa Ibf/in.2 (psi) MPa 6.894 757 E-03 kPa 6.894 757 E+OO bar 6.894 757 E-02 in. Hg (32°F) kPa 3.386 38 E+OO in. Hg (60°F) kPa 3.376 85 E+OO in. H20 (39.2°F) kPa 2.490 82 E-01 in. H20 (60°F) kPa 2.488 4 E-01

mm Hg (O°C) = torr kPa 1.333 224 E-01 cm H20 (4°C) kPa 9.806 38 E-02 Ibf/ft2 (psI) kPa 4.788 026 E-02 ....m Hg (O°C) Pa 1.333 224 E-01 ....bar Pa 1.0* E-01 dyne/cm2 Pa 1.0* E-01 Vacuum, draft Pa in. Hg (60°F) kPa 3.376 85 E+OO in. H20 (39.2°F) kPa 2.490 82 E-01 in. H20 (60°F) kPa 2.488 4 E-01

mm Hg (O°C) = torr kPa 1.333 224 E-01 cm H20 (4°C) kPa 9.806 38 E-02 Liquid head m ft m 3.048* E-01 in. mm 2.54* E+01 cm 2.54* E+OO Pressure drop/length Palm psilft kPalm 2.262 059 E+01 psi/100 ft kPalm 2.262 059 E-01(5)

DENSITY, SPECIFIC VOLUME, CONCENTRATION, DOSAGE Density (gases) kg/m3 Ibm/ft3 kg/m3 1.601 846 E+01 g/m3 1.601 846 E+04 Density (liquids) kg/m3 Ibm/U.S. gal kg/m3 1.198 264 E+02 g/cm3 1.198 264 E-01 Ibm/U.K. gal kg/m3 9.977 633 E+01 kg/dm3 9.977 633 E-02 Ibm/ft3 kg/m3 1.601 846 E+01 g/cm3 1.601 846 E-02 g/cm3 kg/m3 1.0* E+03 kg/dm3 1.0* E+OO °API g/cm3 141 .5/(1 31 .5 + °API) Density (solids) kg/m3 Ibm/ft3 kg/m3 1.601 846 E+01 Specific volume m3/kg ft3/lbm m3/kg 6.242 796 E-02 (gases) m3/g 6.242 796 E-05 Specific volume m3/kg ft3/lbm dm3/kg 6.242 796 E+01 (liquids) U.K. gal/Ibm dm3/kg cm3/g 1.002 242 E+01 U.S. sal/Ibm dm3/kg cm3/g 8.345 404 E+OO Specific volume m3/mol Ug mol m3lkmol 1.0* E+00'3 (mole basis) ft3/lbm mol m3/kmol 6.242 796 E-02'3 Specific volume m3/kg bbl/U.S. ton m3/t 1.752 535 E-01 (clay yield) bbl/U.K. ton m3/t 1.564 763 E-01 Yield (shale m3/kg bbl/U.S. ton dm3/t Ut 1.752 535 E +02 distillation) bbl/U.K. ton dm3/t Ut 1.564 763 E+02 U.S. gal/U.S. ton dm3/t Ut 4.172 702 E+OO U.S. gal/U.K. ton dm3/t Ut 3.725 627 E+OO Concentration kg/kg wt % kg/kg 1.0* E-02 (mass/mass) g/kg 1.0* E+01 wt ppm mg/kg 1.0* E+OO Concentration kg/m3 Ibm/bbl kg/m3 g/dm3 2.853 01 0 E+OO (masslvolume) g/U.S. sal kg/m3 2.641 720 E-01 g/U.K. gal kg/m3 gIL 2.199 692 E-01 29 TABLE 2.2-TABLES OF RECOMMENDED SI UNITS (cont'd.) Conversion Factor· Metric Unit Multiply Customary Customary SPE Other Unit by Factor to auanti� and SI Unit Unit Preferred Allowable Get Metric Unit

DENSITY, SPECIFIC VOLUME, CONCENTRATION, DOSAGE

Concentration kg/m3 Ibm/1000 U.S. gal g/m3 mg/dm3 1.198 264 E+02 (masslvolume) Ibm/1000 U.K. gal g/m3 mg/dm3 9.977 633 E+01 grains/U.S. gal g/m3 mg/dm3 1.71 1 806 E+01 grains/ft3 mg/m3 2.288 352 E+03 Ibm/1000 bbl g/m3 m!i!/dm3 2.853 010 E+OO mg/U.S. gal g/m3 mg/dm3 2.641 720 E-01 grains/100 ft3 m!i!/m3 2.288 352 E+01 Concentration m3/m3 bbl/bbl m3/m3 1.0· E+OO (volumelvolume) ft3/ft3 m3/m3 1.0· E+OO bbl/acre·ft m3/m3 1.288 923 E-04 m3/ha·m 1.288 923 E+OO vol % m3/m3 1.0· E-02 U.K. gal/ft3 dm3/m3 Llm3 1.605 437 E+02 U.S. gal1ft3 dm3/m3 Llm3 1.336 806 E+02 mLlU.S. gal dm3/m3 Llm3 2.641 720 E-01 mLlU.K. gal dm3/m3 Llm3 2.199 692 E-01 vol ppm cm3/m3 1.0· E+OO dm3/m3 Llm3 1.0· E-03 U.K. gal/1000 bbl cm3/m3 2.859 406 E+01 U.S. gal/1000 bbl cm3/m3 2.380 952 E+01 U.K. ptl1000 bbl cm3/m3 3.574 253 E+OO Concentration mol/m3 Ibm moI/U.S. gal kmol/m3 1.198 264 E+02 (mole/volume) Ibm moI/U.K. gal kmol/m3 9.977 633 E+01 Ibm mollft3 kmol/m3 1.601 846 E+01 std ft3 (60°F, kmol/m3 7.518 18 E-03 1 atm)/bbl Concentration m3/mol U.S. gal/1000 std ft3 dm3/kmol Llkmol 3.166 93 E+OO (volume/mole) (60°F/60°F) bbl/million std ft3 dm3/kmol Llkmol 1.330 11 E-01 (60°F/60°F)

FACILITY THROUGHPUT, CAPACITY

Throughput kg/s million Ibm/yr tla Mg/a 4.535 924 E+02 (mass basis) U.K. tonlyr tla Mg/a 1.016 047 E+OO U.S. ton/yr tla Mg/a 9.071 847 E-01 U.K. ton/D tid Mg/d 1.016 047 E+OO tlh, Mg/h 4.233 529 E-02 U.S. ton/D tid 9.071 847 E-01 tlh, Mg/h 3.779 936 E-02 U.K. ton/hr tlh Mg/h 1.016 047 E+OO U.S. ton/hr tlh Mg/h 9.071 847 E-01 Ibm/hr kg/h 4.535 924 E-01 Throughput m3/s bbl/D tla 5.803 036 E+01 (7) (volume basis) m3/d 1.589 873 E-01 m3/h 6.624 471 E-03 ft3/D m3/h 1.179 869 E-03 m3/d 2.831 685 E-02 bbl/hr m3/h 1.589 873 E-01 fP/h m3/h 2.831 685 E-02 U.K. gal/hr m3/h 4.546 092 E-03 LIs 1.262 803 E-03 U.S. gal/hr m3/h 3.785 412 E-03 LIs 1.051 503 E-03 U.K. gal/min m3/h 2.727 655 E-01 LIs 7.576 819 E-02 U.S. gal/min m3/h 2.271 247 E-01 LIs 6.309 020 E-02 30 TA BLE 2.2-TABLES OF RECOMMENDED SI UNITS (cont'd.) Conversion Factor* Metric Unit Multiply Customary Customary SPE Other Unit by Factor to auanti� and SI Unit Unit Preferred Allowable Get Metric Unit

FACILITY THROUGHPUT, CAPACITY (6)

Throughput mol/s Ibm mollhr kmol/h 4.535 924 E-01 (mole basis) kmol/s 1.259 979 E-04

FLOW RATE (6)

Pipeline capacity m3/m bbl/mile m3lkm 9.879 013 E-02 Flow rate kg/s U.K. ton/min kg/s 1.693 412 E+01 (mass basis) U.S. ton/min kg/s 1.51 1 974 E+01 U.K. ton/hr kg/s 2.822 353 E-01 U.S. ton/hr kg/s 2.519 958 E-01 U.K. tontO kg/s 1.175 980 E-02 U.S. tontO kg/s 1.049 982 E-02 million Ibm/yr kg/s 5.249 912 E+OO U.K. ton/�r kg/s 3.221 864 E-05 U.S. ton/yr kg/s 2.876 664 E-05 Ibm/s kg/s 4.535 924 E-01 Ibm/min kg/s 7.559 873 E-03 Ibm/hr kg/s 1.259 979 E-04 Flow rate m3/s bbl/O m3/d 1.589 873 E-01 (volume basis) Us 1.840 131 E-03 ft3/0 m3/d 2.831 685 E-02 Us 3.277 413 E-04 bbl/hr m3/s 4.416314 E-05 Us 4.416314 E-02 ft3/hr m3/s 7.865 791 E-06 Us 7.865 791 E-03 U.K. gal/hr dm3/s Us 1.262 803 E-03 U.S. gal/hr dm3/s Us 1.051 503 E-03 U.K. gal/min dm3/s Us 7.576 820 E-02 U.S. gal/min dm3/s Us 6.309 020 E-02 ft3/min dm3/s Us 4.719 474 E-01 fWs dm3/s Us 2.831 685 E+01 Flow rate mol/s Ibm mol/s kmol/s 4.535 924 E-0113 ' (mole basis) Ibm mol/hr kmol/s 1.259 979 E-04 3 ' million scf/O kmol/s 1.383 449 E-02 3 Flow rate/length kg/s'm Ibm/(s-ft) kg/(s'm) 1.488 164 E+OO (mass basis) Ibm/(hr-ft) kg/(s'm) 4.133 789 E-04 Flow rate/length m2/s U.K. gal/(min-ft) m2/s m3/(s·m) 2.485 833 E-04 (volume basis) U.S. gal/(min-ft) m2/s m3/(s·m) 2.069 888 E-04 U.K. aal/(hr-in.) m2/s m3/(s·m) 4.971 667 E-05 U.S. gal/(hr-in.) m2/s m3/(s·m) 4.139 776 E-05 U.K. gal/(hr-ft) m2/s m3/(s·m) 4.143 055 E-06 U.S. gal/(hr-ft) m2/s m3/(s·m) 3.449 814 E-06 Flow rate/area kg/s'm2 Ibm/(s-ft2) kg/s'm2 4.882 428 E+OO (mass basis) Ibm/(hr-W) kg/s·m2 1.356 230 E-03 Flow rate/area m/s ft3/(S-ft2) m/s m3(s·m2) 3.048* E-01 (volume basis) ft3/(min-ft2) m/s m3/(s·m2) 5.08" E-03 U.K. gal/(hr-in.2) m/s m3/(s'm2) 1.957 349 E-03 U.S. gal/(hr-in.2) m/s m3/(s·m2) 1.629 833 E-03 U.K. gal/(min-ft2) m/s m3/(s'm2) 8.155 621 E-04 U.S. gal/(min-W) m/s m3/(s·m2) 6.790 972 E-04 U.K. gal/(hr-W) m/s m3/(s·m2) 1.359 270 E-05 U.S. gal/(hr-W) m/s m3/(s'm2) 1.131 829 E-05 Flow rate/ m3/s·Pa bbl/(O-psi) m3/(d'kPa) 2.305 916 E-02 pressure drop (productivity index) 31 TA BLE 2.2-TA BLES OF RECOMMENDED SI UNITS (cont'd.) Conversion Factor* Metric Unit Multiply Customary Customary SPE Other Unit by Factor to Quanti!yand SI Unit Unit Preferred Allowable Get Metric Unit

ENERGY, WORK, POWER Energy, work J quad MJ 1.055 056 E+12 TJ 1.055 056 E+06 EJ 1.055 056 E+OO MW·h 2.930 71 1 E+08 GW·h 2.930 711 E+05 TW·h 2.930 711 E+02 therm MJ 1.055 056 E+02 kJ 1.055 056 E+05 kW·h 2.930 71 1 E+01 U.S. tonf-mile MJ 1.431 744 E+01 hp-hr MJ 2.684 520 E+OO kJ 2.684 520 E+03 kW·h 7.456 999 E-01 ch-hr or CV-hr MJ 2.647 796 E+OO Kj 2.647 796 E+03 kW·h 7.354 99 E-01 kW-hr MJ 3.6* E+OO kJ 3.6* E+03 Chu kJ 1.899 101 E+OO kW·h 5.275 280 E-04 Btu kJ 1.055 056 E+OO kW·h 2.930 71 1 E-04 kcal kJ 4.184* E+OO cal kJ 4.184* E-03 ft-Ibf kJ 1.355 818 E-03 Ibf-ft kJ 1.355 818 E-03 J kJ 1.0* E-03 Ibf-ft2/s2 kJ 4.214 011 E-05 erg J 1.0' E-07 Impact energy J kgf-m J 9.806 650' E+OO Ibf-ft J 1.355 818 E+OO Work/length JIm U.S. tonf-mile/ft MJ/m 4.697 322 E+01 Surface energy J/m2 erg/cm2 mJ/m2 1.0' E+OO Specific impact J/m2 kgf·m/cm2 J/cm2 9.806 650' E-OO energy Ibf·ft/in.2 J/cm2 2.101 522 E-01 Power W quad/yr MJ/a 1.055 056 E+12 TJ/a 1.055 056 E+06 EJ/a 1.055 056 E+OO erg/a TW 3.170 979 E-27 GW 3.170 979 E-24 million Btu/hr MW 2.930 71 1 E-01 ton of kW 3.51 6 853 E+OO refrigeration Btu/s kW 1.055 056 E+OO kW kW 1.0* E+OO hydraulic horse- kW 7.460 43 E-01 power -hhp hp (electric) kW 7.46' E-01 hp (550 ft-Ibf/s) kW 7.456 999 E-01 ch or CV kW 7.354 99 E-01 Btu/min kW 1.758 427 E-02 ft·lbf/s kW 1.355 818 E-03 kcal/hr W 1.162 222 E+OO Btu/hr W 2.930 71 1 E-01 ft'lbf/min W 2.259 697 E-02 Power/area W/m2 Btu/s·ft2 kW/m2 1.135 653 E+01 cal/hr'cm2 kW/m2 1.162 222 E-02 Btu/hr·ft2 kW/m2 3.154 591 E-03 32 TA BLE 2.2-TA BLES OF RECOMMENDED SI UNITS (cont'd.) Conversion Factor' Metric Unit Multiply Customary Customary SPE Other Unit by Factor to Quanti� and SI Unit Unit Preferred Allowable Get Metric Unit

ENERGY, WORK, POWER Heat flow unit - hfu j1.Cal/s·cm2 mW/m2 4.184* E+01 (geothermics) Heat release rate, W/m3 hp/ft3 kW/m3 2.633 414 E+01 mixing power cal/(hr·cm3) kW/m3 1.162 222 E+OO Btu/(s·ft3) kW/m3 3.725 895 E+01 Btu/(hr·ft3) kW/m3 1.034 971 E-02 Heat generation cal/(s-cm3) jJ.W/m3 4.184* E+12 unit -hgu (radioactive rocks) Cooling duty WIW Btu/(bhp-hr) W/kW 3.930 148 E-01 (machinery) Specific fuel kg/J Ibm/(hp-hr) mg/J kg/MJ 1.689 659 E-01 consumption kg/(kW'h) 6.082 774 E-01 (mass basis) Specific fuel m3/J m3/(kW-hr) dm3/MJ mm3/J 2.777 778 E+02 consumption dm3/(kW'h) 1.0* E+03 (volume basis) U.S. gal/(hp-hr) dm3/MJ mm3/J 1.410 089 E+OO dm3/(kW'h) 5.076 321 E+OO U.K. pt/(hp-hr) dm3/MJ mm13/J 2.1 16809 E-01 dm3/(kW'h) 7.620 512 E-01 Fuel consumption m3/m U.K. gal/mile dm3/100 km U100 km 2.824 81 1 E+02 (automotive) U.S. gal/mile dm3/1 00 km U100 km 2.352 146 E+02 mile/U.S. gal km/dm3 km/L 4.251 437 E-01 mile/U.K. gal km/dm3 km/L 3.540 060 E-01

MECHANICS Velocity (linear), m/s knot kmlh 1.852* E+OO speed mile/hr km/h 1.609 344* E+OO m/s m/s 1.0* E+OO ftls m/s 3.048* E-01 cm/s 3.048* E+01 m/ms 3.048* E-0418) ftlmin m/s 5.08* E-03 cm/s 5.08' E-01 ftlhr mm/s 8.466 667 E-02 cmls 8.466 667 E-03 ftlD mm/s 3.527 778 E-03 mId 3.048' E-01 in.ls mm/s 2.54* E+01 cm/s 2.54* E+OO in.lmin mm/s 4.233 333 E-01 cm/s 4.233 333 E-02 Velocity (angular) rad/s rev/min rad/s 1.047 198 E-01 rev/s rad/s 6.283 185 E+OO degree/min radls 2.908 882 E-04 Interval transit time s/m sIft slm jJ.s/m 3.280 840 E+0019) Corrosion rate m/s in./yr (ipy) mm/a 2.54* E+01 mil/yr mm/a 2.54* E-02 Rotational frequency rev/s rev/s rev/s 1.0* E+OO rev/min rev/s 1.666 667 E-02 rev/min rad/s 1.047 198 E-01 Acceleration m/s2 ftls2 mls2 3.048* E-01 (linear) cm/s2 3.048' E+01 gal(cm/s2) m/s2 1.0* E-02 Acceleration rad/s2 rad/s2 rad/s2 1.0* E+OO (rotational) rpmls rad/s2 1.047 198 E-01 Momentum kg·m/s Ibm·ftls kg·m/s 1.382 550 E-01

33 TA BLE 2.2-TA BLES OF RECOMMENDED SI UNITS (cont'd.) Conversion Factor· Metric Unit Multiply Customary Customary SPE Other Unit by Factor to Quantity and SI Unit Unit Preferred Allowable Get Metric Unit

MECHANICS Force N U.K. tonf kN 9.964 016 E+OO U.S. tonf kN 8.896 443 E+OO kgf (kp) N 9.806 650· E+OO Ibf N 4.448 222 E+OO N N 1.0· E+OO pdl mN 1.382 550 E+02 dyne mN 1.0· E-02 Bending moment, N'm U.S. tonf·ft kN·m 2.71 1 636 E+OO(lO) torque kgf·m N·m 9.806 650· E+OO('O) Ibf·ft N'm 1.355 818 E+OO('O) Ibf·in. N'm 1.129 848 E-01('O) pdl·ft N·m 4.214011 E-02('O) Bending moment! N'm/m (lbf·ft)/in. (N·m)/m 5.337 866 E+01('O) length (kgf·m)/m (N'm)/m 9.806 650· E+OO('O) (Ibf·in.)/in. (N·m)/m 4.448 222 E+OO(lO) Elastic moduli Pa Ibf/in.2 GPa 6.894 757 E-06 (Young's, Shear bulk) Moment of inertia kg·m2 Ibm·ft2 kg·m2 4.214 011 E-02 Moment of section m' in.' cm' 4.162 314 E+01 Section modulus m3 cu in. cm3 1.638 706 E+01 cu ft cm3 1.638 706 E+04 mm3 2.831 685 E+04 m3 2.831 685 E-02 Stress Pa U.S. tonf/in.2 MPa N/mm2 1.378 951 E+01 kgf/mm2 MPa N/mm2 9.806 650· E+OO U.S. tonf/ft2 MPa N/mm2 9.576 052 E-02 Ibf/in.2 (psi) MPa N/mm2 6.894 757 E-03 Ibf/ft2 (psf) kPa 4.788 026 E-02 dyne/cm2 Pa 1.0· E-01 Yield point, Ibf/100 ft2 Pa 4.788 026 E-01 gel strength (drilling fluid) Mass/length kg/m Ibm/ft kg/m 1.488 164 E+OO

Mass/area kg/m2 U.S. tonlft2 Mg/m2 9.764 855 E+OO structural loading, bearing capacity Ibm/ft2 kg/m2 4.882 428 E+OO (mass basis) Coefficientof m/(m·K) in.l(in.·oF) mm/(mm·K) 5.555 556 E-01 thermal expansion

TRANSPORT PROPERTIES Diffusivity m2/s ft2/s mm2/s 9.290 304· E+04 cm2/s mm2/s 1.0· E+02. ft2/hr mm2/s 2.580 64· E+01 Thermal resistance (k·m2)1W (OC·m2·hr)/kcal (K·m2)/kW 8.604 208 E+02 (OF·ft2 hr)/Btu (K·m2)/kW 1.761 102 E+02 Heat flux W/m2 Btu/(hr'ft2) kW/m2 3.154 591 E-03 Thermal W/(m·K) (cal/s·cm2.°C)/cm W/(m·K) 4.184· E+02 conductivity Btu/(hr·ft2.oF/ft) W/(m·K) 1.730 735 E+OO kJ·m/(h·m2.K) 6.230 646 E+OO kcal/(hr·m2.oC/m) W/(m·K) 1.162 222 E+OO Btu/(hr·ft2.oF/in.) W/(m·K) 1.442 279 E-01 cal/(hr·cm2.oC/cm) W/(m·K) 1.162 222 E-01

34 TA BLE 2.2-TA BLES OF RECOMMENDED SI UNITS (cont'd.) Conversion Factor· Metric Unit Multiply Customary Customary SPE Other Unit by Factor to Quantit:land SI Unit Unit Preferred Allowable Get Metric Unit

TRANSPORT PROPERTIES Heat transfer W/{m2.K) cal/{s-cm2-0C) kW/{m2·K) 4.184· E+01 coefficient Btu/{s-ft2-0F) kW/{m2·K) 2.044 17.5 E+01 cal/{hr-cm2-0C) kW/{m2·K) 1.162 222 E-02 Btu/{hr-ft2_0F) kW/(m2·K) 5.678 263 E-03 kJ/{h·m2.K) 2.044 175 E+01 Btu/{hr-ft2-OR) kW/{m2.K) 5.678 263 E-03 kcall{hr-m2-0C) kW/{m2.K) 1.162 222 E-03 Volumetric heat W/{m3'K) Btu/{s-ft3_0F) kW/{m3·K) 6.706 61 1 E+01 transfer coefficient Btu/{hr-ft3-0F) kW/{m3'K) 1.862 947 E-02 Surface tension N/m dyne/cm mN/m 1.0· E+OO Viscosity Pa's {lbf-s)/in.2 Pa's {N's)/m2 6.894 757 E +03 (dynamic) {lbf-s)/ft2 Pa·s {N's)/m2 4.788 026 E+01 {kgf-s)/m2 Pa·s (N's)/m2 9.806 650· E+OO Ibm/{ft-s) Pa·s {N·s)/m2 1.488 164 E+OO {dyne-s)/cm2 Pa's {N·s)/m2 1.0· E-01 cp Pa's (N's)/m2 1.0· E-03 Ibm/{ft·hr) Pa·s (N·s)/m2 4.133 789 E-04 Viscosity m2/s ft2/s mm2/s 9.290 304· E+04 (kinematic) in.2/s mm2/s 6.451 6· E+02 m2/hr mm2/s 2.777 778 E+02 cm2/s mm2/s 1.0· E+02 ft2lhr mm2/s 2.580 64· E+01 cSt mm2/s 1.0· E+OO Permeability m2 darcy jJ.m2 9.869 233 E-01(11) millidarcy jJ.m2 9.869 233 E-04(11) 10-3 jJ.m2 9.869 233 E-01 (11)

ELECTRICITY, MAGNETISM Admittance S S S 1.0· E+OO Capacitance· F jJ.F jJ.F 1.0· E+OO Capacity, C A-hr kC 3.6· E+OO storage battery Charge density C/m3 C/mm3 C/mm3 1.0· E+OO Conductance S S S 1.0· E+OO U{mho) S 1.0· E+OO Conductivity S/m S/m S/m 1.0· E+OO U/m S/m 1.0· E+OO mU/m mS/m 1.0· E+OO Current density Alm2 Almm2 Almm2 1.0· E+OO Displacement C/m2 C/cm2 C/cm2 1.0· E+OO Electric charge C C C 1.0· E+OO Electric current A A A 1.0· E+OO Electric dipole C·m C·m C·m 1.0· E+OO moment Electric field VIm VIm VIm 1.0· E+OO strength Electric flux C C C 1.0· E+OO Electric polarization C/m2 C/cm2 C/cm2 1.0· E+OO Electric potential V V V 1.0· E+OO mV mV 1.0· E+OO Electromagnetic A·m2 A·m2 A'm2 1.0· E+OO moment Electromotive force V V V 1.0· E+OO Flux of displacement C C C 1.0· E+OO

35 TA BLE 2.2-TA BLES OF RECOMMENDED SI UNITS (cont'd.) Conversion Factor' Metric Unit Multiply Customary Customary SPE Other Unit by Factor to Quantity and SI Unit Unit Preferred Allowable Get Metric Unit

ELECTRICITY, MAGNETISM

Frequency Hz cycles/s Hz 1.0' E+OO Impedance n n n 1.0' E+OO Interval transit time s/m fJos/ft fJos/m 3.280840 E+OO Linear current Aim Almm Almm 1.0' E+OO density Magnetic dipole Wb-m Wb-m Wb-m 1.0' E+OO moment Magnetic field Aim Almm Almm 1.0' E+OO strength oersted Aim 7.957 747 E+01 gamma Aim 7.957 747 E-04 Magnetic flux Wb mWb mWb 1.0' E+OO Magnetic flux T mT mT 1.0' E+OO density gauss T 1.0' E-04 Magnetic induction T mT mT 1.0' E+OO Magnetic moment A-m2 A-m2 A-m2 1.0' E+OO Magnetic T mT mT 1.0' E+OO polarization Magnetic potential A A A 1.0' E+OO difference Magnetic vector Wb/m Wb/mm Wb/mm potential Magnetization Aim Almm Almm Modulus of S S S admittance Modulus of n n n impedance Mutual inductance H H H Permeability Him fJoH/m fJoH/m Permeance H H H Permittivity F/m fJoF/m fJoF/m Potential difference V V V Quantity of C C C electricity Reactance n n n Reluctance H-1 H-1 H-1 Resistance n n n Resistivity nom n-cm n-cm nom nom (12) Self inductance H mH mH Surface density C/m2 mC/m2 mC/m2 of charge Susceptance S S S Volume density C/m3 C/mm3 C/mm3 of charge

ACOUSTICS, LIGHT, RADIATION

Absorbed dose Gy rad Gy 1.0' E-02 Acoustical energy J J J Acoustical intensity W/m2 W/cm2 W/m2 1.0' E+04 Acoustical power W W W Sound pressure N/m2 N/m2 N/m2 1 Illuminance Ix footcandle Ix 1.076 391 E+01 Illumination Ix footcandle Ix 1.076 391 E+01 Irradiance W/m2 W/m2 W/m2 Light exposure Ix's footcandle·s Ix-s 1.076 391 E+01 Luminance cd/m2 cd/m2 cd/m2 Luminous efficacy ImIW ImIW Im/W 36 TA BLE 2.2-TA BLES OF RECOMMENDED SI UNITS (cont'd.) Conversion Factor" Metric Unit Multiply Customary Customary SPE Other Unit by Factor to Quantity and SI Unit Unit Preferred Allowable Get Metric Unit

ACOUSTICS, LIGHT, RADIATION

Luminous exitance Im/m2 Im/m2 Im/m2 Luminous flux 1m 1m 1m Luminous intensity cd cd cd Quantityof light I' m·s talbot I' m·s 1.0' E+OO Radiance W/(m2'sr) W/(m2-sr) W/(m2'sr) Radiant energy J J J Radiant flux W W W Radiant intensity W/sr W/sr W/sr Radiant power W W W 1 Wave length m 'A nm 1.0' E-01 Capture unit m - ' 10-3cm- ' m - ' 1.0' E+01 10-"cm- ' 1 m - ' m - ' 1 Radioactivity curie Bq 3.7' E+10

37 TA BLE 2.3-S0ME ADDITIONAL APPLICATION STANDARDS Conversion Factor- Metric Unit Multiply Customary Customary SPE Other Unit by Factor to Quanti� and SI Unit Unit Preferred Allowable Get Metric Unit Capillary pressure Pa ft (fluid) m (fluid) 3.048- E-Ol Compressibility of Pa-' psi- ' Pa- ' 1.450 377 E-04 reservoirfluid kPa- ' 1.450 377 E-Ol Corrosion allowance m in. mm 2.54- E+Ol Corrosion rate m/s mil/yr mm/a 2.54- E-02 (mpy) Differential orifice Pa in. H2O kPa 2.488 4 E-Ol pressure (at 60°F) cm H2O 2.54- E+OO Gas-oil ratio m3/m3 scf/bbl "standard" 1.801 175 E-Oll')-- m3/m3 Gas rate m3/s scf/D "standard" 2.863 640 E-021') m3/d Geologic time s yr Ma Head (fluid mechanics) m ft m 3.048- E-Ol cm 3.048- E+Ol Heat exchange rate W Btu/hr kW 2.930 71 1 E-04 kJ/h 1.055 056 E+OO Mobility m2/Pa's d/cp /Jom2/mPa·s 9.869 233 E-Ol /Jom2/Pa·s 9.869 233 E+02 Net pay thickness m ft m 3.048- E-Ol Oil rate m3/s bbl/D m3/d 1.589 873 E-Ol short ton/yr Mg/a tla 9.071 847 E-Ol Particle size m micron /Jom 1.0- Permeability-thickness m3 md-ft md'm /Jom2.m 3.008 142 E-04 Pipe diameter (actual) m in. cm 2.54- E+OO mm 2.54- E+Ol Pressure buildup Pa psi kPa 6.894 757 E+00(2) per cycle Productivity index m3/Pa·s bbl/(psi-D) m3/(kPa·d) 2.305 916 E-02(2) Pumping rate m3/s U.S. gal/min m3/h 2.271 247 E-Ol Us 6.309 020 E-02 Revolutions per minute rad/s rpm rad/s 1.047 198 E-Ol rad/m 6.283 185 E+OO Recovery/unit volume m3/m3 bbl/(acre-ft) m3/m3 1.288 931 E-04 (oil) m3/ha·m 1.288 931 E+OO Reservoirarea m2 sq mile km2 2.589 988 E+OO acre ha 4.046 856 E-Ol Reservoirvolume m3 acre-ft m3 1.233 482 E+03 ha'm 1.233 482 E-Ol Specific productivity m3/Pa·s·m bbl/(D-psi-ft) m3/(kPa·d·m) 7.565 341 E-02(2) index Surface or interfacial N/m dyne/cm mN/m 1.0- E+OO tension in reservoir capillaries Torque N'm Ibf-ft N'm 1.355 818 E+00(3) Velocity (fluid flow) m/s fils m/s 3.048- E-Ol Vessel diameter m 10100 cm in. cm 2.54- E+OO above 100 cm ft m 3.048- E-Ol "An asterisk indicates the conversion factor is exact using the numbers shown; all subsequent numbers are zeros. " See Notes '·3 on page 1598.

38 TABLE 2.4-FAHRENHEIT - CELSIUS TEMPERATURE CONVERSION CHART

- 459. 67 to -19 -18to53 54 to 350 360 to 1070 1080 to 1790 1800 to 3000

(O (0 (O (O O ( ( C CF C F C CF C F ( C) F 0 O ) ) ) e ) ) ) e ) ) C ) C) F) 1 l - 27 78 - 1 8 4 111 1 -17J -459 67 -0 II I 14 1 181 160 680 0 181 2 1,080 1 .97 6 0 9!2 2 1,100 1.17l 0 2 2 1 4 -267 7 8 -4 10 - 7 1 -17 12 8 5\ III 0 187 8 1 70 698 0 58/ 1 1,090 1.994 0 917 I 1,110 3.190 0 -2 6 -16 12 III 8 -161 21 -440 6 7 13.3 56 1 9 1 1 180 "16 0 591 1 1,100 2,012.0 993 3 1,120 3,308 0 50 -156 67 -430 -26 12 -I S 13 9 57 134 6 198 9 390 734 0 598 9 1 , 110 2,030 0 991 9 1,130 3 3 16 0 68 -1\1 11 -420 -25 1 6 -14 14 4 18 1 1 6 4 104 4 '00 III 0 60' 4 1,120 2,048 0 1,00' 4 1,140 ),3" 0

8 138 1 -14\ 16 --no - 21 00 - 13 6 110 59 110 0 .10 770 0 610 0 1,1 3 0 2, 066 0 1 ,0 1 00 I.!50 ) , ) 6 1 1 1 10 4 11 6 0 1'0 0 -1'0 00 -400 -1' 44 - 1 6 211 6 410 788 0 611 6 1 , 1 40 2,014 0 1,011 6 UtO U80 0 I 1.1 8 -234 " -190 -13 89 - I II I 16 I 6 1 221 I '10 806 0 611 I 1 ,1 10 2,102 0 1,021 1 1,170 3,39! 0 14 -llB 89 -180 -13 11 - 10 0 1 6 7 61 1 '1 6 226 7 440 8 14 6 626 7 1,160 2,120 0 1,026 7 1 ,110 1 .16 0 -9 1 8 -lll 33 -370 -22 78 1 1 7 2 !l 1 . 1 ' 2 3 1 1 '10 8 4 1 0 611 1 1 ,170 2,118 0 I ,Oll 2 1,190 l.4l4 0

17 - 1 17 78 - 1 60 -11 12 - 8 6 17 8 64 W 2 217 8 460 860 0 637 I IIS0 2 ,116 0 1.017 I 1,900 1,'12 0 -111 11 -lID - 11 61 -I 19 4 18 1 61 149 0 143 1 410 81S 0 64l 3 1,190 2,114 0 1,�l.J 1,910 3,'1 0 0 - -106 67 -1'1 - 1 111 6 2 1 1 1 8 9 66 1 10 8 2'S 9 .SO 8 9 60 6'1 9 1,100 2.192 0 UI8 9 1 ,920 1 418 0 -101 II -330 -10 16 -I 13 0 19 4 61 111 6 114 • 490 9 14 0 614 4 1,2 10 2 , 2 10 0 1,01' • 1.910 3,106 0 . -1'1 16 -m - 10 00 - 14 8 20 a 68 1 14 4 1.0 0 100 9 1 1 0 660 0 1 , 110 2,228 0 1.060 0 1.9.0 3, 51" �

-1'0 00 -31) _19 ,tJ, - 3 16 6 10 6 69 116 1 161 6 1 1 0 9 10 0 6616 1 . 13 0 1,246 0 1,061 1 1.910 l.l'2 0 _184 H -300 - 18 89 - 1 18 • 11 I 10 118 0 171 I 110 9 68 0 611 1 1,140 2.264 C 1,011 1 1,960 3,160 0 -178 87 -190 - 18 31 - I 10 1 2 1 7 II 1 19 8 116 7 130 986 0 616 I 1.210 2.182 0 1,076 7 1 ,970 3,171 n -173 33 -180 - 17 8 0 ll O II I Il 1 6 1 6 18l l 140 1,004 0 68 11 1,160 2.300 0 1,081 ! 1,980 3,196 0 - 1 69 11 -173 II -�SQ 61 - 17 1 I 33 8 22 8 I l 1 63 4 181 8 1 10 1022 0 687 8 1.110 2,318 0 1.081 i 1 .990 1.11' 0

-168 89 -1Il -4\7 6 -167 1 11 6 11 3 14 161 1 293 1 160 1,0'0 0 693 1 1.280 1,336 0 1,091 3 2,000 3 .• 12 , - I!l 78 -lIO _4 14 0 -161 1 37 4 11 ' 71 161 0 198 9 170 1,018 0 698 , 1 190 UI' 0 1.098 9 2 . 0 1 0 3 . 610 e -162 11 -160 -06 0 -11 6 4 19 1 1 : 4 16 168 8 104 • \80 1,076 � 71).1 .1 1,100 1.m 0 1,104 4 2,010 3 , 661 0 -116 61 -210 -418 0 - 11 0 I '1 0 21 0 71 110 6 1 10 0 190 1 094 0 110 0 1,1 1 0 1.1'0 0 1,110 0 2,010 3 .686 ' 6 S _lSI 1 \ -1'0 -400 0 -1.1 4 41 8 l 6 78 I n .1 111 6 600 1,112 0 111 6 1310 1,40S 0 I, III 6 2 , 040 3.70. 0

I - 14\ 16 -210 -181 0 -11 9 7 44 6 26 I 1 9 17' 1 311 6 1 0 1,110 0 711 I 1 , 3 30 2,'16 0 1,121 1 2.050 3 , me -1.0 00 -210 -16< 0 -Il l 8 46 4 2 6 1 80 116 0 116 I 6 20 1,148 0 726 I 1.340 2,U' 0 1,126 I 2,060 ),740 � - 1 34 44 -110 -146 0 - 11 8 9 '! 1 2 12 S I 1 71 8 lll l 610 1.166 0 712 2 1.310 2,462 0 1,112 1 2.070 ) ./18 0 - 1 2! 89 -100 -llS 0 -112 10 10 0 27 8 81 119 6 ll7 S 6.0 1,18' 0 711 8 1,160 2,480 0 1,117 I 2. 080 3.176 C - 111 11 - 1 90 -310 0 _1 1 7 II 1 1 8 18 1 81 181 4 1'1 3 610 1 , 101 0 7'1 1 1,110 2,498 0 1,141 3 2,090 l,7U C

-III IS - 1 8 0 -19 1 0 -1 1 1 1 1 1 36 2S 9 8' 183 2 2 '8 9 660 1,220 0 7'8 9 1 , 3 80 2,116 0 1,141 9 1.100 3,111 e - 111 11 -110 -1 140 -10 6 11 11 4 19 4 81 181 0 1\4 4 610 1,118 0 7 54 . 1,390 2,5H 0 1,15' • 2,1 10 3,110 0 -106 61 - 160 - 1 16 0 -100 U 51 l 30 0 86 186 8 3 60 0 680 1,156 0 760 0 1,400 1.111 0 1 . 1 60 0 2,120 3,1'1 0 _101 11 -110 -218 0 -94 4 1\ \9 0 10 6 81 188 6 361 6 690 1,174 0 761 6 1 , '10 1.110 0 1 ,16 11 2 ,130 3,166 C - 91 16 -1.0 -220 0 - 8 H9 16 60 8 3 11 8S 190 4 1II I 700 1.292 0 711 I 1,'20 2,518 0 1,111.1 2 ,1'0 ],11' 0

- 90 00 -1 30 -201 0 -8ll II 61 6 1 1 7 89 192 1 116 7 110 1,110 0 776 7 1 , 430 2,6060 1,176 7 2 ,1 10 ),901 C - 84 .U -110 -184 0 - 7 1 8 1 8 64 4 1 1 1 90 194 0 181 1 710 1,118 0 781 1 1,440 2,61< 0 1,182 2 2,160 3 ,920 0 - - 78 89 1 1 0 - 166 0 -72 2 19 66 1 31 8 91 195 8 lSI 8 730 1,346 0 781 8 1,4\0 2,641 0 1 , 1 111 2 .170 3 ,931 0 - 11 13 - 100 - 1480 - 661 10 68 0 33 3 91 191 6 393 3 7.0 1,364 0 793 3 1�60 1,6600 I,m.) 1,180 3,911 0 - 70 16 - 95 - 1 19 0 - 6 II 1 1 69 8 ll9 93 199 4 198 9 710 1,181 0 798 9 1 ,4 70 2,611 0 1,191 9 2, 1 90 3,9140

- 67 18 - 90 - 130 0 - \ 16 II 11 6 34 4 94 201 1 404 4 760 1,400 0 804 • 1 ,480 2,696 0 1.204 4 2,200 3,992 0 - 61 00 - 81 - 111 0 - 100 1 3 11 4 31 0 95 203 0 410 0 770 1,418 0 810 0 1 ,490 1.71 4 0 1,110 0 2 ,21 0 4.010 0 - 61 11 - 80 - 111 0 - 444 1 4 II I 11 6 96 1048 4 11 6 780 1,436 0 815 6 1 . 100 2.731 0 1,211 I 2,210 4,021 0 - I' 4\ - I I - 101 0 - 38' 11 7 1 0 16 I 97 106 6 ' 1 1 1 790 1.4 ,.� a 811 I 1.110 2 . 710 0 1,111 I 2 , 1 l0 4,046.0 - 16 61 - 70 - 94 0 - 3 33 16 78 8 36 7 98 208 • 4 16 1 800 1,471 0 S16 7 1.120 1.168 0 1,116 7 2 ,240 4.014 0

-1189 - 61 - 8\ 0 - 118 1 1 80 6 37 1 99 110 2 4 l l l 810 1 , 4 900 831 1 1 ,\30 2 . 1 8 60 l,m 2 2.210 ',012 0 - 51 il - 60 - 16 0 - 111 18 81 ' 31 8 100 1Il 0 431 8 810 1.108 0 837 8 1,140 2,10' 0 1.231 I 2,210 4,100 0 - '8 1' - \\ - 67 0 - 167 19 84 2 431 110 130 0 W3 810 1,116 0 8.l l 1 . 1 50 2.821 0 1,1'3 3 2,110 ',1 11 0 - .\ 16 - 10 - 18 0 - III 30 86 0 48 9 1 1 0 1'8 0 448 9 8 '0 1,544 0 848 9 1 ,\60 1,8'0 0 1,241 9 2,110 ',1)6 0 - ' 178 -4\ - 49 0 - 0 \6 31 81 8 14 4 130 266 0 4 54 4 8 10 1 , 5 62 0 S5" 1.1 70 2.818 0 1.2 14 4 2,290 4 , 1 54 0

- .0 00 - '0 - 40 0 0 1 1 89 6 60 0 1'0 184 0 460 0 860 1 . 180 0 860 0 1,180 2,81 6 0 1,160 0 2,)00 ',11l 0 -19.\ - 19 .- 18 1 o \6 33 91 4 65 6 1 50 302 0 46\ 6 8 10 1,198 0 861 6 1.190 1,89' 0 1,161 6 2,310 ' , 1900 - 38 89 - 18 - 1 6' III 34 9l l II I 160 3 10 0 411 I 880 1,616 0 8 7 1 . 1 1,600 2 ,91 1 0 1,271 1 2,320 4,201 0 - - 38 1. 17 - 34 6 167 J\ 9 1 0 76 I 110 llS O 4 16 7 890 1.634 0 816 I 1 ,61 0 1,930 0 1,276.7 1,llO • , 226 0 - 16 - 31 78 - 31 8 III 3i 96 8 81 1 180 356 0 '81 1 900 1 , 6 11 0 882 2 1,610 2,948 0 1.212 2 l.l'O 4,244 0

- l ll l - 31 - 3 1 0 118 37 98 6 81 8 1ge 37. 0 '81 8 9 1 0 1.670 0 831 8 1 , 630 2,966 0 1.281 1 U 50 ',W O 1 - 1 66 -1' -191 311 38 100 4 93 3 100 3 9 1 0 49l J 9 10 1,688 0 893 3 1.6'0 1,98' 0 1,193 3 '1,360 4,210 0 ' - 36 11 -11 - lI 389 39 lOl l 98 9 110 .10 0 498 9 9 10 1.106 0 898 9 1,650 3,001 0 1 ,29 89 2 ,370 ',291 0 -1116 - 31 -116 444 '0 104 0 1 04 4 1 10 4 18 0 104 4 940 1 . 1 14 0 904 4 1.660 3,020 0 1 ,304 4 2,lIO 4,316 0 - 1 3 00 -11 -138 \ 00 4 1 10\ 8 1 1 00 130 4 46 0 \10 0 950 1 . 74 1 0 910 0 1,610 3,031 0 UIO O 2,390 ',33' 0

- 3..j H - 30 -110 \ 16 41 101 6 111 6 140 4 64 0 515 6 960 1,760 0 911 6 1,680 3,016 0 I,W 3 2.450 .... 1 0 - 31 89 -19 - 10 1 611 43 109 4 111 1 1 10 4 81 0 521 I 9 10 1.118 0 911 I 1,690 3,07' 0 1 ,3711 2,100 ',\3 1 0 -1133 - l8 - 1 8' 661 44 1 1 1 1 1 16 7 160 500 0 116 7 9 80 1.196 0 9 16 7 U OO 3 ,0 9 1 0 I,m 9 2.150 4 ,621 0 - ll l8 -17 -166 III '5 : 13 0 112 1 1 70 118 0 \31 1 990 1 , 8140 9ll 1 UIO 3,110 0 1,416 7 1,600 '.112 0 - 31 11 - 16 -148 778 46 1 14 8 IJI 8 180 \36 0 \37 8 1,000 I,m 0 931 8 1.110 3 , 1 2 1 0 1 , ' \ 4 4 2.6 50 ',102 0

- 31 67 -1\ - 13 0 8 33 41 1166 I4J 3 190 II' 0 143 3 1 ,0 1 0 1,810 0 943 1 1.130 1,\46 0 1,412.2 2,700 ',1 92 0 - 31 11 - l' - Il l 8 S9 '8 118 4 148 9 100 \ 71 0 148 9 1,010 1 , 8 68 0 9.8 9 1.1'0 3 ,164 0 1,11 0 0 2.110 4.912 0 - - 10 16 - 11 9 4 9 44 49 1102 154 4 3 I 0 1 900 114 4 1,010 1,886 0 914 4 1.150 3,181 0 1,531 8 2.100 1,072 0 - 30 00 - 1 1 - 1 6 1 0 0 \0 III 0 16Q 0 310 608 0 560 0 1,0'0 1,904 0 960 0 1 .160 3,100 0 1,\65.1 1. 1 50 1,162 0 - 19 41 - 21 - 1 8 1 0 6 51 I II 8 161 6 330 6160 56\ 6 1,010 1.9ll 0 9 65 6 1 .170 3 , 1 11 0 1,5n3 2.900 1.211 0

1 9 - 88 - 10 - 4 0 II I \1 III 6 11\ I 3'0 644 0 \11 I 1 ,060 1,940.0 911 I 1 . 1 80 3,236 0 1.611 1 2 , 9 10 I,W 0 - 18 1' -19 - 21 I II 13 111 4 176 7 3 10 661 0 5 16 7 1,070 1,958 0 976 7 1.190 3.214 C 1.648 9 3.000 \ . 4 32 0

39 Notes