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Chap01

VIEWS: 238 PAGES: 24

									Section 1

Conversion Factors and Mathematical Symbols*

James O. Maloney, Ph.D., P.E., Emeritus Professor of Chemical Engineering, University of Kansas; Fellow, American Institute of Chemical Engineering; Fellow, American Association for the Advancement of Science; Member, American Chemical Society, American Society for Engineering Education

Fig. 1-1 Table 1-1 Table 1-2a Table 1-2b Table 1-3 Table 1-4 Table 1-5 Table 1-6 Table 1-7 Table 1-8 Table 1-9

CONVERSION FACTORS Graphic Relationships of SI Units with Names . . . . . . . . . SI Base and Supplementary Quantities and Units. . . . . . . Derived Units of SI that Have Special Names. . . . . . . . . . Additional Common Derived Units of SI . . . . . . . . . . . . . SI Prefixes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Conversion Factors: U.S. Customary and Commonly Used Units to SI Units . . . . . . . . . . . . . . . . . . . . . . . . . . . . Metric Conversion Factors as Exact Numerical Multiples of SI Units . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Alphabetical Listing of Common Conversions . . . . . . . . . Common Units and Conversion Factors . . . . . . . . . . . . . . Kinematic-Viscosity Conversion Formulas . . . . . . . . . . . . Values of the Gas-Law Constant. . . . . . . . . . . . . . . . . . . . .

1-2 1-3 1-3 1-3 1-3 1-4 1-13 1-15 1-18 1-18 1-18

Table 1-10 United States Customary System of Weights and Measures. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Table 1-11 Temperature Conversion . . . . . . . . . . . . . . . . . . . . . . . . . . Table 1-12 Specific Gravity, Degrees Baumé, Degrees API, Degrees Twaddell, Pounds per Gallon, Pounds per Cubic Foot . . . Table 1-13 Wire and Sheet-Metal Gauges . . . . . . . . . . . . . . . . . . . . . . Table 1-14 Fundamental Physical Constants . . . . . . . . . . . . . . . . . . . . CONVERSION OF VALUES FROM U.S. CUSTOMARY UNITS TO SI UNITS Table 1-15 Table 1-16 MATHEMATICAL SYMBOLS Mathematical Signs, Symbols, and Abbreviations . . . . . . . Greek Alphabet . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1-19 1-19 1-20 1-21 1-22

1-24 1-24

* Much of the material was taken from Sec. 1. of the fifth edition. The contribution of Cecil H. Chilton in developing that material is acknowledged. 1-1

FIG. 1-1

Graphic relationships of SI units with names (U.S. National Bureau of Standards, LC 1078, December 1976.)

1-2

TABLE 1-1

SI Base and Supplementary Quantities and Units SI unit symbol (“abbreviation”); Use roman (upright) type m kg s A K mol cd rad sr

TABLE 1-2b Additional Common Derived Units of SI Quantity acceleration angular acceleration angular velocity area concentration (of amount of substance) current density density, mass electric-charge density electric-field strength electric-flux density energy density entropy heat capacity heat-flux density, irradiance luminance magnetic-field strength molar energy molar entropy molar-heat capacity moment of force permeability permittivity radiance radiant intensity specific-heat capacity specific energy specific entropy specific volume surface tension thermal conductivity velocity viscosity, dynamic viscosity, kinematic volume wave number Unit meter per second squared radian per second squared radian per second square meter mole per cubic meter ampere per square meter kilogram per cubic meter coulomb per cubic meter volt per meter coulomb per square meter joule per cubic meter joule per kelvin joule per kelvin watt per square meter candela per square meter ampere per meter joule per mole joule per mole-kelvin joule per mole-kelvin newton-meter henry per meter farad per meter watt per square-metersteradian watt per steradian joule per kilogram-kelvin joule per kilogram joule per kilogram-kelvin cubic meter per kilogram newton per meter watt per meter-kelvin meter per second pascal-second square meter per second cubic meter 1 per meter Symbol m/s2 rad/s2 rad/s m2 mol/m3 A/m2 kg/m3 C/m3 V/m C/m2 J/m3 J/K J/K W/m2 cd/m2 A/m J/mol J/(mol⋅K) J/(mol⋅K) N⋅m H/m F/m W/(m2⋅sr) W/sr J/(kg⋅K) J/kg J/(kg⋅K) m3/kg N/m W/(m⋅K) m/s Pa⋅s m2/s m3 1/m

Quantity or “dimension” Base quantity or “dimension” length mass time electric current thermodynamic temperature amount of substance luminous intensity Supplementary quantity or “dimension” plane angle solid angle

SI unit meter kilogram second ampere kelvin mole* candela radian steradian

* When the mole is used, the elementary entities must be specified; they may be atoms, molecules, ions, electrons, other particles, or specified groups of such particles.

TABLE 1-2a Derived Units of SI that Have Special Names Quantity frequency (of a periodic phenomenon) force pressure, stress energy, work, quantity of heat power, radiant flux quantity of electricity, electric charge electric potential, potential difference, electromotive force capacitance electric resistance conductance magnetic flux magnetic-flux density inductance luminous flux illuminance activity (of radionuclides) absorbed dose Unit hertz newton pascal joule watt coulomb volt farad ohm siemens weber tesla henry lumen lux becquerel gray Symbol Hz N Pa J W C V F Ω S Wb T H lm lx Bq Gy Formula l/s (kg⋅m)/s2 N/m2 N⋅m J/s A⋅s W/A C/V V/A A/V V⋅s Wb/m2 Wb/A cd⋅sr lm/m2 l/s J/kg

TABLE 1-3

SI Prefixes Prefix exa peta tera giga mega kilo hecto* deka* deci* centi milli micro nano pico femto atto Symbol E P T G M k h da d c m µ n p f a 000 000 000 000 1 000 000 000 000 000 1

Multiplication factor 1 000 000 000 1 000 000 1 000 1 000 = 1018 000 = 1015 000 = 1012 000 = 109 000 = 106 000 = 103 100 = 102 10 = 101 0.1 = 10−1 0.01 = 10−2 0.001 = 10−3 0.000 001 = 10−6 0.000 000 001 = 10−9 0.000 000 000 001 = 10−12 0.000 000 000 000 001 = 10−15 0.000 000 000 000 000 001 = 10−18 *Generally to be avoided.

1-3

TABLE 1-4

Conversion Factors: U.S. Customary and Commonly Used Units to SI Units Customary or commonly used unit Space,† time naut mi mi chain link fathom yd ft in in mil Alternate SI unit Conversion factor; multiply customary unit by factor to obtain SI unit 1.852* E + 00 1.609 344* E + 00 2.011 68* E + 01 2.011 68* E − 01 1.828 8* E + 00 9.144* E − 01 3.048* E − 01 3.048* E + 01 2.54* E + 01 2.54 E + 00 2.54* E + 01 1.893 939 E − 01 8.051 964 E + 01 1.076 391 E + 01 1.917 134 E + 00 2.589 988 E + 00 2.589 988 E + 02 4.046 856 E − 01 1.000 000* E + 04 8.361 274 E − 01 9.290 304* E − 02 6.451 6* E + 02 6.451 6* E + 00 5.699 291 E − 03 3.280 840 E + 00 4.168 182 1.233 482 1.233 482 7.645 549 1.589 873 2.831 685 2.831 685 4.546 092 4.546 092 3.785 412 3.785 412 1.136 523 9.463 529 4.731 765 2.841 307 2.957 353 1.638 706 E + 00 E + 03 E − 01 E − 01 E − 01 E − 02 E + 01 E − 03 E + 00 E − 03 E + 00 E + 00 E − 01 E − 01 E + 01 E + 01 E + 01

Quantity Length

SI unit km km m m m m m cm mm cm µm m/km m/m3 m/m3 m/m3 km2 ha ha m2 m2 m2 mm2 cm2 m2/cm3 m2/m3 km3 m3 ha⋅m m3 m3 m3 dm3 m3 dm3 m3 dm3 dm3 dm3 dm3 cm3 cm3 cm3 m3m m3/m m3/m m3/m L/m rad rad rad rad sr a d s min s h ns

Length/length Length/volume

ft/mi ft/U.S. gal ft/ft3 ft/bbl mi2 section acre ha yd2 ft2 in2 ft2/in3 ft2/ft3 cubem acre⋅ft yd3 bbl (42 U.S. gal) ft3 U.K. gal U.S. gal U.K. qt U.S. qt U.S. pt U.K. fl oz U.S. fl oz in3

Area

Area/volume Volume

L L L L L L

Volume/length (linear displacement)

bbl/in bbl/ft ft3/ft U.S. gal/ft rad deg (°) min (′) sec (″) sr year week h min mµs Mass, amount of substance

6.259 342 E + 00 5.216 119 E − 01 9.290 304* E − 02 1.241 933 E − 02 1.241 933 E + 01 1 1.745 329 E − 02 2.908 882 E − 04 4.848 137 E − 06 1 1 7.0* 3.6* 6.0* 6.0* 1.666 667 1 t t 1.016 047 9.071 847 5.080 234 4.535 924 4.535 924 3.110 348 2.834 952 6.479 891 E + 00 E + 03 E + 01 E + 01 E − 02

Plane angle

Solid angle Time

Mass

U.K. ton U.S. ton U.K. cwt U.S. cwt lbm oz (troy) oz (av) gr

Mg Mg kg kg kg g g mg

E + 00 E − 01 E + 01 E + 01 E − 01 E + 01 E + 01 E + 01

1-4

TABLE 1-4

Conversion Factors: U.S. Customary and Commonly Used Units to SI Units (Continued ) Customary or commonly used unit lbm⋅mol std m3(0°C, 1 atm) std ft3 (60°F, 1 atm) Btu/lbm cal/g cal/lbm Alternate SI unit Conversion factor; multiply customary unit by factor to obtain SI unit 4.535 924 E − 01 4.461 58 E − 02 1.195 30 E − 03 2.326 000 2.326 000 6.461 112 4.184* 9.224 141 E − 03 E + 00 E − 04 E + 00 E + 00

Quantity Amount of substance

SI unit kmol kmol kmol MJ/kg kJ/kg kWh/kg kJ/kg J/kg kJ/kmol kJ/kmol MJ/m3 kJ/m3 kWh/m3 MJ/m3 kJ/m3 kWh/m3 MJ/m3 kJ/m3 kWh/m3 MJ/m3 kJ/m3 kJ/m3 kJ/m3 kJ/m3 kWh/m3 kJ/(kg⋅K) kJ/(kg⋅K) kJ/(kg⋅K) kJ/(kg⋅K) kJ/(kg⋅K) kJ/(kg⋅K) kJ/(kmol⋅K) kJ/(kmol⋅K) K K °C K, °C MPa kPa bar MPa kPa MPa kPa bar kPa kPa kPa kPa kPa Pa Pa Pa kPa kPa kPa kPa kPa m mm cm kPa/m

Enthalpy, calorific value, heat, entropy, heat capacity Calorific value, enthalpy (mass basis) J/g J/g

Caloric value, enthalpy (mole basis) Calorific value (volume basis—solids and liquids)

kcal/(g⋅mol) Btu/(lb⋅mol) Btu/U.S. gal Btu/U.K. gal Btu/ft3

4.184* E + 03 2.326 000 E + 00 kJ/dm3 kJ/dm3 kJ/dm3 2.787 163 2.787 163 7.742 119 2.320 800 2.320 800 6.446 667 3.725 895 3.725 895 1.034 971 4.184* 3.581 692 4.184* 4.184* 3.725 895 1.034 971 4.186 8* 4.184* 4.184* 3.6* 4.186 8* 4.184* 4.186 8* 4.184* 5/9 1 5/9(°F − 32) 5/9 1.013 250* E − 01 1.013 250* E + 02 1.013 250* E + 00 1.0* E − 01 1.0* E + 02 6.894 757 E − 03 6.894 757 E + 00 6.894 757 E − 02 3.376 85 E + 00 2.488 4 E − 01 1.333 224 E − 01 9.806 38 E − 02 4.788 026 E − 02 1.333 224 E − 01 1.0* E + 05 1.0* E − 01 3.376 85 2.490 82 2.488 4 1.333 224 9.806 38 3.048* 2.54* 2.54* E + 00 E − 01 E − 01 E − 01 E − 02 E − 01 E + 01 E + 00 E − 01 E + 02 E − 02 E − 01 E + 02 E − 02 E − 02 E + 01 E − 02 E + 00 E − 01 E + 03 E + 00 E + 01 E − 02 E + 00 E + 00 E + 00 E + 03 E + 00 E + 00 E + 00 E + 00

cal/mL (ft⋅lbf)/U.S. gal Calorific value (volume basis—gases) cal/mL kcal/m3 Btu/ft3 Btu/(lbm⋅°R) cal/(g⋅K) kcal/(kg⋅°C) kWh/(kg⋅°C) Btu/(lbm⋅°F) kcal/(kg⋅°C) Btu/(lb⋅mol⋅°F) cal/(g⋅mol⋅°C) Temperature, pressure, vacuum Temperature (absolute) Temperature (traditional) Temperature (difference) Pressure °R K °F °F atm (760 mmHg at 0°C or 14,696 psi) bar mmHg (0°C) = torr µmHg (0°C) µ bar mmHg = torr (0°C) cmH2O (4°C) lbf/ft2 (psf) mHg (0°C) bar dyn/cm2 Vacuum, draft inHg (60°F) inH2O (39.2°F) inH2O (60°F) mmHg (0°C) = torr cmH2O (4°C) ft in psi/ft

J/dm3 J/dm3 J/dm3 J/(g⋅K) J/(g⋅K) J/(g⋅K) J/(g⋅K) J/(g⋅K) J/(g⋅K)

Specific entropy

Specific-heat capacity (mass basis) Specific-heat capacity (mole basis)

Liquid head

Pressure drop/length

2.262 059 E + 01

1-5

TABLE 1-4

Conversion Factors: U.S. Customary and Commonly Used Units to SI Units (Continued ) Customary or commonly used unit lbm/ft3 lbm/U.S. gal lbm/U.K. gal lbm/ft3 g/cm3 lbm/ft3 Alternate SI unit Conversion factor; multiply customary unit by factor to obtain SI unit 1.601 846 1.601 846 1.198 264 1.198 264 9.977 633 1.601 846 1.601 846 1.0* 1.601 846 6.242 796 6.242 796 6.242 796 1.002 242 8.345 404 E + 01 E + 04 E + 02 E − 01 E + 01 E + 01 E − 02 E + 03 E + 01 E − 02 E − 05 E + 01 E + 01 E + 00

Quantity Density

SI unit kg/m3 g/m3 kg/m3 g/cm3 kg/m3 kg/m3 g/cm3 kg/m3 kg/m3 m3/kg m3/g dm3/kg dm3/kg dm3/kg m3/kmol m3/kmol m3/t m3/t dm3/t dm3/t dm3/t dm3/t kg/kg g/kg mg/kg kg/m3 kg/m3 kg/m3 g/m3 g/m3 g/m3 mg/m3 g/m3 g/m3 mg/m3 m3/m3 m3/m3 m3/m3 dm3/m3 dm3/m3 dm3/m3 dm3/m3 cm3/m3 dm3/m3 cm3/m3 cm3/m3 cm3/m3 kmol/m3 kmol/m3 kmol/m3 kmol/m3 dm3/kmol dm3/kmol t/a t/a t/d t/h t/d t/h t/h t/h kg/h

Density, specific volume, concentration, dosage

Specific volume

ft3/lbm ft /lbm U.K. gal/lbm U.S. gal/lbm
3

cm3/g cm3/g

Specific volume (mole basis) Specific volume Yield

L/(g⋅mol) ft3/(lb⋅mol) bbl/U.S. ton bbl/U.K. ton bbl/U.S. ton bbl/U.K. ton U.S. gal/U.S. ton U.S. gal/U.K. ton wt % wt ppm

1 6.242 796 E − 02 1.752 535 E − 01 1.564 763 E − 01 L/t L/t L/t L/t 1.752 535 1.564 763 4.172 702 3.725 627 1.0* 1.0* 1 g/dm3 g/L mg/dm3 mg/dm3 mg/dm3 mg/dm3 mg/dm3 2.853 010 2.641 720 2.199 692 1.198 264 9.977 633 1.711 806 2.288 351 2.853 010 2.641 720 2.288 351 1 1.288 931 1.0* 1.605 437 1.336 806 2.641 720 2.199 692 1 1.0* 2.859 403 2.380 952 3.574 253 1.198 264 9.977 644 1.601 846 7.518 21 L/kmol L/kmol 3.166 91 1.330 10 1.016 047 9.071 847 1.016 047 4.233 529 9.071 847 3.779 936 1.016 047 9.071 847 4.535 924 E + 02 E + 02 E + 00 E + 00 E − 02 E + 01 E + 00 E − 01 E − 01 E + 02 E + 01 E + 01 E + 03 E + 00 E − 01 E + 01 E − 04 E − 02 E + 02 E + 02 E − 01 E − 01 E − 03 E + 01 E + 01 E + 00 E + 02 E + 01 E + 01 E − 03 E + 00 E − 01 E + 00 E − 01 E + 00 E − 02 E − 01 E − 02 E + 00 E − 01 E − 01

Concentration (mass/mass)

Concentration (mass/volume)

lbm/bbl g/U.S. gal g/U.K. gal lbm/1000 U.S. gal lbm/1000 U.K. gal gr/U.S. gal gr/ft3 lbm/1000 bbl mg/U.S. gal gr/100 ft3 ft3/ft3 bbl/(acre⋅ft) vol% U.K. gal/ft3 U.S. gal/ft3 mL/U.S. gal mL/U.K. gal vol ppm U.K. gal/1000 bbl U.S. gal/1000 bbl U.K. pt/1000 bbl

Concentration (volume/volume)

L/m3 L/m3 L/m3 L/m3 L/m3

Concentration (mole/volume)

(lb⋅mol)/U.S. gal (lb⋅mol)/U.K. gal (lb⋅mol)/ft3 std ft3 (60°F, 1 atm)/bbl U.S. gal/1000 std ft3 (60°F/60°F) bbl/million std ft3 (60°F/60°F) Facility throughput, capacity U.K. ton/year U.S. ton/year U.K. ton/day U.S. ton/day U.K. ton/h U.S. ton/h lbm/h

Concentration (volume/mole)

Throughput (mass basis)

1-6

TABLE 1-4

Conversion Factors: U.S. Customary and Commonly Used Units to SI Units (Continued ) Customary or commonly used unit bbl/day ft /day bbl/h ft3/h U.K. gal/h U.S. gal/h U.K. gal/min U.S. gal/min
3

Quantity Throughput (volume basis)

SI unit t/a m3/d m3/h m3/h m3/h m3/h L/s m3/h L/s m3/h L/s m3/h L/s kmol/h kmol/s

Alternate SI unit

Conversion factor; multiply customary unit by factor to obtain SI unit 5.803 036 1.589 873 1.179 869 1.589 873 2.831 685 4.546 092 1.262 803 3.785 412 1.051 503 2.727 655 7.576 819 2.271 247 6.309 020 E + 01 E − 01 E − 03 E − 01 E − 02 E − 03 E − 03 E − 03 E − 03 E − 01 E − 02 E − 01 E − 02

Throughput (mole basis)

(lbm⋅mol)/h Flow rate

4.535 924 E − 01 1.259 979 E − 04 1.693 412 1.511 974 2.822 353 2.519 958 1.175 980 1.049 982 5.249 912 3.221 864 2.876 664 4.535 924 7.559 873 1.259 979 1.589 873 1.840 131 2.831 685 3.277 413 4.416 314 4.416 314 7.865 791 7.865 791 1.262 803 1.051 503 7.576 820 6.309 020 4.719 474 2.831 685 E + 01 E + 01 E − 01 E − 01 E − 02 E − 02 E + 00 E − 05 E − 05 E − 01 E − 03 E − 04 E − 01 E − 03 E − 02 E − 04 E − 05 E − 02 E − 06 E − 03 E − 03 E − 03 E − 02 E − 02 E − 01 E + 01

Flow rate (mass basis)

U.K. ton/min U.S. ton/min U.K. ton/h U.S. ton/h U.K. ton/day U.S. ton/day million lbm/year U.K. ton/year U.S. ton/year lbm/s lbm/min lbm/h bbl/day ft /day bbl/h ft3/h U.K. gal/h U.S. gal/h U.K. gal/min U.S. gal/min ft3/min ft3/s
3

kg/s kg/s kg/s kg/s kg/s kg/s kg/s kg/s kg/s kg/s kg/s kg/s m3/d L/s m3/d L/s m3/s L/s m3/s L/s dm3/s dm3/s dm3/s dm3/s dm3/s dm3/s kmol/s kmol/s kmol/s kg/(s⋅m) kg/(s⋅m) m2/s m2/s m2/s m2/s m2/s m2/s kg/(s⋅m2) kg/(s⋅m2) m/s m/s m/s m/s m/s m/s m/s m/s m3/(s⋅m2) m3/(s⋅m2) m3/(s⋅m2) m3/(s⋅m2) m3/(s⋅m2) m3/(s⋅m2) m3/(s⋅m2) m3/(s⋅m2) m3/(s⋅m) m3/(s⋅m) m3/(s⋅m) m3/(s⋅m) m3/(s⋅m) m3/(s⋅m)

Flow rate (volume basis)

L/s L/s L/s L/s L/s L/s

Flow rate (mole basis)

(lb⋅mol)/s (lb⋅mol)/h million scf/D lbm/(s⋅ft) lbm/(h⋅ft) U.K. gal/(min⋅ft) U.S. gal/(min⋅ft) U.K. gal/(h⋅in) U.S. gal/(h⋅in) U.K. gal/(h⋅ft) U.S. gal/(h⋅ft) lbm/(s⋅ft2) lbm/(h⋅ft2) ft3/(s⋅ft2) ft3/(min⋅ft2) U.K. gal/(h⋅in2) U.S. gal/(h⋅in2) U.K. gal/(min⋅ft2) U.S. gal/(min⋅ft2) U.K. gal/(h⋅ft2) U.S. gal/(h⋅ft2)

4.535 924 E − 01 1.259 979 E − 04 1.383 45 E − 02 1.488 164 E + 00 4.133 789 E − 04 2.485 833 2.069 888 4.971 667 4.139 776 4.143 055 3.449 814 E − 04 E − 04 E − 05 E − 05 E − 06 E − 06

Flow rate/length (mass basis) Flow rate/length (volume basis)

Flow rate/area (mass basis) Flow rate/area (volume basis)

4.882 428 E + 00 1.356 230 E − 03 3.048* 5.08* 1.957 349 1.629 833 8.155 621 6.790 972 1.359 270 1.131 829 E − 01 E − 03 E − 03 E − 03 E − 04 E − 04 E − 05 E − 05

1-7

TABLE 1-4

Conversion Factors: U.S. Customary and Commonly Used Units to SI Units (Continued ) Customary or commonly used unit Energy, work, power therm U.S. tonf⋅mi hp⋅h ch⋅h or CV⋅h kWh Chu Btu kcal cal ft⋅lbf lbf⋅ft J (lbf⋅ft2)/s2 erg Alternate SI unit Conversion factor; multiply customary unit by factor to obtain SI unit 1.055 056 1.055 056 2.930 711 1.431 744 2.684 520 2.684 520 7.456 999 2.647 780 2.647 780 7.354 999 3.6* 3.6* 1.899 101 5.275 280 1.055 056 2.930 711 4.184* 4.184* 1.355 818 1.355 818 1.0* 4.214 011 1.0* E + 02 E + 05 E + 01 E + 01 E + 00 E + 03 E − 01 E + 00 E + 03 E − 01 E + 00 E + 03 E + 00 E − 04 E + 00 E − 04 E + 00 E − 03 E − 03 E − 03 E − 03 E − 05 E − 07

Quantity Energy, work

SI unit MJ kJ kWh MJ MJ kJ kWh MJ kJ kWh MJ kJ kJ kWh kJ kWh kJ kJ kJ kJ kJ kJ J J J mJ/m2 J/cm2 J/cm2 MW kW kW kW kW kW kW kW kW kW W W W kW/m2 kW/m2 kW/m2 kW/m3 kW/m3 kW/m3 kW/m3 W/kW mg/J kg/kWh dm3/MJ dm3/MJ dm3/MJ dm3/100 km dm3/100 km km/dm3 km/dm3

Impact energy Surface energy Specific-impact energy Power

kgf⋅m lbf⋅ft erg/cm2 (kgf⋅m)/cm2 (lbf⋅ft)/in2 million Btu/h ton of refrigeration Btu/s kW hydraulic horsepower—hhp hp (electric) hp [(550 ft⋅lbf)/s] ch or CV Btu/min (ft⋅lbf)/s kcal/h Btu/h (ft⋅lbf)/min Btu/(s⋅ft2) cal/(h⋅cm2) Btu/(h⋅ft2) hp/ft3 cal/(h⋅cm3) Btu/(s⋅ft3) Btu/(h⋅ft3) Btu/(bhp⋅h) lbm/(hp⋅h) m3/kWh U.S. gal/(hp⋅h) U.K. pt/(hp⋅h) U.K. gal/mi U.S. gal/mi mi/U.S. gal mi/U.K. gal

9.806 650* E + 00 1.355 818 E + 00 1.0* E + 00 9.806 650* E − 02 2.101 522 E − 03 2.930 711 3.516 853 1.055 056 1 7.460 43 7.46* 7.456 999 7.354 999 1.758 427 1.355 818 1.162 222 2.930 711 2.259 697 E − 01 E + 00 E + 00 E − 01 E − 01 E − 01 E − 01 E − 02 E − 03 E + 00 E − 01 E − 02

Power/area

1.135 653 E + 01 1.162 222 E − 02 3.154 591 E − 03 2.633 414 1.162 222 3.725 895 1.034 971 kg/MJ mm3/J mm3/J mm3/J L/100 km L/100 km km/L km/L E + 01 E + 00 E + 01 E − 02

Heat-release rate, mixing power

Cooling duty (machinery) Specific fuel consumption (mass basis) Specific fuel consumption (volume basis) Fuel consumption

3.930 148 E − 01 1.689 659 E − 01 6.082 774 E − 01 2.777 778 E + 02 1.410 089 E + 00 2.116 806 E − 01 2.824 807 2.352 146 4.251 437 3.540 064 E + 02 E + 02 E − 01 E − 01

1-8

TABLE 1-4

Conversion Factors: U.S. Customary and Commonly Used Units to SI Units (Continued ) Customary or commonly used unit knot mi/h ft/s ft/min ft/h ft/day in/s in/min Alternate SI unit Conversion factor; multiply customary unit by factor to obtain SI unit 1.852* E + 00 1.609 344* E + 00 3.048* E − 01 3.048* E + 01 5.08* E − 03 8.466 667 E − 02 3.527 778 E − 03 3.048* E − 01 2.54* E + 01 4.233 333 E − 01 2.54* 2.54* E + 01 E − 02

Quantity Velocity (linear), speed

SI unit km/h km/h m/s cm/s m/s mm/s mm/s m/d mm/s mm/s mm/a mm/a r/s rad/s m/s2 cm/s2 rad/s2 (kg⋅m)/s kN kN N N mN kN⋅m N⋅m N⋅m N⋅m (N⋅m)/m (N⋅m)/m kg⋅m2

Corrosion rate Rotational frequency Acceleration (linear) Acceleration (rotational) Momentum Force

in/year (ipy) mil/year r/min ft/s2 rpm/s (lbm⋅ft)/s U.K. tonf U.S. tonf kgf (kp) lbf dyn U.S. tonf⋅ft kgf⋅m lbf⋅ft lbf⋅in (lbf⋅ft)/in (lbf⋅in)/in lbm⋅ft2 U.S. tonf/in kgf/mm2 U.S. tonf/ft2 lbf/in2 (psi) lbf/ft2 (psf) dyn/cm2 lbm/ft U.S. ton/ft2 lbm/ft2 Miscellaneous transport properties
2

1.666 667 E − 02 1.047 198 E − 01 3.048* 3.048* E − 01 E + 01

1.047 198 E − 01 1.382 550 E − 01 9.964 016 E + 00 8.896 443 E + 00 9.806 650* E + 00 4.448 222 E + 00 1.0 E − 02 2.711 636 E + 00 9.806 650* E + 00 1.355 818 E + 00 1.129 848 E − 01 5.337 866 E + 01 4.448 222 E + 00 4.214 011 E − 02 N/mm2 N/mm2 N/mm2 N/mm2 1.378 951 E + 01 9.806 650* E + 00 9.576 052 E − 02 6.894 757 E − 03 4.788 026 E − 02 1.0* E − 01 1.488 164 E + 00 9.764 855 E + 00 4.882 428 E + 00

Bending moment, torque

Bending moment/length Moment of inertia Stress

MPa MPa MPa MPa kPa Pa kg/m Mg/m2 kg/m2

Mass/length Mass/area structural loading, bearing capacity (mass basis) Diffusivity

ft2/s m2/s ft2/h (°C⋅m2⋅h)/kcal (°F⋅ft2⋅h)/Btu Btu/(h⋅ft2) (cal⋅cm)/(s⋅cm ⋅°C) (Btu⋅ft)/(h⋅ft2⋅°F)
2

m2/s mm2/s m2/s (K⋅m2)/kW (K⋅m2)/kW kW/m2 W/(m⋅K) W/(m⋅K) (kJ⋅m)/(h⋅m2⋅K) W/(m⋅K) W/(m⋅K) W/(m⋅K) kW/(m2⋅K) kW/(m2⋅K) kW/(m2⋅K) kW/(m2⋅K) kJ/(h⋅m2⋅K) kW/(m2⋅K) kW/(m2⋅K)

9.290 304* E − 02 1.0* E + 06 2.580 64* E − 05 8.604 208 E + 02 1.761 102 E + 02 3.154 591 E − 03 4.184* 1.730 735 6.230 646 1.162 222 1.442 279 1.162 222 4.184* 2.044 175 1.162 222 5.678 263 2.044 175 5.678 263 1.162 222 E + 02 E + 00 E + 00 E + 00 E − 01 E − 01 E + 01 E + 01 E − 02 E − 03 E + 01 E − 03 E − 03

Thermal resistance Heat flux Thermal conductivity

(kcal⋅m)/(h⋅m2⋅°C) (Btu⋅in)/(h⋅ft2⋅°F) (cal⋅cm)/(h⋅cm2⋅°C) Heat-transfer coefficient cal/(s⋅cm2⋅°C) Btu/(s⋅ft2⋅°F) cal/(h⋅cm2⋅°C) Btu/(h⋅ft2⋅°F) Btu/(h⋅ft2⋅°R) kcal/(h⋅m2⋅°C)

1-9

TABLE 1-4

Conversion Factors: U.S. Customary and Commonly Used Units to SI Units (Continued ) Customary or commonly used unit Btu/(s⋅ft3⋅°F) Btu/(h⋅ft3⋅°F) dyn/cm (lbf⋅s)/in2 (lbf⋅s)/ft2 (kgf⋅s)/m2 lbm/(ft⋅s) (dyn⋅s)/cm2 cP lbm/(ft⋅h) ft2/s in2/s m2/h ft2/h cSt darcy millidarcy Btu/(h⋅ft2) Btu/(s⋅ft2) cal/(s⋅cm2) (lb⋅mol)/[h⋅ft2(lb⋅mol/ft3)] (g⋅mol)/[s⋅m2(g⋅mol/L)] Electricity, magnetism S µF C/mm3 S (mho) S/m /m m /m A/mm2 C/cm C A C⋅m V/m C C/cm2 V mV A⋅m2 V C cycles/s Ω A/mm Wb⋅m A/mm Oe gamma mWb
2

Quantity Volumetric heat-transfer coefficient Surface tension Viscosity (dynamic)

SI unit kW/(m3⋅K) kW/(m3⋅K) mN/m Pa⋅s Pa⋅s Pa⋅s Pa⋅s Pa⋅s Pa⋅s Pa⋅s m2/s mm2/s mm2/s m2/s mm2/s µm2 µm2 W/m2 W/m2 W/m2 m/s m/s S µF C/mm3 S S S/m S/m mS/m A/mm2 C/cm2 C A C⋅m V/m C C/cm2 V mV A⋅m2 V C Hz Ω A/mm Wb⋅m A/mm A/m A/m mWb

Alternate SI unit

Conversion factor; multiply customary unit by factor to obtain SI unit 6.706 611 E + 01 1.862 947 E − 02 1

(N⋅s)/m2 (N⋅s)/m2 (N⋅s)/m2 (N⋅s)/m2 (N⋅s)/m2 (N⋅s)/m2 (N⋅s)/m2

6.894 757 E + 03 4.788 026 E + 01 9.806 650* E + 00 1.488 164 E + 00 1.0* E − 01 1.0* E − 03 4.133 789 E − 04 9.290 304* E − 02 6.451 6* E + 02 2.777 778 E + 02 2.580 64* E − 05 1 9.869 233 E − 01 9.869 233 E − 04 3.152 1.135 4.184 8.467 1.0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 7.957 747 E + 01 7.957 747 E − 04 1 E + 00 E + 04 E + 04 E − 05 E + 01

Viscosity (kinematic)

Permeability Thermal flux

Mass-transfer coefficient

Admittance Capacitance Charge density Conductance Conductivity

Current density Displacement Electric charge Electric current Electric-dipole moment Electric-field strength Electric flux Electric polarization Electric potential Electromagnetic moment Electromotive force Flux of displacement Frequency Impedance Linear-current density Magnetic-dipole moment Magnetic-field strength

Magnetic flux

1-10

TABLE 1-4

Conversion Factors: U.S. Customary and Commonly Used Units to SI Units (Continued ) Customary or commonly used unit mT G gamma mT A⋅m2 mT A Wb/mm A/mm S Ω H µH/m H µF/m V C Ω H−1 Ω Ω⋅cm Ω⋅m mH mC/m2 S C/mm3 Acoustics, light, radiation rad J W/cm2 W N/m2 fc fc W/m2 fc⋅s cd/m2 lm/W lm/m2 lm cd W/m2⋅sr J W W/sr W Alternate SI unit Conversion factor; multiply customary unit by factor to obtain SI unit 1 1.0* 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1.0* 1 1.0* 1 1.0* 1.076 391 E + 01 1.076 391 E + 01 1 1.076 391 E + 01 1 1 1 1 1 1 1 1 1 1 E + 04 E − 02 E − 04

Quantity Magnetic-flux density

SI unit mT T nT mT A⋅m2 mT A Wb/mm A/mm S Ω H µH/m H µF/m V C Ω H−1 Ω Ω⋅cm Ω⋅m mH mC/m2 S C/mm3 Gy J W/m2 W N/m2 lx lx W/m2 lx⋅s cd/m2 lm/W lm/m2 lm cd W/m2⋅sr J W W/sr W

Magnetic induction Magnetic moment Magnetic polarization Magnetic potential difference Magnetic-vector potential Magnetization Modulus of admittance Modulus of impedance Mutual inductance Permeability Permeance Permittivity Potential difference Quantity of electricity Reactance Reluctance Resistance Resistivity Self-inductance Surface density of change Susceptance Volume density of charge Absorbed dose Acoustical energy Acoustical intensity Acoustical power Sound pressure Illuminance Illumination Irradiance Light exposure Luminance Luminous efficacy Luminous exitance Luminous flux Luminous intensity Radiance Radiant energy Radiant flux Radiant intensity Radiant power

1-11

TABLE 1-4

Conversion Factors: U.S. Customary and Commonly Used Units to SI Units (Concluded ) Customary or commonly used unit Å 10−3 cm−1 m−1 Alternate SI unit Conversion factor; multiply customary unit by factor to obtain SI unit 1.0* 10−3 cm−1 1.0* 1 1 3.7* E − 01 E + 01

Quantity Wavelength Capture unit

SI unit nm m−1 m−1 Bq

Radioactivity

Ci

E + 10

*An asterisk indicates that the conversion factor is exact. † Conversion factors for length, area, and volume are based on the international foot. The international foot is longer by 2 parts in 1 million than the U.S. Survey foot (land-measurement use). NOTE: The following unit symbols are used in the table: Unit symbol A a Bq C cd Ci d °C ° dyn F fc G g gr Gy H h ha Hz J K L, , l
NOTE:

Name ampere annum (year) becquerel coulomb candela curie day degree Celsius degree dyne farad footcandle gauss gram grain gray henry hour hectare hertz joule kelvin liter

Unit symbol lm lx m min ′ N naut mi Oe Ω Pa rad r S s ″ sr St T t V W Wb

Name lumen lux meter minute minute newton U.S. nautical mile oersted ohm pascal radian revolution siemens second second steradian stokes tesla tonne volt watt weber

Copyright SPE-AIME, The SI Metric System of Units and SPE’s Tentative Metric Standard, Society of Petroleum Engineers, Dallas, 1977.

1-12

TABLE 1-5 Metric Conversion Factors as Exact Numerical Multiples of SI Units The first two digits of each numerical entry represent a power of 10. For example, the entry “−02 2.54” expresses the fact that 1 in = 2.54 × 10−2 m. To convert from abampere abcoulomb abfarad abhenry abmho abohm abvolt acre ampere (international of 1948) angstrom are astronomical unit atmosphere bar barn barrel (petroleum 42 gal) barye British thermal unit (ISO/ TC 12) British thermal unit (International Steam Table) British thermal unit (mean) British thermal unit (thermochemical) British thermal unit (39°F) British thermal unit (60°F) bushel (U.S.) cable caliber calorie (International Steam Table) calorie (mean) calorie (thermochemical) calorie (15°C) calorie (20°C) calorie (kilogram, International Steam Table) calorie (kilogram, mean) calorie (kilogram, thermochemical) carat (metric) Celsius (temperature) centimeter of mercury (0°C) centimeter of water (4°C) chain (engineer’s) chain (surveyor’s or Gunter’s) circular mil cord coulomb (international of 1948) cubit cup curie day (mean solar) day (sidereal) degree (angle) denier (international) dram (avoirdupois) dram (troy or apothecary) dram (U.S. fluid) dyne electron volt erg Fahrenheit (temperature) Fahrenheit (temperature) farad (international of 1948) faraday (based on carbon 12) faraday (chemical) faraday (physical) fathom fermi (femtometer) ampere coulomb farad henry mho ohm volt meter2 ampere meter meter2 meter newton/meter2 newton/meter2 meter2 meter3 newton/meter2 joule joule joule joule joule joule meter3 meter meter joule joule joule joule joule joule joule joule kilogram kelvin newton/meter2 newton/meter2 meter meter meter2 meter3 coulomb meter meter3 disintegration/second second (mean solar) second (mean solar) radian kilogram/meter kilogram kilogram meter3 newton joule joule kelvin Celsius farad coulomb coulomb coulomb meter meter To Multiply by +01 1.00 +01 1.00 +09 1.00 −09 1.00 +09 1.00 −09 1.00 −08 1.00 +03 4.046 856 −01 9.998 35 −10 1.00 +02 1.00 +11 1.495 978 +05 1.013 25 +05 1.00 −28 1.00 −01 1.589 873 −01 1.00 +03 1.055 06 +03 1.055 04 +03 1.055 87 +03 1.054 350 +03 1.059 67 +03 1.054 68 −02 3.523 907 +02 2.194 56 −04 2.54 +00 4.1868 +00 4.190 02 +00 4.184 +00 4.185 80 +00 4.181 90 +03 4.186 8 +03 4.190 02 +03 4.184 −04 2.00 tK = tc + 273.15 +03 1.333 22 +01 9.806 38 +01 3.048 +01 2.011 68 −10 5.067 074 +00 3.624 556 −01 9.998 35 −01 4.572 −04 2.365 882 +10 3.70 +04 8.64 +04 8.616 409 −02 1.745 329 −07 1.111 111 −03 1.771 845 −03 3.887 934 −06 3.696 691 −05 1.00 −19 1.602 10 −07 1.00 tK = (5/9)(tF + 459.67) tc = (5/9)(tF − 32) −01 9.995 05 +04 9.648 70 +04 9.649 57 +04 9.652 19 +00 1.828 8 −15 1.00 To convert from fluid ounce (U.S.) foot foot (U.S. survey) foot of water (39.2°F) footcandle footlambert furlong gal (galileo) gallon (U.K. liquid) gallon (U.S. dry) gallon (U.S. liquid) gamma gauss gilbert gill (U.K.) gill (U.S.) grad grad grain gram hand hectare henry (international of 1948) hogshead (U.S.) horsepower (550 ft lbf/s) horsepower (boiler) horsepower (electric) horsepower (metric) horsepower (U.K.) horsepower (water) hour (mean solar) hour (sidereal) hundredweight (long) hundredweight (short) inch inch of mercury (32°F) inch of mercury (60°F) inch of water (39.2°F) inch of water (60°F) joule (international of 1948) kayser kilocalorie (International Steam Table) kilocalorie (mean) kilocalorie (thermochemical) kilogram mass kilogram-force (kgf) kilopond-force kip knot (international) lambert lambert langley lbf (pound-force, avoirdupois) lbm (pound-mass, avoirdupois) league (British nautical) league (international nautical) league (statute) light-year link (engineer’s) link (surveyor’s or Gunter’s) liter lux maxwell meter micrometer mil mile (U.S. statute) mile (U.K. nautical) mile (international nautical) mile (U.S. nautical) millibar millimeter of mercury (0°C) To meter3 meter meter newton/meter2 lumen/meter2 candela/meter2 meter meter/second2 meter3 meter3 meter3 tesla tesla ampere turn meter3 meter3 degree (angular) radian kilogram kilogram meter meter2 henry meter3 watt watt watt watt watt watt second (mean solar) second (mean solar) kilogram kilogram meter newton/meter2 newton/meter2 newton/meter2 newton/meter2 joule 1/meter joule joule joule kilogram newton newton newton meter/second candela/meter2 candela/meter2 joule/meter2 newton kilogram meter meter meter meter meter meter meter3 lumen/meter2 weber wavelengths Kr 86 meter meter meter meter meter meter newton/meter2 newton/meter2 Multiply by −05 2.957 352 −01 3.048 −01 3.048 006 +03 2.988 98 +01 1.076 391 +00 3.426 259 +02 2.011 68 −02 1.00 −03 4.546 087 −03 4.404 883 −03 3.785 411 −09 1.00 −04 1.00 −01 7.957 747 −04 1.420 652 −04 1.182 941 −01 9.00 −02 1.570 796 −05 6.479 891 −03 1.00 −01 1.016 +04 1.00 +00 1.000 495 −01 2.384 809 +02 7.456 998 +03 9.809 50 +02 7.46 +02 7.354 99 +02 7.457 +02 7.460 43 +03 3.60 +03 3.590 170 +01 5.080 234 +01 4.535 923 −02 2.54 +03 3.386 389 +03 3.376 85 +02 2.490 82 +02 2.4884 +00 1.000 165 +02 1.00 +03 4.186 74 +03 4.190 02 +03 4.184 +00 1.00 +00 9.806 65 +00 9.806 65 +03 4.448 221 −01 5.144 444 +04 1/π +03 3.183 098 +04 4.184 +00 4.448 221 −01 4.535 923 +03 5.559 552 +03 5.556 +03 4.828 032 +15 9.460 55 −01 3.048 −01 2.011 68 −03 1.00 +00 1.00 −08 1.00 +06 1.650 763 −06 1.00 −05 2.54 +03 1.609 344 +03 1.853 184 +03 1.852 +03 1.852 +02 1.00 +02 1.333 224 1-13

TABLE 1-5 Metric Conversion Factors as Exact Numerical Multiples of SI Units (Concluded ) The first two digits of each numerical entry represent a power of 10. For example, the entry “−02 2.54” expresses the fact that 1 in = 2.54 × 10−2 To convert from minute (angle) minute (mean solar) minute (sidereal) month (mean calendar) nautical mile (international) nautical mile (U.S.) nautical mile (U.K.) oersted ohm (international of 1948) ounce-force (avoirdupois) ounce-mass (avoirdupois) ounce-mass (troy or apothecary) ounce (U.S. fluid) pace parsec pascal peck (U.S.) pennyweight perch phot pica (printer’s) pint (U.S. dry) pint (U.S. liquid) point (printer’s) poise pole pound-force (lbf avoirdupois) pound-mass (lbm avoirdupois) pound-mass (troy or apothecary) poundal quart (U.S. dry) quart (U.S. liquid) rad (radiation dose absorbed) Rankine (temperature) rayleigh (rate of photon emission) rhe rod roentgen rutherford second (angle) To radian second (mean solar) second (mean solar) second (mean solar) meter meter meter ampere/meter ohm newton kilogram kilogram meter3 meter meter newton/meter2 meter3 kilogram meter lumen/meter2 meter meter3 meter3 meter (newton-second)/meter2 meter newton kilogram kilogram newton meter3 meter3 joule/kilogram kelvin 1/second-meter2 meter2/(newtonsecond) meter coulomb/kilogram disintegration/second radian Multiply by −04 2.908 882 +01 6.00 +01 5.983 617 +06 2.628 +03 1.852 +03 1.852 +03 1.853 184 +01 7.957 747 +00 1.000 495 −01 2.780 138 −02 2.834 952 −02 3.110 347 −05 2.957 352 −01 7.62 +16 3.083 74 +00 1.00 −03 8.809 767 −03 1.555 173 +00 5.0292 +04 1.00 −03 4.217 517 −04 5.506 104 −04 4.731 764 −04 3.514 598 −01 1.00 +00 5.0292 +00 4.448 221 −01 4.535 923 −01 3.732 417 −01 1.382 549 −03 1.101 220 −04 9.463 529 −02 1.00 tK = (5/9)tR +10 1.00 +01 1.00 +00 5.0292 −04 2.579 76 +06 1.00 −06 4.848 136 To convert from second (ephemeris) second (mean solar) To second second (ephemeris) Multiply by +00 1.000 000 Consult American Ephemeris and Nautical Almanac −01 9.972 695 +06 2.589 988 −03 1.295 978 −08 1.00 +02 1.097 28 +01 1.459 390 −01 2.286 −10 3.335 640 −10 3.335 640 −12 1.112 650 +11 8.987 554 −12 1.112 650 +11 8.987 554 +03 1.609 344 +02 2.997 925 +00 1.00 +04 1.00 −04 1.00 −05 1.478 676 −06 4.928 921 −02 2.916 666 +03 1.016 046 +03 1.00 +09 4.20 +00 2.831 684 +02 9.071 847 +03 1.00 +02 1.333 22 +07 9.323 957 −07 1.256 637 +00 1.000 330 +00 1.000 165 −01 9.144 +07 3.1536 +07 3.155 815 +07 3.155 692 +07 3.155 692 +07 3.155 692

second (sidereal) section scruple (apothecary) shake skein slug span statampere statcoulomb statfarad stathenry statmho statohm statute mile (U.S.) statvolt stere stilb stoke tablespoon teaspoon ton (assay) ton (long) ton (metric) ton (nuclear equivalent of TNT) ton (register) ton (short, 2000 lb) tonne torr (0°C) township unit pole volt (international of 1948) watt (international of 1948) yard year (calendar) year (sidereal) year (tropical) year 1900, tropical, Jan., day 0, hour 12 year 1900, tropical, Jan., day 0, hour 12

second (mean solar) meter2 kilogram second meter kilogram meter ampere coulomb farad henry mho ohm meter volt meter3 candela/meter2 meter2/second meter3 meter3 kilogram kilogram kilogram joule meter3 kilogram kilogram newton/meter2 meter2 weber volt watt meter second (mean solar) second (mean solar) second (mean solar) second (ephemeris) second

1-14

TABLE 1-6

Alphabetical Listing of Common Conversions To Square feet Square meters Square miles Cubic meters Coulombs (absolute) Inches Meters Microns Millimeters of mercury at 32°F Dynes per square centimeter Newtons per square meter Feet of water at 39.1°F Grams per square centimeter Inches of mercury at 32°F Pounds per square foot Pounds per square inch Pounds (cement) Pounds (cement) Cubic meters Gallons Cubic meters Gallons Gallons per minute Atmospheres Newtons per square meter Pounds per square inch Cubic feet B.t.u. per hour Kilowatts Calories (gram) Centigrade heat units (c.h.u. or p.c.u.) Foot-pounds Horsepower-hours Joules Liter-atmospheres Pounds carbon to CO2 Pounds water evaporated from and at 212°F Cubic foot-atmospheres Kilowatt-hours Joules per cubic meter Watts Horsepower Joules per kilogram Calories per gram per degree centigrade Joules per kilogram per degree Kelvin Watts Joules per square meter per second Kilowatts per square foot Calories, gram (15°C.), per square centimeter per second for a temperature gradient of 1°C. per centimeter Multiply by 43,560 4074 0.001563 1233 3600 3.937 × 10−9 1 × 10−10 1 × 10−4 760 1.0133 × 106 101,325 33.90 1033.3 29.921 2116.3 14.696 94 376 0.15899 42 0.11924 31.5 0.02917 0.9869 1 × 105 14.504 1 ⁄12 33,480 9.803 252 0.55556 777.9 3.929 × 10−4 1055.1 10.41 6.88 × 10−5 0.001036 0.3676 2.930 × 10−4 37,260 0.29307 0.02357 2326 1 4186.8 1054.4 3.1546 0.1758 1.2405 To convert from B.t.u. (60°F.) per degree Fahrenheit Bushels (U.S. dry) Bushels (U.S. dry) Calories, gram Calories, gram Calories, gram Calories, gram Calories, gram Calories, gram, per gram per degree C. Calories, kilogram Calories, kilogram per second Candle power (spherical) Carats (metric) Centigrade heat units Centimeters Centimeters Centimeters Centimeters Centimeters Centimeters of mercury at 0°C. Centimeters of mercury at 0°C. Centimeters of mercury at 0°C Centimeters of mercury at 0°C. Centimeters of mercury at 0°C. Centimeters per second Centimeters of water at 4°C. Centistokes Circular mils Circular mils Circular mils Cords Cubic centimeters Cubic centimeters Cubic centimeters Cubic centimeters Cubic feet Cubic feet Cubic feet Cubic feet Cubic feet Cubic feet Cubic foot-atmospheres Cubic foot-atmospheres Cubic feet of water (60°F.) Cubic feet per minute Cubic feet per minute Cubic feet per second Cubic feet per second Cubic inches Cubic yards Curies Curies Degrees Drams (apothecaries’ or troy) To Calories per degree centigrade Cubic feet Cubic meters B.t.u. Foot-pounds Joules Liter-atmospheres Horsepower-hours Joules per kilogram per degree Kelvin Kilowatt-hours Kilowatts Lumens Grams B.t.u. Angstrom units Feet Inches Meters Microns Atmospheres Feet of water at 39.1°F. Newtons per square meter Pounds per square foot Pounds per square inch Feet per minute Newtons per square meter Square meters per second Square centimeters Square inches Square mils Cubic feet Cubic feet Gallons Ounces (U.S. fluid) Quarts (U.S. fluid) Bushels (U.S.) Cubic centimeters Cubic meters Cubic yards Gallons Liters Foot-pounds Liter-atmospheres Pounds Cubic centimeters per second Gallons per second Gallons per minute Million gallons per day Cubic meters Cubic meters Disintegrations per minute Coulombs per minute Radians Grams Multiply by 453.6 1.2444 0.03524 3.968 × 10−3 3.087 4.1868 4.130 × 10−2 1.5591 × 10−6 4186.8 0.0011626 4.185 12.556 0.2 1.8 1 × 108 0.03281 0.3937 0.01 10,000 0.013158 0.4460 1333.2 27.845 0.19337 1.9685 98.064 1 × 10−6 5.067 × 10−6 7.854 × 10−7 0.7854 128 3.532 × 10−5 2.6417 × 10−4 0.03381 0.0010567 0.8036 28,317 0.028317 0.03704 7.481 28.316 2116.3 28.316 62.37 472.0 0.1247 448.8 0.64632 1.6387 × 10−5 0.76456 2.2 × 1012 1.1 × 1012 0.017453 3.888 1-15

To convert from Acres Acres Acres Acre-feet Ampere-hours (absolute) Angstrom units Angstrom units Angstrom units Atmospheres Atmospheres Atmospheres Atmospheres Atmospheres Atmospheres Atmospheres Atmospheres Bags (cement) Barrels (cement) Barrels (oil) Barrels (oil) Barrels (U.S. liquid) Barrels (U.S. liquid) Barrels per day Bars Bars Bars Board feet Boiler horsepower Boiler horsepower B.t.u. B.t.u. B.t.u. B.t.u. B.t.u. B.t.u. B.t.u. B.t.u. B.t.u. B.t.u. B.t.u. per cubic foot B.t.u. per hour B.t.u. per minute B.t.u. per pound B.t.u. per pound per degree Fahrenheit B.t.u. per pound per degree Fahrenheit B.t.u. per second B.t.u. per square foot per hour B.t.u. per square foot per minute B.t.u. per square foot per second for a temperature gradient of 1°F. per inch

TABLE 1-6

Alphabetical Listing of Common Conversions (Concluded ) To Grams Newtons Joules Coulombs (abs.) Feet Meters Centimeters per second Miles per hour Meters per (second)2 Newtons per square meter B.t.u. Joules Liter-atmospheres B.t.u. Calories, gram Foot-poundals Horsepower-hours Kilowatt-hours Liter-atmospheres Joules Horsepower Kilowatts Miles Barrels (U.S. liquid) Cubic meters Cubic feet Gallons (Imperial) Liters Ounces (U.S. fluid) Cubic feet per hour Cubic feet per second Grams Pounds Grams per cubic meter Parts per million Drams (avoirdupois) Drams (troy) Grains Kilograms Pounds (avoirdupois) Pounds (troy) Pounds per cubic foot Multiply by 1.7719 1 × 10−5 1 × 10−7 96,500 6 0.3048 0.5080 0.011364 0.3048 2989 3.995 × 10−5 0.04214 4.159 × 10−4 0.0012856 0.3239 32.174 5.051 × 10−7 3.766 × 10−7 0.013381 1.3558 0.0018182 0.0013558 0.125 0.03175 0.003785 0.13368 0.8327 3.785 128 8.021 0.002228 0.06480 1⁄ 7000 2.2884 17.118 0.5644 0.2572 15.432 0.001 0.0022046 0.002679 62.43 To convert from Horsepower (British) Horsepower (metric) Horsepower (metric) Hours (mean solar) Inches Inches of mercury at 60°F Inches of water at 60°F Joules (absolute) Joules (absolute) Joules (absolute) Joules (absolute) Joules (absolute) Joules (absolute) Kilocalories Kilograms Kilograms force Kilograms per square centimeter Kilometers Kilowatt-hours Kilowatt-hours Kilowatts Knots (international) Knots (nautical miles per hour) Lamberts Liter-atmospheres Liter-atmospheres Liters Liters Liters Lumens Micromicrons Microns Microns Miles (nautical) Miles (nautical) Miles Miles Miles per hour Miles per hour Milliliters Millimeters To Pounds water evaporated per hour at 212°F Foot-pounds per second Kilogram-meters per second Seconds Meters Newtons per square meter Newtons per square meter B.t.u. (mean) Calories, gram (mean) Cubic foot-atmospheres Foot-pounds Kilowatt-hours Liter-atmospheres Joules Pounds (avoirdupois) Newtons Pounds per square inch Miles B.t.u. Foot-pounds Horsepower Meters per second Miles per hour Candles per square inch Cubic foot-atmospheres Foot-pounds Cubic feet Cubic meters Gallons Watts Microns Angstrom units Meters Feet Miles (U.S. statute) Feet Meters Feet per second Meters per second Cubic centimeters Meters Multiply by 2.64 542.47 75.0 3600 0.0254 3376.9 248.84 9.480 × 10−4 0.2389 0.3485 0.7376 2.7778 × 10−7 0.009869 4186.8 2.2046 9.807 14.223 0.6214 3414 2.6552 × 106 1.3410 0.5144 1.1516 2.054 0.03532 74.74 0.03532 0.001 0.26418 0.001496 1 × 10−6 1 × 104 1 × 10−6 6080 1.1516 5280 1609.3 1.4667 0.4470 1 0.001

To convert from Drams (avoirdupois) Dynes Ergs Faradays Fathoms Feet Feet per minute Feet per minute Feet per (second)2 Feet of water at 39.2°F. Foot-poundals Foot-poundals Foot-poundals Foot-pounds Foot-pounds Foot-pounds Foot-pounds Foot-pounds Foot-pounds Foot-pounds force Foot-pounds per second Foot-pounds per second Furlongs Gallons (U.S. liquid) Gallons Gallons Gallons Gallons Gallons Gallons per minute Gallons per minute Grains Grains Grains per cubic foot Grains per gallon Grams Grams Grams Grams Grams Grams Grams per cubic centimeter

1-16

TABLE 1-6

Alphabetical Listing of Common Conversions (Concluded ) To Pounds per gallon Grains per gallon Pounds per cubic foot Pounds per square foot Pounds per square inch Acres Square meters B.t.u. per minute B.t.u. per hour Foot-pounds per minute Foot-pounds per second Watts Horsepower (metric) Pounds carbon to CO2 per hour Grains Kilograms Pounds (troy) Grams per cubic centimeter Kilograms per cubic meter Atmospheres Kilograms per square meter Atmospheres Kilograms per square centimeter Newtons per square meter Newtons Newtons per square meter Horsepower-hours B.t.u. Cubic meters Degrees Radians per second Radians Gee pounds Kilograms Pounds Square feet Multiply by 8.345 58.42 0.0624 2.0482 0.014223 2.471 10,000 42.42 2545 33,000 550 745.7 1.0139 0.175 7000 0.45359 1.2153 0.016018 16.018 4.725 × 10−4 4.882 0.06805 0.07031 6894.8 4.4482 47.88 0.379 1.8 9.464 × 10−4 57.30 0.10472 4.848 × 10−6 1 14.594 32.17 0.0010764 To convert from Millimeters of mercury at 0°C. Millimicrons Mils Mils Minims (U.S.) Minutes (angle) Minutes (mean solar) Newtons Ounces (avoirdupois) Ounces (avoirdupois) Ounces (U.S. fluid) Ounces (troy) Pints (U.S. liquid) Poundals Square feet Square feet per hour Square inches Square inches Square yards Stokes Tons (long) Tons (long) Tons (metric) Tons (metric) Tons (metric) Tons (short) Tons (short) Tons (refrigeration) Tons (British shipping) Tons (U.S. shipping) Torr (mm. mercury, 0°C.) Watts Watts Watts Watt-hours Yards To Newtons per square meter Microns Inches Meters Cubic centimeters Radians Seconds Kilograms Kilograms Ounces (troy) Cubic meters Ounces (apothecaries’) Cubic meters Newtons Square meters Square meters per second Square centimeters Square meters Square meters Square meters per second Kilograms Pounds Kilograms Pounds Tons (short) Kilograms Pounds B.t.u. per hour Cubic feet Cubic feet Newtons per square meter B.t.u. per hour Joules per second Kilogram-meters per second Joules Meters Multiply by 133.32 0.001 0.001 2.54 × 10−5 0.06161 2.909 × 10−4 60 0.10197 0.02835 0.9115 2.957 × 10−5 1.000 4.732 × 10−4 0.13826 0.0929 2.581 × 10−5 6.452 6.452 × 10−4 0.8361 1 × 10−4 1016 2240 1000 2204.6 1.1023 907.18 2000 12,000 42.00 40.00 133.32 3.413 1 0.10197 3600 0.9144

To convert from Grams per cubic centimeter Grams per liter Grams per liter Grams per square centimeter Grams per square centimeter Hectares Hectares Horsepower (British) Horsepower (British) Horsepower (British) Horsepower (British) Horsepower (British) Horsepower (British) Horsepower (British) Pounds (avoirdupois) Pounds (avoirdupois) Pounds (avoirdupois) Pounds per cubic foot Pounds per cubic foot Pounds per square foot Pounds per square foot Pounds per square inch Pounds per square inch Pounds per square inch Pounds force Pounds force per square foot Pounds water evaporated from and at 212°F. Pound-centigrade units (p.c.u.) Quarts (U.S. liquid) Radians Revolutions per minute Seconds (angle) Slugs Slugs Slugs Square centimeters

1-17

TABLE 1-7 Mass (M)

Common Units and Conversion Factors* 1 pound mass = 453.5924 grams = 0.45359 kilograms = 7000 grains 1 slug = 32.174 pounds mass 1 ton (short) = 2000 pounds mass 1 ton (long) = 2240 pounds mass 1 ton (metric) = 1000 kilograms = 2204.62 pounds mass 1 pound mole = 453.59 gram moles = 30.480 centimeters = 0.3048 meters 1 inch = 2.54 centimeters = 0.0254 meters 1 mile (U.S.) = 1.60935 kilometers 1 yard = 0.9144 meters 1 foot 1 square foot = 929.0304 square centimeters = 0.09290304 square meters 1 square inch = 6.4516 square centimeters 1 square yard = 0.836127 square meters 1 cubic foot = 28,316.85 cubic centimeters = 0.02831685 cubic meters = 28.31685 liters = 7.481 gallons (U.S.) = 3.7853 liters = 231 cubic inches = 60 minutes = 3600 seconds 1 atm = 760 millimeters of mercury at 0°C (density 13.5951 g/cm3) = 29.921 inches of mercury at 32°F = 14.696 pounds force/square inch = 33.899 feet of water at 39.1°F = 1.01325 × 106 dynes/square centimeter = 1.01325 × 105 Newtons/square meter Density (M/L3) 1 pound mass/cubic foot = 0.01601846 grams/cubic centimeter = 16.01846 kilogram/cubic meter Energy (H or FL) 1 British thermal unit = 251.98 calories = 1054.4 joules = 777.97 foot-pounds force = 10.409 liter-atmospheres = 0.2930 watt-hour 2 Diffusivity (L /θ) 1 square foot/hour = 0.258 cm2/s = 2.58 × 10−5 m2/s Viscosity (M/Lθ) 1 pound mass/foot hour = 0.00413 g/cm s 0.000413 kg/m s 1 centipoise = 0.01 poise = 0.01 g/cm s = 0.001 kg/m s = 0.000672 lbm/ft s = 0.0000209 lbfs/ft2 Thermal conductivity [H/θL2(T/L)] 2 1 Btu/hr ft (°F/ft) = 0.00413 cal/s cm2 (°C/cm) = 1.728 J/s m2 (°C/m) Heat transfer coefficient 1 Btu/hr ft2 °F = 5.678 J/s m2 °C Heat capacity (H/MT) 1 Btu/lbm °F = 1 cal/g °C = 4184 J/kg °C Gas constant 1.987 Btu/lbm mole °R = 1.987 cal/mol K = 82.057 atm cm3/mol K = 0.7302 atm ft3/lb mole °F = 10.73 (lbf /in.2) (ft3)/lb mole °R = 1545 (lbf /ft2) (ft3)/lb mole °R = 8.314 (N/m2) (m3)/mol K Gravitational acceleration g = 9.8066 m/s2 = 32.174 ft/s2

Length (L)

Area (L2)

Volume (L3)

1 gallon Time (θ) 1 hour

Temperature (T) 1 centigrade or Celsius degree = 1.8 Fahrenheit degree Temperature, Kelvin = T°C + 273.15 Temperature, Rankine = T°F + 459.7 Temperature, Fahrenheit = 9/5 T°C + 32 Temperature, centigrade or Celsius = 5/9 (T°F − 32) Temperature, Rankine = 1.8 T K Force (F) 1 pound force = 444,822.2 dynes = 4.448222 Newtons = 32.174 poundals Pressure (F/L2) Normal atmospheric pressure

NOTE: U.S. customary units; or British units, on left and SI units on right. *Adapted from Faust et al., Principles of Unit Operations, John Wiley and Sons, 1980.

TABLE 1-8

Kinematic-Viscosity Conversion Formulas Range of t, sec 32 < t < 100 t > 100 25 < t < 40 t > 40 34 < t < 100 t > 100 Kinematic viscosity, stokes 0.00226t − 1.95/t 0.00220t − 1.35/t 0.0224t − 1.84/t 0.0216t − 0.60/t 0.00260t − 1.79/t 0.00247t − 0.50/t 0.027t − 20/t 0.00147t − 3.74/t

TABLE 1-9 Temp. scale Kelvin

Values of the Gas-Law Constant Press. units Vol. units Wt. units g-moles g-moles g-moles g-moles g-moles g-moles g-moles g-moles lb-moles lb-moles lb-moles lb-moles lb-moles lb-moles lb-moles lb-moles lb-moles lb-moles lb-moles Energy units calories joules (abs) joules (int) atm cm3 atm liters mm Hg-liters bar-liters kg/(cm2)(liters) atm-ft3 mm Hg-ft3 chu or pcu Btu hp-hr kw-hr atm-ft3 in Hg-ft3 mm Hg-ft3 (lb)(ft3)/in2 ft-lb R 1.9872 8.3144 8.3130 82.057 0.08205 62.361 0.08314 0.08478 1.314 998.9 1.9872 1.9872 0.0007805 0.0005819 0.7302 21.85 555.0 10.73 1545.0

Viscosity scale Saybolt Universal Saybolt Furol Redwood No. 1 Redwood Admiralty Engler

atm. atm. mm. Hg bar kg/cm2 atm mm Hg Rankine atm in Hg mm Hg lb/in2abs lb/ft2abs

cm3 liters liters liters liters ft3 ft3

ft3 ft3 ft3 ft3 ft3

1-18

TABLE 1-10 United States Customary System of Weights and Measures Linear Measure 12 inches (in) or (″) = 1 foot (ft) or (′) 3 feet = 1 yard (yd) 16.5 feet = 1 rod (rd) 5.5 yards 5280 feet = 1 mile (mi) 320 rods 1 mil = 0.001 inch Nautical: 6080.2 feet = 1 nautical mile 6 feet = 1 fathom 120 fathoms = 1 cable length 1 knot = 1 nautical mile per hour 60 nautical miles = 1° of latitude

TABLE 1-11

Temperature Conversion Formulas

°F = (°C × 5/9) + 32 °C = (°F − 32) × 5/9 °R = °F + 459.69 °K = °C + 273.15 °K = °R × 5/9 Temperature difference, T °F = °C × 9/5

NOTE: An extensive table of temperature conversions may be found in the sixth edition of the Handbook (Table 1-12).

Square Measure 144 sq. inches (sq. in) or (in2) or ( ″) = 1 sq. foot (ft2) or ( ′) 9 sq. feet (ft2) ( ′) = 1 sq. yard (yd2) 30.25 sq. yards = 1 sq. rod, pole, or perch 10 sq. chains 160 sq. rods = = 1 acre 43,560 sq. ft 640 acres = 1 sq. mile = 1 section 1 circular inch (area of circle of 1 inch diameter) = 0.7854 sq. inch 1 sq. inch = 1.2732 circular inch 1 circular mil = area of circle of 0.001 inch diameter 1,000,000 circular mils = 1 circular inch Circular Measure 60 seconds (″) (sec) = 1 minute (min) or (′) 60 minutes (′) = 1 degree (°) 90 degrees (°) = 1 quadrant 360 degrees (°) = 1 circumference = 1 radian (rad.) 57.29578 degrees = 57° 17′ 44.81″ Volume Measure 1728 cubic in (cu. in) (in3) = 1 cubic foot (cu. ft)(ft3) 27 cu. ft = 1 cubic yard (cu. yd) Dry Measure: 2 pints = 1 quart 8 quarts = 1 peck 4 pecks = 1 bushel 1 United States Winchester bushel = 2150.42 cubic inches Liquid: 4 gills = 1 pint (pt) 2 pints = 1 quart (qt) 4 quarts = 1 gallon (gal) 7.4805 gallons = 1 cubic foot Apothecaries’ Liquid: 60 minims (min. or ) = 1 fluid dram or drachm 8 drams ( ) = 1 fluid ounce 16 ounces (oz. ) = 1 pint Avoirdupois Weight 16 drams = 437.5 grains = 1 ounce (oz) 16 ounces = 7000 grains = 1 pound (lb) 100 pounds = 1 hundredweight (cwt) 2000 pounds = 1 short ton: 2240 pounds = 1 long ton Troy Weight 24 grains = 1 pennyweight (dwt) 20 pennyweights = 1 ounce (oz) 12 ounces = 1 pound (lb) Apothecaries’ Weight 20 grains (gr) = 1 scruple ( ) 3 scruples = 1 dram ( ) 8 drams = 1 ounce ( ) 12 ounces = 1 pound (lb) Solid:

1-19

TABLE 1-12

Specific Gravity, Degrees Baumé, Degrees API, Degrees Twaddell, Pounds per Gallon, Pounds per Cubic Foot* °Bé = 145 −
Lb per gal at 60°F wt in air 4.9929 5.0346 5.0763 5.1180 5.1597 5.2014 5.2431 5.2848 5.3265 5.3682 5.4098 5.4515 5.4932 5.5349 5.5766 5.6183 5.6600 5.7017 5.7434 5.7851

145 140 sp gr 60°/60°F − 1 141.5 − 130 (lighter than H2O); °Tw = °API = − 131.5 (heavier than H2O); °Bé = sp gr sp gr 0.005 sp gr
Lb per ft3 at 60°F wt in air 37.350 37.662 37.973 38.285 38.597 39.910 39.222 39.534 39.845 40.157 40.468 40.780 41.092 41.404 41.716 42.028 42.340 42.652 42.963 43.275 Lb per gal at 60°F wt in air 5.8268 5.8685 5.9101 5.9518 5.9935 6.0352 6.0769 6.1186 6.1603 6.2020 6.2437 6.2854 6.3271 6.3688 6.4104 6.4521 6.4938 6.5355 6.5772 6.6189 Lb per ft3 at 60°F wt in air 43.587 43.899 44.211 44.523 44.834 45.146 45.458 45.770 46.082 46.394 46.706 47.018 47.330 47.642 47.953 47.265 48.577 48.889 49.201 49.513 Lb per gal at 60°F wt in air 6.6606 6.7023 6.7440 6.7857 6.8274 6.8691 6.9108 6.9525 6.9941 7.0358 7.0775 7.1192 7.1609 7.2026 7.2443 7.2860 7.3277 7.3694 7.4111 7.4528 Lb per ft3 at 60°F wt in air 49.825 50.137 50.448 50.760 51.072 51.384 51.696 52.008 52.320 52.632 52.943 53.255 53.567 53.879 54.191 54.503 54.815 55.127 55.438 55.750 Lb per gal at 60°F wt in air 7.4944 7.5361 7.5777 7.6194 7.6612 7.7029 7.7446 7.7863 7.8280 7.8697 7.9114 7.9531 7.9947 8.0364 8.0780 8.1197 8.1615 8.2032 8.2449 8.2866 8.3283 Lb per gal at 60°F wt in air 14.6238 14.6655 14.7072 14.7489 14.7906 14.8323 14.8740 14.9157 14.9574 14.9990 15.0407 15.0824 15.1241 15.1658 15.2075 15.2492 15.2909 15.3326 15.3743 15.4160 15.4577 15.4993 15.5410 15.5827 15.6244 15.6661 15.7078 15.7495 15.7912 15.8329 15.8746 15.9163 15.9580 15.9996 16.0413 16.0830 16.1247 16.1664 16.2081 16.2498 16.2915 16.3332 16.3749 16.4166 16.4583 16.5000 16.5417 16.5833 16.6250 16.6667 Lb per ft3 at 60°F. wt. in air 56.062 56.374 56.685 56.997 57.310 57.622 57.934 58.246 58.557 58.869 59.181 59.493 59.805 60.117 60.428 60.740 61.052 61.364 61.676 61.988 62.300 Lb per ft3 at 60°F. wt. in air 109.394 109.705 110.017 110.329 110.641 110.953 111.265 111.577 111.889 112.200 112.512 112.824 113.136 113.448 113.760 114.072 114.384 114.696 115.007 115.318 115.630 115.943 116.255 116.567 116.879 117.191 117.503 117.814 118.126 118.438 118.740 119.062 119.374 119.686 119.998 120.309 120.621 120.933 121.245 121.557 121.869 122.181 122.493 122.804 123.116 123.428 123.740 124.052 124.364 124.676

Sp gr 60°/ 60° 0.600 .605 .610 .615 .620 .625 .630 .635 .640 .645 .650 .655 .660 .665 .670 .675 .680 .685 .690 .695

°Bé 103.33 101.40 99.51 97.64 95.81 94.00 92.22 90.47 88.75 87.05 85.38 83.74 82.12 80.53 78.96 77.41 75.88 74.38 72.90 71.44

°API 104.33 102.38 100.47 98.58 96.73 94.90 93.10 91.33 89.59 87.88 86.19 84.53 82.89 81.28 79.69 78.13 76.59 75.07 73.57 72.10

Sp gr 60°/ 60° 0.700 .705 .710 .715 .720 .725 .730 .735 .740 .745 .750 .755 .760 .765 .770 .775 .780 .785 .790 .795

°Bé 70.00 68.58 67.18 65.80 64.44 63.10 61.78 60.48 59.19 57.92 56.67 55.43 54.21 53.01 51.82 50.65 49.49 48.34 47.22 46.10

°API 70.64 69.21 67.80 66.40 65.03 63.67 62.34 61.02 59.72 58.43 57.17 55.92 54.68 53.47 52.27 51.08 49.91 48.75 47.61 46.49

Sp gr 60°/ 60° 0.800 .805 .810 .815 .820 .825 .830 .835 .840 .845 .850 .855 .860 .865 .870 .875 .880 .885 .890 .895

°Bé 45.00 43.91 42.84 41.78 40.73 39.70 38.67 37.66 36.67 35.68 34.71 33.74 32.79 31.85 30.92 30.00 29.09 28.19 27.30 26.42

°API 45.38 44.28 43.19 42.12 41.06 40.02 38.98 37.96 36.95 35.96 34.97 34.00 33.03 32.08 31.14 30.21 29.30 28.39 27.49 26.60

Sp gr 60°/ 60° 0.900 .905 .910 .915 .920 .925 .930 .935 .940 .945 .950 .955 .960 .965 .970 .975 .980 .985 .990 .995 1.000

°Bé 25.56 24.70 23.85 23.01 22.17 21.35 20.54 19.73 18.94 18.15 17.37 16.60 15.83 15.08 14.33 13.59 12.86 12.13 11.41 10.70 10.00

°API 25.72 24.85 23.99 23.14 22.30 21.47 20.65 19.84 19.03 18.24 17.45 16.67 15.90 15.13 14.38 13.63 12.89 12.15 11.43 10.71 10.00

Sp gr 60°/ 60° 1.005 1.010 1.015 1.020 1.025 1.030 1.035 1.040 1.045 1.050 1.055 1.060 1.065 1.070 1.075 1.080 1.085 1.090 1.095 1.100 1.105 1.110 1.115 1.120 1.125 1.130 1.135 1.140 1.145 1.150 1.155 1.160 1.165 1.170 1.175 1.180 1.185 1.190 1.195 1.200 1.205 1.210 1.215 1.220 1.225 1.230 1.235 1.240 1.245 1.250

°Bé 0.72 1.44 2.14 2.84 3.54 4.22 4.90 5.58 6.24 6.91 7.56 8.21 8.85 9.49 10.12 10.74 11.36 11.97 12.58 13.18 13.78 14.37 14.96 15.54 16.11 16.68 17.25 17.81 18.36 18.91 19.46 20.00 20.54 21.07 21.60 22.12 22.64 23.15 23.66 24.17 24.67 25.17 25.66 26.15 26.63 27.11 27.59 28.06 28.53 29.00

°Tw 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50

Lb per gal at 60°F wt in air 8.3700 8.4117 8.4534 8.4950 8.5367 8.5784 8.6201 8.6618 8.7035 8.7452 8.7869 8.8286 8.8703 8.9120 8.9537 8.9954 9.0371 9.0787 9.1204 9.1621 9.2038 9.2455 9.2872 9.3289 9.3706 9.4123 9.4540 9.4957 9.5374 9.5790 9.6207 9.6624 9.7041 9.7458 9.7875 9.8292 9.8709 9.9126 9.9543 9.9960 10.0377 10.0793 10.1210 10.1627 10.2044 10.2461 10.2878 10.3295 10.3712 10.4129

Lb per ft3 at 60°F wt in air 62.612 62.924 63.236 63.547 63.859 64.171 64.483 64.795 65.107 65.419 65.731 66.042 66.354 66.666 66.978 67.290 67.602 67.914 68.226 68.537 68.849 69.161 69.473 69.785 70.097 70.409 70.721 71.032 71.344 71.656 71.968 72.280 72.592 72.904 73.216 73.528 73.840 74.151 74.463 74.775 75.087 75.399 75.711 76.022 76.334 76.646 76.958 77.270 77.582 77.894

Sp gr 60°/ 60° 1.255 1.260 1.265 1.270 1.275 1.280 1.285 1.290 1.295 1.300 1.305 1.310 1.315 1.320 1.325 1.330 1.335 1.340 1.345 1.350 1.355 1.360 1.365 1.370 1.375 1.380 1.385 1.390 1.395 1.400 1.405 1.410 1.415 1.420 1.425 1.430 1.435 1.440 1.445 1.450 1.455 1.460 1.465 1.470 1.475 1.480 1.485 1.490 1.495 1.500

°Bé 29.46 29.92 30.38 30.83 31.27 31.72 32.16 32.60 33.03 33.46 33.89 34.31 34.73 35.15 35.57 35.98 36.39 36.79 37.19 37.59 37.99 38.38 38.77 39.16 39.55 39.93 40.31 40.68 41.06 41.43 41.80 42.16 42.53 42.89 43.25 43.60 43.95 44.31 44.65 45.00 45.34 45.68 46.02 46.36 46.69 47.03 47.36 47.68 48.01 48.33

°Tw 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100

Lb per gal at 60°F wt in air 10.4546 10.4963 10.5380 10.5797 10.6214 10.6630 10.7047 10.7464 10.7881 10.8298 10.8715 10.9132 10.9549 10.9966 11.0383 11.0800 11.1217 11.1634 11.2051 11.2467 11.2884 11.3301 11.3718 11.4135 11.4552 11.4969 11.5386 11.5803 11.6220 11.6637 11.7054 11.7471 11.7888 11.8304 11.8721 11.9138 11.9555 11.9972 12.0389 12.0806 12.1223 12.1640 12.2057 12.2473 12.2890 12.3307 12.3724 12.4141 12.4558 12.4975

Lb per ft3 at 60°F wt in air 78.206 78.518 78.830 79.141 79.453 79.765 80.077 80.389 80.701 81.013 81.325 81.636 81.948 82.260 82.572 82.884 83.196 83.508 83.820 84.131 84.443 84.755 85.067 85.379 85.691 86.003 86.315 86.626 86.938 87.250 87.562 87.874 88.186 88.498 88.810 89.121 89.433 89.745 90.057 90.369 90.681 90.993 91.305 91.616 91.928 92.240 92.552 92.864 93.176 93.488

Sp gr 60°/ 60° 1.505 1.510 1.515 1.520 1.525 1.530 1.535 1.540 1.545 1.550 1.555 1.560 1.565 1.570 1.575 1.580 1.585 1.590 1.595 1.600 1.605 1.610 1.615 1.620 1.625 1.630 1.635 1.640 1.645 1.650 1.655 1.660 1.665 1.670 1.675 1.680 1.685 1.690 1.695 1.700 1.705 1.710 1.715 1.720 1.725 1.730 1.735 1.740 1.745 1.750

°Bé 48.65 48.97 49.29 49.61 49.92 50.23 50.54 50.84 51.15 51.45 51.75 52.05 52.35 52.64 52.94 53.23 53.52 53.81 54.09 54.38 54.66 54.94 55.22 55.49 55.77 56.04 56.32 56.59 56.85 57.12 57.39 57.65 57.91 58.17 58.43 58.69 58.95 59.20 59.45 59.71 59.96 60.20 60.45 60.70 60.94 61.18 61.34 61.67 61.91 62.14

°Tw 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150

Lb per gal at 60°F wt in air 12.5392 12.5809 12.6226 12.6643 12.7060 12.7477 12.7894 12.8310 12.8727 12.9144 12.9561 12.9978 13.0395 13.0812 13.1229 13.1646 13.2063 13.2480 13.2897 13.3313 13.3730 13.4147 13.4564 13.4981 13.5398 13.5815 13.6232 13.6649 13.7066 13.7483 13.7900 13.8317 13.8734 13.9150 13.9567 13.9984 14.0401 14.0818 14.1235 14.1652 14.2069 14.2486 14.2903 14.3320 14.3737 14.4153 14.4570 14.4987 14.5404 14.5821

Lb per ft3 at 60°F wt in air 93.800 94.112 94.424 94.735 95.047 95.359 95.671 95.983 96.295 96.606 96.918 97.230 97.542 97.854 98.166 98.478 98.790 99.102 99.414 99.725 100.037 100.349 100.661 100.973 101.285 101.597 101.909 102.220 102.532 102.844 103.156 103.468 103.780 104.092 104.404 104.715 105.027 105.339 105.651 105.963 106.275 106.587 106.899 107.210 107.522 107.834 108.146 108.458 108.770 109.082

Sp gr 60°/ 60° 1.755 1.760 1.765 1.770 1.775 1.780 1.785 1.790 1.795 1.800 1.805 1.810 1.815 1.820 1.825 1.830 1.835 1.840 1.845 1.850 1.855 1.860 1.865 1.870 1.875 1.880 1.885 1.890 1.895 1.900 1.905 1.910 1.915 1.920 1.925 1.930 1.935 1.940 1.945 1.950 1.955 1.960 1.965 1.970 1.975 1.980 1.985 1.990 1.995 2.000

°Bé 62.38 62.61 62.85 63.08 63.31 63.54 63.77 63.99 64.22 64.44 64.67 64.89 65.11 65.33 65.55 65.77 65.98 66.20 66.41 66.62 66.83 67.04 67.25 67.46 67.67 67.87 68.08 68.28 68.48 68.68 68.88 69.08 69.28 69.48 69.68 69.87 70.06 70.26 70.45 70.64 70.83 71.02 71.21 71.40 71.58 71.77 71.95 72.14 72.32 72.50

°Tw 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200

*Prepared by Lewis V. Judson, Ph.D., Chief of Length Section of National Bureau of Standards with the advice and assistance of E. L. Peffer, B.S., A.M., late Chief of Capacity and Density Section, National Bureau of Standards.

1-20

TABLE 1-13

Wire and Sheet-Metal Gauges* Values in approximate decimals of an inch As a number of gauges are in use for various shapes and metals, it is advisable to state the thickness in thousandths when specifying gauge number. U.S. Steel Wire (Stl WG) or Washburn & Moen or Roebling or Am. Steel & Wire Co. [A. (steel) WG] (for steel wire) 0.4900 .4615 .4305 .3938 .3625 .3310 .3065 .2830 .2625 .2437 .2253 .2070 .1920 .1770 .1620 .1483 .1350 .1205 .1055 .0915 .0800 .0720 .0625 .0540 .0475 .0410 .0348 .0317 .0286 .0258 .0230 .0204 Birmingham (BWG) (for steel wire) or Stubs Iron Wire (for iron or brass wire)‡ — — — 0.454 .425 .380 .340 .300 .284 .259 .238 .220 .203 .180 .165 .148 .134 .120 .109 .095 .083 .072 .065 .058 .049 .042 .035 .032 .028 .025 .022 .020 U.S. Steel Wire (Stl WG) or Washburn & Moen or Roebling or Am. Steel & Wire Co. [A. (steel) WG] (for steel wire) 0.0181 .0173 .0162 .0150 .0140 .0132 .0128 .0118 .0104 .0095 .0090 .0085 .0080 .0075 .0070 .0066 .0062 .0060 .0058 .0055 .0052 .0050 .0048 .0046 .0044 Birmingham (BWG) (for steel wire) or Stubs Iron Wire (for iron or brass wire)‡ 0.018 .016 .014 .013 .012 .010 .009 .008 .007 .005 .004 — — — — — — — — — — — — — —

Gauge number 0000000 000000 00000 0000 000 00 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25

American (AWG) or Brown & Sharpe (B & S) (for nonferrous wire and sheet)† — — — 0.460 .410 .365 .325 .289 .258 .229 .204 .182 .162 .144 .128 .114 .102 .091 .081 .072 .064 .057 .051 .045 .040 .036 .032 .0285 .0253 .0226 .0201 .0179

U.S. Standard (for sheet and plate metal, wrought iron) — — — — — — — — — 0.239 .224 .209 .194 .179 .164 .150 .135 .120 .105 .090 .075 .067 .060 .054 .0478 .0418 .0359 .0329 .0299 .0269 .0239 .0209

Standard Birmingham (BG) (for sheet and hoop metal) 0.6666 .6250 .5883 .5416 .5000 .4452 .3964 .3532 .3147 .2804 .2500 .2225 .1981 .1764 .1570 .1398 .1250 .1113 .0991 .0882 .0785 .0699 .0625 .0556 .0495 .0440 .0392 .0349 .0313 .0278 .0248 .0220

Imperial Standard and Wire Gauge (SWG) (British legal standard) 0.500 .464 .432 .400 .372 .348 .324 .300 .276 .252 .232 .212 .192 .176 .160 .144 .128 .116 .104 .092 .080 .072 .064 .056 .048 .040 .036 .032 .028 .024 .022 .020

Gauge number 0000000 000000 00000 0000 000 00 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25

Gauge number 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50

American (AWG) or Brown & Sharpe (B & S) (for nonferrous wire and sheet)† 0.0159 .0142 .0126 .0113 .0100 .0089 .0080 .0071 .0063 .0056 .0050 .0045 .0040 .0035 .0031 — — — — — — — — — —

U.S. Standard (for sheet and plate metal, wrought iron) 0.0188 .0172 .0156 .0141 .0125 .0109 .0102 .0094 .0086 .0078 .0070 .0066 .0062 — — — — — — — — — — — —

Standard Birmingham (BG) (for sheet and hoop metal) 0.0196 .0175 .0156 .0139 .0123 .0110 .0098 .0087 .0077 .0069 .0061 .0054 .0048 .0043 .0039 .0034 .0031 .0027 .0024 .0022 .0019 .0017 .0015 .0014 .0012

Imperial Standard and Wire Gauge (SWG) (British legal standard) 0.018 .0164 .0148 .0136 .0124 .0116 .0108 .0100 .0092 .0084 .0076 .0068 .0060 .0052 .0048 .0044 .0040 .0036 .0032 .0028 .0024 .0020 .0016 .0012 .0010

Gauge number 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50

Metric wire gauge is 10 times the diameter in millimeters. *Courtesy of Dr. Lewis V. Judson with I. H. Fullmer, National Bureau of Standards. † Sometimes used for iron wire. ‡ Sometimes used for copper plate and for steel plate 12 gauge and heavier and for steel tubes.

1-21

TABLE 1-14

Fundamental Physical Constants sec = mean solar second Definition: g0 = standard gravity Definition: atm = standard atmosphere mm Hg (pressure) = standard millimeter mercury int = international; abs = absolute amp = ampere coul = coulomb

1 sec = 1.00273791 sidereal seconds g0 = 9.80665 m/sec2 1 liter = 0.001 cu. m 1 atm = 101,325 newtons/sq m 1 mm Hg (pressure) = (1⁄ 760) atm = 133.3224 newtons/sq m 1 int ohm = 1.000495 0.000015 abs ohm 1 int amp = 0.999835 0.000025 abs amp 1 int coul = 0.999835 0.000025 abs coul 1 int volt = 1.000330 0.000029 abs volt 1 int watt = 1.000165 0.000052 abs watt 1 int joule = 1.000165 0.000052 abs joule T0°C = 273.150 0.010°K (PV)0°CP=0 = (RT)0°C = 2271.16 0.04 abs joule/mole = 22,414.6 0.4 cu. cm atm/mole = 22.4146 0.0004 liter atm/mole R = 8.31439 0.00034 abs joule/deg mole = 1.98719 0.00013 cal/deg mole = 82.0567 0.0034 cu. cm atm/deg mole = 0.0820567 0.0000034 liter atm/deg mole ln 10 = 2.302585 R ln 10 = 19.14460 0.00078 abs joule/deg mole = 4.57567 0.00030 cal/deg mole N = (6.02283 0.0022) × 1023/mole h = (6.6242 0.0044) × 10−34 joule sec c = (2.99776 0.00008) × 108 m/sec (h2/8π2k) = (4.0258 0.0037) × 10−39 g sq cm deg (h/8π2c) = (2.7986 0.0018) × 10−39 g cm Z = Nhc = 11.9600 0.0036 abs joule cm/mole = 2.85851 0.0009 cal cm/mole (Z/R) = (hc/k) = c2 = 1.43847 0.00045 cm deg = 96,501.2 10.0 int coul/g-equiv or int joule/int volt g-equiv = 96,485.3 10.0 abs coul/g-equiv or abs joule/abs volt g-equiv = 23,068.1 2.4 cal/int volt g-equiv = 23,060.5 2.4 cal/abs volt g-equiv e = (1.60199 0.00060) × 10−19 abs coul = (1.60199 0.00060) × 10−20 abs emu = (4.80239 0.00180) × 10−10 abs esu 1 int electron-volt/molecule = 96,501.2 10 int joule/mole = 23,068.1 2.4 cal/mole 1 abs electron-volt/molecule = 96,485.3 10. abs joule/mole = 23,060.5 2.4 cal/mole 1 int electron-volt = (1.60252 0.00060) × 10−12 erg 1 abs electron-volt = (1.60199 0.00060) × 10−12 erg hc = (1.23916 0.00032) × 10−4 int electron-volt cm = (1.23957 0.00032) × 10−4 abs electron-volt cm k = (8.61442 0.00100) × 10−5 int electron-volt/deg = (8.61727 0.00100) × 10−5 abs electron-volt/deg = (R/N) = (1.38048 0.00050) × 10−23 joule/deg 1 IT cal = (1⁄ 860) = 0.00116279 int watt-hr = 4.18605 int joule = 4.18674 abs joule = 1.000654 cal 1 cal = 4.1840 abs joule = 4.1833 int joule = 41.2929 0.0020 cu. cm atm = 0.0412929 0.0000020 liter atm 1 IT cal/g = 1.8 Btu/lb 1 Btu = 251.996 IT cal = 0.293018 int watt-hr = 1054.866 int joule = 1055.040 abs joule = 252.161 cal 1 horsepower = 550 ft-lb (wt)/sec = 745.578 int watt = 745.70 abs watt 1 in = (1/0.3937) = 2.54 cm 1 ft = 0.304800610 m 1 lb = 453.5924277 g 1 gal = 231 cu. in = 0.133680555 cu. ft = 3.785412 × 10−3 cu. m = 3.785412 liter

Absolute temperature of the ice point, 0°C PV product for ideal gas at 0°C R = gas constant per mole

ln = natural logarithm (base e) N = Avogadro number h = Planck constant c = velocity of light Constant in rotational partition function of gases Constant relating wave number and moment of inertia Z = constant relating wave number and energy per mole c2 = second radiation constant = Faraday constant

e = electronic charge

Constant relating wave number and energy per molecule k = Boltzmann constant Definition of IT cal: IT = International steam tables cal = thermochemical calorie Definition: cal = thermochemical calorie

Definition of Btu: Btu = IT British Thermal Unit

cal = thermochemical calorie Definition of horsepower (mechanical): lb (wt) = weight of 1 lb at standard gravity Definition of in: in = U.S. inch ft = U.S. foot (1 ft = 12 in) Definition; lb = avoirdupois pound Definition; gal = U.S. gallon

1-22

CONVERSION OF VALUES FROM U.S. CUSTOMARY UNITS TO SI UNITS
American engineers are probably more familiar with the magnitude of physical entities in U.S. customary units than in SI units. Consequently, errors made in the conversion from one set of units to the other may go undetected. The following six examples will show how to convert the elements in six dimensionless groups. Proper conversions will result in the same numerical value for the dimensionless number. The dimensionless numbers used as examples are the Reynolds, Prandtl, Nusselt, Grashof, Schmidt, and Archimedes numbers. Table 1-7 provides a number of useful conversion factors. To make a conversion of an element in U.S. customary units to SI units, one multiplies the value of the U.S. customary unit, found on the left side in the table, by the equivalent value on the right side. For example, to convert 10 British thermal units to joules, one multiplies 10 by 1054.4 to obtain 10544 joules. In each example, the initial values of the factors are expressed in U.S. customary units, and the dimensionless value is calculated. Then the factors are converted to SI units, and the dimensionless value is recalculated. The two dimensionless values will be approximately the same. (Small variations occur due to the number of significant figures carried in the solution.) NNu = (200) (5.678) (1.5) (0.0254) = 357.7 (0.07) (1.728)

(Difference due to rounding)

Example 4. Calculation of a Grashof Number
NGr = L3ρ2gβ(∆T)/µ2 U.S. Customary units L = 3 ft ρ = 0.0725 lbm/ft3 g = 32.174 ft/s2 β = 0.00168/°R ∆T = 99 °R µ = 0.019 centipoise = 0.019 × 0.000672 lbm/ft⋅s = 1.277 × 10−5 lbm/ft⋅s NGr = (33) (0.0725)2(32.174) (0.00168) (99) = 4.66 × 109 (1.277 × 10−5)2

Example 1. Calculation of a Reynolds Number
NRe = DVρ µ

U.S. customary units D = 3 in. = 3⁄12 ft V = 6 ft/s ρ = 0.08 lbm/ft3 µ = 0.015 cp = (0.015)(0.000672) lbm/ft⋅s NRe = SI units D = (3)(0.0254) m V = (6)(0.3048) m/s ρ = (0.08)(16.018) kg/m3 µ = (0.015)(0.001) kg/m⋅s NRe = (3 × 0.0254) (6 × 0.3048) (0.08 × 16.018) = 11,904 (0.015) (0.001) (3/12)(6)(0.08) = 11,904 (0.015)(0.000672)

SI units L = (3)(0.3048) = 0.9144 m ρ = (0.0725)(16.018) = 1.1613 kg/m3 g = 9.807 m/s2 β = (0.00168)/(1.8) = 0.000933/°K ∆T = (99)(1.8) = 178.2 °K µ = (0.019)(0.001) = 1.9 × 10−5 kg/m⋅s NGr = (0.9144)3(1.1613)2(9.807)(0.000933)(178.2) = 4.66 × 109 (1.9 × 10−5)2

Example 5. Calculation of a Schmidt Number
NSc = µ ρD

Example 2. Calculation of a Prandtl Number
NPr = Cp µ k

U.S. customary units γp = 0.47 Btu/lbm °F µ = 15 centipoise = (15) (0.000672) (3600) lbm/ft⋅hr k = 0.065 Btu/hr⋅ft2 (°F/ft) (0.47) (15 × 0.000672 × 3600) = 262.4 NPr = 0.065 SI units γ = (0.47)(4184) J/kg °C µ = (15)(0.001) kg/m⋅s k = (0.065)(1.728) J/s⋅m2 (°C/m) (0.47) (4184) (15) (0.001) = 262.6 NPr = (0.065) (1.728) (Difference due to rounding)

U.S. customary units µ = 0.02 centipoise = (0.02)(2.42) lbm/ft⋅hr ρ = 0.08 lbm/ft3 D = 1.0 ft2/hr (diffusivity) (0.02) (2.42) = 0.605 NSc = (0.08)(1.0) SI units µ = (0.02)(0.001) kg/m⋅s ρ = (0.08)(16.02) kg/m2 D = (1.0)(2.58 × 10−5) m2/s NSc = (0.02) (0.001) = 0.605 (0.08)(16.02)(1.0) (2.58 × 10−5)

Example 6. Calculation of an Archimedes Number
NAr = d 3ρf(ρp − ρf)g µ2

Example 3. Calculation of a Nusselt Number
NNu = U.S. customary units h = 200 Btu/hr⋅ft2⋅°F D = 1.5 in. = 1.5/12 ft k = 0.07 Btu/hr⋅ft2 (°F/ft) NNu = (200)(1.5/12) = 357.1 0.07 hD k

U.S. customary units d = 2 mm = 2/[(1000)(0.3048)] = 0.00656 ft ρf = 0.0175 lbm/ft3 ρp = 168.5 lbm/ft3 g = 32.174 ft/s2 µ = 0.04 centipoise = 0.04 × 0.000672 = 2.688−5 lbm/ft⋅s NAr = (0.00656)3 (0.0175) (168.5 − 0.017) (32.174) = 37,064 (2.688 × 10−5)2

SI units d = 2/1000 m ρp = 168.5 × 16.02 = 2699.37 kg/m3 ρf = 0.0175 × 16.02 = 0.2804 g/m3 g = 9.807 m/s2 µ = 0.04 × 0.001 = 4 × 10−5 kg/m⋅s NAr = (2/1000)3 (0.2804) (2699.37 − 0.28) (9.807) = 37,118 (4 × 10−5)2

SI units h = (200)(5.678) J/(s⋅m2⋅°C) D = (1.5)(0.0254) m k = (0.07)(1.728) J/s⋅m2 (°C/m)

(Difference due to rounding)

1-23

MATHEMATICAL SYMBOLS
TABLE 1-15 Mathematical Signs, Symbols, and Abbreviations ( ) : < > ∼ ≠ ∝ ∞ ∴
3 n

TABLE 1-16 Alpha Beta Gamma Delta Epsilon Zeta Eta Theta Iota Kappa Lambda Mu

Greek Alphabet Nu Xi Omicron Pi Rho Sigma Tau Upsilon Phi Chi Psi Omega = Ν, ν = N, n = Ξ, ξ = X, x = Ο, ο = O, o = Π, π = P, p = Ρ, ρ = R, r = Σ, σ = S, s = Τ, τ = T, t = , υ = U, u = Φ, φ = Ph, ph = Χ, χ = Ch, ch = Ψ, ψ = Ps, ps = Ω, ω = O, o

⊥ |x| log or log10 loge or ln e a° a′ a a″ a sin cos tan ctn or cot sec csc vers covers exsec sin−1 sinh cosh tanh sinh−1 f(x) or φ(x) ∆x dx dy/dx or y′ d2y/dx2 or y″ dny/dxn ∂y/∂x ∂ny/∂xn ∂ny ∂x∂y

plus or minus (minus or plus) divided by, ratio sign proportional sign less than not less than greater than not greater than approximately equals, congruent similar to equivalent to not equal to approaches, is approximately equal to varies as infinity therefore square root cube root nth root angle perpendicular to parallel to numerical value of x common logarithm or Briggsian logarithm natural logarithm or hyperbolic logarithm or Naperian logarithm base (2.178) of natural system of logarithms an angle a degrees prime, an angle a minutes double prime, an angle a seconds, a second sine cosine tangent cotangent secant cosecant versed sine coversed sine exsecant anti sine or angle whose sine is hyperbolic sine hyperbolic cosine hyperbolic tangent anti hyperbolic sine or angle whose hyperbolic sine is function of x increment of x summation of differential of x derivative of y with respect to x second derivative of y with respect to x nth derivative of y with respect to x partial derivative of y with respect to x nth partial derivative of y with respect to x nth partial derivative with respect to x and y integral of

= Α, α = A, a = Β, β = B, b = Γ, γ = G, g = ∆, δ = D, d = Ε, ε = E, e = Ζ, ζ = Z, z = Η, η = E, e = Θ, θ = Th, th = Ι, = I, i = Κ, κ = K, k = Λ, λ = L, l = Μ, µ = M, m

b

integral between the limits a and b
a

y ˙ y ¨ ∆ or ∇2

δ

first derivative of y with respect to time second derivative of y with respect to time the “Laplacian” ∂2 ∂2 ∂2 + + ∂x2 ∂y2 ∂z2 sign of a variation sign for integration around a closed path

1-24


								
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