Tài liệu UNITS AND CONVERSION FACTORS E.J. ROSCHKE PROPULSION DIVISION JET PROPULSION LABORATORY doc

They experienced practicalannoyances with the mingling of units from mechanical engineering, electrical engineering andphysics.. Multiply units appearing in left-hand column by appropria

UNITS AND CONVERSION FACTORS

E.J ROSCHKEPROPULSION DIVISIONJET PROPULSION LABORATORY

Many years ago I was given a copy of this document, prepared in handwriting, some time inthe early 1960’s I did not know the author, E.J Roschke I have found it to be such a usefulreference that I decided to have an electronic version prepared Recently, I spoke with Dr.Roschke, now retired from the Jet Propulsion Laboratory to learn of the document’s origin Inthe early 1960’s a group of research engineers, largely having backgrounds in mechanicalengineering, were engaged in the new field of electric propulsion They experienced practicalannoyances with the mingling of units from mechanical engineering, electrical engineering andphysics That situation motivated Dr Roschke to assemble this material

Although I have carefully checked the values given here, it is quite possible that sometypographical errors remain I will appreciate learning any corrections that should be made

F.E.C CulickMechanical EngineeringCalifornia Institute of TechnologyOctober 2001

UNITS AND CONVERSION FACTORS

Table of Contents

II Description of Units

IV Dimensions of esu and emu Electric

Table of Contents – continued

B Values of Universal Gas Constant, Boltzmann’s Constant

References used in compiling these charts and tables are listed below in the order of “mostusage”.

1 Halliday, D & Resnick, R., Physics – For Students of Science and Engineering, John Wiley,New York, 1960

2 Forsythe, W.E., Smithsonian Physical Tables, 9th Revised Edition, Publ 4169, SmithsonianInstitution, Washington, D.C., 1954

3 Scott, R.B., Cryogenic Engineering, D Van Nostrand Inc., Princeton, New Jersey, 1959

4 Hall, N.A., Thermodynamics of Fluid Flow, Second Printing with revisions, Prentice-HallInc., Englewood Cliffs, New Jersey, 1956

5 Gray, D.E (coordinating editor), American Institute of Physics Handbook, McGraw HillInc., New York, 1957

Additional Note on Use of Conversion Tables, Part VII

Multiply units appearing in left-hand column by appropriate numerical factor to obtainunits appearing in upper row

I DECIMAL MULTIPLES AND SUB-MULTIPLES

LengthMassTimeForceWork, Energy

PowerDynamic Viscosity

Kinematic Viscosity

cgs

centimetergramseconddyneerg

−poisestoke

mks

meterkilogramsecondnewtonjoulewatt

−

−ELECTRIC AND MAGNETIC UNITS

The esu and emu unit systems are cgs systems

esu denotes “electrostatic unit”, sometimes given prefix “stat”, e.g statcoulombemu denotes “electromagnetic unit”, sometimes given prefix “ab”, e.g abcoulombSome emu units have special names:

QuantityMagnetic Flux, φ

Magnetic Field Strength, B

Magnetomotive Force, F

Magnetic Vector, H

emulinemaxwellgaussgilbertoersted

mksqweberweber/m2amp-turnamp-turn/m

mksq DIMENSIONS Length L

The fundamental dimensions in both systems are M, L, T cgs units used

ρ

j

VI

B H

εµσCLR

c21/c2

c2

c21/c21/c2

*c = velocity of light (free space) in cm/sec ≈ 3 × 1010

Thus: 1 emu of charge = 2.998 × 1010 esu of charge

or 1 abcoulomb = 2.998 × 1010 statcoulomb

2

−

2 2

− 2

∗

esuemu

V DIMENSIONS AND UNITS FOR PHYSICAL QUANTITIES

mksq SYSTEM

A MECHANICAL QUANTITIESQuantity

T-1

LT-2LM

ML-3MLT-1

ML2T-3

ML-1T-2T

ML2T-2

Derived Units

meter/sec2radianradian/sec2kgm-meter2/secradian/secmeter2joulenewtoncycle/secnewton/kgmmeterkilogramkgm/meter2kgm-meter/secwattnewton/meter2secondnewton/metermeter/seckgm/meter-secmeter2/secmeter3meterjoule

MT-3θ-1

Derived Units

joulejoule/K°

joule/kgm- K°joulejoule/kgm-K°K°

watt/meter- K°meter2/secwatt/meter2- K°

*The dimension of temperature is θ; the unit is K°

C ELECTRIC AND MAGNETIC QUANTITIESQuantity

E D

ρ

j

VI

B H

εµσCLR

Dimensions

QMLT-2Q-1

VI CONVERSION OF mksq UNITS TO GAUSSIAN UNITS

*c = vel of light (free space) in cm/sec ≈ 3 × 1010

Use of table:

1 coulomb = 10-1 (3 × 1010) statcoulomb = 3 × 109 statcoulomb

VII CONVERSION FACTORS

NOTE: mksq UNITS ARE CAPITALIZED

USE OF TABLES: EXAMPLE

′6011.667 × 10-234382.16 × 104

′′

36006012.063 × 1051.296 × 105

RADIAN

1.745 × 10-22.909 × 10-44.848 × 10-416.283

rev2.778 × 10-34.630 × 10-57.716 × 10-70.15921

1 revolution = 2 π RADIANS = 360o , 1o = 60′ = 3600′′

B SOLID ANGLE

1 sphere = 4 π steradians = 12.57 steradians

1052.54030.481.609 × 105

METER

10-2110002.540 × 10-20.30481609

km

10-5

10-312.540 × 10-33.048 × 10-41.609

in

0.393739.373.937 × 10-41126.336 × 104

ft3.281 × 10-23.28132818.333 × 10-215280

mile

6.214 × 10-66.214× 10-40.62141.578 × 10-51.894 × 10-41

cm2

1041929.06.4525.067 × 10-6

ft2

10.761.076 × 10-316.944 × 10-35.454 × 10-3

in2

15500.155014417.854 × 10-7

circ mil

1.974 × 1091.974 × 1051.833 × 1081.273 × 1061

1 square mile = 27,878,400 ft2 = 640 acres

1 acre = 43,560 ft2 1 barn = 10-28 meter2

cm3

106110002.832× 10416.39

liter

10001.000 × 10-3128.321.639 × 10-2

ft3

35.313.531 × 10-83.531 × 10-215.787 × 10-4

in3

6.102 × 1046.102 × 10-261.0217281

1 U.S fluid gallon = 4 U.S fluid quarts = 8 U.S fluid pints

=128 U.S fluid ounces = 231 in3

× 10-4

1.660

× 10-2428.35453.6

9.072

× 10-5

KGM

0.001114.59

1.660

× 10-27

2.835

× 10-20.4536907.2

slug

6.852

× 10-56.852

× 10-21

5.855

× 10-26116

3.660

× 10-27

6.250

× 10-212000

NOTE FOR TABLE F: Portion of table enclosed in heavy lines must be used with caution

because those units are not properly mass units but weight equivalents which depend on standardterrestrial acceleration due to gravity, i.e g

× 10-31.9403.108 × 10-253.71

KGM/M3

515.41100016.022.768 × 104

gm/cm30.51540.00111.602 × 10-227.68

lb/ft332.176.243

× 10-262.4311728

lb/in31.862 × 10-23.613

× 10-53.613 × 10-25.787 × 10-41NOTE FOR TABLE G: Portion of table enclosed in heavy lines must be used with caution

because those units are not mass-density units but weight-density units which depend on g

day365.214.167 × 10-26.944 × 10-41.157 × 10-5

hr8.766 × 1032411.667 × 10-22.778 × 10-4

min5.259 × 10314406011.667 × 10-2

SECOND

3.156 × 1078.640 × 1043600601

1 year = 365.24219879 days

I SPEED

ft/sec10.91133.2811.4673.281 × 10-21.688

km/hr1.09713.6001.6093.600 × 10-21.852

METER/SEC

0.34080.277810.47700.01000.5144

miles/hr0.68180.62142.2371 2.237 × 10-21.151

cm/sec30.4827.7810044.70151.44

knot0.59250.54001.9440.86891.944 × 10-21

1054.480

× 1051.383

× 104980.79.807

× 105

NT

10-5 14.4480.1383

9.807

× 10-39.807

lb2.248

× 10-60.2248 1

3.108

× 10-22.205

× 10-32.205

pdl7.233

× 10-57.23332.17 1

7.093

× 10-270.93

gf1.020

× 10-3102.0453.614.10 11000

kgf1.020

× 10-60.10200.4536

1.410

× 10-20.001 1

NOTE FOR TABLE J: Portion of table enclosed in heavy lines must beused with caution because those units are not force units but weightequivalents of mass which depend on g.

9.869

× 10-72.458

× 10-31.316

× 10-29.869

× 10-66.805

× 10-24.725

× 10-4

dyne/cm2

1.013

× 10612.491

1.333

× 10410

6.895

× 104478.8

inch ofwater406.8

4.015

× 10-415.353

4.015

× 10-327.680.1922

cm Hg76

7.501

× 10-50.18681

7.501

× 10-45.171

6.895

× 10347.88

lb/in214.70

1.450

× 10-53.613

× 10-20.1934

1.450

× 10-41

6.944

× 10-3

lb/ft22116

2.089

× 10-35.20227.85

2.089

× 10-21441

a Where the acceleration of gravity has the standard value 9.80665 meter/sec2

1 bar = 106 dyne/cm2 1 millibar = 103 dyne/cm2

1 torr (mm Hg at 0°C) = 1.93367 × 10-2 lb/ft2

L ENERGY, WORK, HEAT

2.685

× 106

14.186

5.610

× 1029

931.0

kgm1.174

1 meter – kgf = 9.807 joule, 1 watt-sec = 1 joule = 1 nt-meter, 1 cm-dyne = 1 ergSome conversions used in spectroscopy:

NOTES FOR TABLE L: The electron volt is the kinetic energy an electron gains from beingaccelerated through the potential difference of one volt in an electric field The units enclosed byheavy lines are not properly energy units; they arise from the relativistic mass-energy equivalentformula E = mc2

× 10-82.389

× 10-40.55577.142

× 10-41.414

× 103

4.186

× 1071

104

2.326

× 1072.990

× 1045.920

× 1010

4.186

× 103

10-41

2.326

× 1032.990

5.920

× 106

1.8004.299

× 10-84.299

× 10-4 1

1.285

× 10-32.545

1.400

× 1033.346

× 10-50.3346777.911.980

× 106

7.072

× 10-41.690

× 10-111.690

× 10-73.929

× 10-45.051

× 10-71(SEE NOTE FOR TABLE N)

m

lb

hr - hp

N SPECIFIC ENERGY PER UNIT TEMPERATURE

1 calorie per gram

× 10-82.389

× 10-41.000

1.286

× 10-32.546

× 103

4.186

× 1071

104

4.187

× 1075.382

× 1041.066

× 1011

4.186

× 103

10-41

4.187

× 1035.382

× 10-41

1.285

× 10-32.545

777.9

1.859

× 10-50.1859777.91

1.980

× 106

3.929

× 10-49.376

× 10-129.376

× 10-83.929

× 10-45.051

× 10-71

NOTE FOR TABLES M & N: The engineering units enclosed within the heavy lineshave been properly related to the pound mass rather than the pound force because thesespecific thermal quantities depend on unit mass and have nothing to do with weight.However, in engineering practice it is customary to relate energy and energy per degree

to weight Thus we speak of Btu/lb, ft-lb/lb and hp-hr/lb of weight The conversionfactors given in Tables M & N are equally valid for this purpose if the local acceleration

of gravity if the earth standard value of g = 32.174 ft/sec2 = 9.80665 meter/sec2 This istrue because the pound-force and the pound-mass are numerically equal at standardgravity It should be realized that relating specific quantities to weight, rather than mass,involves a change of concept because weight and mass are not dimensional equivalents.The relation between units of mass and weight is not a relation between the concepts ofmass and weight The units are related by

lbf = 32.174 lbm ft/sec2

C gm

m

f

° lb F

hr - hp

m °

× 10-24.628254514.2934133.413

2.778

× 10-41

2.142

× 10-51.286

× 10-30.70690.39500.9481

60

3.3

× 1041.852

× 1024.425

× 10444.25

0.2161777.9

1.667

× 10-215503.087737.60.7376

3.929

× 10-41.414

3.030

× 10-51.818

× 10-31

5.613

× 10-31.341

1.341

× 10-3

7.000

× 10-2252.0

5.399

× 10-30.3239178.21238.90.2389

2.930

× 10-41.055

2.260

× 10-51.356

× 10-30.7457

4.186

× 10-310.001

0.2930

1.055

× 1032.260

× 10-21.356745.74.18610001

sec

lb-

sec

1 British thermal unit

per hour per foot2 =

1 British thermal unit

per sec per inch2 =

3.600

× 10410.86021.3332.713

1.635

× 1068027

2.035

× 10-3

1.055

× 1035.179

1.327

× 1040.36870.3171491.51

3.928

× 10-4203.6

1

*Also power per unit area

Q HEAT TRANSFER COEFFICIENT, h

1 calorie per sec

per centimeter2 - ºC =

per DEG KELVIN =

1 watt per inch2 per

× 10-21.356

× 10-470.310.3452

4.185

× 104115505.675

2.943

× 1061.445

× 104

27.00

6.452

× 10-41

3.663

× 10-31.899

× 1039.322

7.372

× 1030.1762273.11

5.184

× 1052.546

× 103

1.422

× 10-23.398

× 10-75.267

× 10-41.929

× 10-61

3.928

× 10-4203.61

2

cm - sec

cal

2

m hr

Btu

2

in - sec

Btu

2

ft hp

C cm sec

R R THERMAL CONDUCTIVITY, k

1 calorie per sec per

centimeter-deg C =

1 WATT per METER

per DEG KELVIN =

1 watt per inch per

418.5139.371.730

7.474

× 1044403

10.63

2.540

× 10-21

4.394

× 10-2

1.898

× 103111.8

241.90.578122.761

4.320

× 1042546

5.600

× 10-31.338

× 10-55.269

× 10-4

2.315

× 10-31

5.894

× 10-2

9.503

× 10-22.271

× 10-48.939

× 10-3

3.929

× 10-416.971

C

°

− cm sec

S ABSOLUTE OR DYNAMIC VISCOSITY, µ

9.807

× 1034.788

4.788

× 1021014.88

1.020

× 10-41.020

× 10-214.8820.10200.1518

2.089

× 10-52.089

× 10-30.20481

2.089

× 10-23.108

× 10-2

10-30.1009.80747.8811.488

6.720

× 10-46.720

× 10-26.59032.174

0.67201

NOTE FOR TABLE S: The absolute viscosity µ is properly expressed in force units according

to its definition In heat transfer and fluid mechanics it is usually expressed in equivalent units to avoid the use of a conversion factor in Reynolds Number Mass unitshave been used in the portion of the table enclosed in heavy lines The proper force unitsfor µ in the mksq system are NEWTON-SEC per METER2; they are seldom used Thepoise is the cgs force unit and is defined by

1069.290 × 104

stoke

10-21

104929.0

METER 2 /SEC

10-6

10-419.290 × 10-2

ft2/sec1.076 × 10-51.076 × 10-310.761

1 stoke = 1 centimeter2/sec

centipoise poise

2

meter

sec kgm −f

dyne

AA ELECTRIC CHARGE

9.652

× 1033.336

× 10-11

amp-hr2.778

× 10-31

2.778

× 10-426.81

9.266

× 10-14

COUL

1036001

9.652

× 1043.336

× 10-10

faraday1.036

× 10-43.730

× 10-21.036

× 10-51

3.456

× 10-15

statcoul2.998

× 10101.079

× 10132.998

× 1092.893

× 10141

1 electronic charge = 1.602 × 10-19 coulombs

AMP

1013.336 × 10-10

statamp2.998 × 10102.998 × 1091

abv1

1082.998 × 1010

VOLT

10-81299.8

statv3.336 × 10-113.336 × 10-31

1098.987 × 1020

OHM

10-918.987 × 1011

statohm1.113 × 10-211.113 × 10-121

EE ELECTRIC RESISTIVITY, RECIPROCAL CONDUCTIVITY

109

1011

8.987

× 1020166.2

ohm-cm

10-91100

8.987

× 10111.662

× 10-7

OHM-M

10-110.01001

8.987

× 1091.662

× 10-9

statohm-cm

1.113

× 10-211.113

× 10-121.113

× 10-101

1.850

× 10-19

ohm-circmil/ft6.015

× 10-36.015

× 1066.015

× 1085.406

× 10181

× 10118.987

× 1051

8.987

× 1011

µ h0.001

1061

8.987

× 1017

stathenry1.113

× 10-211.113

× 10-121.113

× 10-181

108

kiloline0.0011

105

WEBER

10-8

10-51

7.958

× 10-2

AMP-TURN

1010.7958

gilbert12.571.2571

1 pragilbert = 4 π amp-turn

1 esu = 2.655 × 10-11 amp-turn

JJ MAGNETIC FIELD STRENGTH, B

1 gauss (line per

6.452

× 10-2164.52

6.452

× 10-66.452

× 10-8

2 METER WEBER

10-4

1.550

× 10-21

10-7

10-9

milligauss1000

1.550

× 105

1071

10.100

10-3

3.937

× 10-27.958

× 10-2

cm

turn amp −

101

10-20.39370.7958

METER

TURN AMP−

1000100139.3779.58

in

turn amp −

25.402.54

2.540

× 10-212.021

oersted12.571.257

1.257

× 10-20.49471

1 oersted = 1 gilbert/cm

1 esu = 2.655 × 10-9 amp-turn/meter

1 praoersted = 4 π amp-turn/meter

VIII ELECTROMAGNETIC CONSTANTS OF FREE SPACE

Maxwell was able to show analytically that the constant appearing in a wave equationderived for free space (perfect vacuum), for the case ρe =σc = 0, was the square of thevelocity of propagation of electromagnetic waves in free space The experiments of Hertzverified that this velocity was the velocity of light in free space and that

0 0

1

2

εµ

=

c

where µ0 is the permeability of free space and ε0 is the permittivity of free space This equation

is true for any system of units; in the mksq system

The permeability and permittivity of materials are usually given relative to the values offree space

χm ≶ 0, χ m << 1 χe ≥ 0

κm is temperature possible χe >> 1dependent

X SOME IMPORTANT DIMENSIONAL CONSTANTS (mksq units)

Speed of light c 3.00 × 108 meter/sec (2.997930 ± 0.000003) × 108

Universal Gravitational Const G 6.67 × 10-11 nt-m2/kgm2 (6.673 ± 0.003) × 10-11

Avogadro’s Number N0 6.02 × 1023 /mole (6.02486 ± 0.00016) × 1023

Universal Gas Constant R 8.32 joule/mole °K 8.31696 ± 0.00034

Standard Volume of Ideal Gas 2.24 × 10-2 meter3 (2.24207 ± 0.00006) × 10-2

Planck’s Constant h 6.63 × 10-34 joule/sec (6.62517 ± 0.00023) × 10-34

Boltzmann’s Constant k 1.38 × 10-23 joule/°K (1.38044 ± 0.00007) × 10-23

Mechanical Equiv of Heat J 4.19 joule/cal 4.1855 ± 0.0004

(at 3.98°C, 1 atm)Permeability of Free Space µ0 1.26 × 10-6 henry/meter 4π × 10-7 exactly

Permittivity of Free Space ε0 8.85 × 10-12 farad/meter (8.85415 ± 0.00002) × 10-12

Electronic Charge e 1.60 × 10-19 coulomb (1.60206 ± 0.00003) × 10-19

Electronic Rest Mass m e 9.11 × 10-31 kgm (9.1083 ± 0.0003) × 10-31

Proton Rest Mass m p 1.67 × 10-27 kgm (1.67239 ± 0.00004) × 10-27

Neutron Rest Mass m n 1.67 × 10-27 kgm (1.67470 ± 0.00004) × 10-27

Mass-Energy Relation c2 = E/m 8.99 × 1016 meter2/sec2 (8.98758 ± 0.00003) × 1016

Magnetic Moment of Electron 9.28 × 10-32 joule-m2/weber (9.2837 ± 0.0002) × 10-32

Compton Wavelength of Electron λc 2.43 × 10-12 meter (2.42626 ± 0.00002) × 10-12

First Bohr Orbit Radius in a0 5.29 × 10-11 meter (5.29172 ± 0.00002) × 10-11

Hydrogen AtomStefan-Boltzmann Const σ 5.67 × 10-8 joule/sec(°K)4 meter2 (5.6687 ± 0.0019) × 10-8