Conversion Factors for mksq Units to Gaussian Units, Summaries of Physics

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UNITS AND CONVERSION FACTORS

E.J. ROSCHKE

PROPULSION DIVISION

JET PROPULSION LABORATORY

NOTE:

Many years ago I was given a copy of this document, prepared in handwriting, some time in the early 1960’s. I did not know the author, E.J. Roschke. I have found it to be such a useful reference 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. In the early 1960’s a group of research engineers, largely having backgrounds in mechanical engineering, were engaged in the new field of electric propulsion. They experienced practical annoyances with the mingling of units from mechanical engineering, electrical engineering and physics. That situation motivated Dr. Roschke to assemble this material.

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

F.E.C. Culick Mechanical Engineering California Institute of Technology October 2001

Table of Contents – continued

• References Section Page
• I. Decimal Multiples and Submultiples - Mechanical, Electric, Magnetic II. Description of Units
• III. Equivalent Units mksq System - and Magnetic Quantities IV. Dimensions of esu and emu Electric
• V. Dimensions and Units for Physical Quantities — mksq System 6, - A. Mechanical - B. Thermal - C. Electric and Magnetic
• VI. Conversion of mksq Units to Gaussian Units
• VII. Conversion Factors 8- - A. Plane Angle - B. Solid Angle - C. Length - D. Area - E. Volume - F. Mass - G. Density - H. Time - I. Speed - J. Force - K. Pressure - L. Energy, Work, Heat - M. Specific Energy - N. Specific Energy Per Unit Temp. - O. Power - P. Heat Flux - Q. Heat Transfer Coefficient - R. Thermal Conductivity - S. Absolute Viscosity - T. Kinematic Viscosity - AA. Electric Charge - BB. Electric Current - CC. Electric Potential - DD. Electric Resistance - EE. Electric Resistivity - FF. Capacitance - GG. Inductance
  • HH. Magnetix Flux Section Page
  • I I. Magnetomotive Force
  • J J. Magnetic Field Strength, B
  • KK. Magnetic Vector, H
• VIII. Electromagnetic Constants of Free Space
• IX. Electromagnetic Constants of Materials
• X. Some Important Dimensional Constants
• XI. Some Important Dimensionless Groups
• XII. The Perfect Gas Law 27, - A. Nomenclature, Definitions and Equations - and Avogadro’s Number in Different Units B. Values of Universal Gas Constant, Boltzmann’s Constant

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

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, Smithsonian Institution, 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-Hall Inc., Englewood Cliffs, New Jersey, 1956.
5. Gray, D.E. (coordinating editor), American Institute of Physics Handbook, McGraw Hill Inc., New York, 1957.

Additional Note on Use of Conversion Tables, Part VII.

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

mksq DIMENSIONS

Length L Mass M Time T Current Q/T Charge Q

III. EQUIVALENT UNITS mksq SYSTEM

1 newton = 1 kilogram-meter/(second) 2 1 volt = 1 newton-meter/coulomb 1 amp = 1 coulomb/second 1 joule = 1 newton-meter = 1 coulomb-volt 1 weber = 1 volt-second 1 farad = 1 coulomb/volt 1 henry = 1 weber/amp 1 ohm = 1 volt/amp 1 watt = 1 joule/sec

IV. DIMENSIONS OF esu AND emu ELECTRIC AND MAGNETIC QUANTITIES The fundamental dimensions in both systems are M, L, T. cgs units used.

Quantity

Charge Field Intensity Elec. Displacement Charge Density Current Density Elec. Potential Total Current Mag. Field Strength Mag. Vector Permittivity Permeability Conductivity Capacitance Inductance Resistance

Symbol

q E D ρ j V I B H ε μ σ C L R

esu M x^ LyTz x y z

½ 3 2 - ½ -½ - ½ -½ - ½ - ½ -½ - ½ ½ - ½ - ½ 0 ½ ½ - 0 0 0 0 -2 2 0 0 - 0 1 0 0 -1 2 0 -1 1

emu M x^ LyTz x y z

½ ½ 0 ½ 0 ½ ½ - ½ 0 ½ - ½ - ½ ½ - ½ -½ - ½ -½ - 0 -2 2 0 0 0 0 -2 1 0 -1 2 0 1 0 0 1 -

c 1/c c c c 1/c c 1/c c c 2 1/c 2 c 2 c 2 1/c 2 1/c 2

*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

−^32

(^32) −^32

2 −^3

−^52 −^32 2 3

∗

esu

emu

V. DIMENSIONS AND UNITS FOR PHYSICAL QUANTITIES

mksq SYSTEM

A. MECHANICAL QUANTITIES

Quantity

Acceleration Angle Angular Accleration Angular Momentum Angular Velocity Area Energy Force Frequency Gravitational Field Strength Length Mass Mass Density Momentum Power Pressure Time Torque Velocity Viscosity (Dynamic) Viscosity (Kinematic) Volume Wave Length Work

Dimensions

LT- 0 T- ML^2 T- T- L^2 ML^2 T- MLT- T- LT- L M ML- MLT- ML^2 T- ML-1^ T- T ML^2 T- LT- ML-1^ T- L^2 T- L^3 L ML^2 T-

Derived Units

meter/sec^2 radian radian/sec^2 kgm-meter 2 /sec radian/sec meter 2 joule newton cycle/sec newton/kgm meter kilogram kgm/meter 2 kgm-meter/sec watt newton/meter 2 second newton/meter meter/sec kgm/meter-sec meter 2 /sec meter 3 meter joule

VI. CONVERSION OF mksq UNITS TO GAUSSIAN UNITS

Quantity

q E D ρ j V I B H μ ε σ C L R

mksq Unit

coulomb volt/meter coulomb/meter 2 coulomb/meter 3 amp/meter 2 volt coulomb/sec : = amp weber/meter 2 amp-turn/meter farad/meter henry/meter 1/ohm-meter farad henry ohm

Conversion Factor × Gaussian Unit*

10 -1^ c statcoulomb 10 6 /c statvolt/cm 4 π × 10 -5^ c lines/cm^2 10 -7^ c statcoulomb/cm^3 10 -5^ abamp/cm^2 108 /c statvolt 10 -1^ abamp 104 gauss 4 π × 10 -3^ oersted 4 π × 10 -11^ c 2  107 /4π  10 -11^ 1/abohm-cm 10 -9^ c 2 statfarad 109 abhenry 109 abohm

(esu) (esu) (esu) (esu) (emu) (esu) (emu) (emu) (emu) (esu) (emu) (emu) (esu) (emu) (emu)

*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 1 degree = 2.778 × 10 -3^ revolutions so, 16.7 o^ = 16.7 × 2.778 × 10 -3^ revolutions

A. PLANE ANGLE

1 degree = 1 minute = 1 second = 1 RADIAN = 1 revolution =

o

1 1.667 × 10 - 2.778 × 10 -

360

1.667 × 10 -

2.16 × 104

2.063 × 105

1.296 × 105

RADIAN

1.745 × 10 -

2.909 × 10 -

4.848 × 10 -

rev

2.778 × 10 - 4.630 × 10 - 7.716 × 10 -

1

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

B. SOLID ANGLE

1 sphere = 4 π steradians = 12.57 steradians

C. LENGTH

1 centimeter = 1 METER = 1 kilometer = 1 inch = 1 foot = 1 statute mile =

cm

1 100 105

1.609 × 10 5

METER

2.540 × 10 -

km

10 - 10 - 1 2.540 × 10 - 3.048 × 10 -

in

3.937 × 10 - 1 12 6.336 × 104

ft

3.281 × 10 -

8.333 × 10 -

mile

6.214 × 10 -

6.214× 10 -

1.578 × 10 -

1.894 × 10 -

1 foot = 1200/3937 meter 1 meter = 3937/1200 ft 1 angstrom (Å) = 10 -10^ meter 1 X-unit = 10-13^ meter 1 micron = 10 -6^ meter 1 millimicron (mu) = 10 -9^ meter

1 light-year = 9.460 × 1012 km 1 par-sec = 3.084 × 1013 km 1 fathom = 6 ft 1 yard = 3 ft 1 rod = 16.5 ft 1 mil = 10-3^ in 1 nautical mile = 1852 meters = 1.1508 statute miles 1 nautical mile = 6076.10 ft

D. AREA

1 SQUARE METER =

1 square cm = 1 square foot = 1 square inch = 1 circular mil =

METER^2

9.290 × 10 -

6.452 × 10 -

5.067 × 10 -

cm^2

104 1

5.067 × 10 -

ft 2

1.076 × 10 - 1 6.944 × 10 - 5.454 × 10 -

in^2

1550

144 1 7.854 × 10 -

circ mil

1.974 × 109

1.974 × 105

1.833 × 108

1.273 × 106

1 square mile = 27,878,400 ft 2 = 640 acres 1 acre = 43,560 ft 2 1 barn = 10 -28^ meter 2 1 hectare = 2.417 acres

E. VOLUME

1 CUBIC METER =

1 cubic cm = 1 liter = 1 cubic foot = 1 cubic inch =

METER^3

1.000 × 10 -

2.832 × 10 -

1.639 × 10 -

cm^3

106 1 1000 2.832 × 104

liter

1000 1.000 × 10 - 1

1.639 × 10 -

ft 3

3.531 × 10 - 3.531 × 10 - 1 5.787 × 10 -

in^3

6.102 × 104

6.102 × 10 -

1 U.S. fluid gallon = 4 U.S. fluid quarts = 8 U.S. fluid pints =128 U.S. fluid ounces = 231 in^3 1 British imperial gallon = 277.42 in^3 (volume of 10 lb H 2 O at 62 o^ F) 1 liter = 1000.028 cm^3 (volume of 1 kgm H 2 O at its maximum density)

H. TIME

1 year = 1 day =

1 hour = 1 minute =

1 SECOND =

yr 1

2.738 × 10 -

1.141 × 10 -

1.901 × 10 -

3.169 × 10 -

day

1

4.167 × 10 -

6.944 × 10 -

1.157 × 10 -

hr 8.766 × 103 24 1

1.667 × 10 -

2.778 × 10 -

min 5.259 × 103 1440 60 1 1.667 × 10 -

SECOND

3.156 × 107

8.640 × 104

1 year = 365.24219879 days

I. SPEED

1 foot per second =

1 kilometer per hour =

1 METER per SECOND =

1 mile per hour =

1 centimeter per sec =

1 knot =

ft/sec 1

3.281 × 10 -

km/hr

1

3.600 × 10 -

METER/SEC

miles/hr

1

2.237 × 10 -

cm/sec

100

1

knot

1.944 × 10 - 1 1 knot = 1 nautical mile/hr 1 mile/min = 88 ft/sec = 60 miles/hr

J. FORCE

1 dyne =

1 NEWTON =

1 pound =

1 poundal =

1 gram-force =

1 kilogram-force =

dyne

1

105

× 105

× 104

× 105

NT

× 10 -

lb

× 10 -

1

× 10 -

× 10 -

pdl

× 10 -

× 10 -

gf

× 10 -

kgf

× 10 -

× 10 -

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

1 kgf = 9.80665 newton 1 lb = 32.17398 poundal

K. PRESSURE

1 atmosphere =

1 dyne per cm^2 =

1 inch of water at 4 o^ Ca^ =

1 centimeter of mercury at 0 o^ Ca^ =

1 NEWTON per METER^2 =

1 pound per in^2 =

1 pound per ft 2 =

atm

× 10 -

× 10 -

× 10 -

× 10 -

× 10 -

× 10 -

dyne/cm^2

× 106

× 104

× 104

inch of water

× 10 -

× 10 -

cm Hg

× 10 -

× 10 -

× 10 -

NT/METER^2

× 105

× 103

lb/in^2

× 10 -

× 10 -

× 10 -

× 10 -

lb/ft 2

× 10 -

× 10 -

a (^) Where the acceleration of gravity has the standard value 9.80665 meter/sec 2 1 bar = 10^6 dyne/cm^2 1 millibar = 10 3 dyne/cm^2 1 torr (mm Hg at 0°C) = 1.93367 × 10 -2^ lb/ft 2

1 meter – kgf = 9.807 joule, 1 watt-sec = 1 joule = 1 nt-meter, 1 cm-dyne = 1 erg

Some conversions used in spectroscopy:

1 eV = 8065.7 cm-1^ 1 cm-1^ = 0.000124 eV 1 eV ≈ 6000 °K At 300°K, 23 kT ≈ 0.05 eV

NOTES FOR TABLE L: The electron volt is the kinetic energy an electron gains from being accelerated through the potential difference of one volt in an electric field. The units enclosed by heavy lines are not properly energy units; they arise from the relativistic mass-energy equivalent formula E = mc^2.

M. SPECIFIC ENERGY

gm

cal gm

erg KGM

JOULE

1 calorie per gram =

1 erg per gram =

1 JOULE per KILOGRAM =

1 Btu per pound (mass)=

1 foot-pound per pound (mass)=

1 horsepower-hour per pound (mass)=

× 10 -

× 10 -

× 10 -

× 10 3

× 107

× 107

× 104

× 1010

× 103

× 103

× 106

× 10 -

× 10 -

× 10 -

× 103

× 10 -

× 106

× 10 -

× 10 -

× 10 -

× 10 -

× 10 -

(SEE NOTE FOR TABLE N)

lbm

Btu

m

f lb

ft-lb lbm

hp-hr

N. SPECIFIC ENERGY PER UNIT TEMPERATURE

1 calorie per gram per degree C =

1 erg per gram per degree C =

1 JOULE per KGM per DEGREE K =

1 Btu per lb (mass) per degree F =

1 foot-lb per lb (mass) per degree F =

1 horsepower-hour per lb (mass) per degree F=

× 10 -

× 10 -

× 10 -

× 10 3

× 107

× 107

× 104

× 1011

× 103

× 103

× 107

× 10 -

× 10 -

× 10 -

× 10 -

× 106

× 10 -

× 10 -

× 10 -

× 10 -

× 10 -

NOTE FOR TABLES M & N: The engineering units enclosed within the heavy lines have been properly related to the pound mass rather than the pound force because these specific 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 conversion factors 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/sec 2 = 9.80665 meter/sec 2. This is true because the pound-force and the pound-mass are numerically equal at standard gravity. 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 of mass and weight. The units are related by

lbf = 32.174 lb (^) m ft/sec^2

gmC

cal ° gmC

erg

° KGM K

JOULE

° lb F

Btu m °^ lb F

ft-lb m

f ° lb F

hp-hr m °

P. HEAT FLUX*

1 calorie per sec per centimeter 2 =

1 kilocalorie per hour per meter 2 =

1 WATT per METER^2 =

1 watt per inch^2 =

1 British thermal unit per hour per foot^2 =

1 British thermal unit per sec per inch^2 =

1 horsepower per foot 2 =

× 10 -

× 10 -

× 10 -

× 10 -

× 104

× 106

× 102

× 104

× 106

× 10 -

× 10 -

× 10 -

× 103

× 104

× 105

× 103

× 10 -

× 10 -

× 10 -

× 10 -

× 10 -

× 10 -

× 10 -

× 10 -

× 10 -

*Also power per unit area

Q. HEAT TRANSFER COEFFICIENT, h

1 calorie per sec per centimeter 2 - ºC =

1 WATT per METER^2 per DEG KELVIN =

1 watt per inch^2 per deg Centigrade =

1 Btu per hour per per foot 2 - ºF =

1 Btu per sec per inch 2 - ºF =

1 horsepower per foot 2 - ºF =

× 10 -

× 10 -

× 10 -

× 104

× 106

× 104

× 10 -

× 10 -

× 103

× 103

× 105

× 103

× 10 -

× 10 -

× 10 -

× 10 -

× 10 -

× 10 -

× 10 -

2 sec-cm

cal 2 hr m

kilocal

− 2 M

WATT 2 in

watt 2 hr-ft

Btu 2 sec-in

Btu 2 ft

hp

sec cm C

cal 2 − ° °K

2 M

WATT

in C

watt 2 ° hr-ft F

Btu 2 ° sec-in F

Btu 2 ° (^) ft F

hp 2 °

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 deg Centigrade =

1 Btu per hour per foot-deg F =

1 Btu per sec per inch-deg F =

1 horsepower per foot-deg F =

× 10 -

× 10 -

× 10 -

× 102

× 104

× 10 -

× 10 -

× 103

× 104

× 10 -

× 10 -

× 10 -

× 10 -

× 10 -

× 10 -

× 10 -

× 10 -

× 10 -

sec− cm° C

cal METER °K

WATTS

in C

watts

° hr-ftF

Btu ° sec-inF

Btu ° ft F

hp °