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1
UNITS AND CONVERSION FACTORS
E.J. ROSCHKE
PROPULSION DIVISION
JET PROPULSION LABORATORY
2 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
1UNITS AND CONVERSION FACTORS
Table of Contents
Section Page
References 3
I. Decimal Multiples and Submultiples 4
II. Description of Units
Mechanical, Electric, Magnetic 4
III. Equivalent Units mksq System 5
IV. Dimensions of esu and emu Electric
and Magnetic Quantities 5 V. Dimensions and Units for Physical Quantities - mksq System 6,7A. Mechanical 6
B. Thermal 7
C. Electric and Magnetic 7
VI. Conversion of mksq Units to Gaussian Units 8
VII. Conversion Factors 8-23
A. Plane Angle 8
B. Solid Angle 8
C. Length 9
D. Area 9
E. Volume 9
F. Mass 10
G. Density 10
H. Time 11
I. Speed 11
J. Force 11
K. Pressure 12
L. Energy, Work, Heat 13
M. Specific Energy 14
N. Specific Energy Per Unit Temp. 15
O. Power 16
P. Heat Flux 17
Q. Heat Transfer Coefficient 17
R. Thermal Conductivity 18
S. Absolute Viscosity 19
T. Kinematic Viscosity 19
AA. Electric Charge 20
BB. Electric Current 20
CC. Electric Potential 20
DD. Electric Resistance 21
EE. Electric Resistivity 21
FF. Capacitance 21
GG. Inductance 22
2Table of Contents - continued
Section Page
HH. Magnetix Flux 22
I I. Magnetomotive Force 22
J J. Magnetic Field Strength, B23
KK. Magnetic Vector, H23
VIII. Electromagnetic Constants of Free Space 24
IX. Electromagnetic Constants of Materials 24
X. Some Important Dimensional Constants 25
XI. Some Important Dimensionless Groups 26
XII. The Perfect Gas Law 27,28
A. Nomenclature, Definitions and Equations 27
B. Values of Universal Gas Constant, Boltzmann's Constant and Avogadro's Number in Different Units 28 3 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, 9
thRevised 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. 4I. DECIMAL MULTIPLES AND SUB-MULTIPLES
Name Symbol Equivalent Name Symbol Equivalent
tera T 10 12 deci d 10 -1 giga G 10 9 centi c 10 -2 mega M 10 6 milli m 10 -3 kilo k 10 3 micro 10 -6 hecto h 10 2 nano n 10 -9 deca 10 pico p 10 -12II. DESCRIPTION OF UNITS
MECHANICAL UNITS
Quantity
Length
Mass Time ForceWork, Energy
PowerDynamic Viscosity
Kinematic Viscositycgs
centimeter gram second dyne erg poise stokemks meter kilogram second newton joule wattELECTRIC AND MAGNETIC UNITS
The esu and emu unit systems are cgs systems.
esu denotes "electrostatic unit", sometimes given prefix "stat", e.g. statcoulomb emu denotes "electromagnetic unit", sometimes given prefix "ab", e.g. abcoulombSome emu units have special names:
Quantity
Magnetic Flux,
Magnetic Field Strength, B
Magnetomotive Force,
FMagnetic Vector, Hemu
line maxwell gauss gilbert oerstedmksq weber weber/m 2 amp-turn amp-turn/m. 5 mksq DIMENSIONSLength L
Mass M
Time T
Current Q/T
Charge Q
III. EQUIVALENT UNITS mksq SYSTEM
1 newton = 1 kilogram-meter/(second)
21 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 j V I B H C LR esu
M x L y T z xy z 23-1
½ -½ -1
½ -½ -1
½-1
½ -½ -2
½ ½ -1
½-2
½ 0
½½-2
0 0 0
0-2 2
0 0-10 1 0
0-1 2
0-1 1 emu
M x L y T z xyz½ ½ 0
½ 0
½ ½-2
½ 0
½-1
½-2
½ ½-1
½-½-1
½-½-1
0-2 2
0 0 0
0-2 1
0-1 2
0 1 0
0 1-1c
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 10 10Thus: 1 emu of charge = 2.998 10
10 esu of charge or 1 abcoulomb = 2.998 10 10 statcoulomb 2323
23
23
25
23
23
esuemu 6