UNITS AND CONSTANTS SI,CGS ,MKS CONVERSION FORMULE |UNITS AND CONSTANTS|

APPENDIX C FUNDAMENTAL  UNITS AND CONSTANTS

 1.  FUNDAMENTAL UNITS

At least four unit systems are in use today. The coherent unit systems utilize a set of base quantities from which all derived quantities are obtained by multiplication or division without the introduction of numerical factors. The traditional English units, which continue to see use in the United States, do not form a coherent system. The coherent unit systems include SI units and the MKS and cgs systems. The cgs system is based on three basic quantities for length, mass, and time using the centimeter, gram and second, respectively. In the cgs system, force and energy are quantified with the derived units of dyne (g cm/s2) and erg (g cm2/s2), respectively. The gauss (G) and oersted (Oe) are cgs units for magnetic flux density and magnetic field strength, respec- tively. MKS is a system of units for mechanics based on the three fundamental quanti- ties of length, mass, and time using the meter, kilogram, and second, respectively. The International System of Units (SI units) is a coherent system based on the seven basic quantities, and matching units, specified in Table C.1. The derived SI units and their corresponding constituent base units (dimensions) are given in Table C.2, where the angular measures of the radian and steradian are sometimes referred to as supplementary units. For volume, the liter (L) is actually not a derived unit since it requires a numeric multiplier, that is, 1 L = 10−3 m3. The SI prefixes incorporated with both base and derived units are provided in Table C.3. Corresponding units between the SI, cgs, and English systems are presented in Table C.4. Some selected conversions between the various units are given in Table C.5. Table C.6 lists the physical quantities common to power engineering as well as the symbol and unit utilized for each.

TABLE C.1. Base SI Quantities  and Units

Base Physical Quantity                                            Base Unit                                   Unit Symbol

Length	meter	M
Mass	kilogram	Kg
Time	second	S
Electric current	ampere	A
Thermodynamic temperature	Kelvin	K
Amount of substance	mole	mol
Luminous intensity	candela	Cd

TABLE 2. Derived SI Quantities  and Units

Quantity                             Derived Unit       Unit Symbol                   Unit Dimension(s)

Frequency Force	hertz newton	Hz N	1/s kg × m/s2  = J/m
Pressure Energy, Work, Heat Power	pascal joule watt	Pa J W	N/m2  = kg/(m × s2) N × m = kg × m2/s2 J/s = kg × m2/s3
Electric charge Electric potential Resistance	coulomb volt ohm	C V Ω	A × s J/C = kg × m2/s3/A = W/A V/A = kg × m2/s3/A2
Conductance Capacitance Magnetic flux density Magnetic flux Inductance	siemens farad tesla weber henry	S F T Wb H	1/Ω = A/V C/V = A2  × s4/kg/m2 V × s/m2  = kg/A/s2  = Wb/m2 V × s = kg × m2/s2/A V × s/A = kg × m2/s2/A2 = Wb/A
Plane angle	radian	rad	m/m
Solid angle	steradian	sr	m2/m2

TABLE 3. SI Prefixes

Prefix                 Factor                  Symbol                  Prefix                 Factor                  Symbol

milli                    10−3                                       m                      kilo                      103                                        k micro                  10−6                                       μ                       Mega                   106                                        M nano                   10−9                                       n                       Giga                    109                                         G pico                    10−12                                     p                       Tera                    1012                                      T femto                  10−15                                     f                        Peta                     1015                                      P atto                     10−18                                     a                        Exa                      1018                                      E

TABLE 4. Corresponding Units in the SI, cgs, and English Unit Systems

Quantity                            SI                                   cgs                                         English

Length                      meter, m                    centimeter, cm                      inch, in; foot, ft

Mass                         kilogram, kg             gram, g                                 pound mass, lb or lbm

Time                         second, s                   second, sec                           second, sec

Temperature              kelvin, K                   degree kelvin, °K;

degree Celsius, °C

degree Fahrenheit, °F

Force	newton, N	dyne	pound, lb or lbf
Pressure Energy Power Heat	pascal, Pa joule, J watt, W joule, J	dyne/cm2 erg erg/sec calorie, cal	pound/inch2, psi foot pound, ft lb foot pound/sec, ft lb/sec British thermal unit, Btu

TABLE 5. Unit Conversion Factors

Dimension                                                                  Selected Equalities

Length                                1 m = 39.37 inches = 3.281 ft

1 inch = 2.54 cm

1 ft = 12 inches = 30.48 cm

1 yard = 3 ft = 0.9144 m

1 mile = 5280 ft = 1.609 km

Time                                   1 year = 365.25 days = 8766 hours

Mass                                   1 lbm  = 16 oz = 0.4536 kg

1 ton = 2000 lbm  = 907.2 kg

1 tonne (metric ton) = 1000 kg

Force                                   1 N = 105 dyne = 0.2248 lbf

1 lbf = 4.448 N

Torque                                1 N m = 107 dyne cm = 0.7376 lbf ft

Energy                                1 J = 107 erg = 0.7376 ft lbf = 9.480 × 10−4 Btu = 2.778 × 10−7 kWh

1 Btu = 252 cal = 1055 J

1 erg = 10−7 J

1 kWh = 3412.3 Btu = 3.6 × 106 J Power                                 1 W = 0.7376 ft lbf/s = 1.341 × 10−3 hp

1 Btu/h = 2.93 × 10−4 kW

1 hp = 2545 Btu/h = 0.7457 kW Magnetic                             1 T = 104 G = 1 Wb/m2

1 Oe = 79.577472 ampere-turns/meter

TABLE C.6. Symbols and Units for Various Quantities

Quantity	Quantity Symbol	Unit(s)
Fundamental
Length Mass	ℓ m	meter (m) kilogram (kg)
Time	t	second (s)
Current	I	ampere (A)
Mechanical
Force	F	newton (N)
Torque	T	newton-meter (N m)
Angular displacement	θ	radian (rad)
Velocity	v	meter/second (m/s)
Angular velocity	ω	radian/second (rad/s)
Electrical
Charge	q	coulomb (C)
Electric potential	V	volt (V)
Electric field strength	E	volt/meter (V/m)
Energy	W	joule (J)
Power	P	watt (W)
Electric flux density	D	coulomb/meter2  (C/m2)
Electric flux	ψ	coulomb (C)
Resistance	R	ohm (Ω)
Conductance (G = 1/R)	G	siemens (S); mho
Resistivity	ρ	ohm-meter (Ω m)
Conductivity (σ = 1/ρ)	σ	1/(ohm-meter)
Reactance	X	ohm (Ω)
Susceptance (B = 1/X)	B	siemens (S); mho
Impedance	Z	ohm (Ω)
Admittance (Y = 1/Z)	Y	siemens (S); mho
Capacitance	C	farad (F)
Permittivity (D = ε E)	ε	farad/meter (F/m)
Magnetic
Magnetomotive force (Fm  =  Hs ds)	Fm	ampere-turn
Magnetic field strength	H	oersted (Oe); ampere-turn/meter
Magnetic flux	Φ	weber (Wb)
Magnetic flux density	B	tesla (T); gauss (G)
Inductance	L	henry (H)
Permeability (B = μ H)	μ	henry/meter (H/m)

2.  FUNDAMENTAL  PHYSICAL CONSTANTS

Constant                                                       Symbol                                           Value

Speed of light (in vacuum)	c	2.997925 × 108  m/s
Elementary (electron) charge	e	1.60217646 × 10–19  C
Planck’s constant	h	6.62608 × 10–34  J s
Boltzmann constant	k	1.38065 × 10–23  J/K
Permittivity of vacuum Permeability of vacuum	ε0 μ0	10–9/(36π) = 8.842 × 10–12  F/m 4π × 10–7  = 1.257 × 10–6  H/m

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