RMP Lecture Notes

Systems of Units

Most engineering problems use one of three systems of units

SI (Systeme Internationale, mks) is commonly used by scientists. It is in everyday use in most of the world. The so-called "metric system" is a subset/variant of the SI system, which was officially standardized in 1960.
cgs
Engineering (American, English, fps) is the traditional system of the US and UK. Although the UK changed official systems in the 1970s, the US has not. The vast majority of US industrial concerns still specify parts and equipment using these "Engineering" units.

Every system of units has

a set of "basic units" for the dimensions of mass, length, time, absolute temperature, electric current, luminous intensity, and amount of substance.
derived units, which are special combinations of units or units used to describe combination dimensions (energy, force, volume, etc.)
unit multiples, which are multiples or fractions of the basic units used for convenience (years instead of seconds, kilometers instead of meters, etc.). Often these are not "official" parts of the unit system (liters).

Traditional unit systems were based on customary quantities (yard was distance from King's thumb to his nose), but today all systems use basic units defined in terms of measurable physical constants.

1 meter is the distance equal to 1.65076373x10⁶ wavelengths in vacuum of the radiation corresponding to the transition between two levels of the krypton 86 atom

SI System

Base units:

Mass: kilogram (kg)
Length: meter (m)
Temperature: (degree) Kelvin (K)
Time: second (s)
Electric Current: Ampere (A)
Luminous Intensity: candela (cd)

A multiple system is used based on powers of 10:
tera- (T) 10¹², giga- (G) 10⁹, mega- (M) 10⁶, kilo- (k) 10³, centi- (c) 10^-2, milli- (m) 10^-3, micro- (greek mu) 10^-6, nano- (n) 10^-9 pico- (p) 10^-12.

Common derived units include:

Force: Newton (N) = 1 kg*m/s²
Pressure: Pascal (Pa) = 1 N/m²
Energy: Joule (J) = N*m
Power: Watt (W) = J/s

The "liter" (cubic decimeter) is commonly used, although it hasn't any "official" status.

cgs System

Mass: gram (g)
Length: centimeter (cm)

Other basic units and the multiple prefixes are the same as used in SI. Most of the derived units are the same, although

Force: dyne = 1 g*cm/s²
Energy: erg = 1 dyne*cm

Engineering Units

Mass: pound (lbm)
Length: foot (ft)
Temperature: (degree) Rankine (R)
Time: second (s)

with most others the same as SI. Multiples are a little tricky, and sort of fun, since they are based on tradition -- yds, inches, miles, rods, acres, tons, etc.

Force: pound-force (lbf) = 32.2 lbm*ft/s²
Pressure: pressure (psi) = 1 lbf/in²
Energy: foot-pound-force ft-lbf = 1 ft*lbf
Power: horsepower (hp)
Volume: gallon (gal)

There are others that are used to varying degrees. Of particular interest are the energy units expressed in terms of heat, such as the BTU (British Thermal Unit): the heat required to raise the temperature of 1 lb of water by 1 degree Rankine.

These units have been standardized, since all English units such as the inch, pound, etc. are now officially defined in terms of SI units.

References:

R. M. Felder & R. W. Rousseau, Elementary Principles of Chemical Processes (2nd Ed.), John Wiley, 1986. pp. 12-14.
P.H. Wright, Introduction to Engineering (2nd Ed.), John Wiley, 1994, p. 151-59.

R.M. Price
Original: 5/25/94
Modified: 6/21/94, 9/25/95, 10/30/95; 5/17/2004