### Units and Dimensions

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Systems of Units:

The official international system of units (System International d'Units). Strong efforts are underway for its universal adoption as the exclusive system for all engineering and science, but older systems, particularly the cgs and fps engineering gravitational systems are still in use and probably will be around for some time. The chemical engineer finds many physiochemical data given in cgs units; that many calculations are most conveniently made in fps units; and that SI units are increasingly encountered in science and engineering. Thus it becomes necessary to be expert in the use of all three systems.

SI system:

Primary quantities:

 Quantity Unit Mass in Kilogram kg Length in Meter m Time in Second s or as sec Temperature in Kelvin K Mole gmol or simply as mol

Derived quantities:

 Quantity Unit Force in Newton (1 N = 1 kg.m/s2) N Pressure in Pascal (1 Pa = 1 N/m2) N/m2 Work, energy in Joule ( 1 J = 1 N.m) J Power in Watt (1 W = 1 J/s) W

cgs Units:

The older centimeter-gram-second (cgs) system has the following units for derived quantities:

 Quantity Unit Force in dyne (1 dyn = 1 g.cm/s2) dyn Work, energy in erg ( 1 erg = 1 dyn.cm = 1 x 10-7 J ) erg Heat Energy in calorie ( 1 cal = 4.184 J) cal

fps Units:

The foot-bound-second (fps) system has long been used in commerce and engineering in English-speaking countries.

 Quantity Unit Mass in pound ( 1 lb = 0.454 kg) lb Length in foot (1 ft = 0.3048 m) ft Temperature in Rankine oR Force in lbf ( 1 lbf = 32.2 lb.ft/s2) lbf

Conversion factors:

Mass:

1 lb = 0.454 kg

Length:

1 inch = 2.54 cm = 0.0254 m

1 ft = 12 inch = 0.3048 m

Energy:

1 BTU = 1055 J

1 cal = 4.184 J

Force:

1 kgf = 9.812 N

1 lbf = 4.448 N

1 dyn = 1 g.cm/s2

Power:

1 HP = 736 W

Pressure:

1 Pa = 1 N/m2

1 psi = 1 lbf/inch2

1 atm = 1.01325 x 105 N/m2 = 14.7 psi

1 Bar = 105 N/m2

Viscosity:

1 poise = 1 g/(cm.s)

1 cP = (1/100) poise = 0.001 kg/(m.s)

Kinematic viscosity:

1 Stoke = 1 St = 1 cm2/s

Volume:

1 ft3 = 7.481 U.S. gal

1 U.S. gal = 3.785 litre

Temperature:

ToF = 32 + 1.8oC

ToR = 1.8K

Gas Constant:

R = 8314 J / (kmol.K)

Dimensions:

Dimensions of the primary quantities:

 Fundamental dimension Symbol Length L Mass M Time t Temperature T

Dimensions of derived quantities, can be expressed in terms of the fundamental dimensions.

 Quantity Representative symbol Dimensions Angular velocity w t-1 Area A L2 Density r M/L3 Force F ML/t2 Kinematic viscosity n L2/t Linear velocity v L/t Linear acceleration a L/t2 Mass flow rate m. M/t Power P ML2/t3 Pressure p M/Lt2 Sonic velocity c L/t Shear stress t M/Lt2 Surface tension s M/t2 Viscosity m M/Lt Volume V L3