# Dimensions and Conversions

SI basic units and SI derived units are listed of the major flow, transport, and thermal quantities. In the left column name and symbol are given and in the right column the unit (dimension), with the symbol in ^ [ ] used in Appendix C, and in the line below its conversion to the U. S. customary units.

3 2.75

2.5

2.25 2

1.75

d

1.5

1.25 1

0.75 0.5 0.25 0

0 5 10 15 20 25 30

kT/e

Fig. B.1. Dimensionless collision integrals = Ok, and ODAB of air as functions

of kT/є or kT/єав [4, 6].

SI Basic Units

 length, L [mL ^ [L] 1 m = 100 cm = 3.28084 ft (1,000 m = 1 km) mass, m [kg], ^ [M] 1 kg = 2.20462 lbm time, t [s] (= [sec]), ^ [t] temperature, T [K], ^ [T] 1 K = 1.8 °R ^ TRankine = TFahrenheit + 459.67 TKelvin (5/9) TRankine ^ TKelvin = TCelsius + 273.15

amount of substance, mole

[kg-mol], ^ [mole]

1 kg-mol = 2.20462 lbm-mol

 SI Derived Units area, A [m2], ^ [L2] 1 m2 = 10.76391 ft2 volume, V [m3], ^ [L3] 1.0 m3 = 35.31467 ft3 speed, velocity, v, u [m/sL ^ [L/t] 1.0 m/s = 3.28084 ft/s force, F [N] = [kg m/s2], ^ [M L/t2] 1.0 N = 0.224809 lb/ pressure, p [Pa] = [N/m2], ^ [M/L t2] 1.0 Pa = 10~5 bar = 9.86923-10~6 atm = = 0.020885 lb//ft2 density, p [kg/m3], ^ [M/L3] 1.0 kg/m3 = 0.062428 lbm/ft3 (dynamic) viscosity, p [Pa s] = [N s/m2], ^ [M/L t] 1.0 Pa s = 0.020885 lb/ s/ft2 kinematic viscosity, v [m2/s], ^ [L2/t] 1.0 m2/s = 10.76391 ft2/s shear stress, т [Pa] = [N/m2], ^ [M/L t2] 1.0 Pa = 0.020885 lb/ /ft2 energy, enthalpy, work, quantity of heat [J] = [N m], ^ [M L2/t2] 1.0 J = 9.47813-10-4 BTU = = 23.73036 lbmft2/s2 = 0.737562 lb//s2

(mass specific) internal energy, [J/kg] = [m2/s2], ^ [L2/t2] enthalpy, e, h 1.0 m2/s2 = 10.76391 ft2/s2

 (mass) specific heat, cv, cp specific gas constant, R [J/kg K] = [m2/s2 K], ^ [L2/t2T] 1.0 m2/s2K = 5.97995 ft2/s2 °R power, work per unit time [W] = [J/s] = [N m/s], ^ [M L2/t3] 1.0 W = 9.47813-10-4 BTU/s = = 23.73036 lbmft2/s3 thermal conductivity, к [W/m K] = [N/s K], ^ [M L/t3T] 1.0 W/m K = 1.60496-10-4 BTU/s ft °R

= 4.018342 lbm ft/s3 °R

heat flux, q [W/m2] = [J/m2s], ^ [M/t3]

1.0 W/m2 = 0.88055-10-4 BTU/s ft2 = = 2.204623 lbm/s3

(binary) mass diffusivity, Dab [m2/s], ^ [L2/t]

1.0 m2/s = 10.76391 ft2/s

thermo diffusivity, D’A [kg/m s], ^ [M/L t]

1.0 kg/m s = 0.67197 lbm/ft s

diffusion mass flux, j [kg/m2s], ^ [M/L2t]

1.0 kg/m2s = 0.20482 lbm/ft2s

References

1. Taylor, B. N. (ed.): The International System of Units (SI). US Dept. of Com­merce, National Institute of Standards and Technology, NIST Special Publica­tion 330, 2001, US Government Printing Office, Washington, D. C. (2001)

2. Taylor, B. N. (ed.): Guide for the Use of the International System of Units (SI). US Dept. of Commerce, National Institute of Standards and Technology, NIST Special Publication 811, 1995, US Government Printing Office, Washington, D. C. (1995)

3. Hirschfelder, J. O., Curtiss, C. F., Bird, R. B.: Molecular Theory of Gases and Liquids. John Wiley & Sons, New York (1966)

4. Bird, R. B., Stewart, W. E., Lightfoot, E. N.: Transport Phenomena, 2nd edn. John Wiley & Sons, New York (2002)

5. Vincenti, W. G., Kruger, C. H.: Introduction to Physical Gas Dynamics. John Wiley & Sons, New York (1965), Reprint edition, Krieger Publishing Comp., Melbourne, Fl (1975)

6. Neufeld, P. D., Jansen, A. R., Aziz, R. A.: J. Chem. Phys. 57, 1100-1102 (1972)