394 Table 113 



VISCOSITY AND THERMAL CONDUCTIVITY OF AIR AND DIFFUSIVITY OF 



WATER VAPOR IN AIR 1 



The dynamic viscosity may be defined as the ratio of shearing stress to shear, 



3m 

 dz 



where r is the shearing stress and du/dz is the shear (u is the velocity normal to the 

 direction z). The basic cgs unit is 1 poise = 1 g. cm. _1 s. -1 . The dynamic viscosity of a 

 gas is independent of pressure except at very low pressures. Its temperature dependence 

 was computed from Sutherland's equation: 



_3_ 



f* _ To + C ( T\ 2 

 M, T + C \ To ) 



where T is the absolute temperature, ik> is the dynamic viscosity at absolute temperature 

 To and C is Sutherland's constant, assumed to have the value 120 °C. At To = 296.16 °K. 

 (23 °C), a*o= (1.8325 ±0.0010) X 10"* g. cm.-'s." 1 according to Birge. 2 

 The thermal conductivity k is defined by 



dz 



where H is the rate of heat conduction per unit area and dT/ds is the temperature 

 gradient, k at °C. is given by Chapman and Cowling 3 as 5.80 X 10" 3 cal. cmr's." 1 

 °C."' and it is estimated that the probable error is ± 0.02 X 10" s . Values at other 

 temperatures are assumed proportional to fi. 



Kinematic viscosity, thermometric conductivity, and diffusivity of water vapor in dry 

 air are functions of both temperature and pressure. A pressure of 1000 mb. is assumed 

 in computing these quantities. (See original article for corresponding values of density 

 used in the computations.) The kinematic viscosity v is the ratio of the dynamic viscosity 

 fj. to the density p ; v = fi/p. It is the factor occurring in the relation giving the accelera- 

 tion du/dt due to fluid friction. In the simplest case this relation is of the type 



du d 2 u 



dt ~~ " dz 2 



The thermometric conductivity v c = k/(c P p) determines the rate of heating due to a 

 given temperature distribution : 



dT _ 3 2 T 



-dl- Ve d7 



where c P is the specific heat at constant pressure. A value of 0.1895 cm. 2 s. -1 has been 

 computed for °C. and the ratio v/v c has been assumed constant for other temperatures. 

 A substance having the concentration (mass per total mass) q in a mixture of density 

 P is diffused at the rate, in mass per unit area and time, 



E =-> D Tz 



where D is the diffusivity. The corresponding rate of change of concentration is 



dq _£, d*q 



dt dz 2 



1 Montgomery, R. B., Journ. Meteorol., vol. 4, pp. 193-196, 1947. 



2 Birge, R. T., The 1944 values of certain atomic constants with particlar reference to the electronic 

 charge. Amer. journ. Phys., vol. 13, pp. 63-73, 1945. 



3 Chapman, Sydney, and Cowling, T. G., The mathematical theory of non-uniform gases. 404 pp. 

 Cambridge Univ. Press, 1939. 



(continued) 



SMITHSONIAN METEOROLOGICAL TABLES 



