43* MOLECULAR FREE PATHS 437 



43*. Pressure of Air in Motion 



The same calculations may also be made in the case when the 

 mass of gas is in a state of flow, and we shall estimate the pressure 

 exerted by a gas moving with constant velocity a upon a surface 

 in the mass of gas which we take at right angles to the direction 

 of flow. 



Since the forward velocity a may be taken as equally shared 

 by all the particles of the whole mass of gas, there is no need for 

 this new problem to alter the formulae of 40* except by replacing 

 the function e~ kmojt f expressive of Maxwell's law, by the more 

 general function 



z -2a cos s) 

 



Two integrations then give 



for the momentum carried across unit area in unit time in the 

 positive direction, and 



<o 4 sin s cos 2 s e - 





for that carried over in the negative direction ; and the pressure 

 exerted by the streaming gas in the direction of its flow is, accord- 

 ing to the former formula, given by 



Carrying out the integrations as far as we can, we obtain 

 d = Nm*/(kmf*)l (a/2&ra)e-* 2 +(a 2 + l/2fcm)j" foe-***}, 



or, on introduction of the mean value O ( 19*), 

 Q l = i-Nm^O 2 + a 2 ) 1 1 + (4/VO) J^*r*" 1 "' J + JdQr 



Similarly we have 



g a = - iJVmRjirQ 2 + a 2 ) 1 1 - (4/TrO) due-* 



and thus as result we get the simple formula 

 p = Nm(*& + a 2 ), 



