194 Prof. Osborne Reynolds on 



regards pressure, density, and temperature of that in the 

 orifice; and this is precisely what it is found to be on 

 examining the equations. 



7. The following is the definite expression of the foregoing 

 argument. 



The adiabetic laws for gas are : p being pressure, p density, 

 t absolute temperature, and 7 the ratio of specific heat, 



i=pYT i =^r ' (i> 



The equation of motion, u being the velocity and x the direc- 

 tion of motion, is 



du dp 



P U cU = ~M 

 or 



* Jo P 



Substituting from equations (1), 



r?dp _ 7 />o T . 



Jo P y-l/>oV 



Au^s&i^mm] ( 3) 



v 7-1 Po r l Vpi/ J 



P^Pi/Rf^^ (4) 



PoTl \Pl/ 



Hence along a steady stream, since W is constant, equation 

 (5) gives a relation that must hold between A and p. 



Differentiating A with respect to p and making - — zero, 



it appears 



2i>iV=(7 + l)/MT (6) 



or 



P 



Pi 



For air 7 = 1-408. 



-lw <" 



^ = •527 (8) 



Pi 



