592 Effect of Variable Specific Heat on Gas Discharges . 



A 2 -?/ 2 i 2 ii 2 



But Q 2 = ~ and v 2 = J -^- from (5). 



X m 





v 2 m x ) 



••• Q=Q={i-!5d--)} 



If, however, K P = A + ST + S"F 



and K^B+ST + S'T 2 



with A/ = — 9 

 B 



then the formulae (6) and (7) become respectively 



approximation. 

 . . . . (7) 



.nd 



• • (8) 

 /V JL "\ k 1 — x m \\ 



Q=a{l-3(xT 1+ ^)i— L}. . . (9) 



It will be observed from formulae (6) to (9) that, when S 

 (or what is the same thing, X) is positive, the velocity u is 

 greater under variable than under constant specific heat 

 conditions, while Q, the quantity discharged, is less. The 

 same applies, of course, to S' and V. If X and V are nega- 

 tive, then the velocity u is less and the discharge Q is greater 

 than under constant specific heat conditions. 



The foregoing analysis suggests another method of specific 

 heat determination, besides those already in use. By the 

 provision of a suitably short convergent nozzle of invariable 

 coefficient of contraction under all conditions, the application 

 of equations (6) to (9) to the discharges obtained would 

 enable the values of X and V to be derived. -This method 

 has, at least, decided advantages over most others, particularly 

 in the simplicity both of the experimental work and calcu- 

 lations involved. 



It is to be observed, of course, that the same qualification 

 must be applied to these variable specific heat equations (6) 

 to (9) as are applied to the usual constant specific heat 

 formulae. That is, they must be used as they stand, only 

 for cases of flow in which the discharge pressure is above or 

 equal to the critical pressure, i. e., when the stream velocity at 



