L 5-89 ] 



LXIX. The Effect of Variable Specific Heat on the Discharge 

 of Gases through Orifices or Nozzles. By William J. 

 Walker, Ph.D., University College, Dundee*. 



Summary. The following paper raises the question whether 

 or not it is desirable to account for abnormal orifice or 

 nozzle discharges by the consideration of changes in the 

 value of 7, the index in the equation pvy= constant, for 

 adiabatic changes of state. This appears, generally, to have 

 been the custom hitherto, but, since the actual adiabatic 

 equation under linear variable specific heat conditions is 

 p V m e KT = constant, the analysis in this paper has been carried 

 out on the latter basis for the purpose of determining, as 

 nearly as possible, what effect such specific heat variation 

 has on discharges. An exact solution does not appear to be 

 derivable, but the method of analysis adopted here may be 

 carried to any degree of accuracy required. The method of 

 analysis is somewhat similar to that adopted in a previous 

 paper dealing with another effect of variable specific heat, 

 The result obtained in the present paper brings out promi- 

 nently the' fact that the error in computing discharges, by the 

 usual constant specific heat theory, increases as the density of 

 the medium in the reservoir is diminished. This fact appears 

 to have been neglected in previous considerations of the 

 subject. It is pointed out, also, that, by means of the dis- 

 charge formulae obtained, the method of orifice discharge 

 may be used as a reliable and convenient one for the deter- 

 mination of specific heat variations with temperature. 



In the How of gases through nozzles and orifices the 

 analysis generally applied to any interpretation of test results 

 is that based on the constancy of the specific heat of the gas 

 concerned. The formulae derived under such an assumption 

 are, for the velocity of the gas, 



r y Y ~ 1 ~P 



u e = \ 2g — — *piVi{l — x y } feetpersec, . (1) 



and for the quantity discharged, 



Q c =A[2 i /^- 1 ^(.4-xT i )] i lb.persec., . (2) 



* Communicated by the Author. 



