THE 



LONDON, EDINBURGH, and DUBLIN 



PHILOSOPHICAL MAGAZINE 



AND 



JOURNAL OF SCIENCE. 



[SIXTH SERIES.] 



AUGUST 1916. 

 



XVI. On the Discharge of Gases under Hiqh Pressures. 

 By Lord Rayleigh, O.M., F.R&* 



THE problem of the passage of gas through a small 

 aperture or nozzle from one vessel to another in which 

 there is a much lower pressure has had a curious history. 

 It was treated theoretically and experimentally a long while 

 ago by Saint- Venant and Wantzel t in a remarkable memoir, 

 where they point out the absurd result which follows from 

 the usual formula, when we introduce the supposition that 

 the pressure in the escaping jet is the same as that which 

 prevails generally in the recipient vessel. In Lamb's 

 notation J, if the gas be subject to the adiabatic law {pocp y ), 



n p°dp > _ Zy p ( _ 

 P ~ Y- 1 Po 



where q 

 po, po the 



«r 



-•ii-(ipj. 



7-1 



W-c 2 ), (1) 



is the velocity corresponding to pressure p ; 



pressure and density in the discharging vessel 

 where q = Q ; c the velocity of sound in the gas when at 

 pressure p and density p ; c that corresponding to p , p . 

 According to (1) the velocity increases as p diminishes, but 

 only up to a maximum, equal to c Q ^/{2/(y — l)}, when p = 0. 



* Communicated by the Author. 



f " Memoire et experiences sur l'ecoulement de l'air, determine par 

 des differences de pressions considerables," Joum. de TEcole Polyt. t. xvi. 

 p. 85 (1839). 



X 'Hydrodynamics,' §§ 28, 25 (1916). 



Phil. Mag. S. 6. Vol. 32. No. 188. Aug. 1916. N 



