THE 

 LONDON, EDINBURGH, and DUBLIN 



PHILOSOPHICAL MAGAZINE 



AND 



JOURNAL OF SCIENCE. 



[SIXTH SERIES.] 



| 



JUL Y 1916. 



I. On the Flow of Compressible Fluid past an Obstacle. 

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



IT is well known that according to classical Hydro- 

 dynamics a steady stream of frictionless incompressible 

 fluid exercises no resultant force upon an obstacle, such as 

 a rigid sphere, immersed in it. The development of a 

 " resistance " is usually attributed to viscosity, or when 

 there is a sharp edge to the negative pressure which may 

 accompany it (Helmholtz). In either case it would seem 

 that resistance involves something of the nature of a wake, 

 extending behind the obstacle to an infinite distance. When 

 the system of disturbed velocities, although it may mathe- 

 matically extend to infinity, remains as it were attached to 

 the obstacle, there can be no resistance. 



The absence of resistance is asserted for an incompressible 

 fluid ; but it can hardly be supposed that a small degree of 

 compressibility, as in water, would atf'ect the conclusion. 

 On the other hand, high relative velocities, exceeding that 

 of sound in the fluid, must entirely alter the conditions. It 

 seems worth while to examine this question more closely, 

 especially as the first effects of compressibility are amenable 

 to mathematical treatment. 



The equation of continuity for a compressible fluid in 



* Communicated by the Author. 



Phil. Mag. S. 6. Vol. 32. No. 187. July 1916. B 



