THE UNSTEADY, SUBSONIC MOTION OF A SPHERE IN A COMPRESSIBLE INVISCID FLUID

Abstract

In this paper we investigate the effect of compressibility on the work required to accelerate a rigid sphere, immersed in a fluid, from rest to a final uniform velocity. Viscosity is neglected, but it is shown that for the accelerations for which compressibility is important, the additional work (which is used in sending out sound, waves) is all done before the boundary layer separates from the rear of the sphere. The work done on the fluid is increased twofold as a result of compressibility in the limiting case of infinite acceleration, but by a smaller factor for a finite acceleration. These results apply when the Mach number is low; there is some discussion of how they are affected by increase of Mach number.