A mechanical method for solving problems of flow in compressible fluids

Abstract

At the present time the chief study of aerodynamical laboratories is concerned with the steady flow of air past solid bodies at speeds which are so low that the effect of compressibility is inappreciable. In recent years, however, the rapid increase in the speed of aircraft has very much increased the importance of the study of the effect of compressibility on air flow. The highest speeds of aircraft at the present time are of the order of 280 miles per hour or 400 feet per second, i. e ., 0.4 of the speed of sound. The tips of the propellers of these high speed machines may move at speeds as high as 1.3 times the speed of sound. At low speeds when air behaves like an incompressible fluid, the classical theory of hydrodynamics which is concerned with irrotational motion predicts that a body moving steadily will experience no resistance or lift. In the simpler form of the theory of Prandtl the motion is still irrotational, but the existence of a circulation round the body and of vortex sheets trailing down-wind permit the possibility of resistance and lift. At speeds higher than that of sound it is known that a nearly discontinuous wave is formed in front of the body. This wave has been photographed and has been studied theoretically by many writers. It involves a dissipation of energy so that even on the classical theory which involves no viscosity, bodies moving at speeds higher than that of sound should have a resistance.