On the Flow of a Compressible Fluid past a Circular Cylinder, II

Abstract

§10. In continuation of a previous paper the third approximation of JANZEN-PAYLEIGH method is carried out for the irrotational flow of a compressible fluid past a circular cylinder. Formulae correct to the order of M⁶ are thus obtained for the velocity potential and for the velocity distributions on the surface of the cylinder as well as on the radial line perpendicular to the direction of the undisturbed stream. As in the previous paper, theoretical velocity distribution for the latter is compared with TAYLOR'S experiments. It is seen that the agreement is somewhat improved. Next, taking air as the fluid, values of the critical MACH number are given for each successive stage of approximation and the true value is estimated to bye 0.4. Further, the accuracy of the PRANDTL-GLAUERT'S linear theory (JACOBS' formula) and TSIEN'S hodograph method is discussed with reference to the critical MACH number. Lastly, an asymptotic expression for the velocity potential at a great distauce from a cylindrical body of arbitrary cross-section is given, in case when there is no circulation round the body, which seems to provide some evidence for the correctness of the formulae obtained in this paper