The laminar boundary-layer equations of bodies of revolution. Motion of a sphere

Abstract

In a previous paper (Meksyn 1948) the author gave a method of calculating the velocity distribution in a laminar boundary layer on cylindrical bodies. The aim of the present paper is to extend the method to the case of laminar boundary layers on bodies of revolution. The problem has been treated, so far, only in a few papers (Goldstein 1938, §§51, 52, 61). Millikan (1932) has derived boundary-layer equations and Kármán’s momentum equation for bodies of revolution, and, assuming a parabolic distribution for the velocity u in the laminar part, and u ~ y 1/η in the turbulent part (where y is the distance from the surface), he has applied the momentum equation to airship-line bodies. Fediaersky (1934) derived independently the momentum equation for bodies of revolution and applied it to airship-like bodies by assuming u ~ u n , where n is arbitrary. Tomotika (1935) applied the momentum equation to the evaluation of various boundary-layer quantities for bodies of revolution, in particular for a sphere. Fage (1936) used Tomotika’s results to evaluate the surface friction at the forward part of a sphere. In the present paper the general boundary-layer equations are derived for axially symmetrical motions of bodies of revolution; the equations are partially solved for a sphere, and the results compared with Fage’s (1936) measurements.