On the shearing motion of fluid past a projection

Abstract

1. In this paper, a continuation of an earlier paper(1), we consider the two-dimensional motion of incompressible viscous liquid past a projection, the motion being one of uniform shear apart from the disturbance caused by the projection. A special form is assumed for the boundary, so that the area in the z-plane (Fig. 1) can be represented conformally on a circle in the ζ-plane by a rational function of ζ; this function contains a parameter a (0 < a ≤ 1), and by varying a the shape of the projection can be varied. Since a rational function is concerned in the conformal transformation a method lately developed by N. Muschelišvili(2) can be used in solving the biharmonic equation for the stream function, though the method actually used differs in some points of detail from that originally proposed by Muschelišvili and appears to be somewhat simpler.