Note on the shearing motion of fluid past a projection

Abstract

1. A method has lately been developed by N. Muschelišvili (1) for the solution of problems of the slow two-dimensional motion of viscous liquid and of the corresponding problems of plane stress and plane strain, in cases in which the area in the x, y-plane that is concerned can be represented conformally on the interior of the circle |ζ| = 1 in the ζ-plane by a relation of the form z = x + iy = r(ζ), where r(ζ) is a rational function of ζ. In most problems in which the method has been used the function r(ζ) has been a simple one, but it is of importance to consider a rational function of as general a form as possible since, given any relation z = f(ζ), it will usually be possible to find a rational function that approximates to f(ζ) throughout the circle |ζ| = 1 and for a close approximation a complicated function r(ζ) will in general be required.