ON A FUNCTION-THEORY METHOD FOR OBTAINING POTENTIAL-FLOW PATTERNS OF A COMPRESSIBLE FLUID

摘要

A scheme for obtaining exact potential-flow patterns in a compressible fluid is presented. The method is based on a complex-function theory developed recently for the solutions of the simultaneous first-order partial differential equations in the hodograph variables. The procedure suggested is to take a given incompressible-flow pattern given by an analytic function and to replace this function by an associated complex function, a solution of the compressible-flow equations, which will represent an associated compressible-flow pattern. This method formally solves the problem for obtaining an exact flow past a body in a compressible fluid;however, before such general flow patterns can be obtained, the new complex functions involved must first be studied and tabulated.