The solution of boundary value problems for a general hodograph equation
A. G. Mackie · Mathematical Proceedings of the Cambridge Philosophical Society · 1958
ABSTRACT In this paper the solution is found of certain boundary value problems appropriate to the flow of an invisoid, compressible fluid past a wedge-shaped profile. The most general hodograph equation in the form is used. Expressions are found for the position coordinates and the drag. The resulting solutions are then discussed for functions k(σ) appropriate to Chaplygin's equation, Tricomi's equation and the equation of Tomotika and Tamada. The case of Helmholtz flow past a wedge with sonic velocity upstream is treated in detail, and the resulting expressions for the drag enable an estimate to be made of the error which results in using approximations to Chaplygin's equation.