Two-dimensional irrotational mixed subsonic and supersonic flow of a compressible fluid and the upper critical Mach number

The problem of flow of a compressible fluid past a body with subsonic flow at infinite is formulated by the hodograph method. The solution in the hodograph plane is first constructed about the origin by superposition of the particular integrals of the transformed equations of motion with a set of constants which would determine, in the limiting case, a known incompressible flow. This solution is then extended outside the circle of convergence by analytic continuation.