Compressible Flows Obtainable From Two-Dimensional Flows Through the Addition of a Constant Normal Velocity

This paper demonstrates that exact solutions of the flow of compressible fluids can be obtained by starting with two-dimensional steady-state flows and superposing upon them a velocity of constant magnitude and direction at right angles to the planes of the two-dimensional flows, while at the same time, the pressure, density, and temperature of the fluid at each point are unchanged. The procedure is demonstrated by several examples, one of which is of interest in connection with the discharge of exhaust gases from a gas engine through the tail cone and tail pipe in cases where the circulation has not been completely removed from the flow. Another example is the flow around a “sweepback” or “arrow” wing. This example is illustrated for supersonic flows on plane oblique shocks and on the Meyer-Prandtl expansion around an edge.