Note on a Generalised Velocity Parameter in Two-Dimensional Fluid Dynamics

Extract

The purpose of this note is to draw a formal parallel between the fundamental hodograph flow equations in subsonic and supersonic regimes when expressed in terms of a generalised velocity parameter. This parameter can cover, by simple algebraic extension, hodograph flows in either regime; it has simple geometrical and dynamical interpretations and models of the combined hodograph plans in terms of this parameter are also suggested.

A similar, and perhaps familiar, velocity parameter appears to have been first used in the solution of certain subsonic flow problems by Tsien, following a suggestion of von Kármán, although a more general and basic form was not described.