The intrinsic geometrical and physical properties of plane steady gas flow

The main purpose of the present paper is to establish a relation between the intrinsic geometrical and physical properties of plane steady gas flow, i.e., between the geometry of the flow pattern on one side and the flow variables on the other. This is accomplished by complete integration of the governing fluid dynamics equations in an a priori unknown system of curvilinear coordinates. The complete solution is presented by explicit expressions for the metric tensor components associated with the curvilinear system in terms of the flow Mach number and the Bernoulli constant along the streamlines. Several examples including subsonic, sonic, supersonic, rotational, and irrotational flow are discussed to illuminate the special technique and its potential for determining flow patterns that result from particular geometrical and/or physical specifications.