Two dimensional viscous flow of a compressible fluid

The Navier-Stokes equations for the two dimensional steady motion of a viscous compressible fluid are transformed to a system of equations in which the stream function is one of the two independent coordinates while the second coordinate is arbitrary. Vorticity, speed, density, pressure and the velocity gradient are the unknown functions of the equations. Three systems of equations are developed, all of them underdeveloped. The equations are applied to flows with pre-assigned forms and it is shown that if the stream lines are straight lines, they must be either parallel or concurrent and if the stream lines are involutes of a curve, then they must be concentric circles.