On intrinsic properties of steady gas flows

Summary

Considering the geometric theory of triply orthogonal spatial curves, the basic equations governing a steady gas flow are transformed into the intrinsic form and the results obtained are:

(1) The pressure is uniform along the binormal to the stream line and the radius of curvature varies as the square of the velocity along it, for the baratropic fluids.

(2) Acceleration is irrotational field when the fluid is compressible but baratropic or incompressible, in which case the relations existing between the flow quantities, curvature and torsions of the curves under consideration are obtained.

(3) Considering incompressible flows, it is observed that either velocity in magnitude is uniform or the vorticity lies in the normal plane, in which case the stream lines are orthogonal to the vortex lines.

Stream lines are observed to be either right circular helices or circles or straight lines.

If the stream lines are not straight then the torsions of the binormal congruences and stream lines are equal.

(4) The compatibility conditions of Berker¹) are transformed into intrinsic form, involving the curvatures and torsions of the above curves.