Some geometrical properties of plane flows

Abstract

The geometrical configuration consisting of five straight lines tangent to the stream line (ψ = const.), isobar (p = const.), isocline (θ = const.), isovel (q = const.) and isopycnic (ρ = const.) at a point P of the physical plane in the plane flow of a fluid has a number of interesting properties. The study of this geometric configuration for a wide class of ideal fluids (which includes polytropic gases and incompressible fluids), in particular its properties at sonic points, is the purpose of this paper.