A new derivation of the method of characteristics for axially symmetrical supersonic flow
is a differential equation [Eq. (17) of this paper] expressing the change in the magnitude and the direction of the velocity vector along a Mach wave. The purpose of this note is to give a simple derivation of this equation. Two-dimensional flows and irrotational flows can be obtained by specializing Eq. (17). 1. Bernoulli's equation. If V denotes the velocity, p the pressure, p the density, and 5 the arc length of the stream line, Bernoulli's equation can be written in the form