Question

Which of these is the compatibility equation along C+ characteristic line?

(a) du + \(\frac {dp}{ρa}\) = 0

(b) du – \(\frac {dp}{ρa}\) = 0

(c) \(\frac {dpu}{ρa}\) = 0

(d) \(\frac {du}{ρa}\) = 0

This question was posed to me in my homework.

My question is from Finite Waves in division Unsteady Wave Motion of Aerodynamics

Answer 1

Right choice is (a) du + \(\frac {dp}{ρa}\) = 0

Best explanation: C+ characteristic line is the path along which the governing partial equation can be reduced to the ordinary differential equation. The compatibility equation along C+ line is:

du + \(\frac {dp}{ρa}\) = 0

The compatibility equation along C– line is:

du – \(\frac {dp}{ρa}\) = 0