Question

What is the Riemann invariant for C+ characteristic line?

(a) J+ = u + ∫\(\frac {dp}{ρa}\) = constant

(b) J+ = u – ∫\(\frac {dp}{ρa}\) = constant

(c) J+ = u + \(\frac {dp}{ρa}\)

(d) J+ = u – \(\frac {dp}{ρa}\)

I had been asked this question during a job interview.

This interesting question is from Finite Waves in portion Unsteady Wave Motion of Aerodynamics

Answer 1

The correct choice is (a) J+ = u + ∫\(\frac {dp}{ρa}\) = constant

Explanation: Riemann invariant for a compatibility equation of the C+ characteristic line is obtained by integrating the compatibility equation.

The compatibility equation along C+ characteristic line is given by:

du + \(\frac {dp}{ρa}\) = 0

On integrating the above equation, we get:

J+ = u + ∫\(\frac {dp}{ρa}\) = constant

Where, J+ is the Riemann invariant