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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»

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



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