Question

What is the slope of the right running wave characteristic equation?

(a) u + a

(b) u – a

(c) 2u

(d) 2a

This question was addressed to me in unit test.

Origin of the question is Philosophy of Method of Characteristics in division Numerical Techniques for Steady Supersonic Flow of Aerodynamics

Answer 1

Right option is (a) u + a

To explain I would say: The right running wave has a characteristic line as C+ which has a positive slope. It’s slope is given by \(\frac {dy}{dx}\) = u + a, where a is the local speed of sound which is equal to \(\sqrt {γRT}\). Its compatibility equation is given by du + \(\frac {dp}{ρa}\) = 0.