Question

The incorrect relation for properties associated with the flow, for a point in the flow where the speed of sound is a, is_______

(a) \(\frac {\gamma +1}{2(\gamma -1)}\) a^*2=\(\frac {a_0^2}{\gamma -1}\)≠const

(b) \(\frac {\gamma +1}{2(\gamma -1)}\) a^*2=const

(c) \(\frac {a_0^2}{\gamma -1}\)=const

(d) \(\frac {\gamma +1}{2(\gamma -1)}\) a^*2=\(\frac {a_0^2}{\gamma -1}\)=const

This question was posed to me in my homework.

This interesting question is from The Basic Normal Shock Equations topic in portion Normal Shock Waves of Aerodynamics

Answer 1

Correct option is (a) \(\frac {\gamma +1}{2(\gamma -1)}\) a^*2=\(\frac {a_0^2}{\gamma -1}\)≠const

The best explanation: The two properties, a* and a0, of the flow are related to each other by the relation: \(\frac {\gamma +1}{2(\gamma -1)}\) a^*2=\(\frac {a_0^2}{\gamma -1}\). These two (a* and a0) are defined quantities and are constant at a point in the flow. Thus, the correct relation is \(\frac {\gamma +1}{2(\gamma -1)}\) a^*2=\(\frac {a_0^2}{\gamma -1}\)=const, since gamma is also a constant.