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

The incorrect relation for properties associated with the flow, for a

1.	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=\(\frac {a_0^2}{\gamma -1}\)=constThis 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» 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.

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