Chapter 1, Problem 1.8P

The shock waves on a vehicle in supersonic flight cause a component of drag called supersonic wave drag $D_w$. Define the wave-drag coefficient as $C_{D,w}=D_w/q\infty S$, where S is a suitable reference area for the body. In supersonic flight, the flow is governed in part by its thermodynamic properties, given by the specific heats at constant pressure $c_p$ and at constant volume $c_v$. Define the ratio $c_p/c_v\equiv \gamma$. Using Buckingham’s pi theorem, show that $C_{D,w}=f\left(M\infty ,\gamma \right)$. Neglect the influence of friction.