Buckingham's Pi theorem on Supersonic wave drag

[FOBoi1122]

Hi all,

I am working on aerodyanmics homework, and I've been stuck on this problem for a while.

"The shockwaves on a vehicle in supersonic flight cause a component of drag called supersonic wave drag Dw. Defined the wave-drag coefficient as Cdw = Dw/(qS), 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 cp at constant volume cv. Define the ratio cp/cv = gamma. Using Buckingham's pi theorem, show that Cdw = f(M, gamma). Neglect influence of friction."

Since i recently learned the theorem, I'm not completely proficcient at using it. I assumed that the problem would be a function of f(Dw, rho (denisity), V (velocity), and S (area)), but when i try that, i don't get the right answer. Also does anyone know why the problem gives this part: "In supersonic flight, the flow is governed in part by its thermodynamic properties, given by the specific heats at constant pressure cp at constant volume cv. Define the ratio cp/cv = gamma. "?

Thanks for your help.

 

[ziaf004]

hey, now I'm having the exact same problem. I bet u figured out how to do it by now right?

Do u mind sharing? Please lol

 

[rocketscience08]

Are you confused as to what exactly Buckingham Pi is, or what the question is asking?