Buckingham's Pi theorem on Supersonic wave drag

In summary, the conversation is about a problem involving shockwaves on a vehicle in supersonic flight and the component of drag it causes called supersonic wave drag. The problem also involves using Buckingham's Pi theorem and the specific heats at constant pressure and volume to determine the wave-drag coefficient. The individuals involved are struggling with understanding how to use the theorem and what the problem is asking for. They also wonder why the problem includes information about thermodynamic properties. One person asks for help with solving the problem.
  • #1
FOBoi1122
4
0
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.
 
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  • #2
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
 
  • #3
Are you confused as to what exactly Buckingham Pi is, or what the question is asking?
 

1. What is Buckingham's Pi theorem on Supersonic wave drag?

Buckingham's Pi theorem is a mathematical tool used to determine the dimensionless groups and scaling laws that govern a physical system. In the context of supersonic wave drag, it can be used to predict the amount of drag experienced by an object traveling at supersonic speeds.

2. How does Buckingham's Pi theorem apply to supersonic wave drag?

In the case of supersonic wave drag, Buckingham's Pi theorem can be used to determine the dimensionless groups that affect the drag force. These groups include the Mach number, Reynolds number, and angle of attack, among others. By analyzing these dimensionless groups, we can better understand and predict the behavior of supersonic wave drag.

3. Can Buckingham's Pi theorem be used to design supersonic aircraft?

Yes, Buckingham's Pi theorem can be a useful tool in the design of supersonic aircraft. By using this theorem to analyze the dimensionless groups that affect supersonic wave drag, engineers can make more informed decisions when designing aircraft that will travel at supersonic speeds.

4. What are some limitations of Buckingham's Pi theorem in relation to supersonic wave drag?

One limitation of Buckingham's Pi theorem is that it assumes a linear relationship between the variables being analyzed. In the case of supersonic wave drag, this may not always be the case, as the drag force can change significantly depending on the angle of attack and other factors. Additionally, the theorem may not take into account other factors that affect supersonic wave drag, such as shock waves and boundary layer interactions.

5. How can Buckingham's Pi theorem be applied to other areas of supersonic research?

Buckingham's Pi theorem can be applied to other areas of supersonic research, such as supersonic combustion, shock wave/boundary layer interactions, and supersonic wind tunnel design. By using this theorem, researchers can gain a better understanding of the underlying principles and scaling laws that govern these phenomena, leading to more efficient and effective designs and experiments.

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