Determine Local Velocity at Cp Point: Incompressible Cp=-0.18

[physicsCU]

Quick question from my last aero test

We are given an incompressible Cp of -0.18, the freestream V and the altitude. The question is to determine the local velocity at the Cp point.

The flow is compressible.

Can I simply do -0.18 = 1 - (VL/V0)^2 and solve VL?

Or do I need the Prandtl-Glaubert approximation of Cp = Cp_incompressible/Sqrt(1-M0^2) ?

I did it without using prandtl, but I don't know if that is ok or not. I can't seem to get a clear answer from the prof and solutions haven't been posted.

Thanks all!

 

[Navin A S]

Yes, you can simply do -0.18 = 1 - (VL/V0)^2 and solve VL. This is the correct way to determine the local velocity at the Cp point. The Prandtl-Glaubert approximation is not necessary in this case.

 

[ravenprp]

It is important to use the correct formula to determine the local velocity at the Cp point in order to get an accurate answer. In this case, since the flow is compressible, you should use the Prandtl-Glauert approximation of Cp = Cp_incompressible/Sqrt(1-M0^2). This formula takes into account the compressibility effects of the flow. Using the incorrect formula could lead to an inaccurate result. It is always best to double check with your professor or reference materials to make sure you are using the correct formula for the given scenario.