I am doing a project on Bernoulli's principal for my High School physics course. I made an airfoil in accordance with NACA 2412 (same as a C-152).

I am going to put it in a wind tunnel where the wind speed is going to be measured. How can I find the wind speed on top of and on the bottom of the airfoil, once I know what the outside wind speed (or velocity of the airfoil) is?

My end goal is to find the pressure differences on the outside of the wing, and I can do that very easily once I know the speed on each side of the airfoil.


The problem here is that measuring velocity is really very difficult. It needs to be measured slightly above the surface (because the velocity at the surface is zero due to viscosity, so you need to get above the boundary layer edge) but you don't want to introduce a physical probe to measure that because then you are disrupting the very flow you want to measure!

There are less invasive techniques that involve putting small seed particles in the flow and hitting them with lasers (Laser Doppler Velocimetry for one). But unless you have tens of thousands of dollars to spend on such a system, that's not really going to work either.

So you have to go back to basics. Pressure differences create velocity, not the other way around. And it turns out, pressure is very easy to measure without being invasive, and comparatively inexpensive.

Since the flow is low speed (I assume), you know that the stagnation pressure is (approximately) constant. This means if you know the pressure in the flow at rest, you can find the velocity of the flow in motion simply by measuring it's static pressure. You know this because (Bernoulli's Principle):

$P_0 = P_{static} + \frac{1}{2}\rho V^2$

where $P_0$ is the stagnation pressure and $P_{static}$ is what you measure if you were to put a pressure probe with the opening perpendicular to the flow. In other words, you drill a small hole in the surface of the body and hook up a pressure sensor to the hole. Since you know $P_0$ and you measure $P_{static}$, you will be able to calculate the velocity.

I won't get into the details of it, but the pressure normal to the surface is a constant. In other words, unlike velocity, the pressure you measure at the surface is the same as the pressure you measure at the edge of the boundary layer. This is how you can measure non-invasively.

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