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If you take an infinitely thin sheet of metal and stick it out of the window of an airplane at exactly 0 AOA, will the surfaces of it become low pressure if you speed up? In a wind tunnel, there is the fan making high pressure (which converts to lower pressure because of the faster moving air as you go down the tunnel, I think). In real flight, there is no fan or anything to make pressure differences around the plane that I'm aware of, like there is in a wind tunnel. Why are flows in a wind tunnel basically the same as real flight in that case?

Another way to ask this. From the perspective of the ground to a plane flying, no air is moving that fast so Bernoulli wouldn't work, right? If you could see air molecules, they wouldn't be moving that much compared to you on the ground. (besides downwash and other obvious effects)

This also might help : If you're going faster density decreases. From the perspective of the ground to the airplane, the same amount of air molecules are colliding and interacting with the plane, as if you were moving slower. Why would density decrease around a plane in that case, at high speed? (ignoring the fact that as you go faster air molecules will bunch up and make higher density air)

This question might seem all over the place, but it was really hard to explain.

Last thing that I just thought of : Bernoulli works by ‘stretching’ out air by using low pressure (making the air move faster in the process). In a wind tunnel, the fan does that. In real flight, there is no such function?

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    $\begingroup$ Bernoulli's theorem only compares the energy of the same flow at different speeds and elevations. There is no "absolute" Bernoulli value, it is all relative. Like with energy itself. $\endgroup$ Jan 27 at 10:45

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Your questions follow a common theme. You tend to use your intuition to try to work through the questions -- but without the required math and rigor. Intuition can give guidance, but it can also easily mislead. You tend to over-complicate things when you're trying to simplify them.

In this case, comparing a 'real' flow perspective to a wind tunnel perspective, is simply a matter of a reference frame transformation. You should look into Eulerian vs. Lagrangian frames. The equivalence of these perspectives is developed for all Newtonian physics -- whether it is fluid mechanics, or a car driving down the road.

In particular, this idea works for wind tunnels of all speeds -- from incompressible (nearly Mach zero) to hypersonic. This tells us that variation of density does not matter (as the density is constant in an incompressible flow). So you don't need to consider any ideas about density change when thinking about changes in frames of reference.

Furthermore, almost all flows of interest for aircraft can be considered continuum -- i.e. we do not treat the flow as a bunch of particles bouncing off of one another. Instead, we treat the flow as a continuous medium.

The exception occurs in the very upper reaches of the atmosphere as you reach the edge of space. There, you transition from a continuum flow to free molecular flow (where everything is based on particle collisions). This idea is expressed by the Knudsen number $Kn=\lambda/L$. It is the ratio of the mean free path $\lambda$ (the average distance a particle travels before colliding with something) to $L$ the characteristic length scale of the object in the flow. When $Kn<0.01$, you have a continuum flow. The mean free path at sea level conditions is less than 70 nm=$70x10^{-9}$m. A 1mm gnat is about 150,000 times too big to be worried about non-continuum effects.

Engineers use particle collision theory to derive the perfect gas equation of state $P=\rho\,R\,T$ (and a few other things), but then we leave it behind and just take the equation of state with us.

Stop thinking about particle collisions and density changes (in incompressible flows). They aren't significant to the answers you seek and are just getting you wrapped around the axle.

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If you take an infinitely thin sheet of metal and stick it out of the window of an airplane at exactly 0 AOA, will the surfaces of it become low pressure if you speed up?

No.

In that condition the speed is exactly the same on the whole surface of the thin plate (apart in the boundary layer that we can disregard) so there's no change of pressure either. As soon as the AoA changes then the airflow on the surface of the plate experiences local changes in speed and in pressure, changes which are quite well described by the Bernoulli's equation.

In real flight, there is no fan or anything to make pressure differences around the plane

As just said, if the plate is at 0° AoA then the pressure difference around the plate is always 0, full stop. It doesn't matter if the plate at 0° is moving in low pressure air, high pressure air, in a wind tunnel, in water, in lava, in the airflow of an air dryer or in the martian atmosphere: pressure and speed around a flat plate at 0° AoA is constant, it doesn't change, and the relevant aerodynamic force is zero as well.

Bernoulli works by ‘stretching’ out air by using low pressure

Bernoulli is just an equation that, within its limitations, describes how reality works. In particular, it just mathematically translates the fact that if a body immersed in a fluid makes the fluid change its speed locally around the body, then also pressure changes locally, inversely proportional to the square of the speed's change.

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