I recently read this from Wikipedia in an article discussing lift.

A fluid flowing over the surface of a body exerts a force on it. It makes no difference whether the fluid is flowing past a stationary body or the body is moving through a stationary volume of fluid.

Can someone elaborate on this specifically in the case of a wing moving through air. I understand with a moving fluid like in an air tunnel but not when the object moves through a fluid.

  • $\begingroup$ As an intuitive sort of way to think about it, think about your frame of reference - if you picture an airplane flying, the air appears still and the airplane moving through it. On the other hand, if you imagine the air moving, the airplane appears still. (Sort of like if you're in the car and imagine you aren't moving but your surroundings are.) With a change of frame of reference, the situation appears the same. $\endgroup$ – heather Dec 31 '17 at 0:20

They are saying a wing moving through the stationary air is the equivalent of air moving around a stationary wing in a wind tunnel.

A wing moving through stationary air would be like in the case of planes for example. That is why we can test a plane wing design in a wind tunnel for instance.

It would also apply to any object moving through a fluid. It is saying that the situation is the equivalent to the fluid moving around the object.

What it boils down to is, fluid flows only care about relative movement. Wind blowing past a wing at $25 \ \frac ms$ is the same as that wing moving $25 \ \frac ms$ through stationary air; as far as the fluid dynamics are concerned.


I'll introduce an idea called reference frames. In a nutshell, reference frames are where you fix your head on when making observations. (Sticking a camera would be easier to imagine.)

1st scenario where the air flows across a stationary wing. Imagine sticking a camera on the wing itself. You'll see that the wing is not moving while air particles fly over it.

2nd scenario where the wing moves in stationary air. Stick the camera on the wing again and you'll see the exact same thing. Air particles fly over the wing. The two situations are also the same when you stick the camera on the moving air; you'll see the wing slide past while the air doesn't move. (Unless it's disturbed by the wing, but you get my idea.)

What conclusion can you draw from this? With only air particles and the wing, there is no way to tell if it's the air moving or the wing is moving. This means that any force exerted in one of the scenarios will exist and will be exactly the same in the other scenario.


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