# Why does a fluid follow the wing?

When air is moving above and under a wing that is curved, why does the air at the top of the wing follow the wings shape and go downwards when it could just go in a straight line? It doesn't make sense to me.

• If it went in a straight line, wouldn't there be a vacuum underneath it? Aug 12, 2021 at 10:56

The air above the wing is accelerated down towards the wing by the air pressure from the air further above

When a wing flows through air, if the air strikes the the top surface of the wing, and then moves off in a straight line, there would be lower pressure on the top surface of the wing. For this not to happen, the wind must flow around the surface of the wing.

You can also think about it as if the air above the wing has higher pressure than the air just on its surface due to the motion of the air, and so it gets pushed down onto the wing.

When air flows over a wing (or more generally, when any fluid flows over a solid surface), viscosity tends to make the air stick to the surface and creates a region of sheared flow (the boundary layer) where the speed varies between zero at the surface and a larger value farther out in the flow. Assuming sufficiently large Reynolds numbers, the boundary layer is thin and its effects on the surrounding flow can be modelled by distributed vorticity on the wing's surface.

Because of the vorticity, the previously uniform flow (before encountering the wing) is modified, typically producing low-pressure regions forward on the upper surface and adverse pressure gradients farther aft as the flow approaches the trailing edge, where it has to match the pressure from the lower surface.

For sufficiently streamlined cases and mild enough flow conditions (i.e. large enough Reynolds numbers and small enough lift coefficients), the inertia of the flow is enough to allow the flow to overpower the adverse pressure gradients and continue to the trailing edge without separating from the surface.

A similar process is responsible for the so-called Coanda effect, in which a jet passing over a flap is deflected downward so it contributes to the lift as well as the thrust.

In summary: the viscosity of the flow is what allows it to follow the wing's surface. Without viscosity, airfoils would have no lift or drag (in 2D, at least).

• The point of the boundary layer is only the assumption that the velocity of the surface matches the velocity of gas at the surface. It only “sticks” in the direction of the surface’s velocity, which is all viscosity can do because it only provides force in response to velocity. Viscosity does not provide any forces or sticking power in a direction perpendicular to the surface. So it doesn’t explain at all what makes the gas go to the surface against the gas’ momentum, which is the question. In particular there is no surface region of higher concentration. Aug 16, 2021 at 14:16
• @Al Brown The boundary layer is directly responsible for creating the vorticity that perturbs the flow and allows it to follow the surface of the wing. Aug 16, 2021 at 14:19
• @Al Brown Sorry, but that's just wrong. The link you give seems to be someone's personal opinion. Aug 16, 2021 at 14:52
• @Al Brown Molecules colliding with the surface just means there is pressure. None of the theories dispute that. Aug 16, 2021 at 15:15
• @Al Brown I'm getting messages about avoiding extended discussions in comments, so I'm through commenting for now. Aug 16, 2021 at 21:34

The air can respond quickly enough to the pressure difference and achieve equilibrium because the molecules are so numerous (trillions of them in even a billionth of a cc) and moving so fast (average particle speed of “still” room air is over 1,000 mph).

So any empty space will be immediately filled until that space is pushing back with enough pressure to keep the inflow and outflow of molecules balanced.

In short, it’s pressure equalization that makes the final amount of gas in the space, but it’s the particle energy and small size that can make it happen fast enough to fill the backside of a wing even though momentum doesn’t seem to be pushing any air in that direction