# Behavior of air over a wing [duplicate]

Venturi´s effect states that air over the wing accelerates and static pressure drops. There's a different theory which states that as air is viscous, once it impacts the wing, slows down... Can those two theories coexist?

• Yeah, air behaves very differently at sub and supersonic speeds. – SMS von der Tann Oct 16 '16 at 21:36
• Venturi effect is not actually applicable to a wing. It works with pipes. But Bernoulli's principle still applies. – mins Oct 17 '16 at 10:57

Yes. In different regions.

A fluid flowing through a constricted section of a tube undergoes a decrease in pressure, which is known as the Venturi effect. This is a consequence of Bernoulli's principle, which says that total pressure is constant. Basically,

$P_{1} - P{2} = \frac{\rho}{2} (v_{2}^{2} - v_{1}^{2})$

along a streamline. But here's the catch- it is applicable only for steady, inviscid, incompressible flows. This condition is satisfied when the flow speed is small (subsonic) and at a certain distance from the body (i.e. wing) and can be used to calculate the velocity or pressure fields at some distance from it.

However, in real world, the fluid (i.e. air) is viscous, though its effects are restricted to a certain region immediately near the body, as seen below:

By F l a n k e r - Own work, CC BY-SA 3.0, Link

You can see that in the immediate region of the immersed body, the fluid is slowed down- there is a velocity gradient between the different layers of the fluid as they are being slowed down. However, after some distance from the body, the fluid behaves as if it is inviscid- there is no velocity gradient.

In the end, we choose the situation that is more useful for us- in case of subsonic flow, for calculating lift etc. the flow can safely be assumed as inviscid, while the boundary layer is very important when we consider cases like heat transfer etc. There is nothing right or wrong here (the air follows the same laws, wherever it is)- it is simply the case of using the theory that makes more sense for easier understanding and computation.