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The Bernoulli Principle describes the relation of a fluid speed to its pressure. Air, being a fluid, experiences this same correlation and because such, the Bernoulli Principle has often been misrepresented as what causes the lifting affect on an airplane wing.

In reality, the Bernoulli Principle has negligible affect on an airplane's wing, generating lift or otherwise. I'll qualify this as being below mach speeds.

The common explanations are:
1. Air has farther to travel across the top than across the bottom of the wing, so it goes faster, which generates lower pressure, relative to the bottom. The difference in pressures produces the force known as lift.
2. A cutaway of an airfoil is compared to the cutaway of a venturi. Because the Bernoulli Principle explains the lower pressure at the greatest restriction, say in a carburetor, that similar shapes mean the airfoil works the same way.

Both explanations are flawed.

Ex.1 - Air does not travel faster over the top of a wing. This misconception was probably someone thinking that two air molecules need to come back together at the tail end, but they don't. This is what generates the vortex behind the wing.
Ex.2 - A pure stretch of the imagination. Similar in shape, but not environment. The venturi encircles the air flow, the airfoil does not. This changes how the air reacts to these different surfaces. Air above the wing actually has to compress to get out the way of the wing. The faster the wing speed, the greater the compression.

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