Lift and airfoils in 2D
common misconceptions and basic explanation
Bernoulli's equation is derived from the momentum equation, assuming an incompressible, steady, inviscid flow with no body forces.
Even at Mach 0.15, the density variations near the leading edge exceed ±5%, which is the limit for assuming incompressible flow.
There’s though a small region close to the airfoil surface where the influence of friction, thermal conduction, and diffusion is important: the boundary layer.
Flows at high Reynolds numbers can be considered inviscid for most practical purposes.
Forces due to gravity, electric fields and magnetic fields are usually negligible. In the case we are most interested in, which is gravity, the difference in height is so small that the variation in potential energy is inconsequential.
Equal transit times
But actually, the fluid parcels over the airfoil are accelerated and reach the trailing edge faster.
This explanation suggests that fluid parcels have to meet up again at the trailing edge.
The curvature is an obstacle in the passage of the fluid that the fluid avoids by pinching a streamtube.
The issue with this explanation is that is does not really explain how the pinching occurs, nor why it is grater over the upper surface than over the lower surface.
The pressure, even near the absolute vacuum, always points in the direction of the wall; therefore, it would be more correct to say that lift is produced by the push that the air exerts in the lower part of the airfoil, and that the upper surface contributes by pushing, not so much, in the opposite direction.
A proper explanation of lift should not treat the velocity field and the pressure field separately. The cause-and-effect relationship is reciprocal; thus, an explanation based on downward turning alone or on Bernoulli alone would be incomplete.