A wrong --but simple to understand-- theory for lift states:
Air molecules that were close before being separated at the leading edge must be close again after they join back at the trailing edge. For this to happen, molecules must travel the two paths in the same time.
As the path is longer on the upper side, due to the camber of the wing, air is accelerated on the upper side. By Bernoulli's equation, static pressure decreases when velocity increases, so the pressure is lower on the upper side, and higher on the lower side.
Lift is the force created by this pressure differential on the wing sides.
(What is wrong is not Bernoulli's equation, but the assumed relationship between path length and speed.)
Such theory is, for instance, presented as correct in this book.
More at Nasa.
We know this theory is wrong and lift created by path length difference would be a very small percentage of the lift actually measured (and even null for symmetrical airfoils).
Let's assume a rectangular wing with a simple cambered airfoil, at the critical angle of attack:
- What would be the pressure differential according to equal transit time difference? What percentage of actual lift does it represent?