The theory under consideration is often called as 'Equal Transit' theory. It is true that, a high static pressure is created at the bottom of airfoil and low pressure on the top. But this pressure difference is not created by the so called 'Equal Transit' theory. The 2 big mistakes people did while applying Bernoulli's principle were
- Why should the 2 particles starting together, meet at the trailing edge at the same time. It is completely an absurd argument, there is no law in physics to support this. The 2 particles can leave for a completely different path and they may not even meet in their life time.
- You cannot apply Bernoulli's equation across 2 streamlines. It should applied strictly along a stream line.
Bernoulli's equation is completely true, it is conservation of energy along a streamline. Some people applied Bernoulli's equation without properly understanding what it is. That caused the whole confusion.
If you are interested in learn more about the lift generation (truth & myth), watch this excellent lecture from Dr Holger Babinsky of Cambridge university.
You can download the slides he used for the lecture from here SLIDES