Lift is what keeps flying objects from falling out of the sky which makes it perhaps the most important element of foils. The most popular theory for how lift works is known as the equal transit time hypothesis which suggests that since wings are often shaped with a longer surface on top and a shorter surface on the bottom, that the air moves faster over the top surface causing a pressure decrease and thus a lift upwards through the Bernoulli equation. However it can be easily found that this is not an entirely correct explanation for lift. Some modern low drag wings are actually designed with a longer surface on the bottom. Also planes can fly upside down. In reality in a fluid energy, momentum, and mass must be conserved, and while Bernoulli's equation concerns energy and Newtons laws of motion are in concern to the conservation of momentum they cannot fully explain lift. The more complete explanation of lift is much more complex than often taught. In order to fully understand lift mass of the fluid must be taken into account, and the dynamics of fluid mass are different to solid mass which results in it being necessary to have a good understanding of Euler equations and Navier-Stokes Equations.
This is not meant to scare or attack anyone for their predisposition, the Bernoulli equation can explain some parts of lift but it is important to remember that the concept of lift is much more complex than you might believe and that the equal transit time hypothesis is not the complete story. I personally do not know the ins and outs of Euler and Navier-Stokes Equations but I think it is fascinating how complex lift really is. Keep being interested!
This is not meant to scare or attack anyone for their predisposition, the Bernoulli equation can explain some parts of lift but it is important to remember that the concept of lift is much more complex than you might believe and that the equal transit time hypothesis is not the complete story. I personally do not know the ins and outs of Euler and Navier-Stokes Equations but I think it is fascinating how complex lift really is. Keep being interested!