I know that there are dozens of questions about lift generation here but after reading them I still don't understand everything. My question is: why does air accelerate over the (upper side) wing? I know that it accelerates because there is pressure differential etc. but why wouldn't the air just flow over both sides of the wing with equal speed?
The Abdullah's answer is correct to it's level of approximation, but I'd like to expand on why the pressure is reduced on the leeward side.
As the air encounters the leading edge, it is pushed out of the way. Due to first law of motion, it would like to continue moving outward from the wing and avoid the area just above the wing. But besides inertia, air also has viscosity, which prevents sharp changes in air velocity, so the incoming air trying to pass high above the wing drags the air near the wing along. But when the air just above the wing is pulled out aft, there is shortage of air just over the wing, which means low pressure.
This low pressure causes the air bend around the wing, and since it pulls air from all sides, accelerate as it enters the low pressure region over the leading edge and decelerate again as it leaves it over the trailing edge.
Without viscosity (e.g. in liquid helium) the pressure would not be reduced, because the oncoming fluid would just continue straight over the highest point and the area over the receding part of the upper surface would be filled with stagnant fluid moving with the wing. In fact that's exactly what happens in stall – as the curvature increases (due to higher angle of attack), at some point the viscosity is no longer enough to keep the air moving, the area over the wing gets filled with air just whirling around and not moving away, so there is no longer shortage of air, the sucking of oncoming air stops and the generated lift rapidly decreases – just the lower surface still generates some.
Air accelerates over the upper side. The reason is simple: As the wing - or anything else in air - moves, it creates high pressure at the front and low pressure at the back. The air flowing around the wing gets sucked into this low pressure region, and the suction accelerates it. (It will slow down again at the end of the low pressure zone) But the downturned trailing edge means that only the air coming over the upper surface can access this suction. The air flowing over the bottom has no idea of the suction zone above.
From a layman’s point of view:
As far as lift generation, it is more precise to say that the lower static pressure generated perpendicular to the chord line of the wing is created by an increase in velocity of the air molecules instead of saying that the acceleration is created by the lower pressure. The acceleration of air molecules is greatest on the side (Upper or lower) of the wing with the greatest curvature. Basic aircraft wings are usually curved more on the upper-side of the wing than it is on the lower-side. This curvature creates a greater distance to travel in the same amount of time. Hence, the molecules are accelerated.
Think of it like a marching band or a column of soldiers marching. When soldiers or musicians have to march, they do so at the same speed. Both the cadence and the length of everyone’s steps are identical. When soldiers or musicians have to turn their column to march around an object, the individuals at the outside of the turn will move at a faster pace than the ones on the inside by lengthening their strides. If the turn is very sharp (like a 90° turn), the individuals on the inside of the turn will slow their pace by shortening the their strides. They do this because their is now a difference in the distance they have to travel in the same amount of time. Because there is a greater distance on the outside of the turn, there are fewer individuals per square feet of space on the outside of the turn than the amount of individuals on the inside. But since the column is not stopping, the file of individuals will continue to build up on the inside of the turn while waiting on the individuals on the outside of the turn to catch up. The column viewed from above will look like an accordion or a spring bent in the middle: a lot of material on the inside of the bend; very little material on the outside of the bend.
Let’s transfer this analogy to air molecules that are stationary relative to an airmass. The wing is actually moving through the airmass instead of the airmass moving over the wing. Either way, the side of the wing that makes the molecules move the furthest will temporarily have a lower static pressure and a higher velocity as the same mass of air on the other side of the wing. The lower static pressure creates a vacuum along the curved side of the wing. The molecules that were adjacent to one another at the wings leading edge, before encountering the wing, do not have to necessarily meet at the trailing edge. The average static pressure difference along the wing is enough to create this vacuum. The dynamic pressure of the air mass build up on the other side of the wing will also contribute to lift and increase with angle of attack.