the "equal transit-time"... states that the parcels of air which are divided by an airfoil must rejoin again; because of the greater curvature (and hence longer path) of the upper surface of an aerofoil, the air going over the top must go faster in order to "catch up" with the air flowing around the bottom. Therefore, because of its higher speed the pressure of the air above the airfoil must be lower.
Turns out this it has been proven wrong. See these pictures for evidence that air does not need to rejoin at the same place at all, though of course that doesn't mean that no air acceleration occurs at all.
As Wikipedia points out in its article on lift,
Such an explanation would predict that an aircraft could not fly inverted, which is demonstrably not the case. When an aircraft is flying inverted, the air moving over the bottom (in the aircraft reference frame) surface of the airfoil is moving faster. The explanation also fails to account for airfoils which are fully symmetrical yet still develop significant lift.
It is unclear why this explanation has gained such currency, except by repetition by authors of populist (rather than rigorously scientific) books, and perhaps the fact that the explanation is easiest to grasp intuitively without mathematics.
best expl is from "See How it Flies", an online book about airplane physics: http://www.av8n.com/how/htm/airfoils.html
you can see how a curveball works with any ordinary business card...!
The famous aerodynamicist Flettner once built a ship that “sailed” all the way across the Atlantic using huge rotating cylinders as “sails” to catch the wind...
Also, it is easier than you might think to demonstrate this important concept. You don’t need four vanes on the rotating paddle; a single flat surface will do. A business card works fairly well. Drop the card from shoulder height, with its long axis horizontal. As you release it, give it a little bit of backspin around the long axis. It will fly surprisingly well;
Jef Raskin, who started the Macintosh project within Apple, has a great page about what makes airplanes fly, which gets into curveball aerodynamics, upside-down flight, and the wing Albert Einstein designed for the Luftwaffe in WWI.
...the most common explanation of lift seen in elementary texts and popular articles today... is based on the Bernoulli effect, which correctly correlates the increased speed with which air moves over a surface and the lowered air pressure measured at that surface.
In fact, most airplane wings do have considerably more curvature on the top than the bottom, lending credence to this explanation. But, even as a child, I found that it presented me with a puzzle: how can a plane fly inverted (upside down). When I pressed my 6th grade science teacher on this question, he just got mad, denied that planes could fly inverted and tried to continue his lecture. I was very frustrated and argued until he said, "Shut up, Raskin!" I will relate what happened next later in this essay. A few years later I carried out a calculation according to a naive interpretation of the common explanation of how a wing works. Using data from a model airplane I found that the calculated lift was only 2% of that needed to fly the model.