The FAA graphic is a tad useless as it doesn't show the extent of streamline displacement as the cylinder speed cranks up. Indeed, it is more confusing than illuminating in my isolated view.
If one compares the situation with the main field flowing (cylinder off/on) the rotating cylinder effectively constitutes a vortex within the main flow field (don't fuss too much about how you might get a vortex to sit in the middle of a steady flow without being blown away .. mathematics stuff).
The resulting interaction of the two flows is to force the main flow (in the region of the rotating cylinder)
to be deflected so that the incoming stream approaches the cylinder from in front
and below and departs to the rear
and below. This gives a significant change in flow direction to the local main flow and that causes a significant change in momentum .. which provides a vertical force (up/down according to the direction of cylinder rotation) which we call lift (for some strange reason).
The faster the cylinder rotates, the more pronounced is the lift effect.
If you now look at the flow past a wing (say with LE and TE devices), it is pretty similar. This idea then leads to one of the ways of describing lift mathematically using vortex flows.
You might like to have a play with the Jave applet in this
NASA page and you'll see the effect far better than I can explain in words.
Easiest way to play is to move the slider bar to the right and watch the spin rate increase, the flow interaction increase, and the lift force increase. The graph to the right of the flow graphic has a little red dot which slides up and down the line to give you an idea of the force developed.
Neat presentation I thought.
I think the whole point of using the cylinder theory is to prove that air flow to the top of the wing has a higher velocity
One of the problems in teaching is trying to match the description to the needs of the person who is trying to come to grips with the problem. Hence we tend to dumb things down so we can emphasise some of the important things happening.
The speed over the top idea is part of the usual way we talk about Bernoulli (and Euler - although he doesn't get any credit in pilot training) flow to emphasise some aspects.
For the cylinder trick, the important thing to emphasise is not the local flow speeds (and your thought is fine - the top flow close to the cylinder will go faster than that on the bottom) but the fact that
the spinning cylinder causes the flow to be distorted so that it approaches from front/below and departs to the rear/below.
To me, this is a much more useful way of explaning lift as it gets down to simple action and reaction stuff which we see in lots of places in everyday life.
And, as to the "cylinder theory", it's not a case of its just being theory. If you put a cylinder in a smoke tunnel and spin it up .. the streamline smoke tell tails do
JUST what the NASA applet shows.
Figuring out clever ways to change flow direction is all about how you develop desirable forces (lift) in fluids while minimising undesirable forces (drag) .. and this is what aerodynamicists get paid for.