Derfred.
I am not going to waste my time attempting to defend the Bernoulli explanation for lift, because I am well aware of its faults and some of the alternative explanations and theories.
But a few of your comments do deserve examination:
Unfortunately, the idea keeps perpetuating because people like Keith keep peddling it.
I am not peddling anything. The OP asked for an explanation based on Bernoulli’s theorem, so the only possible answer must be based on Bernoulli’s theorem. It is all very well saying “Ah but it isn’t true”, but many courses include this subject, and if the student is to pass the exams he/she must learn it. I suspect that the OP is doing such a course. If this is the case, simply saying “Bernoulli does not do it” is of no use to him/her.
The air does not know it has a longer path to take, and it does not speed up because of it. The air speeds up because the wing moving through the air causes an area of lower pressure above the wing, and an area of higher pressure below.
You appear to be suggesting that because the air is not aware of the longer path it cannot react to it. You are of course correct in that the air has no brain, no intelligence, no self-awareness, indeed no awareness whatsoever. So it cannot ever be aware of anything. But does this lack of awareness mean that it cannot react to things around it? Let’s try a few tests:
If I place a mass of air into a sealed container then reduce the volume of the container, the air will be unaware of this reduction in volume (it is not aware of anything). Does this mean that the air pressure and temperature will not increase? Of course it doesn’t.
If I take a parcel of air and lift it upwards in the atmosphere, the air will be unaware of the fact that its altitude has increased (it is not aware of anything). Does this mean that it will not expand and cool down? Of course it doesn’t.
If I take a mass of air an pass it through a venturi, it will be unaware of the changes in cross-sectional-area (it is not aware of anything). Does this mean that the velocity, pressure and temperature of the air will not change? Of course it doesn’t.
We could of course do more similar tests, but hopefully you have got the point. The fact that air is not aware of anything whatsoever does not prevent it from reacting to events.
You then say:
Bernoulli states that there is a relationship between speed and pressure. In this instance, it is the pressure change that causes the speed change, not vice versa.
But as we have already established, the air is not aware of anything, so how can changes in pressure cause changes in velocity. So which is it to be? Can the air react to things of which it is unaware, or can it not? You cannot have it both ways.
By all means argue that Bernoulli cannot explain how lift is generated, but please, please, try to use more rational arguments.
Those who wish to argue that airflow around wings and the generation of lift have nothing to do with Bernoulli should ask themselves a simply question. Bernoulli’s Theorem is a well established method of providing reasonably accurate predictions of how air velocity and pressure are related in a wide range of circumstance. So if Bernoulli does not apply to wings in flight, how does this come about? Does the approaching air say to itself “oh that’s just an aeroplane wing so I do not need to react in the usual bernolli-esq manner?