I'm not saying ditch Bernouillis'Theorem
Oh I'm sorry -- I must have misunderstood your original post where you twice claimed that it is "wrong".
To say that it's "just a theory" is all very well, but as Genghis conjectures, everything in science is "just a theory". Next time you want to find the length of the hypotenuse of a right-angled triangle, be careful when applying Pythagoras's Theorem -- it is, after all, "just a theory".
Ultimately, all the mechanics we do is derived from Newton's Laws of motion -- even Bernoulli's theorem. The Newtonian approach that you cite is fine as far as it goes, but I have two issues with it:
1) It's just another way of calculating the lift once you know the flow field. It's not a very direct one.
Imagine I placed a watepaper bin in a corridor (in a very litter conscious office
) and wanted to know the weight of the contents at the end of the day. Compare the following methods:
a) Weigh every person entering the corridor during the day as they enter. Weigh every person leaving the corridor during the day as they leave. Subtract the totals and deduce the weight of the contents added to the bin during the day.
b) Weigh the contents.
In principle, both are possible and correct. Applying Newton's Second Law (using the
Momentum Theorem) to find the lift of a wing is a bit like method a). It's good to know it works, and perhaps it adds some insight to the understanding of the problem. But if you know the speed of flow at each point over the surface of the wing, why not use it directly to find the pressure?
2) It often leads to some incorrect assertions. For example, it's common to hear that the "lift of the wing is equal to the rate at which air momentum is tranfered downwards" or worse that "an aerodynamic force can only be generated by changing the momentum of air". Neither give a very complete picture of the physics -- for example in ground effect you have to add in the increased pressure on the ground as well as any momentum changes. Even in free flow, you have to be very careful about the way you add up the momentum to make it work. I note, BTW, that the Lift from Turning Flow page avoids any of these horrors.
I'm sorry to rant. I'm just a bit fed up with seeing a load of "Shock horror -- Established Aerodynamics Proved Wrong" headlines from people who don't understand the physics. I appreciate that yours was a genuine attempt to highlight some important shortcomings in the way pilots are taught aerodynamics. I hope you've enjoyed the debate.