Bernouilli’s principle applied to flight is this: the speed of the air flowing over the top of the wing is faster than the speed of the air flowing under the wing and so the air pressure is less on the top of the wing. The difference in pressure results in a net lift to act on the bird.
This is a curious topic. It is incredible that we can actually build air planes, because there is so much confusion about why they (or indeed birds) fly. The common explanation using Bernoulli’s equation is overly simplified because does not take properly into account why the air flows faster on top of the wing than under it, and when you try to do that you note that there are other forces involved. It is good that they test the wings in wind tunnel before building airplanes.
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