Relation between Bernoulli's theorem and aeroplanes

[abhijithmatt]

i heard that aeroplanes are an application of benoulis theorem. Can you please explain it to me.

 

[boneh3ad]

In a way, they are. Provided you take on faith the fact that the air flowing over a wing moves faster over the top than over the bottom, then Bernoulli's theorem, which describes the inverse relationship between pressure and velocity, will allow you to calculate the pressure on the top and the bottom of the wing, and therefore the lift.

Understanding why the air moves faster over the wing is more difficult.

 

[CWatters]

If you read enough forums you will eventually come across an argument between two groups of people. One camp will be arguing that the lift produced by a wing is due to the application of Benoulis theorem, the other camp will be arguing that lift is produced by the wing accelerating the airflow downwards. It's a false dichotomy.

 

[rcgldr]

A wing produces lift by diverting air downwards. This process involves creation of pressure differentials that coexist with acceleration of air, and the acceleration of air from higher pressure areas to lower pressure areas created by a wing approximately follows Bernoulii's theorem. Bernoulli's basic equation assumes that total energy of the air is not changed, but a wing affects the total energy somewhat, so Bernoulli's equation is an approximation.

The point made by CWatters is that Bernoulli's theorem and downwash theorem both apply to aeroplanes, and that they aren't in conflict.

Using an ideal wing as a frame of reference, it diverts the relative flow downwards without changing the speed, so the total energy remains constant and Bernoulli isn't violated, but from the air's frame of reference, the once still air ends up being accelerated downwards (lift) and somewhat forwards (drag), resulting in a non-zero "exit velocity" (the speed of the affected air when it's pressure first returns to ambient), and in the air's frame of reference work is performed on the air, violating Bernoulli's equation. An efficient wing diverts a large amount of air by a small angle, and from the air's frame of reference, the total energy added to the air is relatively small.

 

[CWatters]

Nice explanation.

Just for info.. I recall seeing a demonstration in the London Science Museum some years ago that comprised a section of wing in a simple wind tunnel. It had a set of water filled tubes connected to holes in the top and bottom wing surface that showed the pressure difference between top and bottom surfaces at various points on the chord. You could rotate the wing to change the angle of attack and see how the pressure distribution changed. Nice simple demo of the Bernoulli part of the story but you couldn't see what the airflow behind the wing was doing as there was no smoke system or similar.