3 ms·

> The issue is that once you recognize that lift is the reaction to accelerating the airflow downwards You need bernoulli to explain why the flow field is chan

by nimish 7y ago

> The issue is that once you recognize that lift is the reaction to accelerating the airflow downwards You need bernoulli to explain why the flow field is changed beyond just the area in contact with the flow. This induces the measured pressure differential, explaining part of lift along with the reaction effects of deflected flow for momentum conservation (NS, Newton's 2nd law). It's simply not _enough_ to say that it's purely angle-of-attack or geometry, and it's definitely not enough to say it's just pressure difference caused by Bernoulli, it's _both at once_. >One significant issue is that if you do this without taking into account friction at the surface of the wing, and the boundary layer that results, you will find that there is no lift at all! Your solution will show the air that passes under the wing turning around the trailing edge, and flowing forward for some distance over the upper surface. In practice, the presence of a boundary layer causes the flow to separate at the trailing edge (if not before). Not really true for 2d inviscid flows, a very useful approximation -- you need to enforce the K-J condition IIRC (which includes viscosity in a sense) In short: fluid dynamics is complex, and you need more than just newton's laws to explain it thoroughly (newton's laws don't explain conservation of mass either...)

mannykannot 7y ago
No, you do not need Bernoulli, it is merely convenient (but only if compressibility is not an issue, which it is, of course, for cruising airliners as well as supersonic aircraft.) Bernoulli does not give you the velocity field. If you are looking for just one thing that is sufficient, it is Newton's laws applied to viscous fluids - i.e. Navier-Stokes. I may have made one mistake in that the the separation at a sharp trailing edge may be inevitable simply because of the high acceleration that would be needed to go around it, together with the impossibility of negative absolute pressures, but in more general cases, such as the flow around a sphere, the effect of the boundary layer in triggering separation is important - as it is when we consider a stall, for that matter. The Kutta condition is merely a way of putting trailing-edge separation into Kutta–Joukowski. It is not a law of nature, it is a rule of thumb that makes K-J a realistic and useful model. Conservation of mass? well, you need that, but who doubts it? You mentioned conservation of energy, and I simply pointed out that you do not need it as an additional constraint, whether or not you are using Bernoulli.
- deleted 7y ago
  [deleted]
mannykannot 7y ago
In my previous reply, I overlooked this sentence, which gets to the heart of the misunderstanding: > It's simply not _enough_ to say that it's purely angle-of-attack or geometry, and it's definitely not enough to say it's just pressure difference caused by Bernoulli, it's _both at once_. Given a situation where Bernoulli is applicable (steady-state flow and inignificant compressibility effects), if you were to measure the airflow velocity and pressure fields around the wing, you would find both that they conform to Bernoulli, and that the pressure summed over the whole wing would account for the entirety of its lift. Alternatively, if you were to calculate the rate of change of momentum of the entire airflow affected by the wing, you would find that this also accounts for the entirety of its lift. This works even in those cases where Bernoulli is not applicable. So we have two different approaches to calculating the lift, and summing them would give the wrong answer. Both approaches can themselves be explained in more fundamental terms, and in both cases, it comes down to Newtonian mechanics. Neither approach allows us to calculate what the airflow looks like and how the presence of the wing shapes it, so neither approach offers a complete explanation. For that, we need Navier-Stokes, which is also reducible to Newtonian mechanics. What's wrong with many attempted explanations of lift, by either principle, is that they don't get the details right: they try to simplify the issues to the point where they are simply wrong.
- nimish 7y ago
  Not quite. You can't just derive the equation of state that's equivalent to Bernoulli's principle from Newton's laws. Only for incompressible flow is it a consequence of Newton's second law (NS) See https://en.wikipedia.org/wiki/Bernoulli%27s_principle#Derivations_of_the_Bernoulli_equation https://en.wikipedia.org/wiki/Bernoulli%27s_principle#Deriva... -- the broader (applies to compressible flow too) derivation is via conservation of energy and mass
  - mannykannot 7y ago
    That is a fair point, but to be clear, it does nothing to rehabilitate the notion that Newton and Bernoulli provide independent components of lift that have to be added (or, for that matter, that one is right and therefore the other is wrong, which is another common misunderstanding that has shown up elsewhere.)

by nimish 7y ago

mannykannot 7y ago

No, you do not need Bernoulli, it is merely convenient (but only if compressibility is not an issue, which it is, of course, for cruising airliners as well as supersonic aircraft.) Bernoulli does not give you the velocity field. If you are looking for just one thing that is sufficient, it is Newton's laws applied to viscous fluids - i.e. Navier-Stokes. I may have made one mistake in that the the separation at a sharp trailing edge may be inevitable simply because of the high acceleration that would be needed to go around it, together with the impossibility of negative absolute pressures, but in more general cases, such as the flow around a sphere, the effect of the boundary layer in triggering separation is important - as it is when we consider a stall, for that matter. The Kutta condition is merely a way of putting trailing-edge separation into Kutta–Joukowski. It is not a law of nature, it is a rule of thumb that makes K-J a realistic and useful model. Conservation of mass? well, you need that, but who doubts it? You mentioned conservation of energy, and I simply pointed out that you do not need it as an additional constraint, whether or not you are using Bernoulli.

deleted 7y ago
[deleted]

mannykannot 7y ago

In my previous reply, I overlooked this sentence, which gets to the heart of the misunderstanding: > It's simply not _enough_ to say that it's purely angle-of-attack or geometry, and it's definitely not enough to say it's just pressure difference caused by Bernoulli, it's _both at once_. Given a situation where Bernoulli is applicable (steady-state flow and inignificant compressibility effects), if you were to measure the airflow velocity and pressure fields around the wing, you would find both that they conform to Bernoulli, and that the pressure summed over the whole wing would account for the entirety of its lift. Alternatively, if you were to calculate the rate of change of momentum of the entire airflow affected by the wing, you would find that this also accounts for the entirety of its lift. This works even in those cases where Bernoulli is not applicable. So we have two different approaches to calculating the lift, and summing them would give the wrong answer. Both approaches can themselves be explained in more fundamental terms, and in both cases, it comes down to Newtonian mechanics. Neither approach allows us to calculate what the airflow looks like and how the presence of the wing shapes it, so neither approach offers a complete explanation. For that, we need Navier-Stokes, which is also reducible to Newtonian mechanics. What's wrong with many attempted explanations of lift, by either principle, is that they don't get the details right: they try to simplify the issues to the point where they are simply wrong.

nimish 7y ago
Not quite. You can't just derive the equation of state that's equivalent to Bernoulli's principle from Newton's laws. Only for incompressible flow is it a consequence of Newton's second law (NS) See https://en.wikipedia.org/wiki/Bernoulli%27s_principle#Derivations_of_the_Bernoulli_equation https://en.wikipedia.org/wiki/Bernoulli%27s_principle#Deriva... -- the broader (applies to compressible flow too) derivation is via conservation of energy and mass
- mannykannot 7y ago
  That is a fair point, but to be clear, it does nothing to rehabilitate the notion that Newton and Bernoulli provide independent components of lift that have to be added (or, for that matter, that one is right and therefore the other is wrong, which is another common misunderstanding that has shown up elsewhere.)