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According to Bernoulli's equation if a fluid gains speed its subject to less pressure and exerts less pressure consequently. Would this not mean that for a mass of air that is flowing between two layers of still air, the moving air (or let's call it wind) would be subject to atmospheric pressure from above and below that is greater than the wind's pressure? And would the still air not crush the wind? How can any type of air flow with less pressure than the corresponding atmospheric pressure at that altitude exist, since it would be crushed by the still air?

I hope my question makes sense and is logically consistent.

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  • $\begingroup$ Is your case of wind moving in between two still layers of air realistic? Does it actually occur in nature? It seems to me to be a highly idealized scenario similar to a Couette flow. I would expect in reality such a wind to exert a shear stress on the still air which consequently would start dragging with the wind until it is one large body of moving air. Bernoulli doesn't account for such viscous action. $\endgroup$ – nluigi Jul 5 '17 at 9:42
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I can't visualise what you are tryig to describe. You speak of air flowing between two layers of still air. Can you draw any kind of surface (real or imaginary) that divides the sill air from the moving air? What happens on that surface?

What may be confusing you is that Berouilli only holds for steady flow, and along one streamline. That is $$p+\frac{1}{2}\rho q^2+\rho gh=p_0$$ is constant along such a streamline, and $p_0$ is called the Bernouilli constant or the total pressure for that streamline. Its value may be different on other streamlines, for example due to heating or cooling, and it may vary along the given streamline if there are irreversible events like friction. Therefore, in any argument involving Bernouilli, you must be careful to describe the whole setup involved and I don't think that you have done that.

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I think what you are referring to is something like a jet of air issued from a nozzle into the ambient. The pressure inside the jet will be everywhere atmospheric (atmosphere acts like a pressure reservoir, the jet being assumed subsonic). Bernoulli equation is not applicable here since viscous forces dominate the motion of the air inside the jet, evident by the fact that beyond a certain distance from the point of issue the jet loses all its momentum and you cant "feel" the air flow anymore.

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