For example, when the wing moves horizontally, the direction of fluid flow changes first to upward at the leading edge of the wing and then to downward at the trailing edge. Does it rotate? If the direction of motion of the fluid at the trailing edge changes to horizontal, does this also rotate?
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If you approach it from a related direction, when does potential flow exist, my answer here may help: https://physics.stackexchange.com/q/46131/ – tpg2114 Jul 01 '19 at 02:45
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What is the question here, in theory or in experiment, in an ideal or viscous flow? – Alex Trounev Jul 01 '19 at 05:40
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@AlexTrounev Ideal fluid – enbin Jul 01 '19 at 06:39
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What is your doubt exactly? @enbinzheng – Shishir Maharana Aug 28 '19 at 16:04
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@ShishirMaharana Assuming that air is a non-viscous fluid, is the flow of air on the wing rotational or non-rotational? – enbin Aug 28 '19 at 22:57
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@enbinzheng, I have edited my answer. – Shishir Maharana Aug 29 '19 at 04:03
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@ShishirMaharana Non-viscous fluids also have lift? – enbin Aug 29 '19 at 13:46
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The phenomenon of lift can be produced in an ideal (non-viscous) fluid by the addition of a free vortex (circulation) around a cylinder in a rectilinear flow stream. – Shishir Maharana Aug 29 '19 at 14:33
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@enbinzheng, actually, YES, because lift is produced when the fluid momentum is redirected. – Shishir Maharana Aug 29 '19 at 14:36
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@enbinzheng, but, you have to add a free vortex as I stated above. – Shishir Maharana Aug 29 '19 at 15:45
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Irrotational flow occurs when the cross gradient of the velocity or shear is zero.
i.e. $\nabla \times \vec {v}=0$
If the air is not deflected downwards by the trailing edge, it wouldn't be able to create a lift. Now, the streamlines should meet (nearly) behind the trailing edge.
An irrotational flow is one where the curl is zero. You can imagine it being like this. If you drop something at a point in the field, would it spin? This can be caused by a difference in magnitude of forces facing the same direction, perpendicular forces on certain faces etc.
If you think about it in terms of a differential element it makes sense. Think of all of the different ways you can make a piece of paper spin. This is where the curl comes from.
EDIT: To sum all of this up and to directly answer your question: yes, wings do have lift in incompressible (and compressible), irrotational, inviscid flow.
Shishir Maharana
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If your question is about how airplane wings work, they cannot work without inducing a vortex. Read this.
Mike Dunlavey
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