Is circulation real?

The thickness of the portion of the boundary layer with zero speed relative is smaller than can be resolved using the scales of fluid mechanics. Velocity and speed in fluid mechanics only have meaning at resolutions significantly larger than the mean free path of individual molecules of the fluid.

 

It’s worse than that…

Quantum Approaches to Consciousness (Stanford Encyclopedia of Philosophy) https://plato.stanford.edu/entries/qt-consciousness/

 

Nothing heard.

 

Yes, I agree. The mean free path of Nitrogen at STP is (according to Mean Free Path Calculator https://www.omnicalculator.com/physics/mean-free-path) 0.000006319 centimetres.
That's 6 x 10^-6 centimetres.
I would suggest velocity and speed in fluid mechanics only have meaning at least the scale of centimetres. That's a million times larger!

For theoretical aerodynamics to work, there has to be a no-slip boundary, but for Kinetic Theory to work, that boundary has to be measurably thick (in centimetres).
But you are saying that it "is smaller than can be resolved using the scales of fluid mechanics".
And that's just the zero-velocity part of the overall boundary layer.

In which case, isn't there a paradox with Prandtl's no-slip boundary?

 

Not at all. It is basic Calculus: a function with an asymptote at zero.

 

You are still not understanding that the theory is not referring to any one particular molecule. It is based on Calculus where a value can approach a limit (asymptote). The interface between the solid surface and the air is where the limit (asymptote) is.

 

If your theory requires an impossible physical condition (a single layer of stationary air molecules) then the theory must be wrong!

 

There was an America’s cup boat that iirr attached its stern or bustle or something (?) to the rest of the hull with a gap in between. There was conjecture that this was to cheat the rule using the boundary layer, the notion being that the boundary layer thickened towards the stern. It was I think called the magic hula or something. It did not work.

Comment?

 

Which "rule using the boundary layer" ?
More information, please.

 

Splitting hairs here but your are incorrect in suggesting that there are air molecules. Air is a mixture of elements and compounds. Nitrogen, Oxygen, elements, water vapor-compounds
And whatever else is floating around with it

Another aspect regarding boundary layers. Fluids seem to be the dominant words that Prandtl etc use. Gasses and liquids. The current argument is that SA says that the velocity even infinitely close to the
interface cannot be zero. Certainly the smoke pulses in air show that the velocity approaches zero
But with liquids perhaps the first molecular layer in contact with the interface will not move.
If the first layer of molecules contact the interface and wet the surface, in order for the layer to move, it would require the liquid at the interface to evaporate to permit the next adjacent layer to wet the surface.
I would not think that this is possible as it would not anywhere to evaporate to

 

I wondered how long it would take for that. Yes, you're right, but the accent is not on "air" but "molecules".

It has been a very long thread and you can be forgiven for not following the whole argument, but many pages ago I made the point that the difference between "none" and "a little" is not a matter of degree. Prandtl and his followers insist that it has to be zero. Any chink in that assertion opens the floodgates of how little. I can accept that the air may slow down towards a surface. We are all aware of wind shear between the top of the mast and the water, but I am adamant that it cannot be brought to zero.

It was Prandtl's pottering with the potable that pitched us into this pickle in the first place!
Let's stay focused on air. The paradox exists for liquids as well but it's much more apparent when applied to gases. And it's aerodynamic theory that is being discussed with Circulation.

 

All I’ve got, and impossible to find on the web, going by memory, but at the time the boundary layer getting thicker aft was received knowledge, or at least in sailing magazines etc.

I’ll keep looking- I think there’s a shot of it on SA somewhere…

 

Ah ha!

Team New Zealand NZL-82 Hula Design & Breakdowns https://forums.sailinganarchy.com/threads/team-new-zealand-nzl-82-hula-design-breakdowns.156481/

pics too!

 

Nope, not going to sailinganarchy. On principle.

 

Coward.

here’s another publication’s anodyne description

Team New Zealand reveals total commitment to the Hula https://www.sail-world.com/USA/Team-New-Zealand-reveals-total-commitment-to-the-Hula/-8282?source=google