Angular motion in a fluid

[Endercreeper01]

If you had a spinning disk inside a fluid, what would describe the motion of the fluid?

Edited November 24, 2013 by Endercreeper01

[John Cuthber]

If you had a spinning disk inside a fluid, what would describe the motion of the fluid?

The word "complicated" would describe it in most cases.

[doG]

Like the air around a flying saucer?

[studiot]

 

If you had a spinning disk inside a fluid, what would describe the motion of the fluid?

 

 

That would rather depend upon the Reynold's number of the motion, which in turn is influenced by the viscoscity of the fluid and the speed and size of the spinner.

 

It is quite possible that you would get what is known as a Rankine vortex where there is a small rotational core aound the spinner and the rest of the fluid executes irrotational circular flow around this, rather like a line vortex, which is irrotational.

Edited November 24, 2013 by studiot

[J.C.MacSwell]

If you had a spinning disk inside a fluid, what would describe the motion of the fluid?

Fluid would be drawn toward the centre of the disc from either side, and outward and in the direction of rotation along the surface and outer edge. This flow would effectively stop the Reynolds number from increasing without limit (by limiting the effective length, which can be chosen arbitrarily for the equation) and continuously increasing turbulence...so it would either fluctuate in some manner or approach a constant state depending on whether it was shedding vortices or not.

[Bignose]

If you had a spinning disk inside a fluid, what would describe the motion of the fluid?

The Navier-Stokes equations if it is a Newtonian fluid. Your problem here isn't even all that uncommon -- it is the basis of why centrifugal pumps work. Any good undergraduate fluid mechanics text or class should discuss the workings of a centrifugal pump in detail.

[Endercreeper01]

Wouldn't angular motion in a fluid create lift?

[J.C.MacSwell]

Wouldn't angular motion in a fluid create lift?

If there was flow in the main stream relative to the spinning disc in any direction except parallel to the axis of the disc, then yes

[Bignose]

Wouldn't angular motion in a fluid create lift?

It is complicated. It is often nice to break the lift into to parts: shear lift and spin lift. Shear lift occurs on an object where there is a gradient in the shear over the surface of that object. If there is angular motion of the fluid, in all likelihood there will be a shear gradient, but it isn't always true, and isn't always a very large effect. Spin lift occurs when the object itself is rotating (a really good example is the movement when a pitcher throws a breaking ball), which of course will then drive angular motion of the fluid.

 

In short, you have to analyze every situation uniquely. You have to figure out if a rotating fluid flow is causing an object to more, a moving object causing a rotating fluid flow, or both. Therefore there is no straightforward simple answer to your question. The answer comes from analyzing the fluid flow with the conservation of mass, linear momentum, angular momentum, and energy equations.

[J.C.MacSwell]

It is complicated. It is often nice to break the lift into to parts: shear lift and spin lift. Shear lift occurs on an object where there is a gradient in the shear over the surface of that object. If there is angular motion of the fluid, in all likelihood there will be a shear gradient, but it isn't always true, and isn't always a very large effect. Spin lift occurs when the object itself is rotating (a really good example is the movement when a pitcher throws a breaking ball), which of course will then drive angular motion of the fluid.

 

In short, you have to analyze every situation uniquely. You have to figure out if a rotating fluid flow is causing an object to more, a moving object causing a rotating fluid flow, or both. Therefore there is no straightforward simple answer to your question. The answer comes from analyzing the fluid flow with the conservation of mass, linear momentum, angular momentum, and energy equations.

I assumed his question was wrt the spinning disc in the OP, and for the simplest cases of uniform mainstream flow, the answer is fairly straightforward. There would be both lift and drag, except in the case of the main flow parallel to the axis of the disc and spin, in which case there would be just drag (oscillations from vortex shedding not withstanding but lift should average zero)

 

It can certainly get complicated beyond that.