Contradictions in Irrotational Vortex?

[Stevenyzs]

So I was reading about Vortices in Wikipedia, when I stumbled upon the explanation about Irrotational Vortices.

It states there that in Irrotational vortices, the fluid's flow velocity u, is inversely proportional to the distance r, from the vortex's axis.

Then, at the end of the explanation, it says that: "In an irrotational vortex, fluid moves at different speed in adjacent streamlines, so there is friction and therefore energy loss throughout the vortex, especially near the core." So the fluid's speed increases and decreases at the same time near the core/axis??

http://en.m.wikipedia.org/wiki/Vortex

 

[mfb]

So the fluid's speed increases and decreases at the same time near the core/axis??

Is that question meant in time or in space?

You need some external force to keep the fluid rotating.

 

[Stevenyzs]

Is that question meant in time or in space?

You need some external force to keep the fluid rotating.

Nah, I'm referring to general physics, not the space time stuff.
Like for example, when you whirl your hand in a bucket of water, you'll create an Irrotational vortex right? And the explanation provided by
Wikipedia first says that the fluid's speed in an Irrotational vortex is inversely proportional to the distance from it's axis.

It then proceeds to say that the different speed in adjacent streamlines, will cause friction between the streamlines, thus causing energy loss throughout the vortex, especially near the core/axis.

So isn't that a contradiction...?

 

[mfb]

Nah, I'm referring to general physics, not the space time stuff.

Classical physics, sure.
There is a difference between "it gets hotter towards the equator" and "it gets hotter towards noon". So "it gets hotter" is ambiguous if you have both a space direction (towards/away from the center) and time (evolution of the system due to friction).

You have more energy loss near the core, so what? Your input power is also near the core.
A car on the highway has more friction and more speed than a car on other roads. Same comparison, no contradiction. The car on the highway just needs more gas.

 

[Stevenyzs]

You have more energy loss near the core, so what? Your input power is also near the core.
A car on the highway has more friction and more speed than a car on other roads. Same comparison, no contradiction. The car on the highway just needs more gas.

So are you saying that the friction between the streamlines are somewhat constant, and more input energy is needed for a narrow Irrotational vortex...?

 

[mfb]

Constant in which aspect?

and more input energy is needed for a narrow Irrotational vortex...?

If that is the only difference: sure.

 

[Stevenyzs]

Constant, like the coefficient of friction mew, between the streamlines. Cos the more input energy you use to induce a faster vortex, the larger the frictional forces...right?

 

[mfb]

You have a fluid, friction in fluids is not a dimensionless coefficient.
Yes, the faster your vortex the larger your friction (in terms of power), similar to the highway&car example from above.

 

[Stevenyzs]

You have a fluid, friction in fluids is not a dimensionless coefficient.
Yes, the faster your vortex the larger your friction (in terms of power)

So for example, if I were to pass a vortex through a Venturi tube, would the rotational velocity increase due the vortex being closer to it's axis, or would the increase in frictional forces cancel it out?

 

[mfb]

That depends on details of the setup.