# Can we agitate a classical non viscous fluid?

Suppose we have an infinite amount of a non viscous liquid (No boundary). Inside that liquid works a rotating impeller. Can the impeller agitate the liquid at all?

The question arise from thinking about "What is quantum about a super fluid?". I mean in a super fluid, the impeller does agitate the liquid, but that agitation depends in a quantized manner on the speed of the impeller. So the question is, if we suppose a non viscous fluid would behave with respect to classical fluid dynamics instead, would there be no agitation at all, or else a continuous agitation, that depends in a non quantized way on the speed of the impeller?

Edit:

Maybe I should add, that with agitation I mean some transport of energy or momentum/velocity, creating a vortex or something in some distance to the impeller.

## 2 Answers

Yes the impellor can agitate the fluid.

When dealing with fluid flow there are two things to consider: viscous forces and inertial forces. By setting the viscosity to zero you make all the viscous forces zero, but you would still have inertial forces.

As your impellor blade (or whatever) rotates it pushes the liquid. Even though the viscosity of the liquid is zero it still can't instantly flow out of the way because it has a mass and therefore requires a force to accelerate it. The result is that the impellor blade will create currents of moving liquid, and the inertia of the liquid in those currents will mean the currents persist away from the impellor blade i.e. into the bulk of the liquid.

• Is this also happening in the super liquid, say super fluid helium? Because my motivation is still to see, if a super fluid is a non viscous classical fluid + something quantum. Loosely speaking. – Mark Neuhaus Jun 17 '15 at 14:17

Nothing that moves inside a classical inviscid fluid can generate vorticity, but if you are willing to accept irrotational flows as being agitated, that certainly happens. There is a concept of added mass. Suppose I try to accelerate a sphere that is immersed in an inviscid fluid. I will also have to accelerate the fluid around it and the sphere will feel heavier than it really is. To be precise, heavier by half the mass of the fluid displaced by the sphere. See the Wikipedia article