So when a ball falls through a fluid in which it is submerged, it keeps displaci

Question

So when a ball falls through a fluid in which it is submerged, it keeps displacing fluid as it descends, but the level of the fluid doesn't rise. So does the ball do work on the fluid?

(Assuming there is no viscosity, the K.E would keep increasing, while potential energy decreases....that's the only energy conversion there's supposed to be...) So even if there is viscosity, the ball reaches a terminal velocity and at that stage, the PE gets converted in to heat energy wholly...But in a question we did in class, the teacher said we should also include work done by the ball on the fluid being displaced...I don't get it!

Explanation / Answer

There is a boundary layer of fluid that is carried along with the ball. At the interface between ball and fluid, the fluid is moving along with the ball. There is a force by the ball on the fluid at the interface. The fluid is moving at the interface. So there is work being done by the ball on the fluid at the interface.

The work being done by the ball on the fluid shows up as turbulent energy in the fluid. This eventually damps out and becomes heat energy.

The above view focuses on the boundary between ball and fluid and the fact that at that boundary the ball and the fluid are moving at the same velocity. Because they are moving at the same velocity the work done by the fluid on the ball is equal and opposite to the work done by the ball on the fluid.

There is another viewpoint that can be taken...

If you ignore the details of the interface and pretend that the ball and fluid are non-rotating, rigid objects in relative motion then you could conclude that the fluid is motionless and that, accordingly, no work is being done. [If you have trouble with the notion of a "rigid fluid", think of a fireman sliding down a pole instead].

Taking this viewpoint, the work done by the ball on the fluid and the work done by the fluid on the ball are no longer equal and opposite. If you add the work done by the ball on the fluid to the work done by the fluid on the ball you get a total that is negative. This is an energy deficit in the interaction. But energy is conserved. The "lost" energy in this sort of interaction usually ends up as heat.

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