Drag/friction on a cylinder rotating in water of different volumes

AI Thread Summary
The energy required to maintain the speed of a rotating cylinder in water depends on the size of the gap between the cylinder and the tank. In smaller gaps, shear force and shear stress become significant, leading to increased energy demands in larger tanks. If the gap is minimal, the larger tank may require more energy due to the increased shear effects. Conversely, with larger gaps, the tank size becomes less relevant, and energy requirements may equalize. Ultimately, the relationship between tank size and energy consumption is contingent on the gap dimensions relative to the cylinder.
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This is not a homework question, but a tipsy bar question.The question being:

There are two tanks of water, one large and one small, full of water of the same density. You are using engines to rotate one cylinder in each tank, the cylinders being of equal size. Will the cylinder in the larger tank of water take more energy to maintain speed than the cylinder in the smaller tank will?
 
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It will depend on how large your tanks are compared to the cylinders. The only thing opposing the constant angular velocity rotation of the cylinders is shear force and shear stress is proportional to the velocity gradient normal to the surface. If the gap between the cylinder is small (a few millimeters maybe) and there is a difference in the gap size between the two tanks there could be a noticeable difference. However is the gap between the cylinder and the tank is much larger (several meters) I don't think it will matter which tank the cylinder is in.
 

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