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

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SUMMARY

The discussion centers on the energy required to maintain the rotational speed of a cylinder in two different-sized water tanks. It concludes that the energy needed depends on the relative size of the tanks compared to the cylinder. Specifically, shear force and shear stress, which are proportional to the velocity gradient normal to the cylinder's surface, play a crucial role. If the gap between the cylinder and the tank is small, variations in tank size can significantly affect energy consumption; however, if the gap is large, the tank size becomes less relevant.

PREREQUISITES
  • Understanding of shear force and shear stress in fluid dynamics
  • Knowledge of angular velocity and its implications in rotational motion
  • Familiarity with the concept of velocity gradients in fluid mechanics
  • Basic principles of energy consumption in mechanical systems
NEXT STEPS
  • Research the effects of shear stress on rotational dynamics in fluids
  • Explore the principles of fluid dynamics related to cylinder motion
  • Learn about the impact of gap size on energy efficiency in rotating systems
  • Investigate the relationship between tank size and fluid resistance in mechanical applications
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Mechanical engineers, fluid dynamics researchers, and anyone interested in the energy dynamics of rotating systems in fluids.

kitkatkipling
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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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