Why are liquid surfaces at constant pressure?

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SUMMARY

The discussion centers on the behavior of liquid surfaces under constant angular speed, specifically addressing why the surface of a spinning bucket of water maintains a constant pressure. The conclusion is that the surface must be at the same pressure to prevent fluid flow along the surface, ensuring equilibrium. The participants also confirm that this principle holds true even when viscosity is introduced, as the surface pressure remains equal to the atmospheric pressure, which is assumed constant throughout the fluid.

PREREQUISITES
  • Understanding of fluid dynamics principles
  • Knowledge of angular momentum and its effects on fluids
  • Familiarity with pressure concepts in liquids
  • Basic grasp of viscosity and its implications in fluid behavior
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  • Research the effects of angular velocity on fluid pressure distribution
  • Explore the role of viscosity in fluid dynamics
  • Study the principles of hydrostatics in rotating fluids
  • Learn about the mathematical modeling of fluid surfaces under rotation
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Students and professionals in physics, engineering, and fluid mechanics who seek to deepen their understanding of fluid behavior under rotational forces.

dEdt
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This is probably a stupid question with a simple answer, but please bear with me.

Suppose we have a bucket of water that we begin to spin at a constant angular speed. My textbook asked to find the shape of the surface of water, with the hint that the surface would be a surface of constant pressure. I got the right answer, but I don't fully understand why the surface should all be at the same pressure. I thought it had to do with preventing water from flowing along the surface, but I don't think that's it because different points of the fluid could be at different pressures without fluid flowing between them.

Also, does this (surface liquid makes = surface of constant pressure) hold if viscosity is introduces?
 
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Surface pressure is equal to the atmospheric pressure which is assumed constant. Isn't it?
 
Ah of course, that makes sense. Thanks.
 

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