Fluid in Equilibrium: Internal Motions, Velocity & Beyond

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    Equilibrium Fluids
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SUMMARY

The discussion centers on the behavior of a uniform density fluid confined within a rotating cylinder of radius r, rotating at an angular speed of Ω. It establishes that when the fluid is in equilibrium in the rotating frame, internal motions do not exist, and the velocity of the fluid is effectively zero relative to the rotating frame. The conversation draws parallels to "Newton's bucket," which illustrates the concept of a preferred frame of reference, emphasizing the importance of understanding motion in non-inertial frames.

PREREQUISITES
  • Understanding of fluid dynamics principles
  • Familiarity with rotational motion concepts
  • Knowledge of non-inertial reference frames
  • Basic grasp of Newtonian mechanics
NEXT STEPS
  • Research the implications of fluid dynamics in rotating systems
  • Study the concept of non-inertial frames in detail
  • Explore the historical context and significance of Newton's bucket
  • Learn about angular momentum conservation in fluid systems
USEFUL FOR

This discussion is beneficial for physicists, fluid dynamicists, and students studying mechanics, particularly those interested in the behavior of fluids in rotating systems and the implications of non-inertial reference frames.

xnd996
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Suppose I have a fluid of uniform density confined to a roating cylinder of radius [tex]r[/tex] turning at an angular speed of [tex]\Omega[/tex].

Now I am considering the fluid in the rotating frame and I know that the fluid is in equilibrium. What does this imply?

If the fluid is in equilibrium are there any internal motions? Is the velocity 0? Why?
 
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