Fluid in Equilibrium: Internal Motions, Velocity & Beyond

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In a rotating cylinder with a uniform density fluid, equilibrium implies that the fluid experiences no net forces acting on it, resulting in a stable state. Despite being in equilibrium, internal motions can still exist, as the fluid's particles may have velocities relative to the rotating frame. The velocity is not zero because the fluid's rotation creates a centrifugal effect, causing the particles to move outward. This scenario is reminiscent of "Newton's bucket," which illustrates the concept of a preferred frame of reference, highlighting the distinction between absolute motion and relative motion. Understanding these dynamics is crucial for analyzing fluid behavior in rotating systems.
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Suppose I have a fluid of uniform density confined to a roating cylinder of radius r turning at an angular speed of \Omega.

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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