Prove: Rotation of Flows Satisfies Equation of Continuity

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SUMMARY

The discussion centers on proving that the rotation of a liquid within a closed circular cylinder satisfies the equation of continuity and boundary conditions using the velocity vector V = (omega) x r. Here, 'omega' represents the angular velocity of the fluid, which is time-dependent, while r is the position vector from the axis of rotation. The continuity equation in cylindrical coordinates is referenced as part of the problem statement, indicating the mathematical framework necessary for the proof.

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Homework Statement



If liquid contained within a closed circular cylinder rotates about the axis of the cylinder, prove that the equation of continuity and boundary conditions are satisfied by V = (omega) x r, where 'omega' is the angular velocity of fluid supposed to be dependent on time only, and r is the position vector measured from a point on the axis of rotation.

Homework Equations



V = 'omega' x r

The continuity equation in the cylindrical co-ordinates is attached as a word document

The Attempt at a Solution



I need a hint as to how to start the solution.
 

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Sorry but did you write the question exactly as it was posed and with everything included? I'm a bit startled.
 
Yes i wrote the question out exactly as it was given to me.
 

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