- #1
ritwik06
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Homework Statement
A U tube of uniform cross sectional area A and base length 'L' contains a liquid of density "p". It is rotated about one of its vertical limbs with constant angular velocity [tex]\omega[/tex]. If the diameter of the tube is small compared to the base length, find the difference in levels of liquids in the to limbs.
The Attempt at a Solution
the shift will be because of the force exerted by the rotation on the liquid contained in the base.
I integrate to find this force [I am not posting the integration, because I think its right, if your answer dos not match with mine, tell me I will post my working on this integration.]
The force on the liquid in th base=[tex]\frac{Ap\omega^{2}L^{2}}{2}[/tex]
Now the work done by this force = change in potential energy due to rise of liquid in one limb
[tex]\frac{Ap\omega^{2}L^{2}}{2} * h = \frac{AP h^{2}g}{2}[/tex]
Is this step right to find "h"?
I was also thinking what is the net work done on water. Is it zero, because the rise in one limb=fall in the other?