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77 (b). Problem 17.23 (RHK) Two identical cylindrical vessels with their bases at the
same level each contain a liquid of density
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.
The area of either base is A, but in one vessel the liquid height is h1 and
in the other h2. We have to find the work done by gravity in equalizing the
levels when the two vessels are connected.
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Solution: Click For PDF Version Problem has been described through the diagram. In the
initial situation liquid in the left vessel is filled to height
Potential energy of a liquid of density
Using this result we find that the potential energy of the system in the initial situation is
Potential energy of the system in the final situation is
Therefore, the work done by gravity in equalising the levels is
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and the height of liquid in the right vessel is
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When the tap joining the two vessels is removed, liquid will flow from the
container that has higher liquid level to the other. We assume that there is
sufficient friction so that the flow speed is nearly zero. The flow will stop
when liquid levels in both containers equalise and attain equal height,
.
We will find the work done by gravity in the changing the system from the
initial to the final situation shown in the diagram by computing the change in
potential energy of the system. 
contained in a cylindrical vessel of cross-section A up to height h
from the base is
