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One can, at this point mention the problem of the water tanks. Two
identical cylindrical water tanks are connected at the bottom by a pipe
with a valve which is closed. One is filled with water to height h, the
other is empty. The valve is opened and water flows. Finally the tanks
reach equilibrium with each being filled to height h/2.
But the potential energy of the water in the tanks is only half that of
the potential energy in the one initially filled tank. Where did the
energy go?