Question

Two identical cylindrical vessel with their bases at the same level each contain a liquid of density `rho`. The height of the liquid in one vessel is `h_(1)` and in the other is `h_(2)` the area of either base is A. What is the work done by gravity is equalising the levels when the two vessels are connected?

Answer 1

Since the total volume of the water is constant, the height in each vessel after interconnection will be `(h_1+h_2)/2`. The level in the left vessel shown in the ure, drops form A to C and that in the right vessel rises from B to D. Effectively, the water in the part AC has dropped down to DB.

The mass of this volume of water is
`m=rhoA(h_1-(h_1+h_2)/2)`
`rho A((h_1-h_2)/2)`
The height descended by this waster is `AC=(h_1-h_2)/2`. The work done by the force of gravity during this process is therefore,
`rhoA((h_1-h_2)/2)^2g`.