4.1.18. Prove that in two communicating vessels the liquid in the field of gravity has minimal potential energy when the liquid levels in both vessels are at the same height.
Solution
For problem $4.1.18$
Comparing the moment when the levels ($A$ and $B$) of liquid in both vessels are different to the moment when they are the same ($C$), we see that the decrease in gravitational potential energy of the system is that of the liquid in light blue dropping to where the liquid in dark blue (with the same volume and mass) is. Thus, the gravitational potential energy of the system is lowest when the levels of liquid in both vessels are the same.
