When water equalizes in the "water seeks its own level" demonstration (in a series of connected glass tubes of various shapes, the water is at the same level in

When water equalizes in the "water seeks its own level" demonstration (in a series of connected glass tubes of various shapes, the water is at the same level in the whole system, as here: https://www.physics.purdue.edu/demos/display_page.php?item=2B-03 https://www.physics.purdue.edu/demos/display_page.php?item=2... ), does the system lose a lot of potential energy as the water equalizes? The demonstration is called Pascal's vases.