[Karto]

If I think straight, the initial potential energy in a column of liquid would be the integration of mgh (actually integration of density * g * section * height), therefore mgh/2 at the beginning of the situation. Or said intuitively : the center of gravity of the column at half its height.

But obviously, even with this 1/2, your relation after dividing between two tanks still holds. :)

[thomasahle]

I was thinking that too, the initial potential energy should be proportional to h^2/2. However then we still have 2*(h/2)^2/2 = h^2/4.

[Karto]

Yes, one h is hidden inside m... Ending up with energy = something * h^2 actually makes the relationship show the same face as the one for capacitors, where energy = something * v^2.

[unkulunkulu]

* where h = half the water level in the first barrel.

[sirusdas]

Good observation!