Prove that the law of equality of work (the “golden rule” of mechanics) applies to a hydraulic machine.

To prove this statement, we need some simple formula from hydraulics or the division of pressure with forces.

So, let it be the formula P = F / S.

We know that in a hydraulic machine, due to the well-known Pascal’s law, P1 = P2.

Hence, from here we can deduce the following:

F1 / S1 = F2 / S2.

Well, because of the communicating vessels, the amount of overflowing liquid will be the same.

V1 = V2, which means S1 * 11 = S2 * 12.

Now, taking into account the previous formula, we get:

F1 / F2 = 12/11.

Namely, this is the very golden rule of mechanics.