Pascal's principle

Also called Pascal's law, Hydraulic principle

Pascal's principle states that a pressure change applied to an enclosed fluid is transmitted undiminished to every point in the fluid and to the walls of its container. A hydraulic lift is the standard payoff.

Push down on a piston sealing a confined liquid and the pressure everywhere in that liquid rises by the same amount. Nothing is lost along the way, because the liquid is treated as incompressible and so has no way to absorb the change.

The hydraulic lift turns that into force multiplication. Two pistons of area $A_1$ and $A_2$ sit on the same confined fluid, so the pressure change matches at both:

\frac{F_1}{A_1} = \frac{F_2}{A_2}

A piston with a hundred times the area returns a hundred times the force. What it does not return is free energy: the fluid pushed out from under the small piston has to go somewhere, so $A_1 d_1 = A_2 d_2$ and the big piston moves a hundredth as far. The work in equals the work out, exactly as a lever or a pulley system does it.

Worth knowing before you memorise it: the AP Physics 1 CED never names Pascal's principle, and no hydraulic equation appears on any of the four AP equation sheets. The exam gets to the same place through the depth relation $P = P_0 + \rho g h$ , which already says that connected points at equal depth in one fluid are at equal pressure.

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