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Hydraulic machines exploit Pascal's law to amplify forces. The hydraulic press, lift, and brake all use the same principle: $F_1/A_1 = F_2/A_2$, giving force multiplication ratio $= A_2/A_1$.

In a hydraulic car lift with area ratio 100:1, applying 100 N to the small piston produces 10,000 N at the large piston — enough to lift a car. The trade-off: the large piston moves 100 times less than the small piston (conservation of energy: $F_1 d_1 = F_2 d_2$).

Hydraulic brakes use the same principle in reverse — a small pedal force creates large braking forces at all four wheels simultaneously. The brake fluid must be incompressible (hence the danger of air bubbles in brake lines — air is compressible and reduces force transmission).

Key assumptions: the fluid is incompressible, the system is sealed, and the fluid is in static equilibrium (flow effects are negligible).