Hydraulic machines

Push the piston of a horizontal cylinder fitted with three vertical tubes, and the liquid climbs to the same new height in every tube: the extra pressure reaches every part of the liquid.

Second form of Pascal's law: a pressure change applied to any part of an enclosed fluid is passed on, without loss and equally in all directions, to every point of the fluid and the vessel walls.

Hydraulic lift: a small piston of area A₁ pushed with force F₁ sets up pressure P = F₁/A₁. The same P acts on a large piston of area A₂, giving an upward force F₂ = PA₂ = F₁A₂/A₁.

The force is multiplied by A₂/A₁, the mechanical advantage of the device. Changing F₁ raises or lowers the platform carrying a car or truck.

Liquid is incompressible, so the volume swept in by the small piston equals the volume swept out by the large one: A₁L₁ = A₂L₂. The large piston moves a shorter distance, in the ratio A₁/A₂.

Two water-filled syringes joined by a rubber tube, piston diameters 1.0 cm and 3.0 cm: 10 N on the small one gives 10 × (3/1)² = 90 N on the large one. Pushing the small piston in 6.0 cm moves the large one out 6.0/9 ≈ 0.67 cm. Atmospheric pressure acts on both and cancels.

Car lift with pistons of radius 5.0 cm and 15 cm, car mass 1350 kg, g = 9.8 m s⁻²: F₁ = 1350 × 9.8 × (5/15)² = 1470 N ≈ 1.5 × 10³ N. The air pressure needed, F₁/(π × 0.05²) ≈ 1.9 × 10⁵ Pa, is almost twice atmospheric pressure.

Hydraulic brakes: a light push on the pedal moves the master piston; brake oil carries the pressure to larger pistons that press the brake shoes against the lining. The same pressure reaches the cylinders at all four wheels, so the braking effort is equal on every wheel.