Hydraulic Press

Pressure. Pressure is the force acting perpendicular to a surface divided by the area of that surface: p = F/S. Its unit is the pascal: 1 Pa = 1 N/m². The same force presses harder on a smaller area. In the press the hand pushes a small piston, so even a modest force creates a large pressure in the oil: 300 N on 4 cm² is 750 kPa, seven and a half times atmospheric pressure.

Pascal's law in the press. Pressure applied to a liquid is transmitted unchanged to every point of it. So the pressure created by the hand in the small cylinder is the same under the big piston. In the simulator you can see it in the colour of the oil: during the down-stroke both cylinders have the same colour, and the gauges p₁ and p₂ read the same number.

Force gain. Since the pressure under the pistons is the same, F₁/S₁ = F₂/S₂, and the force on the big piston is F₂ = F₁·S₂/S₁. The press multiplies force by the ratio of the big piston's area to the small one's. With S₁ = 4 cm² and S₂ = 200 cm² the gain is 50: a 300 N push produces 15 kN — enough to lift a 1.5-tonne car (its weight is 14.7 kN). Compare areas, not diameters: a piston with twice the diameter has four times the area.

How a jack works. A real jack is a pump with two check valves. On the down-stroke valve K2 lets oil from the small cylinder into the big one — at that moment the cylinders are connected, exactly like the textbook press. On the up-stroke K2 closes and holds the load while the small cylinder draws oil from the tank through valve K1. The release valve K3 lets the oil back into the tank, and the load goes down smoothly. The p(t) graph shows the valves at work: on the down-stroke the pressures in the cylinders are equal, on the up-stroke the pressure in the small cylinder drops to zero while the big one keeps it.

The 'golden rule' of mechanics. Oil is practically incompressible, so the volume that leaves the small cylinder arrives in the big one: S₁h₁ = S₂h₂. The big piston moves a distance as many times smaller as the force is larger: one 15 cm stroke of the hand lifts the car by only 3 mm. Lifting it by 12 cm takes 40 strokes, and the hand travels 6 m. The work done by the hand equals the work done by the oil on the big piston: F₁h₁ = F₂h₂. A press gives no gain in work — the Force, Distance and Work bars below the scene show this at a glance.

Try it yourself. Set the hand force to 200 N and try to lift the car — the press stops, and the hint tells you how much force is missing. Increase S₂ and watch the force gain grow while the load rises more slowly. Choose the brick: it withstands about 78 kN, and to crush it with a 300 N push you need an area ratio above 260. The egg has a catch: with S₂/S₁ = 2 a 50 N push will not crush it — part of F₂ goes into holding up the platform itself, which weighs about 59 N.