Pascal's law: how a small push lifts a heavy load

In simple terms

Oil hardly squashes at all. When you push on it, it doesn’t get smaller, it moves somewhere else and pushes on whatever is in the way.

Pressure is how hard the oil pushes on each square centimetre of surface. If the small piston is 20 mm across and the big one is 100 mm across, the big piston has 25 times the area. The same pressure on 25 times the area gives 25 times the force. That’s how a 40 kg push holds up 1,000 kg.

There is a catch, and the animation shows it. To lift the load by 1 mm, you have to push 25 mm of oil out of the small cylinder. The force is multiplied, the distance is divided by the same number. No energy is created: a long, easy push becomes a short, strong lift.

A real jack does this in many small strokes. Two little one-way valves (check valves) make it work: one lets oil out of the small cylinder into the big one, the other lets the small cylinder refill from the reservoir when you lift the handle. Open the release valve and the oil flows back to the reservoir, so the load comes down under its own weight.

For engineers

Pressure is force divided by area:

Worked example from the default setting: a 1,000 kg load weighs 9,810 N. On a 100 mm piston (7,854 mm²) that needs 1.25 N/mm², which is 12.5 bar. The 20 mm pump piston (314 mm²) needs the same 12.5 bar, so the push is 1.25 × 314 = 393 N, about 40 kg. A 110 mm stroke displaces 34.6 cm³, which lifts the big piston 4.4 mm.

Because force times distance is the same on both sides (ignoring friction), the work in equals the work out. Hydraulics is a lever made of oil: it doesn’t save energy, it lets you put the force exactly where you need it, through hoses, around corners, at any distance from the pump.

Two things this simple model leaves out, both covered in later lessons:

• Oil compresses slightly. Mineral oil shrinks about 0.7% per 100 bar, so at high pressure some of each stroke goes into squeezing the oil before the load moves. Trapped air makes this far worse, which is why a jack with air in it feels spongy.
• Seals and valves leak. Any leak path from the loaded side back to the reservoir lets the load sink. On a jack that is usually the outlet check valve or the release valve seat. On a machine it is the piston seal or a holding valve: see cylinder drift.

Deep dive

Pascal’s principle holds for a fluid at rest. In a working machine the oil moves, and some pressure is lost pushing it through hoses and valves, so the pressure at the pump is a little higher than at the cylinder. At jack speeds that loss is tiny, but in a crane circuit at 100 L/min it can be 10 to 20 bar.

The weight of the oil also adds pressure with depth (about 0.09 bar per metre for mineral oil). That is negligible next to 200 bar of working pressure, but it is why a pump’s suction inlet should sit below the tank’s oil level: a pump that has to lift its own oil starts to cavitate.

Where force multiplication turns up on real equipment:

• Hand pumps and bottle jacks, as in the animation. Workshop hand pumps for testing reach 700 bar with a pump piston of only a few millimetres.
• Hydraulic presses and pullers, where the big ram may be 200 to 300 mm across.
• Brakes on winches, cars and cranes: a small master cylinder drives bigger calipers.
• Every cylinder on a ship or crane. A luffing cylinder with a 200 mm bore at 250 bar pushes 785 kN, about 80 tonnes, from oil delivered through a hose the thickness of your thumb.

The check valves are where a jack fails. A seat worn by dirt, or a ball that can’t close because a particle is trapped under it, lets oil back. The symptom is exactly what the “Break it” switch shows: the load holds while you pump and creeps down while you rest. On a machine, the same job is done by pilot-operated check valves and counterbalance valves, which have their own lessons.