Hydraulic Press
Press a small piston and lift a big load — Pascal's law made tangible.
About this simulation
Two connected pistons of different area share one fluid; a force on the small piston multiplies onto the large one by the area ratio, lifting a heavy load. Because the fluid volume is conserved, the big piston rises only as far as the force is magnified — force traded for distance, energy conserved.
How to use it
- Set Input force and watch the F₁ arrow push down on the small piston while the larger F₂ arrow lifts the load on the big piston.
- Change Small piston and Large piston radii and read the F₂ label on the output arrow, the × factor above it and the mass on the load block; the pressure label in the connecting pipe stays the same everywhere.
- Press 'Four times the radius' and check that the output force is sixteen times the input, because area goes as radius squared.
- Select Stroke under Show and compare d₁ and d₂: the large piston moves only d₁ divided by the mechanical advantage.
- Move the Depth probe slider to see the extra pressure ρgh that a depth of fluid adds.
What to notice
- Pressure applied to an enclosed liquid is passed on undiminished to every part of it, so both pistons feel the same pressure.
- The same pressure on a bigger area gives a bigger force: F₂ = F₁ × A₂/A₁.
- The liquid is incompressible, so the volume pushed out by the small piston equals the volume lifted under the big one, and the big piston moves a shorter distance.
- Force is multiplied but work is not: F₁d₁ = F₂d₂, so the press trades distance for force.
The formulas
- P = F₁ ⁄ A₁ = F₂ ⁄ A₂
- Pascal's law: the pressure P is the same under the small piston (force F₁, area A₁) and the large one (force F₂, area A₂).
- A₁d₁ = A₂d₂
- The volume of liquid moved is the same on both sides, so the piston strokes d₁ and d₂ are in inverse ratio to the areas.
- P = ρgh
- Pressure due to a depth h of liquid of density ρ; g is 9.8 m/s².
Questions
What is Pascal's law?
Pascal's law states that a change in pressure applied to an enclosed fluid at rest is transmitted equally and undiminished to every point of the fluid and to the walls of its container. A hydraulic press, a car's hydraulic brakes and a hydraulic jack all rely on it.
How does a hydraulic press multiply force?
A small force on a small piston creates a pressure F₁/A₁ in the liquid. That same pressure acts on a much larger piston, producing F₂ = PA₂. The output force is larger by the ratio of the areas. In the simulation, with radii of 4 cm and 16 cm the area ratio is 16, so 120 N of input supports about 1920 N.
Does a hydraulic lift violate conservation of energy?
No. The large piston rises much less than the small piston moves down, because the liquid's volume is conserved. Work in, F₁d₁, equals work out, F₂d₂, ignoring friction. Choose Stroke under Show in the simulation to see the large piston's short travel next to the small piston's long one.
What is the mechanical advantage of a hydraulic press?
Mechanical advantage is output force divided by input force, which for an ideal hydraulic press equals A₂/A₁, or (r₂/r₁)² for circular pistons. Equal pistons give no advantage, as the 'No advantage' preset shows, while a large piston ten times the radius of the small one gives an advantage of 100; the top line of the simulation reads MA ×100.
Why does pressure increase with depth in a liquid?
Each layer of liquid has to support the weight of the liquid above it, so the deeper you go the more liquid presses down. For a liquid of density ρ the extra pressure at depth h is ρgh. In water, every metre of depth adds about 9.8 kPa, which you can read off with the Depth probe slider.
