PRESS
F₂ = F₁(D₂/D₁)² — the lever’s bargain with a liquid arm.
Use the simulation above to change the variables and play through the guided stages. The explanation below describes the default starting values; the simulation updates its explanation as you experiment.
Setup
Piston 2 is larger, so a push on piston 1 trades distance for force. The drawing uses one shared diameter scale, so the visible size ratio is the real one.
Pascal
A confined fluid is a perfect gossip: pressure applied anywhere is repeated everywhere, undiminished, to every wall and every piston. Pressure — not force — is the fluid’s common currency, and both pistons trade at exactly the same rate.
Solve
Same pressure gives F₂ = F₁(D₂/D₁)². Incompressibility gives A₁d₁ = A₂d₂, so piston 2 gains force and loses stroke.
Stroke
One full quasi-static stroke. Piston 1 moves down and piston 2 rises by d₂ = d₁/MA. Force is multiplied and distance divided. The two work meters remain equal.
Audit
The books close exactly: F₁d₁ = F₂d₂ to machine precision, mechanical advantage (D₂/D₁)², not a joule created or lost. It is the lever’s bargain with a liquid arm — same trade, same audit, no beam required. Every car brake and shop jack is this page.