Pascal's law — the hydraulic press
Press the small piston — the pressure is transmitted through the liquid and lifts a large load on the large piston. Because F₁/S₁=F₂/S₂: the larger the ratio of areas, the greater the force multiplication. Change the piston areas and observe.
I'll give you a target force on the large piston — set the piston areas to reach it. F₂ = F₁·S₂/S₁.
What just happened?
You enlarged the large piston, and the force F₂ lifting the load grew. The liquid transmits pressure equally in every direction, so a larger area means a larger force.
Pascal's law:
— pressure applied to an enclosed liquid is transmitted unchanged to every point. F — force (N), S — piston area (cm² or m²), p — pressure (N/cm² or Pa).
What does that mean in practice?
Since the pressure is the same on both sides, you get the force on the large piston from the ratio of areas:
For free? No — the cost is distance.
However many times you win on force, you lose the same number of times on distance: the small piston must move times farther than the large one rises. The work is the same — this is how hydraulic jacks and brakes work.
Why you need this for the exam:
p = F₁/S₁ = F₂/S₂ plus F₂ = F₁·S₂/S₁ solve almost every problem about a hydraulic press and jack. The trick: write down that the pressure is equal on both sides, and translate that into the ratio of areas.
Remember: the liquid transmits pressure equally, so a larger piston gives a larger force — F₂ = F₁·S₂/S₁. This is the foundation of hydraulics.
Theory & formulas
Pascal's law
Pressure applied to an enclosed liquid is transmitted equally in every direction. In a hydraulic press the same pressure acts on both pistons:
Force multiplication
Hence the force on the large piston: The larger the ratio of areas, the greater the force multiplication.
No free energy
The large piston moves as many times less as the force is greater () — the work on both sides is equal. Applications: brakes, presses, jacks.
Symbols: — forces on the pistons, — piston areas, — piston displacements.
Frequently asked questions
›How does a hydraulic press multiply force?
The pressure p=F/S is the same everywhere in the liquid, so a larger piston (larger S) produces a proportionally larger force F₂=F₁·S₂/S₁.
›Does a hydraulic press give free energy?
No — the large piston moves as many times less as the force is greater; the work (F·s) on both sides is equal.
›Where is Pascal's law applied?
Hydraulic brakes, presses, car jacks, machine control systems.
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