Pascal's Law
Simple Explanation
Pascal's law states that pressure applied to an enclosed fluid is transmitted equally, undiminished, throughout the fluid in all directions. This is the principle behind hydraulic systems, where a small force on a small piston can produce a much larger force on a larger piston.
Why Do We Need It?
Pascal's law is the working principle behind hydraulic brakes, car jacks, hydraulic presses, and countless other machines that multiply force using fluids.
Formula
Pascal's Law (Hydraulic Press)
F₁/A₁ = F₂/A₂
Pressure applied to an enclosed fluid is transmitted equally throughout the fluid — a small force on a small piston can therefore produce a much larger force on a larger piston, since the pressure (F/A) must be the same at both.
- F₁, A₁
- — Force applied to, and area of, the smaller (input) piston
- F₂, A₂
- — Resulting force on, and area of, the larger (output) piston
When to use it: Use to calculate the force multiplication produced by a hydraulic system, such as a car jack or hydraulic press.
Worked Example
Finding output force in a hydraulic press
A hydraulic press has a small piston of area 0.02 m² and a large piston of area 0.5 m². A force of 100 N is applied to the small piston. Find the force produced on the large piston.
Why Does This Work?
Since pressure (P = F/A) is transmitted equally throughout the enclosed fluid, the pressure at both pistons must be the same — this forces F₁/A₁ to equal F₂/A₂, meaning a larger piston area must correspondingly produce a larger output force to maintain that equal pressure.
Real-Life Example
Hydraulic car jacks
A hydraulic car jack lets one person lift a car weighing over a tonne using only modest hand force on a lever.
The jack's small piston (pumped by hand) has a much smaller area than its large piston (supporting the car) — Pascal's law means the small force is multiplied in proportion to the ratio of piston areas, making it possible to lift the heavy car with modest effort.
Practice
A hydraulic system has a small piston of area 0.01 m² and large piston of area 0.3 m². A force of 50 N is applied to the small piston. Find the force on the large piston.
MediumCommon mistake
Thinking a hydraulic system creates energy from nothing — it multiplies FORCE, but the large piston moves a proportionally smaller distance than the small piston, so the work done (force × distance) is conserved, not increased.
Quick Review
- Pascal's law: pressure in an enclosed fluid is transmitted equally in all directions.
- F₁/A₁ = F₂/A₂ — a larger output piston area means a proportionally larger output force.
- Force is multiplied, but the large piston moves a smaller distance (work is conserved).