Pascal's Law
Pascal's law states that pressure applied to a confined fluid is transmitted equally in all directions.
Learn with examples.
The Formula
Pascal's law states that a change in pressure applied to an enclosed fluid is transmitted undiminished throughout the fluid and to the walls of its container. This principle is the foundation of all hydraulic systems.
Blaise Pascal, a French mathematician and physicist, established this principle in 1653. It means that a small force applied to a small piston can create a much larger force on a larger piston. This is how hydraulic jacks, car brakes, and heavy machinery lifts work.
The key insight is that pressure is the same everywhere in the connected fluid. Since pressure equals force divided by area, a larger piston area produces a proportionally larger output force. The trade-off is that the smaller piston must move a greater distance to displace the same volume of fluid.
Variables
| Symbol | Meaning |
|---|---|
| F₁ | Force applied to the input piston (newtons, N) |
| A₁ | Area of the input piston (m²) |
| F₂ | Force produced at the output piston (newtons, N) |
| A₂ | Area of the output piston (m²) |
Example 1
A hydraulic jack has an input piston of area 0.01 m² and output piston of area 0.5 m². If you push with 200 N on the input, what force is produced?
Apply Pascal's law: F₂ = F₁ × A₂/A₁ = 200 × 0.5/0.01
F₂ = 200 × 50
F₂ = 10,000 N (enough to lift a small car)
Example 2
A hydraulic brake system needs to produce 8,000 N at the brake caliper (area 0.004 m²). The master cylinder has area 0.0005 m². What force must the driver apply?
Rearrange: F₁ = F₂ × A₁/A₂ = 8,000 × 0.0005/0.004
F₁ = 8,000 × 0.125
F₁ = 1,000 N (the pedal mechanism further reduces the effort needed)
When to Use It
Use Pascal's law to analyze any hydraulic system that transmits force through a fluid.
- Designing hydraulic jacks, presses, and lifts
- Calculating brake system forces in vehicles
- Engineering heavy construction equipment
- Understanding how hydraulic flight controls work in aircraft