Pascal's principle
Summary
Pascal's principle says a pressure change applied to an enclosed, incompressible fluid at rest is transmitted undiminished to every point in the fluid. In a hydraulic lift, F₁/A₁ = F₂/A₂, so a small input force can balance a large load, but the input piston moves proportionally farther.
Detail
Meaning: A pressure change applied to an enclosed, incompressible fluid at rest is transmitted undiminished to every point in the fluid and to the container walls. Since P = F/A, a small force on a small piston can balance a large force on a large piston. Force is multiplied, but energy is not: the small piston moves farther.
Equation: ΔP = F₁/A₁ = F₂/A₂ and A₁d₁ = A₂d₂, where ΔP is the pressure change (Pa), F is force (N), A is piston area (m²), and d is piston displacement (m).
On the MCAT: Passages describe a hydraulic lift, press, or brake. You are given the piston areas and an input force and asked for the output force, or asked how far the input piston must move to raise the load a set distance. A larger output piston gives a larger output force, and the input piston moves farther than the load.
Common confusion: A hydraulic system does not give free work. The gain in force is paid for in distance, so the work F × d is the same on both sides in the ideal case. Also, the principle is about the change in pressure. Absolute pressure still varies with depth, P = P₀ + ρgh.
Sources
- Physics (Cutnell and Johnson)
- Fundamentals of Physics (Halliday, Resnick and Walker)
- University Physics (Young and Freedman)
Written for the MCAT and checked before it was published. For study reference only. Spotted an error? Let us know.