EASA / CAR Part-66 · Module 2 · 2.2.4 Fluid Dynamics · Cat A
Objective: define pressure as force per unit area, state Pascal's principle, and show how a hydraulic jack multiplies force by the ratio of its piston areas — and what that multiplication costs in stroke.
The same pressure acting on a larger piston produces a larger force.
Pressure is force spread over an area, P = F/A, measured in pascals (1 Pa = 1 N/m²) or more usefully in kPa, bar or psi. The same force on a smaller area gives a higher pressure — which is why a sharp chisel cuts and a snowshoe does not sink.
Pascal's principle says that pressure applied to a confined fluid is transmitted undiminished and in all directions throughout that fluid. In this jack the small piston raises the pressure, and that identical pressure pushes on every square millimetre of the large piston. Since force is pressure times area, the large piston delivers a much larger force: F₂ = F₁ × A₂/A₁. Liquids work for this because they are effectively incompressible — a gas would just squash and absorb the stroke, which is why air is used for springing and fluid for power.
Once again the gain is paid for in movement. The fluid that leaves the small cylinder has to reappear in the large one, so if the output rises 1 cm with a ratio of 8, the input piston must travel 8 cm. Force out × distance out equals force in × distance in: the same energy bargain as a lever. This is exactly how aircraft brakes, jacks and flying-control actuators turn a modest pilot or pump input into a very large output force.