Connect pressure, piston area and movement without mistaking force multiplication for free energy.
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Pressure is force divided by area. A confined fluid transmits an applied pressure change through the fluid. For a slow ideal hydraulic comparison at the same height, F₁/A₁ = F₂/A₂. Equal pressure changes do not imply equal forces on pistons of different areas.
With an effectively incompressible liquid and no leaks, the displaced volumes balance: A₁d₁ = A₂d₂. A piston five times larger in area can produce five times the force ideally, but moves one fifth as far.
A bottle jack uses a lever, a small pump piston, check valves, a reservoir and a larger lifting piston. Repeated handle strokes move more liquid to the lifting side. The release valve allows controlled lowering.
Pneumatic systems use gases, which compress substantially. Hydraulic systems commonly use liquids with much smaller compressibility. Compressibility affects response and energy storage. Both systems require controls and pressure-rated components.
Change one measurement, predict the result, then compare the calculated account. These are editable teaching measurements, not a physical simulation.
Deconstructed · Mechanism in action
Find the lever, pump piston, check valves and release valve. Follow one complete pumping stroke before explaining the larger lifting force.
If a piston’s diameter doubles, by what factor does its area increase?
Area increases by 4 because circle area is proportional to diameter squared. Under equal applied pressure, its ideal force is four times as large.
Compare a syringe containing air with one containing water only under teacher-approved low-pressure conditions. Predict the difference before pressing.
Apply it to the design challenge →Read further: OpenStax · Simple Machines → · NASA · Pascal’s principle →
