Formulas & tables/Physics/Hydrostatics and hydrodynamics/Pascal's law (hydraulic press)

Pascal's law (hydraulic press)

F1S1=F2S2\dfrac{F_1}{S_1}=\dfrac{F_2}{S_2}

Result unit: Pa (pressure on both sides)

What it describes

Pressure in a fluid is transmitted equally in all directions — the principle of the hydraulic press.

Symbols

F1,F2F_1, F_2
forces on the pistons
[N]
S1,S2S_1, S_2
cross-sectional areas of the pistons
[m²]

Where it comes from

The pressure exerted on a fluid is transmitted undiminished in all directions. A small piston can balance a large force on a large piston — this is the principle of the hydraulic press.

When to use it

Hydraulic presses, hydraulic brakes, presses.

Example

A force of 100 N acts on a small piston S1=0.01S_1=0.01 m². What force will the large piston S2=0.5S_2=0.5 m² lift?
SubstitutionF1=100F_1=100, S1=0.01S_1=0.01, S2=0.5S_2=0.5.
ResultF2=100⋅0.50.01=5000F_2=100\cdot\dfrac{0.5}{0.01}=5000 N.

Related formulas

Hydrostatic pressure Buoyant force (Archimedes' principle)

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