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Hydraulic press

Pascal's principle says the pressure in a closed, connected fluid is equal everywhere. In a hydraulic press this gives a force amplification: a small force on a small piston creates the same pressure as a much larger force on a large piston, because pressure is force divided by area.

p = \dfrac{F_1}{A_1} = \dfrac{F_2}{A_2}

equal pressure on both pistons

F_2 = F_1\dfrac{A_2}{A_1}

force amplification

Symbols

$F_1,\ F_2$	forces on the two pistons	N
$A_1,\ A_2$	areas of the pistons	m²

Example

A hydraulic jack has $A_1 = 5$ cm² and $A_2 = 150$ cm². A force $F_1 = 100$ N gives $F_2 = 100\cdot 150/5 = 3000$ N.

The force amplification costs you displacement – the small piston must move much farther than the large one.

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Part of Fluid Mechanics: Hydrostatics.