• Pixel-art sticker of Pascalla, personifying Pascal's Principle, with the caption “Small Push, Big Lift.”

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Pascalla

Pascal's Principle Physics

\[\frac{F_1}{A_1} = \frac{F_2}{A_2}\]
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Meet Pascalla, who multiplies a push: pressure applied to an enclosed fluid is passed on equally everywhere, so F₁/A₁ = F₂/A₂. A piston with ten times the area pushes with ten times the force, which is how a hydraulic lift raises a car. Pixel-art kiss-cut sticker in 2, 3, 4 and 6 inches; equation, symbols and sources in the physics panel below.

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Flat $6 shipping worldwideMade to order, ships in 2–5 business days

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Size3″ × 3″

3″ × 3″ kiss-cut sticker.

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Flat $6 shipping on every order, worldwide, whatever's in it.

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Returns & replacements21 days

Every item is printed to order, so we can’t accept returns or exchanges for change of mind, or if you ordered the wrong size or colour.

Print defect, misprint, damage or the wrong item? We’ll send a free replacement, or a refund if you prefer. Report it within 21 days of delivery with a photo; no need to send it back.

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The physics

Meet Pascalla, a hydraulic lift who turns a small push into a big one.

Blaise Pascal stated in the 1600s that pressure applied to an enclosed fluid is passed on undiminished to every part of it. Push on a small piston with force F₁ over area A₁ and you create a pressure F₁/A₁. That same pressure acts on a large piston of area A₂, which feels F₂ = F₁ × A₂/A₁.

With a large piston ten times the area of the small one, ten times the force comes out. A 500 newton push can lift a 5,000 newton load, about half a tonne. Energy is still conserved: the small piston must travel ten times as far as the large one rises.

Car brakes, hydraulic jacks, excavators and aircraft control systems all use this. Liquids are used because they barely compress, so the pressure is transmitted almost instantly.

Real systems lose some force to friction and to differences in fluid height between the pistons. Air bubbles, which do compress, make brakes feel spongy.

Equations

\[\frac{F_1}{A_1} = \frac{F_2}{A_2}\]
SymbolMeaningUnit
\(F_1\) force on the small piston \(\mathrm{N}\)
\(A_1\) area of the small piston \(\mathrm{m²}\)
\(F_2\) force on the large piston \(\mathrm{N}\)
\(A_2\) area of the large piston \(\mathrm{m²}\)

Sources

  1. OpenStax University Physics Vol. 1 — Pascal's Principle and Hydraulics
  2. Wikipedia — Pascal's law

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