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Pressure in fluids

Air and fluids · level 5, lesson 1 of 6

A question to start

A mechanic lifts a whole car with one hand on a small hydraulic jack. How can a small push lift something so heavy?

The idea

Pressure is force on each square metre, \(p = F/A\), measured in pascals (Pa).

In a liquid or gas at rest, pressure acts equally in every direction at each point. And if you push on a liquid in a closed system, the extra pressure spreads to every part of it. This is Pascal's principle.

A hydraulic jack uses it. A small piston pushes on oil; the pressure spreads to a big piston:

\[\frac{F_1}{A_1} = \frac{F_2}{A_2}.\]

The big piston has a bigger area, so the same pressure gives a bigger force.

small forcelarge forceoil: same pressure

Worked examples

1. The jack. The small piston is 0.0005 m², the big one 0.05 m², 100 times bigger. A push of 150 N gives a pressure of \(150/0.0005 = 300{,}000\) Pa, and the big piston pushes with \(300{,}000 \times 0.05 = 15{,}000\) N, enough to lift a car's corner.

2. The cost. Energy is not free. To lift the big piston by 1 cm, the oil from the small piston must fill 100 times the area by 1 cm, so the small piston must move 100 cm.

3. Car brakes. Your foot pushes a small piston; the pressure spreads through the brake fluid to bigger pistons at each wheel that squeeze the brake pads.

Try it

  1. State Pascal's principle.
  2. A jack's pistons are 0.001 m² and 0.04 m². What force on the small one lifts 8,000 N on the big one?
  3. In question 2, how far must the small piston move to raise the load 2 cm?
  4. Why must the oil in a jack have no air bubbles in it?
Answers
  1. Extra pressure on a fluid at rest in a closed system spreads to every part of it.
  2. \(8{,}000 \times 0.001/0.04 = 200\) N.
  3. 40 times as far: 80 cm.
  4. Air squashes easily, so the push would squash the bubbles instead of moving the big piston.

Common mistake

"A jack makes energy." It gives a bigger force over a smaller distance. Force times distance, the work, is the same on both sides (less a little lost to friction).

Where it leads