Pressure in Solids and Liquids
Senior 2 · Physics
Pressure in Solids and Liquids
Lesson 5 of 5
25 min
Let's begin
A mechanic at a roadside garage lifts a whole minibus with one hand, using a small hydraulic jack. A moto rider squeezes a brake lever gently and stops a heavy machine. Both depend on a discovery made by the French scientist Blaise Pascal in the 1600s: a liquid passes pressure on, undiminished, to every part of itself.
Pascal's principle: a change in pressure applied to an enclosed fluid is transmitted undiminished to every part of the fluid and to the walls of its container.
Liquids are almost incompressible: they cannot be squashed into a smaller volume. So a push on one part of an enclosed liquid is passed on at once to every other part.
Two pistons of different areas are connected by a tube full of oil. A small force F₁ on the small piston (area A₁) creates a pressure P = F₁ ÷ A₁. That same pressure acts on the large piston (area A₂), producing a force F₂ = P × A₂. So:
F₁ ÷ A₁ = F₂ ÷ A₂, which gives F₂ = F₁ × (A₂ ÷ A₁)
The small piston of a jack has an area of 2.0 cm². The large piston has an area of 80 cm². The mechanic pushes with 150 N.
In the chamber pool of the Under Pressure simulation, add masses to the small opening and watch the water level and pressure change throughout the whole pool, just as Pascal's principle predicts.
Tip
Same PRESSURE on both pistons, not the same FORCE
Force multiplier = A₂ ÷ A₁ (big area ÷ small area). If the question gives radii or diameters, the area ratio is the SQUARE of the radius ratio.
State Pascal's principle.
Solution: Pressure applied to an enclosed fluid is transmitted undiminished to every part of the fluid and to the walls of the container.
A garage lift has a small piston of area 0.0010 m² and a large piston of area 0.10 m². What force on the small piston lifts a 12 000 N car?
Solution: F₁ = F₂ × A₁ ÷ A₂ = 12 000 × 0.0010 ÷ 0.10 = 120 N.
In a brake system, a force of 200 N acts on a master piston of area 4.0 cm². Each wheel piston has an area of 16 cm². What force does each wheel piston exert?
Solution: F = 200 × 16 ÷ 4.0 = 800 N.
Why is oil, not air, used in hydraulic machines?
Solution: Oil is almost incompressible, so it passes the pressure on fully. Air would be squashed, wasting the push. Oil also lubricates the pistons.
Summary
Sources and credits
The Rwandan examples, worked examples and practice items are written by Ganzaa.
