Pressure in liquids and gasesIB MYP Physics: Revision notes

Pressure is the force acting on each unit of area: p = F ÷ A. It is measured in pascals (Pa), where 1 Pa = 1 N/m².

The same force on a smaller area gives a bigger pressure, which is why a sharp knife cuts better than a blunt one.

Worked example: a force of 600 N on an area of 0.03 m² gives p = 600 ÷ 0.03 = 20 000 Pa.

A liquid has weight, so the liquid above any point pushes down on it. This means:

• Pressure increases with depth because there is more liquid above.
• Pressure increases with density because denser liquids weigh more for the same volume.
• At the same depth, pressure is equal in all directions and acts at right angles to any surface.

This is why dam walls are thicker at the bottom and why a deep-sea diver feels more pressure than a swimmer near the surface.

The pressure due to a column of liquid is p = h ρ g, where h is the depth in metres, ρ (rho) is the density in kg/m³ and g is the gravitational field strength (10 N/kg).

Worked example: the pressure at 12 m below the surface of sea water (ρ = 1030 kg/m³) is p = 12 × 1030 × 10 = 123 600 Pa.

Doubling the depth doubles the pressure from the liquid.

In a hydraulic system a liquid transmits pressure. Liquids are almost incompressible, so a pressure applied at one piston is passed on equally to the other piston.

Since pressure is the same everywhere in the liquid: F₁ ÷ A₁ = F₂ ÷ A₂.

Worked example: 50 N on a piston of area 0.002 m² produces a pressure of 25 000 Pa. On a piston of area 0.10 m², F₂ = 25 000 × 0.10 = 2500 N.

The larger piston moves a smaller distance, so energy is not gained. Car brakes and garage lifts use hydraulics.

The atmosphere has weight, so the air above you creates atmospheric pressure. At sea level it is about 100 000 Pa (101 kPa). It acts in all directions.

Atmospheric pressure decreases with height because there is less air above you. Gases are not incompressible, so the air is also thinner at altitude.

A barometer measures atmospheric pressure. In a mercury barometer, the pressure of the air holds up a column of mercury about 760 mm tall at sea level. The column becomes shorter on a mountain or when the weather brings lower pressure. Mercury is used because it is very dense, so the column is short enough to be practical.

An object in a fluid feels an upward force called upthrust. It happens because the pressure at the bottom of the object is greater than at the top.

Archimedes' principle: the upthrust on an object equals the weight of the fluid it displaces.

• If the upthrust equals the object's weight, it floats.
• If the weight is greater than the largest possible upthrust, it sinks.

A steel ship floats because its hollow shape displaces a lot of water. If the load is increased, the ship sinks lower until the upthrust again equals the weight.