Pressure in Liquids

Section 1 of 7How a fluid exerts pressure

What is a fluid

• What is a fluid A fluid is any substance that can flow, so both liquids and gases are fluids.

Pressure in all directions

• Pressure in all directions An object that is stationary in a fluid is squeezed by it.
  • At any given depth the pressure is the same in every direction.

Force at right angles

• Force at right angles The force that the fluid exerts on a surface always acts at 90° (normal) to that surface.
• So the force on the walls of a container, or on a submarine hull, points at right angles to the metal.

Section 2 of 7Why pressure increases with depth

1Weight above

• Weight above At any point, the fluid above it has weight and pushes down.

2More fluid, more weight

• More fluid, more weight The deeper the point, the taller the column of fluid above it, so the weight is greater.

3Pressure increases

• Pressure increases Pressure is force per unit area, so a larger weight on the same area gives a larger pressure.

4Density matters

• Density matters A denser liquid has more mass in the same volume, so it produces a higher pressure at the same depth.

Section 3 of 7The equation for pressure in a liquid

Quantity	Symbol	Unit
Pressure due to the liquid	p	pascal, Pa
Depth (height of liquid column)	h	metre, m
Density of the liquid	ρ	kilogram per metre cubed, kg/m3
Gravitational field strength	g	newton per kilogram, N/kg (about 9.8 on Earth)

Section 4 of 7Using the equation

1

Write the equation: p = h × ρ × g. To find the depth, rearrange it to h = p ÷ (ρ × g).

2

Convert all quantities to the correct units first. For example 20 kPa = 20 000 Pa.

3

Substitute the values. Example: the pressure is 20 000 Pa in water of density 1000 kg/m³ and g = 9.8 N/kg.

4

Calculate h = 20 000 ÷ (1000 × 9.8) = 2.04 m, which is 2.0 m to two significant figures.

5

Check that the answer is sensible: a pool depth of about 2 m is realistic.

Section 5 of 7Applying the idea

p = h × ρ × g

Double the depth

• Double the depth The pressure due to the liquid doubles, because p is proportional to h.

Change the liquid

• Change the liquid In sea water (density about 1030 kg/m³) the pressure at a given depth is slightly higher than in fresh water.

Shape does not matter

• Shape does not matter Only the vertical depth matters, not the width of the container or the amount of liquid.

Dam walls

• Dam walls Dams are built thicker at the base because the pressure on the wall is greatest at the bottom.

Section 6 of 7Key terms

Term	Meaning
Fluid	A liquid or gas, a substance whose particles can flow.
Pressure	Force acting at right angles per unit area, measured in pascals (Pa).
Density	Mass per unit volume, measured in kg/m3.
Gravitational field strength	The force per kilogram acting on a mass in a gravitational field (N/kg).
Pascal	The unit of pressure; 1 Pa = 1 N/m2.

Section 7 of 7Exam technique

1

Forgetting to convert kPa to Pa before substituting into the equation.

2

Using the width or volume of the container as the depth. Only the vertical depth below the surface matters.

3

Saying fluid pressure acts only downwards. At a given depth it acts equally in all directions.

4

Writing the unit of density as kg/m instead of kg/m³.