Section 1 of 5Why Liquids Exert Pressure
A liquid presses on everything in it because of the weight of the liquid above.
Cause
- The weight of the column of liquid above a point presses downwards and the liquid passes the push on in all directions.
Equal in all directions
- At a particular depth the pressure is the same sideways, upwards and downwards on a small object.
Depth
- The deeper the point, the greater the weight of liquid above it, so the greater the pressure.
Density
- A denser liquid has more mass in each cubic metre, so it gives a larger pressure at the same depth.
Section 2 of 5The Equation
The Equation
Equation
- p = h × ρ × g where p is pressure, h is depth, ρ is density and g is gravitational field strength.
Units
- Pressure is in pascals, depth in metres, density in kg/m³ and g in N/kg.
Proportional
- Pressure is directly proportional to depth, so doubling the depth doubles the pressure from the liquid.
Not shape
- The result depends on vertical depth only and does not depend on the width or shape of the container.
| Quantity | Symbol | Unit |
|---|---|---|
| Pressure | p | Pa |
| Depth (height of column) | h | m |
| Density of liquid | ρ | kg/m³ |
| Gravitational field strength | g | N/kg |
Section 3 of 5Observing the Effect
A tall container with holes at different heights shows the pattern clearly.
1
Fill a tall plastic bottle with water after making three small holes at different heights in its side.
2
Water squirts out of the lowest hole fastest and furthest, because the pressure there is greatest.
3
The middle hole produces a weaker jet, and the highest hole gives only a gentle flow.
4
This shows that pressure increases with depth below the surface of the water.
5
Repeating with a denser liquid would give stronger jets, showing the effect of density.
Section 4 of 5Worked Example
Question
- Calculate the pressure caused by the water at the bottom of a 30 m deep lake.
- The density of water is 1000 kg/m³ and g = 10 N/kg.
- Write the equationp = h × ρ × g.What the symbols mean: p = pressure due to the liquid (Pa) · ρ = density of the liquid (kg m−3) · g = 9.81 N kg−1 · h = depth (m)
- Substitute the valuesp = 30 × 1000 × 10.
- Calculatep = 300 000 Pa, so p = 3.0 × 10⁵ Pa (300 kPa).
- State that this is the pressure from the water alone, and atmospheric pressure at the surface would be extra.
Answer 3.0 × 10⁵ Pa
Section 5 of 5Exam Checklist & Tips
1.3.6 – Key Points for the Exam
- Liquid pressure Pressure in a liquid caused by the weight of the liquid above.
- Depth The vertical distance below the surface of a liquid.
- Density The mass of a substance per unit volume.
- Gravitational field strength The force per kilogram acting on a mass in a gravitational field, about 10 N/kg on Earth.
Common Mistakes
- Using the length of the container instead of the vertical depth in the equation.
- Forgetting to convert kPa to Pa before substituting into p = hρg.
- Thinking pressure acts only downwards; in a liquid it acts equally in all directions.
- Leaving out atmospheric pressure when the question asks for the total pressure at depth.