Pressure in a liquid increases with depth and with the liquid’s density. The shape of the container and the total amount of liquid do not change it.
This lesson follows calculating pressure from force and area within the force and pressure topic. It prepares you for explaining buoyancy conceptually.
How do I compare pressure in fluids?
Use pressure = depth × density × g, where depth is in metres, density in kg/m³ and g is the value your question gives. Compare two points by comparing depth first, then density.
If the depth doubles in the same liquid, the pressure due to the liquid doubles. If the liquid is denser at the same depth, the pressure is greater.
Worked example: two invented liquids
Take g = 10 N/kg. Liquid A is water, with a density of 1 000 kg/m³. Liquid B is an invented oil with a density of 800 kg/m³.
| Liquid | Depth | Density (kg/m³) | Pressure (Pa) |
|---|---|---|---|
| A | 0.50 m | 1 000 | 0.50 × 1 000 × 10 = 5 000 |
| A | 1.00 m | 1 000 | 1.00 × 1 000 × 10 = 10 000 |
| B | 0.50 m | 800 | 0.50 × 800 × 10 = 4 000 |
| B | 1.00 m | 800 | 1.00 × 800 × 10 = 8 000 |
Compare depth. In liquid A the pressure at 1.00 m is 10 000 Pa, twice the 5 000 Pa at 0.50 m, because the depth doubled.
Compare density. At the same 0.50 m, A gives 5 000 Pa and B gives 4 000 Pa, so the denser liquid gives the greater pressure.
Assumption. These values are the pressure from the liquid only. The air above the surface adds atmospheric pressure to each one, equally for both liquids.
The mistake that costs marks
The common slip is to say a wide container gives a greater pressure because it holds more liquid. A student compares a narrow tube and a wide tank filled to the same depth and claims the tank has the larger pressure at the bottom.
The correct reasoning is that pressure depends on depth and density, and both tubes have the same depth of the same liquid. So the pressure at the bottom is equal. The wide tank holds more liquid, but that weight is spread over a larger base, so the pressure at the bottom is the same.
Check yourself
Using g = 10 N/kg, find the pressure due to the liquid at a depth of 2.0 m in an invented liquid of density 900 kg/m³. Then state the pressure at 1.0 m in the same liquid.
Answer
At 2.0 m: 2.0 × 900 × 10 = 18 000 Pa.
At 1.0 m: 1.0 × 900 × 10 = 9 000 Pa, which is half, because the depth is half.
What to study next
Read explaining buoyancy conceptually, where the pressure difference between top and bottom explains upthrust. Then try the force and pressure practice set.
The graph evidence and fair-comparison lab offers more data to compare. If you want a teacher to quiz you on predictions like these, see online one-to-one Science tuition.