Liquid pressure depends on vertical depth, density and g, and on nothing else. Comparing two points therefore means comparing their depths and densities.
This lesson follows calculating pressure in solids and liquids and sits in SPM Physics pressure.
What does pressure depend on in a liquid?
Three things: the density ρ of the liquid, the gravitational field strength g, and the depth h below the free surface. Depth is always measured vertically.
Because P = ρgh, doubling the depth doubles the pressure in the same liquid. A liquid twice as dense gives twice the pressure at the same depth.
Worked example: three tanks, one pressure
An original experiment fills a tall thin tube, a wide bowl and a funnel-shaped vessel with water to 0.80 m above their bases.
Each base has P = 1000 × 10 × 0.80 = 8000 Pa. The tube holds far less water than the bowl, but the pressure is identical.
The bowl has a larger base, so the force on its base is larger, since F = PA. The pressures are equal, but the forces are not.
How do I compare two depths?
Use a ratio to skip the full calculation. A point at 6 m depth in a lake has three times the pressure of a point at 2 m, because 6 ÷ 2 = 3.
For two liquids, compare ρh. Point X is 0.30 m deep in oil of density 800 kg m⁻³ and point Y is 0.25 m deep in water of density 1000 kg m⁻³. ρh for X is 240 and for Y is 250, so Y has the slightly larger pressure.
When do I add atmospheric pressure?
Add it when the question asks for total or absolute pressure, because the air presses on the free surface. Take atmospheric pressure as 1.0 × 10⁵ Pa if your paper gives no value.
At 10 m depth in water, ρgh = 1000 × 10 × 10 = 1.0 × 10⁵ Pa. The total pressure is 1.0 × 10⁵ + 1.0 × 10⁵ = 2.0 × 10⁵ Pa.
The mistake that costs marks
A tube is tilted, and 0.50 m of liquid lies along it. The top of the liquid is only 0.30 m above the point in question.
| Step | Wrong | Right |
|---|---|---|
| Depth used | 0.50 m (length along tube) | 0.30 m (vertical height) |
| Pressure | 1000 × 10 × 0.50 = 5000 Pa | 1000 × 10 × 0.30 = 3000 Pa |
Draw a horizontal line at the liquid surface and a vertical line down to the point. That vertical line is h.
Check yourself
In an original aquarium, point A is 0.15 m below the water surface and point B is 0.45 m below it. Find the ratio of pressure at B to pressure at A. Does the answer change if the aquarium is replaced by a wider one?
Answer
The ratio is 0.45 ÷ 0.15 = 3, so the pressure at B is three times that at A.
The answer does not change with a wider aquarium, because depth, not width, controls liquid pressure.
What to study next
Pressure that changes with depth leads to buoyancy, because the bottom of a submerged object feels more pressure than its top. Continue with applying Archimedes’ principle or go to Pascal’s principle.
For help building clear comparison answers, see online one-to-one Physics tuition.