Pressure in Fluids
Simple Explanation
Within a liquid, pressure increases with depth: P = hρg. This is because a deeper point has a taller, heavier column of liquid pressing down on it. Atmospheric pressure works the same way — it is the weight of the whole column of air above pressing down, which is why atmospheric pressure decreases with altitude.
Why Do We Need It?
This principle explains why deep-sea divers need pressurized suits, why dams are built thicker at the bottom than the top, and why your ears "pop" when you dive to the bottom of a swimming pool.
Formula
Pressure Due to a Liquid Column
P = hρg
The pressure at a depth within a liquid depends only on how deep the point is, the density of the liquid, and gravity — not on the shape or width of the container.
- P
- — pressure due to the liquid column, in pascals (Pa)
- h
- — depth below the liquid surface, in metres (m)
- ρ
- — density of the liquid, in kilograms per cubic metre (kg/m³)
- g
- — the acceleration due to gravity, approximately 9.8 m/s²
When to use it: Whenever the pressure at a given depth within a liquid needs to be found — for example, water pressure at the bottom of a tank, or atmospheric pressure modeled as a column of air.
Worked Example
Find the pressure at the bottom of a water tank
A water tank is filled to a depth of 3 m. Using the density of water (1000 kg/m³) and g = 9.8 m/s², find the pressure due to the water at the bottom of the tank.
Why Does This Work?
The weight of the liquid column directly above a point is what presses down on it — a taller column (bigger h) or a denser liquid (bigger ρ) both mean more weight pressing down on the same area, and therefore more pressure.
Real-Life Example
Why dams are thicker at the base
Large dams holding back a reservoir are noticeably thicker and stronger at the bottom than near the top of the water.
Since water pressure increases with depth, the base of the dam must withstand far greater pressure than the top, which is why engineers build it thicker there.
Practice
Find the pressure due to a 1.5 m depth of water (density 1000 kg/m³, g = 9.8 m/s²).
MediumCommon mistake
Assuming pressure at a given depth depends on the shape or width of the container — it does not; pressure only depends on the depth, the liquid's density, and gravity, regardless of the container's width or shape.
Quick Review
- P = hρg — pressure due to a liquid column.
- Pressure in a fluid increases with depth.
- Atmospheric pressure decreases with altitude for the same reason, in reverse.