Pressure in a Liquid
Simple Explanation
Pressure in a liquid increases with depth, because deeper points must support the weight of all the liquid above them (plus any pressure already at the surface, such as the atmosphere). This pressure acts equally in all directions at a given depth.
Why Do We Need It?
Understanding how pressure varies with depth in a liquid explains phenomena from why deep-sea submarines need reinforced hulls to why dams are built thicker at the base.
Formula
Pressure at a Depth in a Liquid
P = P₀ + hρg
The total pressure at a depth in a liquid equals the pressure already present at the surface (usually atmospheric pressure) plus the additional pressure from the weight of the liquid above that depth.
- P
- — Total pressure at depth h, in Pa
- P₀
- — Pressure at the liquid surface (often atmospheric pressure), in Pa
- h
- — Depth below the surface, in metres
- ρ
- — Density of the liquid, in kg/m³
- g
- — Acceleration due to gravity, 9.8 m/s²
When to use it: Use to find the total pressure at any depth within a liquid, such as at the bottom of a swimming pool or tank.
Worked Example
Finding pressure at a depth in water
Find the total pressure at a depth of 10 m in water (ρ = 1000 kg/m³, g = 9.8 m/s², atmospheric pressure P₀ = 100,000 Pa).
Why Does This Work?
Pressure at a given depth results from the accumulated weight of all the liquid stacked above that point — the deeper the point, the more liquid weight is pressing down on it, so pressure increases linearly with depth (for a liquid of constant density).
Real-Life Example
Why dams are built thicker at the base
Dam walls are noticeably thicker at the bottom than at the top.
Since water pressure increases with depth, the base of a dam experiences far greater pressure from the water than the top does — engineers design dams thicker at the base specifically to withstand this much larger pressure.
Practice
Find the additional pressure (beyond atmospheric) at a depth of 5 m in water (ρ = 1000 kg/m³, g = 9.8 m/s²).
MediumCommon mistake
Forgetting to add atmospheric pressure (P₀) when finding the TOTAL pressure at a depth — hρg alone gives only the additional pressure due to the liquid, not the full pressure including the atmosphere pressing on the surface above.
Quick Review
- Pressure increases with depth: P = P₀ + hρg.
- Pressure at a given depth acts equally in all directions.
- Deeper structures (dam bases, submarine hulls) must withstand much greater pressure.