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Fundamentals
Hydrostatic pressure
Pressure increase with depth in a still liquid.
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- Δp [kPa]
Pressure difference in pascals, ρ in kg/m³, g = 9.80665 m/s², h in metres of depth below point 1. Shown here in kilopascals.
In a liquid at rest, pressure increases with depth because of the weight of the liquid above. Every extra metre of water adds about 10 kPa.
Calculator
- Pressure rise10.05 bar
- Absolute pressure (with 101.325 kPa at surface)1,107 kPa
What drives the result
Each variable is moved across its typical range while the others stay at the values above. The longest bar is the key driver.
- About 10 m of water adds about 1 bar (100 kPa), a handy rule of thumb for divers and submarine crew.
- Pressure depends only on depth, not on the shape or width of the container.
- This is the pressure on top of the surface pressure. Add atmospheric pressure for the absolute value.
Chart data as tables
Ranked variables
| Variable | Typical range | Lowest result | Highest result | Swing (kPa) | Local step | Change in result |
|---|---|---|---|---|---|---|
| h Depth | 1 to 1,000 m | 10.05 | 10,050 | 10,040 | +10% | +10 % |
| ρ Liquid density | 800 to 1,400 kg/m³ | 784.5 | 1,373 | 588.4 | +10% | +10 % |
Sweep of Depth
| Depth (m) | Pressure rise (kPa) |
|---|---|
| 1 | 10.05 |
| 2.371 | 23.84 |
| 5.623 | 56.53 |
| 13.34 | 134 |
| 31.62 | 317.9 |
| 74.99 | 753.8 |
| 177.8 | 1,787 |
| 421.7 | 4,239 |
| 1,000 | 10,050 |
Sweep one variable
Variables and how each one contributes
Pressure rise
What the equation gives you. Everything else feeds it.
Liquid density
Density of the liquid (seawater is about 1025 kg/m³, fresh water 1000). Directly proportional, but liquids vary little, so this is a minor driver compared with depth.
Depth
Vertical depth below the reference point. Directly proportional: the dominant driver. Doubling the depth doubles the pressure rise.
Worked example with the values above
- ρgh = 1,025 kg/m³ × 9.80665 m/s² × 100 m = 1,005,000 Pa.
- Divide by 1000 to get kilopascals: 1,005 kPa.
- In bar that is 10.05 bar above the surface pressure.
Assumptions and limits
- Stationary liquid of constant density (incompressible).
- Depth measured vertically.
- Uniform gravity.
Common mistakes
- Forgetting to add atmospheric pressure when absolute pressure is needed.
- Mixing gauge and absolute pressure.
- Using the slant length of a pipe instead of the vertical depth.
Statistics and uncertainty
Depth dominates the uncertainty. With ρ known to 1% and depth to 2%, δp/p ≈ √(0.01² + 0.02²) ≈ 2.2%. Density varies with temperature and salinity, typically by up to 3% in seawater.
Where it is used
- Pressure on a submarine hull or a diving bell at depth.
- Tank, dam and bulkhead loads.
- Pressure sensors used as depth gauges.
Maths you need
- Density and weight: pressure from the weight of a column of liquid
- Pascal and bar: 1 bar = 100 kPa