Hydrostatic pressure
ΔP = ρ × g × h
The pressure under a column of fluid, both ways: what pressure reigns h metres below the surface, or at what depth a given gauge pressure is reached. The tool always returns the gauge value (what the manometer reads) and the absolute one (what the gas law wants), in pascals, bars and atmospheres, because confusing them is the classic trap of the chapter. The usual fluids are preset, the surface pressure is adjustable (0 for a vacuum tank), and the diver’s rule "one bar every ten metres" is given with its exact value.
201840 Pa
- Calculation
- ΔP = ρ·g·h = 1025 kg/m³ × 9.80665 × 10 m = 100520 Pa
- Absolute pressure
- 2.0184 bar, that is 1.992 atm
The column adds 100520 Pa of gauge pressure: the absolute pressure is 2.0184 bar, that is 1.992 atm.
Gauge or absolute, the trap of the chapter: the diver’s gauge and the tyre inflator show the overpressure (zero at the surface), the ideal gas law and physiology want the absolute (one atmosphere at the surface). The tool always returns both, named.
The diver’s rule "one bar every ten metres" is a convenient approximation: the exact value is 9.95 m per bar in sea water, 10.2 m in fresh water. At 30 m, a diver breathes air at 4 atm absolute: that absolute is what governs nitrogen dissolution.
The pressure depends only on the depth, not on the shape of the container nor the amount of water: a one-square-centimetre tube and a lake produce the same pressure at ten metres. That is the hydrostatic paradox, and the reason a dam is sized by its water height, not by the volume held back.
Scientific dossier
What the tool computes, what it assumes, where it stops being valid, and where its data comes from.
Method & formulasΔP = ρ × g × h
ΔP = ρ × g × h
P_absolute = P_surface + ρ·g·h
h = ΔP / (ρ·g)
The gauge pressure is the weight of the fluid column per unit area: ρ·g·h. It adds to the surface pressure, the atmosphere in ordinary conditions. The inverse calculation gives the column height equivalent to a pressure, the barometer reading: 760 mm of mercury, 10.3 m of water.
- Gauge pressure
- · the pressure counted from the surface: zero at the surface. It is what usual manometers read, diving and tyres included.
- Absolute pressure
- · the pressure counted from vacuum: the surface is already at one atmosphere. It is what the ideal gas law and physiology expect.
- Standard atmosphere
- · exactly 101,325 Pa, by definition. Equals 1.01325 bar.
- Column height
- · the depth of fluid that produces a given pressure: the unit of barometers (mmHg) and head losses (metres of water column).
Validity domainThe formula holds for an incompressible fluid at rest: exact for liquids at usual depths (water compresses by only 0.
The formula holds for an incompressible fluid at rest: exact for liquids at usual depths (water compresses by only 0.5% per kilometre), it does not apply to the atmosphere over large heights, where the air density decreases with altitude (the pressure follows an exponential there, not a line). It also assumes uniform g, the conventional standard value 9.80665 m/s².
Reading the resultThe line "one more atmosphere every X metres" places the fluid at a glance: 10.
The line "one more atmosphere every X metres" places the fluid at a glance: 10.3 m for fresh water, 76 cm for mercury, and that is exactly why Torricelli chose mercury for his barometer. In diving, the absolute governs everything that matters: at 30 m, the breathed air is at 4 atm, nitrogen dissolves four times more, and decompression stops follow from it. The shape of the container never plays: only the vertical height counts.