Fluid Pressure by Depth

Hydrostatic pressure: P = ρ·g·h

Stevin's law (1586) says the pressure from a column of fluid at rest comes down to three things: its density ρ, the gravity g (≈ 9.81 m/s²) and the depth h. Put them together and you get P = ρ·g·h. The shape of the container plays no part, which is the so-called hydrostatic paradox. In seawater (ρ ≈ 1025 kg/m³) every 10 m down piles on about 1 atm (≈ 101 325 Pa) of gauge pressure, so a diver at 30 m feels 4 atm absolute: the one atmosphere overhead plus three from the water. Work it through for fresh water at h = 10 m (ρ = 1000 kg/m³) and you get P = 1000·9.81·10 = 98 100 Pa, roughly 0.97 atm gauge, or 1.97 atm absolute once you count the atmosphere sitting on the surface.

Applications

Scuba diving leans on it heavily: DAN safety tables and decompression schedules use P to work out nitrogen partial pressures and keep divers clear of decompression sickness. Dam design does too, since the load on the base grows with h and the wall has to get thicker the deeper it goes. You'll also run into it in pressurized vessels and water reservoirs, submarine engineering, hemodynamics (the blood-pressure gap between head and feet), siphons and water-supply networks where pumping head matters, and in industrial level sensors and manometers.

FAQ

Why doesn't the shape of the container matter? Pressure tracks depth, not the volume of fluid sitting above. Fill two glasses to the same water height and the pressure at the bottom is identical, however wide or narrow each one is.

Is the result absolute or gauge pressure? P = ρ·g·h hands you gauge pressure, measured above the local atmosphere. Tack on 1 atm (≈ 101 325 Pa) and you have absolute pressure, the figure divers actually need for their gas calculations.

Does it apply to compressible fluids like air? Only as a rough approximation over short heights. Across a big altitude range the density itself shifts, so the linear ρgh gives way to the barometric formula with its exponential decay.