Hydrostatic Pressure

Hydrostatic pressure: P = ρ·g·h

Hydrostatic pressure measures the force per unit area exerted by a fluid column at rest due to gravity: P = ρ·g·h (gauge pressure, above atmospheric) or P_total = P_atm + ρ·g·h (absolute pressure). It depends only on fluid density (ρ), gravity (g) and depth (h) — never on the shape or cross-sectional area of the container. This counter-intuitive fact is known as the hydrostatic paradox and was first formalized by Simon Stevin in 1586 as Stevin's law. Example: each 10 m of fresh water adds roughly 1 atm (≈ 101,325 Pa) to the pressure. A scuba diver at 30 m experiences about 4 atm absolute — 3 atm from the water plus 1 atm from the atmosphere — which compresses the lungs and dissolves more nitrogen in the blood, leading to narcosis if not properly managed.

Applications

Scuba diving (decompression tables from DAN), dam engineering (wall thickness grows with depth because pressure grows linearly), submarine and deep-sea vessel design, water-supply networks, and clinical medicine (arterial pressure must be measured at heart level, since each 10 cm offset changes the reading by about 7.5 mmHg of liquid column).

FAQ

Does the container's shape change the pressure? No. At the same depth in the same fluid, pressure is identical in a thin straw and a wide tank — this is the hydrostatic paradox.

Why does pressure rise so quickly with depth in water? Because water is roughly 800× denser than air; 10 m of water weighs the same column as the entire atmosphere above us.

Gauge or absolute pressure? Use gauge (P = ρ·g·h) for structural calculations like dams; use absolute (P_atm + ρ·g·h) for diving physiology and gas-solubility problems.