Pressure in a static fluid increases linearly with depth, regardless of container shape. This is the foundation of dam design, tank engineering, and why your ears hurt at the bottom of a pool but not at the top.

The governing equation is beautifully simple:

P = ρ·g·h

• P = gauge pressure (Pa)
• ρ = fluid density (kg/m³) — water is 1000, seawater ~1025, mercury 13,560
• g = 9.81 m/s²
• h = depth below the free surface (m)

Rule of thumb: water adds ~9.81 kPa per meter of depth, or roughly 0.433 psi per foot. So a 10 m water column produces ~98 kPa — almost exactly one atmosphere. Submarine designers and scuba divers internalize this immediately: every 10 m of seawater adds another atmosphere of pressure.

The shape doesn't matter — only depth does. This is the "hydrostatic paradox." A narrow vertical tube and a wide swimming pool, both filled to the same height, exert the same pressure at the bottom. The pressure pushes equally in all directions at any given point.

Why dams taper: Pressure at the base of a 50 m dam is 50 × 9.81 = 490 kPa (~71 psi). At the top, it's zero. Because force grows with depth, the wall must resist a triangular load distribution — maximum at the bottom, zero at the surface. The total horizontal force per unit width is:

F = ½·ρ·g·h²

For that 50 m dam: F = 0.5 × 1000 × 9.81 × 2500 = 12.26 MN per meter of dam length. And critically, this resultant acts at h/3 above the base — the centroid of the triangle — which dictates the overturning moment the foundation must resist.

Real-world example: The Hoover Dam is 221 m tall. Base pressure is ~2.17 MPa (315 psi) — about the pressure inside a typical bicycle CO₂ cartridge, pushing constantly against millions of square meters. The dam is 200 m thick at the base but only 14 m thick at the crest. That ratio isn't aesthetic; it's the triangular pressure profile rendered in concrete.

Practical implications for engineers:

• Tall storage tanks need thicker lower courses (often staggered plate thickness).
• Submerged pipes resist crushing loads that scale with depth.
• Pressure-rated fittings on tank outlets are sized for filled head, not nominal pressure.
• Atmospheric pressure adds ~101 kPa for absolute calculations — usually ignored for gauge-pressure structural design but critical for cavitation and boiling-point work.