Hydrostatic

Hydrostatics is the branch of fluid statics that studies fluids at rest and the forces they exert on submerged bodies and container walls. It explains how pressure is transmitted and distributed in fluids when there is no motion.

In a fluid at rest, pressure is isotropic and increases with depth. The pressure at a point depends only on vertical position and the density of the fluid, not on container shape. The hydrostatic equation describes this change: dP/dz = -ρ g. For a constant density ρ, the pressure at a depth h below a reference surface is P = P0 + ρ g h, where P0 is the pressure at the reference point.

Pascal's law states that pressure applied to a confined fluid is transmitted equally in all directions; this principle underpins hydraulic systems and pressure measurement.

Buoyancy, described by Archimedes’ principle, arises from hydrostatic pressure on submerged surfaces: a body experiences an upward force equal to the weight of the displaced fluid.

Applications include design of dams, water tanks, pipelines, submarines and ships, as well as devices such as manometers and barometers, which rely on liquid columns to measure pressure.

Assumptions include incompressible, non-flowing fluids with uniform density; real fluids may exhibit density variation with depth due to temperature or salinity, and in gases compressibility and stratification must be considered.

Historically, hydrostatics drew on the work of Archimedes and later experiments by Pascal and Torricelli, whose insights laid the foundation for modern fluid statics.