hydrostatically

Hydrostatically is an adverb relating to hydrostatics, the branch of physics and engineering concerned with fluids at rest and the pressure they exert due to gravity. In hydrostatics, pressure at a given depth in a liquid increases with depth, following P = P0 + ρ g h, where P0 is the surface pressure, ρ is the liquid density, g is gravitational acceleration, and h is depth. This relation implies that the shape of the container does not affect bottom pressure.

Key concepts include that the pressure difference with depth leads to buoyancy, described by Archimedes' principle, and that fluids in communicating vessels equilibrate to a common height. In many cases ρ varies with depth or altitude, such as in the atmosphere, but hydrostatic approximations assume small variations or constant density.

Applications include the design and analysis of dams, water supply and irrigation systems, ships and submarines, and manometers and barometers. In meteorology, the hydrostatic equation describes the vertical balance between gravity and pressure gradient in the atmosphere, used to model atmospheric pressure profiles.

Limitations: hydrostatics applies to fluids at rest; when fluids move, hydraulics or fluid dynamics must be used. Incompressible flow is a common assumption; compressibility introduces corrections, especially in gases at high altitude or velocity.

Etymology: hydrostatic derives from Greek hydōr water and statikos standing, implying a stationary fluid.