Hydrostatic

A fluid is hydrostatic when it is at rest, or moving slowly enough that viscous and inertial forces are negligible compared to gravity. In that limit, pressure depends only on vertical position and the column of fluid above: dp/dz = −ρg, so p(z) = p_atm + ρ·g·h for depth h.

The hydrostatic equation underpins barometers, manometers, the depth-dependent pressure divers experience, and the stratified equilibrium of stars and planetary atmospheres. It fails when the fluid has significant motion — pipe flow, wind, ocean currents — where Bernoulli and Navier-Stokes take over.