= Hydrostatics
<Hydrostatics> describes <fluids> at rest under applied <forces>. For a fluid with <mass density> $\rho$ in uniform downward <gravity>, vertical force balance gives $dp/dz=-\rho g$, where $z$ increases upward and $p$ is <pressure>.
For constant $\rho$, the pressure at depth $h$ below a free surface is $p=p_0+\rho gh$. Integrating the pressure over a submerged body yields <Archimedes' principle>: the upward <buoyant force> equals the weight of displaced fluid. The same balance explains both a liquid column in a manometer and the increase of atmospheric pressure toward the ground, although atmospheric density cannot generally be treated as constant.
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