 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.

Hydrostatics is a branch of physics and fluid mechanics that deals with the behavior of stationary fluids. It focuses on the study of fluids at rest and the forces exerted by these fluids on surrounding surfaces. Key concepts in hydrostatics include: 1. **Pressure**: Hydrostatic pressure is the pressure exerted by a fluid due to the weight of the fluid above it.