# Hydrostatic Equation

## Table of Contents

The hydrostatic pressure in a system is the pressure exerted by a fluid at equilibrium due to the force of gravity. The following equations are used to describe the hydrostatic pressure force:

$$ \frac{dP}{dz} = - \rho g $$

$$ P = P_0 - \rho g z $$

$$ \Delta P = \rho g \Delta z $$

Where

- \( \small P \) is the pressure,
- \( \small P_0 \) is the pressure at some reference point,
- \( \small z \) is the height above the reference point,
- \( \small \small \rho \) is the density of the fluid, and
- \( \small \small g \) is the acceleration due to gravity.

Note that the negative sign means that the pressure decreases with increasing height.