# 4.3.6 Liquid Phase


While for most practical purposes, the Cartesian coordinates provides sufficient treatment to the problem, there are situations where the spherical coordinates must be considered and used. Derivations of the fluid static in spherical coordinates are

Pressure Spherical Coordinates

$\label{static:eq:spherical} \dfrac{1} {r^2} \dfrac{d}{dr} \left( \dfrac{r^2}{\rho} \dfrac{dP}{dr}\right) + 4\,\pi\,G\rho = 0$

Or in a vector form as

$\nabla \bullet \left( \dfrac{1}{\rho}\nabla P \right) + 4\,\pi\,G\rho = 0 \label{static:eq:vSpherical}$