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Engineering LibreTexts

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

\[
\label{static:eq:spherical}
    \dfrac{1} {r^2} \dfrac{d}{dr}  
        \left( \dfrac{r^2}{\rho} \dfrac{dP}{dr}\right)  
            + 4\,\pi\,G\rho = 0   \tag{120}
\]

Or in a vector form as  
\[
    \nabla \bullet \left( \dfrac{1}{\rho}\nabla P  \right) +  
        4\,\pi\,G\rho = 0  
    \label{static:eq:vSpherical} \tag{121}
\]

Contributors

  • Dr. Genick Bar-Meir. Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.2 or later or Potto license.