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\begin{equation}  \frac{\partial P}{\partial z} = \rho \frac{GMz}{\left( r^2 + z^2 \right)^{3/2}}  \end{equation}  or when the disk scale height is much smaller than the disk radius, $H \ll r$ r$,  \begin{equation}  \frac{P}{H} = \rho \frac{GMH}{r^{3}}  \end{equation}