= Wind-powered mass loss from a steady accretion disk
{title2=$\dot M'=2\pi RS,\quad\nu\Sigma=R\dot M'/(9\pi f)$}
For a <Keplerian disk>, let $S$ be the total loss through both faces per unit projected area and $\dot M>0$ the inward <accretion rate>. Annular <mass conservation> gives $\dot M'=2\pi RS$. A circular orbit has <specific orbital energy> $-GM/(2R)$, so a marginally escaping wind requires additional energy $GM/(2R)$ per unit lost mass. Equating this sink to a fraction $f$ of the two-face <viscous dissipation> $(9/4)\nu\Sigma\Omega^2$ gives the displayed relation. If the wind carries the local <specific angular momentum> $h=\sqrt{GMR}$, <conservation of angular momentum> gives $(\dot Mh-\mathcal G)'=h\dot M'$, with <viscous torque in an accretion disk> $\mathcal G=3\pi\nu\Sigma h$. Eliminating the torque yields $R^2\dot M''+\tfrac32R\dot M'=\tfrac32f\dot M$.
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