= Steady accretion disk with arbitrary rotation law
For inward <accretion rate> $\dot M>0$, the steady <conservation of angular momentum> equation is $\mathcal G=\dot M(h-h_{\rm in})$ when the inner torque vanishes. The <viscous torque in an accretion disk> is $\mathcal G=2\pi qh\bar\nu\Sigma$, where $h=r^2\Omega$ and $q$ is the <orbital shear parameter>. Thus
$$
\bar\nu\Sigma=\frac{\dot M}{2\pi q}\left(1-\frac{h_{\rm in}}h\right).
$$
The familiar <Keplerian accretion disk> follows when $q=3/2$ and $h\propto r^{1/2}$. The general form also applies to the non-Keplerian <Paczyński-Wiita circular orbit> rotation law.
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