  We address the dusty wind problem, from the point where dust formation has
been completed and outward. Given grain properties, both radiative transfer and
hydrodynamics components of the problem are fully defined by four additional
input parameters. The wind radiative emission and the shape of its velocity
profile are both independent of the actual magnitude of the velocity and are
determined by just three dimensionless free parameters. Of the three, only one
is always significant---for most of phase space the solution is described by a
set of similarity functions of a single independent variable, which can be
chosen as the overall optical depth at visual \tV. The self-similarity implies
general scaling relations among mass loss rate (\Mdot), luminosity ($L$) and
terminal velocity (\vf). Systems with different \Mdot, $L$ and \vf but the same
combination $\Mdot/L^{3/4}$ necessarily have also the same $\Mdot\vf/L$.
  ... Eliminating \tV produces $\vf^3 = A \Mdot(1 + B \Mdot^{4/3}/L)^{-1.5}$,
where $A$ and $B$ are coefficients that contain the only dependence of this
universal correlation on chemical composition. At a given $L$, the maximal
velocity of a dusty wind is $v\sub{max} \propto L^{1/4}$ attained at $\Mdot
\propto L^{3/4}$, with proportionality coefficients derived from $A$ and $B$.
