  I review the multiphase cooling flow equations that reduce to a relatively
simple form for a wide class of self-similar density distributions described by
a single parameter, $k$. It is shown that steady-state cooling flows are
\emph{not} consistent with all possible emissivity profiles which can therefore
be used as a test of the theory. In combination, they provide strong
constraints on the temperature profile and mass distribution within the cooling
radius. The model is applied to ROSAT HRI data for 3 Abell clusters. At one
extreme ($k\sim1$) these show evidence for cores in the mass distribution of
size 110--140$ h_{50}^{-1}$kpc and have temperatures which decline towards the
flow centre. At the other ($k\mapsto\infty$), the mass density and gas
temperature both rise sharply towards the flow centre. The former are more
consistent with measured temperatures, which suggests that the density
distribution in the intracluster medium contains the minimum possible mixture
of low-density components.
