  Here, we model the effect of non-uniform dynamical mass distributions and
their associated gravitational fields on the stationary galactic superwind
solution. We do this by considering an analogue injection of mass and energy
from stellar winds and SNe. We consider both compact dark-matter and baryonic
haloes that does not extend further from the galaxies optical radii $R_{\rm
opt}$ as well as extended gravitationally-interacting ones. We consider halo
profiles that emulate the results of recent cosmological simulations and
coincide also with observational estimations from galaxy surveys. This allows
to compare the analytical superwind solution with outflows from different kinds
of galaxies. We give analytical formulae that establish when an outflow is
possible and also characterize distinct flow regimes and enrichment scenarios.
We also constraint the parameter space by giving approximate limits above which
gravitation, self-gravitation and radiative cooling can inhibit the stationary
flow. We obtain analytical expressions for the free superwind hydrodynamical
profiles. We find that the existence or inhibition of the superwind solution
highly depends on the steepness and concentration of the dynamical mass and the
mass and energy injection rates. We compare our results with observational data
and a recent numerical work. We put our results in the context of the
mass-metallicity relationship to discuss observational evidence related to the
selective loss of metals from the least massive galaxies and also discuss the
case of massive galaxies.
