  We present a versatile family of model galactic outflows including
non-uniform mass and energy source distributions, a gravitational potential
from an extended mass source, and radiative losses. The model easily produces
steady-state wind solutions for a range of mass-loading factors, energy-loading
factors, galaxy mass and galaxy radius. We find that, with radiative losses
included, highly mass-loaded winds must be driven at high central temperatures,
whereas low mass-loaded winds can be driven at low temperatures just above the
peak of the cooling curve, meaning radiative losses can drastically affect the
wind solution even for low mass-loading factors. By including radiative losses,
we are able to show that subsonic flows can be ignored as a possible mechanism
for expelling mass and energy from a galaxy compared to the more efficient
transonic solutions. Specifically, the transonic solutions with low
mass-loading and high energy-loading are the most efficient. Our model also
produces low-temperature, high-velocity winds that could explain the prevalence
of low-temperature material in observed outflows. Finally, we show that our
model, unlike the well-known Chevalier & Clegg (1985) model, can reproduce the
observed linear relationship between wind X-ray luminosity and star formation
rate (SFR) over a large range of SFR from $1-1000$ M$_{\odot}$/yr assuming the
wind mass-loading factor is higher for low-mass, and hence, low-SFR galaxies.
We also constrain the allowed mass-loading factors that can fit the observed
X-ray luminosity vs. SFR trend, further suggesting an inverse relationship
between mass-loading and SFR as explored in advanced numerical simulations.
