  Winds arising from galaxies, star clusters, and active galactic nuclei are
crucial players in star and galaxy formation, but it has proven remarkably
difficult to use observations of them to determine physical properties of
interest, particularly mass fluxes. Much of the difficulty stems from a lack of
a theory that links a physically-realistic model for winds' density, velocity,
and covering factors to calculations of light emission and absorption. In this
paper we provide such a model. We consider a wind launched from a turbulent
region with a range of column densities, derive the differential acceleration
of gas as a function of column density, and use this result to compute winds'
absorption profiles, emission profiles, and emission intensity maps in both
optically thin and optically thick species. The model is sufficiently simple
that all required computations can be done analytically up to straightforward
numerical integrals, rendering it suitable for the problem of deriving physical
parameters by fitting models to observed data. We show that our model produces
realistic absorption and emission profiles for some example cases, and argue
that the most promising methods of deducing mass fluxes are based on
combinations of absorption lines of different optical depths, or on combining
absorption with measurements of molecular line emission. In the second paper in
this series, we expand on these ideas by introducing a set of observational
diagnostics that are significantly more robust that those commonly in use, and
that can be used to obtain improved estimates of wind properties.
