  An analytical MHD model of a normal-polarity prominence with compressible
flow is presented. The exact solution is constructed via a systematic nonlinear
separation of variables method used to calculate several classes of MHD
equilibria in Cartesian geometry and uniform gravity. Although the model is 2D,
a third magnetic/velocity vector field component is included and the highly
sheared fields observed in prominences are reproduced. A description is given
of the balance of gas pressure gradient with gravity and the Lorentz or
inertial forces acting along and across the prominence. It is found that the
flow does not significantly influence the heating profile. The analyzed model
has dimensions, plasma density, temperature and velocity profiles which agree
with those in the observations literature.
