  An analytic model is proposed for non-radiating accretion flows accompanied
by up or down winds in a global magnetic field. Physical quantities in this
model solution are written in variable-separated forms, and their radial parts
are simple power law functions including one parameter for wind strength.
Several, mathematically equivalent but physically different expressions of the
criterion for wind generation are obtained. It is suggested also that the
generation of wind is a consequence of the intervention of some mechanism that
redistributes the locally available gravitational energy, and that the
Bernoulli sum can be a good indicator of the existence of such mechanisms.
