  A simple 1D dynamical model of thermally driven disc winds is proposed, based
on the results of recent, 2.5D axi-symmetric simulations. Our formulation of
the disc wind problem is in the spirit of the original Parker (1958) and Bondi
(1952) problems, namely we assume an elementary flow configuration consisting
of an outflow following pre-defined trajectories in the presence of a central
gravitating point mass. Viscosity and heat conduction are neglected. We
consider two different streamline geometries, both comprised of straight lines
in the (x,z)-plane: (i) streamlines that converge to a geometric point located
at (x,z)=(0,-d) and (ii) streamlines that emerge at a constant inclination
angle from the disc midplane (the x-axis, as we consider geometrically thin
accretion discs). The former geometry is commonly used in kinematic models to
compute synthetic spectra, while the latter, which exhibits self-similarity, is
likely unused for this purpose, although it easily can be with existing
kinematic models. We make the case that it should be, i.e. that geometry (ii)
leads to transonic wind solutions with substantially different properties owing
to its lack of streamline divergence. Both geometries can be used to complement
recent efforts to estimate photoevaporative mass loss rates from protoplanetary
discs. Pertinent to understanding our disc wind results, which are also
applicable to X-ray binaries and active galactic nuclei, is a focused
discussion on lesser known properties of classic Parker wind solutions. We find
that the parameter space corresponding to decelerating Parker wind solutions is
made larger due to rotation and leads instead to disc wind solutions that
always accelerate after the bulk velocity is slowed to a minimum value.
Surprisingly, Keplerian rotation may allow for two different transonic wind
solutions for the same physical conditions.
