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.
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