  We construct models of the inner part of a transonic adiabatic accretion disc
assuming constant specific angular momentum taking the vertical structure fully
into account.\\ For comparison purposes, we construct the corresponding one
dimensional viscous disc models derived under vertical averaging assumptions.
The conditions under which a unique location for the critical/sonic point is
obtained, given an appropriate set of exterior boundary conditions for these
models, is also discussed. This is not unique if the standard '$\alpha $'
prescription with viscous stress proportional to the angular velocity gradient
is used.\\ We use a simple model to discuss the possible limitations on the
form of the viscous stress arising from the requirement that viscous
information must travel at a finite speed. Contrary to results in the existing
literature, the viscous stress tends to be {\it increased} rather than reduced
for the type of flows we consider in which the angular momentum and angular
velocity gradients have opposite signs. However, finite propagation effects may
result in a unique location for the sonic point.\\ We found good agreement
between the radial flow and specific angular momentum profiles in the inner
regions of the one dimensional models and those in the equatorial plane for
corresponding two dimensional models which may be matched for a range of
$\alpha $ between 0.1 and 10$^{-4}$.
