  Spectral and timing properties of accretion flows on a black hole depend on
their density and temperature distributions, which in turn come from the
underlying dynamics. Thus, an accurate description of the flow which includes
hydrodynamics and radiative transfer is a must to interpret the observational
results. In the case of non-rotating black holes, Pseudo-Newtonian description
of surrounding space-time enables one to make a significant progress in
predicting spectral and timing properties. This formalism is lacking for
spinning black holes. In this paper, we show that there exists an exact form of
'natural' potential derivable from the general relativistic (GR) radial
momentum equation. Use of this potential in an otherwise Newtonian set of
equations allows to describe transonic flows very accurately as is evidenced by
comparing with solutions obtained from the full GR framework. We study the
properties of the critical points and the centrifugal pressure supported shocks
in the parameter space spanned by the specific energy and the angular momentum,
and compare with the results of GR hydrodynamics. We show that this potential
can safely be used for the entire range of Kerr parameter $-1<a<1$ for modeling
of observational results around spinning black holes. We assume the flow to be
inviscid. Thus, it is non-dissipative with constant energy and angular
momentum. These assumptions are valid very close to the black hole as the
infall timescale is much shorter as compared to the viscous timescale.
