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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.