Model Dependence of Transonic Properties of Accretion Flows Around Black   Holes
  We analytically study how the behaviour of accretion flows changes when the flow model is varied. We study the transonic properties of the conical flow, a flow of constant height and a flow in vertical equilibrium and show that all these models are basically identical provided the polytropic constant is suitably changed from one model to another. We show that this behaviour is extendible even when standing shocks are produced in the flow. The parameter space where shocks are produced remain roughly identical in all these models when the same transformation among the polytropic indices is used. We present applications of these findings. 
S.K. Chakrabarti and Santabrata Das