Separated flow models are of great interest to model two-phase flow such as Stratified, Stratified-Wavy and Annular flow patterns. Taitel and Dukler proposed a model for Stratified flow assuming that the interfacial effects can be neglected and modelled the pressure drop assuming smooth walls. Based on a new definition of hydraulic diameter for two-phase flows in channels and including the effect of shear on the interface, it is possible to obtain a more general analytical solution for Stratified flow. An extension to Annular flow is possible with the same model, but here the roughness of the tube walls and the interface is taken into account. This model allows a comprehensive approach to modelling of two-phase flow phenomena in the form of partial Reynolds numbers, partial pressure drops, partial rates of dissipation and partial rates of interfacial entrainment, and allows a direct comparison to be made between Stratified and Annular flows. This new model is an interesting platform that can be related to experimental data by the friction factors of the four surfaces of contact.