Semi-empirical correlations Newitt et al. [4] have lead experiments in a 25.4 mm in diameter horizontal pipe, with various particles covering four specific masses (s = 1.18, s = 1.4, s = 2.6 and s = 4.1) and various sizes, the largest being of equivalent diameter 2.6 mm (10% of the pipe diameter). Theoretical considerations are used to derive expressions of the hydraulic gradient for different flow regimes (homogeneous, heterogeneous and flow with moving beds), and of the transition velocities between those regimes. For heterogeneous flows, i.e. for 17V0 6 V , the excess of friction is considered proportional to the energy dissipated by the particles as they fall under the action of gravity. This hypothesis leads to: