Theoretical analysis of the turbulent flow of non‐newtonian slurries in pipes

A theoretical model is derived which permits the analytical calculation of the friction factor‐Reynolds number curves for non‐Newtonian slurries flowing isothermally in smooth pipes. This model is based upon the Bingham plastic rheological equation of state. A change of mechanism in the transition phenomenon is observed to occur for NHe = 5 (105), where NHe is the familiar Hedstrom number. Below this value turbulence is suppressed relative to Newtonian flow, while above this value the transition is delayed but turbulence is enhanced relative to Newtonian flow. A set of theoretical design curves of friction factor versus Reynolds number covering laminar, transitional, and turbulent flows is calculated and presented for a range of NHe values from 103 to 109.