The flow of non-Newtonian materials through open channels has been little-studied compared to research on circular pipes. This paper presents a new Reynolds number to predict the flow of non-Newtonian thickened mining tailings slurries in open channels. Our aim is to model the frictional forces caused by a material's rheology in the laminar regime. The flow behaviour predictions by this and previous models are discussed and validated against previously published experimental data. It is shown that the newly-defined Reynolds number achieves an appropriate evaluation of the friction at the boundary and average velocities, when compared with the experimental data for Kaolin and Bentonite suspensions. The new model requires rheometer data to determine the fluid index (n*). It is preferred, as with tube viscometry, to set up a lab-scale flume from which n* can be determined graphically or by numerical differentiation. Alternatively the fluid index can be obtained from conventional rotational viscometry results.