Power law and composite power law friction factor correlations for laminar and turbulent non-Newtonian open channel flow

Abstract

Extensive experimental results conducted in a 10-m flume for various types of non-Newtonian fluids spanning a range of cross-sectional open channel shapes are presented and analysed in depth in this work. Open channel flow of non-Newtonian slurries is relevant in mining and chemical engineering applications. This database coupled with the literature data is used to develop the generalised friction factor–Reynolds number correlations in a unified fashion. Much confusion still exists in the literature regarding the definition of non-Newtonian Reynolds numbers. This difficulty is circumvented by considering two widely accepted definitions of the Reynolds number, namely due to Haldenwang et al. (Hydrotransport 15: 15th international conference on the hydraulic transport of solids in pipes, Banff, pp 755–768, 2002) for open channel flow and the modified Metzner–Reed pipe flow Reynolds number adapted for open channel flow. Three different types of purely viscous non-Newtonian fluids in rectangular, trapezoidal, triangular and semi-circular channel shapes were tested. The modelling procedure of Garcia et al. (Int J Multiph Flow 29:1605–1624, 2003) used for pipe flow predictions was extended to the present work. The logistic dose curves based on the Reynolds number proposed by Haldenwang et al. [14] performed better than those based on the adapted Metzner–Reed Reynolds number. Correlations developed can be used for the design of open channels of various shapes to transport non-Newtonian fluids.