Friction factor-Reynolds number relationship for laminar flow of non-Newtonian fluids in open channels of different cross-sectional shapes

Abstract

The effect of channel shape on the friction factor-Reynolds number relationship for laminar, open channel flow of three non-Newtonian fluids was investigated. For each channel shape, the data can be described by a general relationship, f=K/Re where f is the Fanning friction factor and Re is the appropriate Haldenwang et al. (2002) Reynolds number corresponding to the flow curve model used to describe the non-Newtonian behaviour exhibited by the test fluid. The K values were found to be 14.6 for triangular channels with a vertex angle of 90°, 16.2 for semi-circular channels, 16.4 for rectangular channels and 17.6 for trapezoidal channels with 60° sides. These K values were found to be in line with those reported by Straub et al. (1958) and Chow (1959) for open channel flow of Newtonian fluids as opposed to the assumption made by Haldenwang et al., 2002 and Haldenwang et al., 2004 of using a constant value of 16 based on the pipe flow paradigm for all channel shapes.