The effect of shape on laminar flow in open channels for non-Newtonian fluids

Abstract

The effect of the cross-sectional shape on the laminar flow of fluids in open channels has been investigated by researchers such as Straub et al. (1) for Newtonian fluids and Kozicki and Tiu (2) for non-Newtonian fluids. These researchers deemed it necessary to include reasonably complex shape factors to accommodate the effect of the cross-sectional shape on the flow behaviour. The Flow Process Research Centre at the Cape Technikon is currently investigating the shape effect, and open channels of three different shapes, namely rectangular, semi-circular and trapezoidal were used. Two smooth tilting flumes that could accommodate the three shapes with flow widths of 150 and 300 mm were used to test various concentrations of kaolin and bentonite suspensions as well as Carboxymethylcellulose (CMC) solutions in water. By using the appropriate Reynolds numbers Haldenwang et al. (3) have shown that laminar data can be correlated on a standard Moody diagram. In laminar flow, the friction factor can be predicted for all the materials tested. The objective of this paper is to test the efficacy of the definitions of the Reynolds numbers due to Haldenwang et al (3) and that of Kozicki and Tiu (2) in correlating the laminar friction factor data for these shapes. Based on extensive comparisons, it can be concluded that for the shapes and fluids tested, the shape issue is adequately accounted for by the much simpler Reynolds number proposed by Haldenwang et al. (3), which entails the use of only the hydraulic radius as opposed to the two parameters introduced by Kozicki and Tiu (2).