Non-Newtonian fluid flow measurement using sharp crested notches

Abstract

Notches, particularly rectangular and V shaped are the cheapest and most common devices used to measure the flow rate of water in open channels. However, they have not been used to measure the flow rate of non-Newtonian fluids. These viscous fluids behave differently from water. It is difficult to predict the flow rate of such fluids during transportation in open channels due to their complex viscous properties. The aim of this work was to explore the possibility of extending the application of especially rectangular and V-shaped notches to non-Newtonian fluids. The tests reported in this document were carried out in the Flow Process and Rheology Centre laboratory. Notches fitted to the entrance of a 10 m flume and an in-line tube viscometer were calibrated using water. The in-line tube viscometer with 13 and 28 mm diameter tubes was used to determine the fluid rheology. Flow depth was determined using digital depth gauges and flow rate measurements using magnetic flow meters. Three different non-Newtonian fluids, namely, aqueous solutions of Carboxymethyl Cellulose (CMC) and water-based suspensions of kaolin and bentonite were used as model non-Newtonian test fluids. From these the coefficient of discharge (Cd) values and appropriate non-Newtonian Reynolds numbers for each fluid and concentration were calculated. The experimental values of the coefficient of discharge (Cd) were plotted against three different definitions of the Reynolds number. Under laminar flow conditions, the discharge coefficient exhibited a typical dependence on the Reynolds number with slopes of ~0.43-0.44 for rectangular and V notches respectively. The discharge coefficient was nearly constant in the turbulent flow regime. Single composite power-law functions were used to correlate the Cd-Re relationship for each of the two notch shapes used. Using these correlations, the Cd values could be predicted to within ±5% for the rectangular and V notches. This is the first time that such a prediction has been done for a range of non-Newtonian fluids through sharp crested notches. The research will benefit the mining and food processing industries where high concentrations of non-Newtonian fluids are transported to either disposal sites or during processing.