Flow Rate Measurement of Non-Newtonian Fluids through Sharp Crested Notches

Sharp crested notches, particularly rectangular and V-shaped ones, have been used to measure the flow rate of water in open channels for a long time. However, they have not been used to measure the flow rate of non-Newtonian fluids. The aim of this work is to explore the possibility of extending their range of application to non-Newtonian fluids, especially for rectangular and V-shaped notches. An experimental facility in the flow process research laboratory was used to perform the extensive tests reported herein. The notches and an in-line tube viscometer were calibrated using water. The in-line tube viscometer was used to determine the fluid rheology. Three different types of non-Newtonian fluids [namely, aqueous solution of carboxymethyl cellulose (CMC) solutions and water-based suspensions of kaolin and bentonite] were used as model test fluids. The experimental values of the coefficient of discharge ($C_d$) were plotted against three different definitions of the Reynolds number denoting different underlying physical ideas. In the laminar conditions, the discharge coefficient exhibited the classical dependence on the Reynolds number with slopes of approximately 0.43–0.44. On the other hand, the discharge coefficient was nearly constant in the turbulent flow regime. Single composite power-law function was used to correlate the present $C_d-\mathsf{R}$ for each of the two notch shapes used here. Using these correlations, the $C_d$ values could be predicted to within $\pm 5\%$ for the rectangular and the V notches.