Effect of sharp crested orifice shape and Newtonian and Non-Newtonian fluid properties on discharge from a tank

Abstract

The flow rate measurement of Newtonian liquids through orifices of various shapes from tanks and pipes has been extensively studied, but not for non-Newtonian liquids. Non-Newtonian liquids have complex rheological properties that make it difficult to determine the discharge through orifices, from tanks. The only literature available was the flow rate measurement of Power law liquids through circular orifices, from a tank. Therefore, the aim of this work was to determine the flow rate of Newtonian and non-Newtonian liquids using circular, square and triangular sharp crested orifices out of a tank, as a function of liquids flow properties. The sharp-crested circular, square and triangular orifices with 8 mm, 12 mm, 16 mm, and 20 mm hydraulic diameters were fitted at the bottom of a square cross-sectioned tank to measure the flow rate of the liquids. A rectangular tank was suspended from a weighbridge with a load cell to capture the flow rate data. A high-speed camera was used to capture the videos for water test calibration purposes. A concentric cylinder viscometer was used to obtain the rheological parameters of the test liquids. The liquids tested included: Newtonian, Power law, Bingham and Herschel–Bulkley model systems. The discharge coefficient (Cd) and Reynolds number (Re) were calculated from the experimental results. The calibration average Cd value for all the orifices was 0.62, which is close to the oft-quoted value of 0.61 for Newtonian liquids and equal to the average Cd value found from a similar study. The Cd-Re relationship indicated that the orifice shape did not have an effect on the flow rate measurement of Newtonian and non-Newtonian liquids from a tank. It was found that for each model test liquid, there is a unique flow curve in the laminar region. The Newtonian, Power-Law, Herschel–Bulkley and Bingham liquids started at Re 11, 53, 232 and 330 respectively, for all orifice shapes. This was due to the varying rheological behavior of the liquids. In the turbulent region, all data coincided with Newtonian Cd values, with an average value of 0.64, not far off from the average Cd value of 0.67 found in previous studies. The range of Reynolds numbers tested in this study was between Re=11 and Re=63000. The idea of an effective shear rate for flow through the orifice was used to develop a new Reynolds number for different liquids, to consolidate the Cd-Re relationship to the Newtonian liquid curve in the laminar flow regime. The effective shear rate of 0.3v/dh was developed to consolidate the Power-law liquids Cd-Re relationship to Newtonian liquid curve. To collapse the Bingham and Herschel-Bulkley liquids on the Newtonian liquid data for the Cd- Re relationship in the laminar and transitional flow, the Bingham number was used to account for yield stress. The Herschel–Bulkley liquids were adjusted by alpha to change the Reynolds number to Newtonian liquids Re. A single composite model was used to predict the relationship between Cd and Re and the discharge equation was determined for all liquidorifice combinations used in this work. The discharge equation is only applicable for 8 mm<d<20 mm, 0<L/d<0.125 and 11<Re2< 63000. The predicted model can be used in engineering designs and processes.