Effect of round orifice aspect ratios on Non-Newtonian fluid discharge from tanks

Abstract

Flow rate measurement of Newtonian and non-Newtonian liquids out of tanks and reservoirs has been conducted broadly dating as far back as the 16th century. However, as far as can be ascertained, the outflow of non-Newtonian liquids from the bottom of a tank has only been reported in a few papers. Non-Newtonian liquids behave differently from water; they have complex rheological characteristics. It is therefore difficult to determine the flow rate of these liquids when they are discharged from the bottom of a tank. The aim of this work is to establish the impact of round orifice aspect ratios (L/d) on the gravitational discharge of non-Newtonian liquids from a tank, as a function of liquid properties. Tests were carried out in the Flow Process and Rheology Centre laboratory of the Cape Peninsula University of Technology. A rectangular tank with clear Perspex walls (0.4, 0.4 and 0.6) m was used for conducting the tests. Four circular orifices – 20 mm in diameter with lengths of 1, 20, 60 and 100 mm and L/d ratios 0.05 (sharp-crested), 1, 3 and 5, respectively – were each fitted in the bottom centre of the tank, flush with the inside surface. The change in liquid weight was measured by a load cell. For calibration purposes, water was used. Various concentrations of glycerine solutions were used as Newtonian liquids, and aqueous solutions of carboxymethylcellulose (CMC) and water-based suspensions of kaolin and bentonite were used as non-Newtonian liquids. The rheology of the tested liquids was established using a Paar-Physica MCR 300 rotational rheometer. Flow rate measurements were conducted for each liquid and concentration. From these, the coefficient of discharge (Cd) values and appropriate Reynolds number was calculated. Data analysis was presented in the form of Cd against the Reynolds number. The existing literature shows that in the turbulent region, Newtonian and non-Newtonian liquids have an average Cd value of 0.62 and 0.67, respectively, irrespective of the L/d ratio used. Calibration results of the current study showed that in the turbulent flow there was a non-consistent increase in Cd values as the L/d ratio increased. For Newtonian liquids the Cd was nearly constant with average Cd values of 0.60, 0.59, 0.80 and 0.78 for L/d ratios of 0.05, 1, 3 and 5, respectively. For Newtonian liquids, a single composite power-law function was used to relate the Cd versus Re relationship for each L/d ratio. The correlations estimated the Cd values to within ±3 % error margins. This thesis adds new coefficient of discharge and Reynolds number data from laminar to turbulent region for an L/d ratio of 5 to the literature. It also adds other kinds of non-Newtonian liquids. Findings from this research will benefit the food processing and engineering industries where high concentrations of non-Newtonian liquids are stored and transported from one tank to the other.