Non-Newtonian fluid flow from bottom of tank using orifices of different shapes

Abstract

The use of orifices in measuring and regulating the discharge of Newtonian liquids from tanks has been studied extensively. For non-Newtonian liquids, this is not the case mainly due to the complex rheological properties of such liquids. To date only circular orifices have been used to measure the flow of Power-Law liquids from a tank. In this work, a range of non-Newtonian liquids flowing from a tank through different sizes of sharp crested circular, square and triangular orifices have been tested. A rectangular tank suspended from a weighbridge with a load cell was used and the orifices were fitted at the bottom of the tank for the discharge measurement. The rheological parameters of the test liquids were obtained using a concentric cylinder viscometer. The liquids tested included Newtonian, Power-law, Bingham and Herschel–Bulkley model liquids. The height-time data was transformed into discharge coefficient (Cd)-Reynolds number (Re) format for each liquid-orifice combination in all cases. The average Cd value was 0.64 in the turbulent region. Each model liquid in the laminar regime resulted in a unique relationship. Using an idea of an effective shear rate for flow through the orifice, a new Reynolds number has been defined for the different liquids to consolidate the Cd-Re relationship to the Newtonian liquid curve. A single composite model was used to predict the relationship between Cd and Re for all liquids-orifices combinations used in this work. This can be used in the engineering designs and processes.