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Numerical solution for stratified laminar flow of two immiscible Newtonian liquids in a circular pipe Gemmell, Alan Robert

Abstract

Numerical solutions of the velocity profiles for laminar, stratified flow of two immiscible, Newtonian liquids in a circular pipe were determined for viscosity ratios of 1, 10, 100 and 1000 at various interface positions. These results were used to calculate the theoretical volumetric flow rate enhancement factors, power reduction factors and hold-up ratios, which for laminar flow depend only upon the viscosity ratio and the interface position. The maximum volumetric flow rate enhancement factors and maximum power reduction factors, and the corresponding input volume ratios, were determined. Dimensionless quantities were used, making the results applicable to any pipe diameter, any liquid viscosities and any pressure gradient, providing laminar flow of both phases prevails. The theoretical results were compared to the experimental results of Russell, Hodgson and Govier for horizontal cocurrent flow of a mineral oil and water in a circular pipe. As expected, the two sets of results differed considerably in the region of turbulent water flow. As turbulence decreased however, the difference decreased, until in the laminar region very good agreement between the theoretical and experimental results was obtained.

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