Scaling in pipeline flow of Kaolin suspensions

Abstract

The dimensionless analysis is applied to pipeline transportation of Kaolin suspensions. Experimental data were obtained for flow through pipes of different diameters. The rheological properties of materials under study were characterized by the Hershel–Bulkley equation. The method of constructing the modified Reynolds number, Rem for visco-plastic materials was discussed. It was shown that in a wide range of the Reynolds number (up to five decimal orders) the experimental data is well fitted by the standard f = 16/Rem dependence up to the laminar-to-turbulent transition point. The transition point (critical Reynolds number, View the MathML source) is a linear function of the pipe diameter. At View the MathML source, the f(Rem) becomes dependent upon pipe diameter. Using the View the MathML source value as a scaling factor, it is possible to construct a universal dependence of View the MathML source versus View the MathML source, which is valid for the entire range of velocities and pipe diameters under study. In the laminar-to-turbulent transition zone this dependence approaches the asymptote View the MathML source and the pressure gradient becomes a quadratic function of average velocity.