Scaling in pipeline flow of Kaolin suspensions

The dimensionless analysis is applied to pipeline transportation of Kaolin suspensions. Experimental data were obtained for flow through pipes of different diameters. The theological properties of materials under study were characterized by the Hershel-Bulkley equation. The method of constructing the modified Reynolds number, Re-m 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/Re-m dependence up to the laminar-to-turbulent transition point. The transition point (critical Reynolds number, Re*(m)) is a linear function of the pipe diameter. At Re-m > Re*(m), the f(Re-m) becomes dependent upon pipe diameter. Using the Re*(m) value as a scaling factor, it is possible to construct a universal dependence of fRe*(m) versus Re-m/Re*(m), 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 f Re*(m) = 14 and the pressure gradient becomes a quadratic function of average velocity. (c) 2006 Elsevier B.V. All rights reserved.