Notice of Retraction: The Friction Coefficient for Solid-Liquid Two-Phase Flows with Coarse Particles in Vertical Pipes

Abstract

The hydraulic transport of solid mineral particles in a vertical pipe is used in many engineering applications, for example in ocean mining. Tested pipe friction data of solid- liquid two-phase flow on vertical pipes, both stationary and horizontally vibrating, were analyzed and expressed in dimensionless formula to show the pipe frictional factor in relation with Reynolds number. It was shown that the solid- liquid two-phase flow produces higher friction than pure water flow when Reynolds number is less than about , the lower Reynolds number is the difference is higher. It was also shown that for the vibrating pipe, the friction factor of the pure water does not change with the frequency of the pipe vibration. The solid-liquid two-phase pipe flow's friction factor in the vibrating pipe, however, is not only higher than pure flow's, but also higher than the friction factor of stationary two-phase pipe flow. The increase is more when the vibrating frequency is higher.