Settling velocities of particulate systems 15: Velocities in turbulent Newtonian flows

The success in previous papers of this series in obtaining closed form solutions to the sedimentation of individual particles and to the suspensions of particles in fluids motivated the application of the same procedure to the turbulent flow of Newtonian fluids in conduits.The purpose of this paper is to present explicit equations for the Fanning friction factor and of the average velocity of a Newtonian fluid in a cylindrical tube, for any value of the Reynolds number and dimensionless roughness.Previously published equations for the friction coefficient are either implicit or explicit in the friction coefficient but dependent on the Reynolds number. Since the Reynolds number depends on the pipe diameter and fluid velocity, in both cases iterative method must be used to calculate the flowrate.By defining a dimensionless pipe diameter and a dimensionless average fluid velocity, and using conduit-flow material properties to define characteristic size and velocity parameters, explicit equations were obtained for the friction coefficient and for the average flow velocity valid for different roughness and flow regimes.