Explicit equations for laminar flow of Bingham plastic fluids

There are three typical problems encountered in pipe flows, which are: unknown friction factor, unknown flow rate, and unknown diameter problems. A major problem in determining the solution to these flow problems occurs due to the implicit nature of the Darcy–Weisbach friction factor. Though explicit equations for flow of Newtonian fluids and Power Law fluids are available, no such usable equations exist for Bingham plastic fluids. In this paper, explicit equations have been developed for flow of Bingham plastic fluids in the laminar regime. The equations thus developed aim at reducing the computational efforts and the need for using complex and time-consuming iterative solutions of the governing implicit equations for calculating the friction factor, discharge and pipe diameter. An explicit equation for an easier calculation of the critical Reynolds number has also been provided, simplifying the calculation of determining whether the flow is in laminar or turbulent regime.