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.