Prabhata K. Swamee, Pushpa N. Rathie, Nitin Aggarwal
In this paper, mathematically equivalent representations of the Buckingham-Reiner equation to compute friction factor and of the diameter equation to compute circular pipe diameter for laminar flow of Bingham plastic fluids in pipes have been given. The new forms are simple and very wellsuited for accurately estimating the friction factor and diameter, because no iterative calculations are necessary. Specifically, the friction factor and diameter are expressed as computable series using Lagrange’s theorem. The equations presented in this study eliminate the need for bestfit parameters that are an integral part of the various explicit approximations proposed to date. The exact equations can also be utilized with advantage in optimization studies of pipelines. The ease, with which the new equations can be used, along with their smooth and predictable behavior, should make them the first choice of use for estimating the friction factor and diameter for laminar flow of Bingham plastic fluids in circular pipes.
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