Accurate Explicit Equations for the Determination of Pipe Diameters

Abstract

The determination of diameter in pipe flow problems requires the use of diagrams or iterative solutions of the Colebrook – White equation. Diagrams are inaccurate because of reading errors and are impossible to use when the whole problem is going to be solved by a computer. Iteration type solutions can be very time consuming when large water distribution networks are involved. In this paper, accurate explicit equations for the determination of pipe diameter are developed. Two equations are presented, a simple and a more complex one. The maximum relative errors in the computation of the diameter, <i>D,</i>for 4x10<SUP>3</SUP>≤ <i>Re</i> ≤10<SUP>8</SUP> and 10<SUP>-5</SUP>≤ <i>ε/D</i> ≤5x10<SUP>-2</SUP> are 0.36% and 5.65x10<SUP>-3</SUP> % respectively. It was found that the complex equation is far superior to other explicit equations available in the literature.