Accurate solutions of Colebrook-White’s friction factor formulae

Abstract

Estimations of friction factor (Ff) in pipeline systems and fluid transport are essential ingredients in engineering fields and processes. In this paper explicit friction factor formulae (Fff) were proposed and evaluated with an aim of developing error free Fff. General Fff that relate Ff, Reynolds number (Re) and relative roughness (Rr) were proposed. Colebrook – White's formula was used to compute different Ff for Re between 4 x 10 3 and 1.704 x 10 8 , and Rr between 1.0 x 10 -7 and 0.052 using Microsoft Excel Solver to fix the Fff. The fixed Fff were used to compute Ff for Re between 4 x 10 3 and 1.704 x 10 8 and Rr between 1.0 x 10 -7 and 0.052. Accuracy of the fixed Fff was evaluated using relative error; model of selection (MSC) and Akaike Information Criterion (AIC) and compared with the previous Fff using Colebrook –White's Ff as the reference. The study revealed that Ff estimated using the fixed Fff were the same as Ff estimated using Colebrook – White's Fff. The fixed Fff provided the lowest relative error of (0.02 %; 0.06 % and 0.04 %), the highest MSC (14.03; 12.42 and 13.07); and the lowest AIC (-73006; -64580 and -67982). The study concluded that modeling of Fff using numerical methods and Microsoft Excel Solver are better tools for estimating Ff in pipeline flow problems.