ACCURATE SOLUTIONS OF COLEBROOK- WHITE’S FRICTION FACTOR FORMULAE

Estimations of friction factor (F f ) in pipeline systems and fluid transport are essential ingredients in engineering fields and processes. In this paper explicit friction factor formulae (F ff ) were proposed and evaluated with an aim of developing error free F ff . General F ff that relate F f , Reynolds number (R e ) and relative roughness (R r ) were proposed. Colebrook – White’s formula was used to compute different F f for R e between 4 x 10 3 and 1.704 x 10 8 , and R r between 1.0 x 10-7 and 0.052 using Microsoft Excel Solver to fix the F ff . The fixed F ff were used to compute F f for R e between 4 x 10 3 and 1.704 x 10 8 and R r between 1.0 x 10 -7 and 0.052. Accuracy of the fixed F ff was evaluated using relative error; model of selection (MSC) and Akaike Information Criterion (AIC) and compared with the previous F ff using Colebrook–White’s F f as the reference. The study revealed that F f estimated using the fixed F ff were the same as F f estimated using Colebrook – White’s F ff . The fixed F ff 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 F ff using numerical methods and Microsoft Excel Solver are better tools for estimating F f in pipeline flow problems. Keywords: Friction factor, MSC; AIC; Reynolds number; Engineering Field; pipe flow, statistical methods