A Comprehensive Update and Performance Evaluation of Friction Factor Formulae

Abstract

In this paper, explicit friction factor formulae (Fff), which is a function of Reynolds number (Re) and relative roughness (Rr) were updated and evaluated. Fff were obtained from archive and conduct performance evaluation. Performance evaluation of the Fff were conducted using relative error; model of selection (MSC) and the Akaike Information Criterion (AIC) using Colebrook-White's friction factors as the reference Ff. The study revealed that there are 47 Fff in use. The growth of the Fff can be grouped into four subgroups based on the pattern and into three subgroups based on number of authors and into three subgroups, based on the accuracy. The growth rates were combinations of linear and exponential based on the pattern. The study revealed that Fff provided the lowest relative error of less than 1.00%, the highest MSC of greater than 6.64 and the lowest AIC of less than -34324.17. The study concluded that the recent and third generation Fff are the best and using Microsoft Excel Solver for calculating Ff in the pipe flow systems is a good tool for engineers.