Predicting the Colebrook–White Friction Factor in the Pipe Flow by New Explicit Correlations

Abstract

Determination of friction factor (f) in pipe flow is necessary for various applications dealing with fluid flow. The Colebrook–White equation is the most accepted technique for the f-values estimation in turbulent flow. The biggest problem with this equation is that it can only be solved using numerical iteration methods. This paper contributes two new formulas based on the Colebrook–White equation to calculate f for the turbulent flow regime. To determine the new correlations, several equations were first suggested and then their coefficients were determined using the curve fitting method. Thereafter, based on various statistical error calculations, two equations with the highest accuracies were selected for the further modification. The advantages of the proposed correlations are that they are explicit in f so they do not need any iteration to compute friction factor and the results of calculating f-values reveal that the two new equations are of maximum absolute percent errors (APE) of 0.91% and 3.49% over the entire applicability range of Colebrook–White equation.