Accuracy/Speed Analysis of Pipe Friction Factor Correlations

Abstract

The Colebrook [1] equation is considered the standard for the calculation of friction factor for turbulent flow in commercial pipes, but it is implicit, and therefore it must be computed by iterative methods. Although such iterative computation quickly converges, the computational time in large pipe system simulations can be reduced using an accurate explicit correlation. A review of the up to date literature identified 30 different explicit correlations. In order to determine which correlation is the best alternative to Colebrook’s, both accuracy and computational burden were compared. The accuracy of each explicit correlation was compared against Colebrook’s correlation using the mean and maximum relative errors and the coefficient of determination. Also, the computational time of each equation was measured using the tic and toc functions in GNU Octave software. It was found that the iterative computation of the Colebrook equation demands about 2.6 times the computational time of the slowest explicit correlation. The correlations with the best balance between accuracy and computational burden are, in decreasing order of accuracy and increasing order of speed, correlations by Serghides [13] (Eqs. (17), (18), (19), and (20)), by Shacham [8] (Eqs. (10) and (11)), by Brkić and Praks [33] (Eqs. (53), (54), (55), and (56)), and by Fang et al. [19] (Eq. (28)).