Explicit Friction Factor Accuracy and Computational Efficiency for Turbulent Flow in Pipes

The implicit Colebrook–White equation is the accepted method for accurately estimating the friction factor for turbulent flow in pipes. This study reviews 28 explicit equations for approximating the friction factor to integrate both the accuracy to the implicit Colebrook–White equation and the relative computational

efficiency of the explicit equations.

A range of 901 Reynolds numbers were selected for the review between Re ≥ 4 × 103 and ≤ 4 × 108 and 20 relative pipe roughness values were selected between ε/D ≥ 10−6 ≤ 10−1, thus producing a matrix of 18,020 points for each explicit equation, covering all the values to be encountered in pipeline hydraulic analysis for turbulent flow. The accuracy of the estimation of the friction factor using the explicit equations to the value obtained using the implicit Colebrook–White equation were calculated and reported as absolute, relative percentage and mean square errors.

To determine the relative computational efficiency, 300 million friction factor calculations were performed using randomly generated values for the Reynolds number and the relative pipe roughness values between the limits specified for each of the explicit equations and compared to the time taken by the Colebrook–White equation. Finally, 2D and 3D contour models were generated showing both the range and magnitude of the relative percentage accuracy across the complete range of 18,020 points for each explicit equation.