Computer-based analysis of explicit approximations to the implicit ColebrookWhite equation in turbulent flow friction factor calculation
The implicit ColebrookWhite equation has been widely used to estimate the friction factor for turbulent fluid-flow in rough-pipes. In this paper, the state-of-the-art review for the most currently available explicit alternatives to the ColebrookWhite equation, is presented. An extensive comparison test was established on the 20500 grid, for a wide range of relative roughness (?/D) and Reynolds number (R) values (110?6??/D?510?2; 4103?R?108), covering a large portion of turbulent flow zone in Moodys diagram. Based on the comprehensive error analysis, the magnitude points in which the maximum absolute and the maximum relative error are occurred at the pair of ?/D and R values, are observed. A limiting case of the most of these approximations provided friction factor estimates that are characterized by a mean absolute error of 510?4, a maximum absolute error of 410?3 whereas, a mean relative error of 1.3% and a maximum relative error of 5.8%, over the entire range of ?/D and R values, respectively. For practical purposes, the complete results for the maximum and the mean relative errors versus the 20 sets of ?/D value, are also indicated in two comparative figures. The examination results for error properties of these approximations gives one an opportunity to practically evaluate the most accurate formula among of all the previous explicit models; and showing in this way its great flexibility for estimating turbulent flow friction factor. Comparative analysis for the mean relative error profile revealed, the classification for the best-fitted six equations examined was in a good agreement with those of the best model selection criterion claimed in the recent literature, for all performed simulations.
analysis turbulent flow moodys diagram fluid mechanics cw friction factor closed form solution explicit scheme excel spreadsheet techdig 2.0 software