Review of new flow friction equations: Constructing Colebrook explicit correlations accurately

Abstract: Using only a limited number of computationally expensive functions, we show a way how to construct accurate and computationally efficient approximations of the Colebrook equation for flow friction. The presented approximations are based on the asymptotic series expansion of the Wright Omega-function and symbolic regression. The results are verified with 8 million of Quasi-Monte Carlo points covering the domain of interest for engineers. In comparison with the built-in wrightOmega feature of Matlab R2016a, the herein introduced related approximations of the Wright Omega-function significantly accelerate the computation. With only two logarithms and several basic arithmetic operations used, the presented approximations are not only computationally efficient but also extremely accurate. The maximal relative error of the most promising approximation which is given in the form suitable for engineers use is limited to 0.0012%, while for a little bit more complex variant is limited to 0.000024%.