Suitability for coding of the Colebrook’s flow friction relation expressed through the Wright ω-function

  • Pavel Praks IT4Innovations, VSB – Technical University of Ostrava, Ostrava, Czechia
  • Dejan Brkić IT4Innovations, VSB – Technical University of Ostrava, Ostrava, Czechia
Keywords: Flow friction, Colebrook equation, Wright ω-function, Artificial intelligence, Symbolic regression, Computational speed


This article analyses a form of the empirical Colebrook’s pipe flow friction equation given originally by the Lambert W-function and recently also by the Wright ω-function. These special functions are used to explicitly express the unknown flow friction factor of the Colebrook equation, which is in its classical formulation given implicitly. Explicit approximations of the Colebrook equation based on approximations of the Wright ω-function given by an asymptotic expansion and symbolic regression were analyzed in respect of speed and accuracy. Numerical experiments on 8 million Sobol’s quasi-Monte points clearly show that also both approaches lead to the approximately same complexity in terms of speed of execution in computers. However, the relative error of the developed symbolic regression-based approximations is reduced significantly, in comparison with the classical basic asymptotic expansion. These numerical results indicate promising results of artificial intelligence (symbolic regression) for developing fast and accurate explicit approximations.


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How to Cite
Praks, P., & Brkić, D. (2020). Suitability for coding of the Colebrook’s flow friction relation expressed through the Wright ω-function. Reports in Mechanical Engineering, 1(1), 174-179.