PERFORMANCE EVALUATION OF THE EXPLICIT APPROXIMATIONS OF THE IMPLICT COLEBROOK EQUATION

U. H. Offor, S. B. Alabi

Abstract: The implicit Colebrook equation has been the standard for estimating pipe friction factor in a fully developed turbulent regime. Several artificial intelligence (AI)-based and non AI-based explicit models have been developed as viable replacement for the implicit Colebrook equation. However, it is not obvious which of the models and/or approaches is the best. In this paper, the performances of the available non AI-based explicit models were compared with those of the AI-based models. The results show that genetic algorithm has been successfully utilized in optimizing the explicit model parameters with the best improvements being from 0.12% to 0.0026% based on maximum relative error index. Although genetic programming and gene expression programming techniques offer the advantage of producing explicit analytical formulas for determination of output parameters, they are found to be grossly inaccurate with errors up to 7% for most accurate model developed. Artificial neural network, a prominent AI-based method has been used to significantly improve friction factor predictions with a high accuracy of 0.004% equivalent to that obtainable with the non-AI based models. The most accurate models are among those developed using the non AI -based techniques with errors up to 1.04 ×10-1 0 %. There is still possibility of improving on the gains made using the artificial intelligence techniques

Keywords: Colebrook Equation, Artificial Intelligence, Genetic Algorithm, Artificial Neural Network and Gene Expression Programming

DOI: https://doi.org/10.15623/ijret.2016.0508001