The implicit Colebrook equation has been the standard for estimating pipe friction factor in a fully developed turbulent regime. Several alternative explicit models to the Colebrook equation have been proposed. To date, most of the accurate explicit models have been those with three logarithmic functions, but they require more computational time than the Colebrook equation. In this study, a new explicit non-linear regression model which has only two logarithmic functions is developed. The new model, when compared with the existing extremely accurate models, gives rise to the least average and maximum relative errors of 0.0025% and 0.0664%, respectively. Moreover, it requires far less computational time than the Colebrook equation. It is therefore concluded that the new explicit model provides a good trade-off between accuracy and relative computational efficiency for pipe friction factor estimation in the fully developed turbulent flow regime.

Friction factor estimation is essential in fluid flow in pipes calculations. The Colebrook equation, which is a referential standard for its estimation, is implicit in friction factor, f. This implies that f can only be obtained via iterative solution. Sequel to this, explicit approximations of the Colebrook equation developed using analytical approaches have been proposed. A shift in paradigm is the application of artificial intelligence in the area of fluid flow. The use of artificial neural network, an artificial intelligence technique for prediction of friction factor was investigated in this study. The network having a 2-30-30-1 topology was trained using the Levenberg-Marquardt back propagation algorithm. The inputs to the network consisted of 60,000 dataset of Reynolds number and relative roughness which were transformed to logarithmic scales. The performance evaluation of the model gives rise to a mean square error value of 2.456 × 10 −15 and a relative error of not more than 0.004%. The error indices are less than those of previously developed neural network models and a vast majority of the non neural networks are based on explicit analytical approximations of the Colebrook equation.

No abstract

No 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.