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Computational Intelligence and Neuroscience
Volume 2016 (2016), Article ID 5242596, 10 pages
Research Article

Intelligent Flow Friction Estimation

1European Commission, DG Joint Research Centre (JRC), Institute for Energy and Transport (IET), Energy Security, Systems and Market Unit, Via Enrico Fermi 2749, 21027 Ispra, Italy
2Faculty of Mechanical Engineering in Niš, University of Niš, Aleksandra Medvedeva 14, 18000 Niš, Serbia

Received 1 December 2015; Revised 5 February 2016; Accepted 7 February 2016

Academic Editor: Reinoud Maex

Copyright © 2016 Dejan Brkić and Žarko Ćojbašić. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Nowadays, the Colebrook equation is used as a mostly accepted relation for the calculation of fluid flow friction factor. However, the Colebrook equation is implicit with respect to the friction factor (). In the present study, a noniterative approach using Artificial Neural Network (ANN) was developed to calculate the friction factor. To configure the ANN model, the input parameters of the Reynolds Number (Re) and the relative roughness of pipe () were transformed to logarithmic scales. The 90,000 sets of data were fed to the ANN model involving three layers: input, hidden, and output layers with, 2, 50, and 1 neurons, respectively. This configuration was capable of predicting the values of friction factor in the Colebrook equation for any given values of the Reynolds number (Re) and the relative roughness () ranging between 5000 and 108 and between 10−7 and 0.1, respectively. The proposed ANN demonstrates the relative error up to 0.07% which had the high accuracy compared with the vast majority of the precise explicit approximations of the Colebrook equation.