A study of friction factor formulation in pipes using artificial intelligence techniques and explicit equations

The hydraulic design and analysis of flow conditions in pipe networks are dependent upon estimating the friction factor, f . The performance of its explicit formulations and those of artificial intelligence (AI) techniques are studied in this paper. The AI techniques used here include artificial neural networks (ANNs) and genetic programming (GP); both use the same data generated numerically by systematically changing the values of Reynolds numbers, Re , and relative roughness, ε/D , and solving the Colebrook-White equation for the value of f by using the successive substitution method. The tests included the transformation of Re and ε/D using a logarithmic scale. This study shows that some of the explicit formulations for friction factor induce undue errors, but a number of them have good accuracy. The ANN formulation for the solving of the friction factor in the Colebrook-White equation is less successful than that by GP. The implementation of GP offers another explicit formulation for the friction factor; the performance of GP in terms of R2 (0.997) and the root-mean-square error (0.013) is good, but its numerically obtained values are slightly perturbed