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

Authors : Farzin SALMASI, Rahman KHATIBI, Mohammad Ali GHORBANI

Pages : 121-138

Doi:10.3906/kim-1302-71

View : 20 | Download : 11

Publication Date : 0000-00-00

Article Type : Research Paper

Abstract :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 insert ignore into journalissuearticles values(AI); techniques are studied in this paper. The AI techniques used here include artificial neural networks insert ignore into journalissuearticles values(ANNs); and genetic programming insert ignore into journalissuearticles values(GP);; both use the same data generated numerically by systematically changing the values of Reynolds numbers, Re, and relative roughness, e/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 e/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 insert ignore into journalissuearticles values(0.997); and the root-mean-square error insert ignore into journalissuearticles values(0.013); is good, but its numerically obtained values are slightly perturbed.
Keywords : Pipe friction factor, Darcy Weisbach equation, implicit explicit equations, artificial neural network, genetic programming