Neural network based non-iterative calculation of the friction factor for power law fluids Original Research Article

An artificial neural network (ANN) approach was used to develop an explicit procedure for calculating the friction factor, f, for power law fluids under turbulent flow conditions in closed pipes. The Regula–Falsi method was used as an iterative procedure to estimate the f values for a range of Reynolds number, Re′, and flow behavior index, n. In developing the ANN model, three configurations were evaluated: the input parameters Re′ and n were taken initially on a linear scale; the first input parameter (Re′) was transformed using a logarithmic scale to the base 10; and both input parameters (Re′ and n) were transformed using the logarithmic scale. The third configuration yielded an optimal ANN model with 12 neurons in each of two hidden layers. However, the simplest ANN model (with one hidden layer and two neurons) also produced good predictions. These values were in close agreement with those obtained using the numerical technique. The developed ANN model may offer significant advantages when dealing with flow problems that involve repetitive calculations of friction factor such as those encountered in the hydraulic analysis of viscous non-Newtonian fluids in pipe networks.