Explicit calculation of the friction factor in pipeline flow of Bingham plastic fluids: a neural network approach

An artificial neural network (ANN) approach was used in this paper to develop an explicit procedure for calculating the friction factor, f, under both laminar and turbulent flow conditions of Bingham plastic fluids in closed conduits and pipe networks. The procedure aims at reducing the computational efforts as well as eliminating the need for conducting complex and time-consuming iterative solutions of the governing implicit equations for calculating the friction factor, f. The ANN approach involved the establishment of an explicit relationship among the Reynolds number, Re, Hedstrom number, He, and the friction factor, f, under both laminar and turbulent flow conditions. Although, an analytical solution of the governing equation under the laminar flow regime was also feasible (such an equation is also provided in this paper), the ANN model is applicable under both laminar and turbulent flow conditions where the analytical approach will have major limitations (especially when considering the implicit equation that govern the turbulent flow regime).