An artificial neural network for non-iterative calculation of the friction factor in pipeline flow

Abstract

Abstract A non-iterative procedure was developed, using an artificial neural network (ANN), for calculating the friction factor, f, in the Darcy-Weisbach equation when estimating head losses due to friction in closed pipes. The Regula-Falsi method was used as an implicit solution procedure to estimate the f values for a range of Reynolds numbers, Re, and relative roughness e/D values (where e is the pipe roughness and D is the pipe diameter). In developing the ANN model, three configurations were evaluated: (i) the input parameters Re and e/D were taken initially on a linear scale; (ii) the first input parameter Re was transformed to a logarithmic scale; and (iii) both input parameters (Re and e/D) were transformed to a logarithmic scale. Configuration (iii) yielded an optimal ANN model with 14 neurons in each of three hidden layers. This configuration was capable of predicting the values of f in the Darcy-Weisbach equation for any given Re in the range of 2×103–1×108 and e/D in the range of 1×10−6–5×10−2. 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 the friction factor such as those encountered in the hydraulic analysis of pipe networks and pressurized irrigation systems.