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

A non-iterative procedure was developed, using an artificial neural network (ANN), for calculating the friction factor, f, in the Darcy-Weisbach equat ion 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 valu es (where e is the pipe roughness and D is the pipe diameter). In developin g the ANN model, three configurations were evaluated: (i) the input paramet ers 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. Configurat ion (iii) yielded an optimal ANN model with 14 neurons in each of three hid den layers. This configuration was capable of predicting the values off in the Darcy-Weisbach equation for any given Re in the range of 2 x 10(3)-1 x 10(8) and e/D in the range of 1 x 10(-6)-5 x 10(-2). These values were in c lose agreement with those obtained using the numerical technique. The devel oped ANN model may offer significant advantages when dealing with flow prob lems that involve repetitive calculations of the friction factor such as th ose encountered in the hydraulic analysis of pipe networks and pressurized irrigation systems. (C) 1998 Elsevier Science B.V. All rights reserved.