Neuro-fuzzy approach in estimating Hazen-Williams friction coefficient for small-diameter polyethylene pipes

Low-pressurized multiple outlet pipelines are extensively used to uniformly distribute irrigation water under different types of low-volume micro-irrigation systems. Polyethylene (PE) is the main pipe material for smooth pipes in sub-main unit of a micro-irrigation system due to its flexibility and resistibility to the sun. For computing friction loss in PE pipes, many practicing engineers hesitate to use the generalized Darcy-Weisbach equation since the friction coefficient varies at each section of the lateral. Although its non-dimensional homogeneity and limitations in applicability, the empirical Hazen-Williams equation is still commonly preferred, because of its simplicity in practice. In the current hydraulic computations for friction loss, some typical fixed values for the Hazen-Williams coefficient (C_HW) in PE pipes are still recommended regardless of pipe diameter. Experimental works have confirmed that there is a strong dependence of the C_HW on pipe diameter (D), therefore a single value of the C_HW cannot be used for all ranges of pipe diameters. The primary focus of this research is to investigate the accuracy of a fuzzy rule system approach to estimate the proper value of the C_HW coefficient for different pipe diameters because of the imprecise, insufficient, ambiguous and uncertain data available. A neuro-fuzzy approach was developed to relate the input (flow rate and pipe diameter) and output (C_HW and friction loss) variables. The application of the proposed approach was performed using the measured data for friction losses available from the recent experimental analysis, hence its performance was tested using some statistic parameters for error estimation. The examination results indicated that through fuzzy rules and membership functions the proposed model can be successfully used to identify the proper values of C_HW coefficient hence accurately estimate friction losses through smooth PE pipes.