Determining turbulent flow friction coefficient using adaptive neuro-fuzzy computing technique

In the analysis of water distribution networks, the main required design parameters are the lengths, diameters, and friction coefficients of rough-pipes, as well as nodal demands and water levels in the reservoirs. Although some of these parameters such as the pipe lengths are precisely known and would remain the same at different points of the networks whereas some parameters such as the pipe diameters and friction coefficients would changed during the life of network and therefore they can be treated as imprecise information. The primary focus of this study is to investigate the accuracy of a fuzzy rule system approach to determine the relationship between pipe roughness, Reynolds number and friction factor because of the imprecise, insufficient, ambiguous and uncertain data available. A neuro-fuzzy approach was developed to relate the input (pipe roughness and Reynolds number) and output (friction coefficient) variables. The application of the proposed approach was performed for the data derived from the Moody's diagram. The performance of the proposed model was compared with respect to the conventional procedures using some statistic parameters for error estimation. The comparison test results reveal that through fuzzy rules and membership functions, the friction factor can be identified, precisely.