Determination of the Inside Diameter of Pressure Pipes for Drinking Water Systems Using Artificial Neural Networks

The fifth-degree polynomial equation determines the diameter in pressurized drinking water systems. input variables are Q: flow (m3/s), H: pressure drop (m); L: pipe length ε: roughness (m), ϑ: kinematic viscosity (m2/s), and Ʃk: sum of minor loss coefficients (dimensionless). After applying energy for a hydraulic system composed two tanks connected to constant accepting Colebrook-White Darcy-Weisbach equations, an undetermined expression is obtained since more unknowns than equations established. This problem solved by implementing nested loop coefficient friction diameter. article proposes Artificial Neural Network (ANN) Levenberg-Marquardt backpropagation method estimate from log-sigmoidal transfer function under stationary conditions. training signals set consists 5,000 random data that follow normal distribution, calculated Visual Basic (®Excel). statistics used network evaluation correspond mean square error, regression analysis, cross-entropy function. architecture with best performance had hidden layer 25 neurons (6-25-1) presenting MSE equal 5.41E-6 9.98E+00 Pearson Correlation Coefficient. cross-validation neural scheme was carried out 1,000 independent set, obtaining 6.91E-6. proposed calculates relative error 0.01% concerning values ​​obtained ®Epanet, evidencing generalizability optimized system.