Prediction of Pressure–Discharge Curves of Trapezoidal Labyrinth Channels from Nonlinear Regression and Artificial Neural Networks

Emitters are important components of drip irrigation systems, and the use of labyrinths as a mechanism of energy dissipation stands out in the drippers’ design. Relating the geometric characteristics of labyrinths with their operational and hydraulic characteristics is not trivial and generally requires the use of computational simulation tools. This study developed and evaluated models that can predict the discharge of labyrinth channels as a function of their geometry to make possible the rapid prediction of pressure–discharge curves due to modifications in the labyrinth geometry. An empirical mathematical model was developed based on nonlinear regression, and a computational model was trained based on artificial neural networks (ANNs). Twenty-four designs of prototypes were built in polymethyl methacrylate to operate at a discharge of approximately $1.4\mathrm{L}{\mathrm{h}}^{-1}$ under 100 kPa. The pressure–discharge curve of each prototype was determined in the laboratory in the range 50–350 kPa. Based on the experimental data, the coefficients of an empirical nonlinear model were fitted, and 11 single-hidden-layer ANN architectures were compared. The best accuracy was provided by an ANN architecture with an input layer with six neurons, six neurons in the hidden layer, and an output layer with a single neuron. The maximum relative errors of the predicted discharges were 9.5% and 9.4% for the ANN and nonlinear models, respectively. Both models were accurate and enabled rapid prediction of the emitter’s discharge. An open-source web application was developed to simulate the pressure–discharge curve of labyrinths within a range of geometric and operational characteristics.