This paper details a hybrid computational and analytical model to predict the performance of inline pressure-compensating (PC) drip irrigation emitters. The term inline refers to flow control devices mounted within the irrigation tubing. Pressure-compensating emitters deliver a relatively constant flow rate over a range applied pressure to accurately meter water to crops. Flow rate is controlled within the emitter by directing the water through a tortuous path (which imposes a fixed resistance), and then through a variable resistor composed of a flexible membrane that deflects under changes in pressure, restricting the flow path. An experimentally validated computational fluid dynamics (CFD) model was used to predict flow behavior through tortuous paths, and a pressure resistance parameter was derived to represent the pressure drop with a single variable. The bending and shearing mechanics of the membrane were modeled analytically and refined for accuracy by deriving a correction factor using finite element analysis. A least-squares matrix formulation that calculates the force applied by a line load of any shape, along which there is a prescribed deflection applied on a rectangular membrane, was derived and was found to be accurate to within one percent. The applicability of the assumption of locally fully developed flow through the pressure compensating chamber in a drip emitter was analyzed.
The combined hybrid computational-analytical model reduces the computational time of modeling drip emitter performance from days to less than 30 minutes, dramatically lowering the time required to iterate and select optimal designs. The model was validated using three commercially available drip emitters, rated at 1.1, 2, and 3.8 L/hr. For each, the model predicted the flow rate with an error of twenty percent or less, as compared to the emitter performance published by the manufacturer.