Mathematical models to optimize lateral line length using two spacing between drippers
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In drip irrigation systems, longer lateral lines can provide cost reduction, but it is limited by the required irrigation uniformity. Non-pressure compensating drip hose is widely used for vegetables and orchards irrigation and its flow rate decreases as the pressure is reduced, resulting in shorter lateral lines in order to obtain the desired uniformity. The lateral line length can be increased using two emitters spacing in different sections; in this case, the system design consists in determining the length of each section and its respective emitter spacing which has a large number of possible combinations. The best alternative can be identified using mathematical simulation models or mathematical optimization models based on operational research techniques as Nonlinear Programming (NLP). This study aimed to evaluate two developed mathematical models that increase the lateral line length of an irrigation system using non-pressure compensating drip hose with different spacing between emitters but maintaining irrigation uniformity at appropriate levels. The models were compared with the conventional procedure obtained from the combination of Darcy-Weisbach equation and Blasius equation. The NLP model generated the longest total length (152.1 m) of the lateral line which cqonsisted of 67.7 m with emitter spacing of 47 cm and 84.4 m with emitter spacing 44 cm, with emission uniformity of 92.5% and it was 16.2% longer than the lateral length obtained with the conventional analytical procedure, for the pressure variation of 20% in the lateral line. The simulation model was the second best option, generating an increase in total length of 7% when compared with the standard procedure.