MATHEMATICAL MODELING OF THE FACTORS AFFECTING THE PERFORMANCE OF THE DRIP IRRIGATION SYSTEM

Abstract

Mathematical modeling considered as one of the influencing means for drip irrigation improvement to develop efficient and economical system designs. Inadequate mathematical models may lead to an underestimation of head losses calculations. This study concerns the factors affect friction head losses in lateral line and to establish the relationship between them. The accurate design of drip irrigation laterals needs to determine the total energy losses that include the pipe friction losses along the lateral line and minor losses due to emitter connections. Laboratory experiments were conducted to measure friction head losses for emitter spacing from 0.3 to 2.4 m, pipe inner diameter 13.1, 15.6, and 17 mm, protrusion barb area 14.49, 21.375, 28.78 mm2 (for on-line emitters), emitter cylinder length from 30 to 68 mm, and emitter inner diameter from 11.2 to 15.5 mm (for built-in emitters) at values of Reynolds number varied from 6000 to 21000. Two mathematical models were developed to predict the friction head losses in lateral equipped with on-line and integrated built-in emitters. The parameters affecting the friction head losses in lateral defined in dimensionless terms using Buckingham’s Π theorem. The developed models were accounted for 98% of the variation in measured data. The friction head losses were calculated using the developed models and there was an acceptable accuracy comparing with the previously proposed models. A friendly user interface computer program named EGY-DRIP SYSTEMS had developed for drip irrigation system design. The program had written in Microsoft visual basic 2013. EGY-Drip SYSTEMS program carries out hydraulic calculations of a sub-unit design for drip irrigation system. The hydraulic calculation based on data inputs about water supply, soil, evapotranspiration, crop (vegetables, fruit, and field crops), and irrigation system components (drippers, pipes, and fittings). The program supported with an upgradable Microsoft access database to facilitate data input by the user. EGY-DRIP SYSTEMS program is outfitted with an open source computer aided drafting program (QCAD) for pipeline network layout drafting.

Key words: Mathematical modeling, drip irrigation, laterals, friction head losses, dimensional analysis, and computer program.