Optimal design of sprinkler laterals based on overlapped pattern and set time of irrigation
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Date
2019-07
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G.B. Pant University of Agriculture and Technology, Pantnagar - 263145 (Uttarakhand)
Abstract
In this study optimization models were developed for designing a single, double and multi-diameter sprinkler lateral lines for various values of uniform upward and downward slopes. It is assumed that a set of suitable pipe diameters as 𝑑1 𝑑2 …………𝑑𝑝 in ascending order are available to be selected completely for each section of lateral pipeline connecting outlets. The optimization model has to select only that diameter out of the available diameters for each section which will result in the minimum total cost. The energy cost of operating lateral line is added with the fixed cost of the lateral line to obtain the total cost of the lateral line. The main constraints imposed in the optimization model are the length constraint, allowable frictional head of the lateral line for acceptable pressure variation in form of energy conservation and distribution coefficient to consider desired value of uniformity coefficient. The equations related to discharge pressure head relationship, adequacy of irrigation, application rate and set time are also written as constraints along with non negative length constraints. The Hazen-Williams equation with multi-outlet factor was used to computing the frictional head loss in single, double and multi-diameter pipelines respectively. The applicability of the optimization models was illustrated by solving different design problems using LINGO 17.0. The optimal solutions obtained are compared by already available solutions. The effects of slopes, fraction of area adequately irrigated, and depth of irrigation on optimal solution were studied. The single pipe size lateral line with bigger diameter was resulting in lesser total cost than the smaller diameter. The pressure variation of the bigger pipe size lateral was lesser with higher initial cost whereas the smaller diameter lateral line is having lower initial cost with higher pressure variation. The optimal design of two and three pipe sizes lateral lines were resulting in lower total cost and pressure variation for the pressure variation constraint as less than equal to 20 % than the pressure variation constraint as equal to 20 %. However, the selected lengths with their corresponding diameters were having higher initial cost due to bigger pipe sizes with more number of pipe sizes than smaller pipe sizes with lesser number of pipe sizes.
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