Abstract
A mathematical linear programming model based on Microsoft Excel spreadsheet was developed to design mainline of sprinkler irrigation system. The line considered has a length of 522 m combined with five different nominal diameters of 3', 3-1/2, 4, 5 and (internal diameter of 73.7, 85.4, 97.2, 122.3and 149.3 mm) which are commercially available in the Egyptian markets. The objective function was to minimize the cost of the mainline pipe; and the constraints considered were commercial availability of diameters. The head loss calculations are based on four different head loss formulas. These are the Hazen-Williams, Manning, Scobey, and Darcy-Weisbach equations. The model estimates the number of pipe unit according to the available manufacturer length. ( taken as 6 meter long). The lowest cost of 7924 US$ was found by the Darcy Wiesbach equation followed by Manning as 8030, Hazen–Williams as 8051 and Scobey as 8385. Validity and sensitivity of the model were confirmed. The effect of land slope and inlet pressure to the system was studied. The results indicated that increasing in inlet pressure decreases the cost of the mainline. Meanwhile, the cost of the mainline is proportionally increased by increasing the up slope of the land, and inversely increases by increasing the down slope of the land.
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