Economic Design of Center-Pivot Sprinkler Laterals

Abstract

Center-pivot laterals are characterized by important friction loss, so therefore the energy consumption is also significant. In this paper, a new, particularly simple, equation is derived to solve explicitly the economic design problem of tapered center-pivot laterals taking into account the energy cost. The appropriate lengths of center-pivot lateral segments with different pipe sizes are calculated directly from the proposed equation in such a way that the total cost of energy and lateral segments is minimized. Friction loss can be calculated using the simple empirical Hazen–Williams formula but also can be calculated using the more general Darcy–Weisbach friction equation. The explicit economic design is applied in two design examples. A detailed economic analysis and comparison between different systems with and without multiple pipe lateral sizes also is performed. A stepwise economic design method determining the most economic pipe diameter at each section of the lateral included between two consecutive sprinklers also is applied. Comparison between the two methods indicates the good performance of the analytical method.