Inlet Pressure, Energy Cost, and Economic Design of Tapered Irrigation Submains

A new particularly simple equation is derived to solve explicitly the economic design problem of submain lines (microirrigation manifold and sprinkle irrigation submains) with pumping. The appropriate lengths of the submain line segments with different diameters are directly calculated from the proposed equation in such a way the total cost of energy and pipes is minimized. It is shown that the portion of energy cost affected by changes in the submain pipe sizes is proportional to the inlet pressure head of the submain. A new equation is derived relating the inlet pressure head of a tapered multioutlet pipeline to the average pressure head value. Direct design solutions were obtained for two different cases ensuring two different hydraulic conditions. In the first case, the average value of outflow over all the outlets (emitters) of the system is imposed to be identical to the required average outlet discharge. This implies that the average pressure head value in the submain is imposed to be equal to an a priori known constant. In the second case the energy cost is assumed proportional to the friction losses along the submain. The explicit economic design is demonstrated in two design examples. Comparisons with previous methods and numerical models indicated the good performance of the suggested solution.