Explicit optimum design of a simple irrigation delivery system

While pipe selection for collective irrigation networks, in the framework of optimal design, is based on methods that have been successfully developed and applied, it is often given insufficient attention in the case of simple irrigation systems. In these projects, designers use very simple empirical pipe selection methods based on arbitrary concepts, which do not lead to an optimal solution. In this article, a simple method is presented, which allows the user to determine directly the optimum pipe size to use in simple irrigation delivery systems with pumps. A detailed theoretical analysis of the behavior of the total cost variable (energy and pipe cost per unit length), expressed as a function of discharge for the various available diameters, was carried out. The proposed method led to the derivation of a simple equation from which the critical values of discharge corresponding to the available pipe diameters are explicitly calculated. The direct computational optimal solution is demonstrated in application examples. The examples used in this application are systems with horizontal and sloping topography with identical outlets (same discharge and pressure head) or systems having outlets with various pressure heads. For simple, non-looping, irrigation delivery systems (single main or submain delivery pipeline), it is sufficient to directly calculate the values of critical discharge corresponding to the various available commercial diameters using the proposed equation. For sloping or branched delivery networks, the equation is applied to the critical path portion of the network that is affected by the energy cost. For the rest of the system, the design is based on hydraulic criteria only. Comparison with previous empirical explicit methods indicates good performance by this new method.