Comparative calculation of irrigation networks using Labye's method, the linear programming method and a simplified nonlinear method

The designating factors in the design of branched irrigation networks are the cost of pipes and the cost of pumping. They both depend directly on the hydraulic pump head. It is mandatory for this reason to calculate the optimal pump head as well as the corresponding economic pipe diameters, in order the minimal total cost of the irrigation network to be produced. The classical optimization techniques, which have been proposed so long, are the following: the linear programming optimization method, the nonlinear programming optimization method, the dynamic programming optimization method and Labye's method. The mathematical research of the problem using the above classical optimization techniques is very complex and the numerical solution calls for a lot of calculations, especially in the case of a network with many branches. For this reason, many researchers have developed simplified calculation methods with satisfactory results and with less calculation time needed. A simplified nonlinear optimization method has been developed at the Aristotle University of Thessaloniki, Greece by M. Theocharis. The required calculating procedure is much shorter when using Theocharis' simplified method than when using the classic optimization methods, because Theocharis' method requires only a handheld calculator and just a few numerical calculations. In this paper a comparative calculation of the pump optimal head as well as the corresponded economic pipe diameters, using: (a) Labye's optimization method, (b) the linear programming optimization method and (c) Theocharis' simplified nonlinear programming method is presented. Application and comparative evaluation in a particular irrigation network is also developed. From the study it is concluded that Theocharis' simplified method can be equally used with the classical methods.