Adaptações de modelos matemáticos para dimensionamento hidráulico em sistemas de irrigação pressurizada.

Abstract

This research aimed at developing mathematic models (set of equations) to choose emitters and hydraulic design of irrigation by sprinkler, in irrigation subunits in a rectangular, triangular and trapezoidal geometric form. The proposed model for the emitter's choice involves soil, water, plants and atmosphere parameters, workday and available time for the system to vvork in an optimized selection of emitters based on the demand of pressure for the area installed (sprinklers) and the approach flow (drip and micro-sprinklers). The model for hydraulic design of rectangular irrigation subunits offers the determination of the best position for the pipe shunt (lower demand pressure, shorter pipe length and higher approximation of maximum pressure variation in the subunit), favoring, in this process, the use of Darcy-Weisbach, Hazen-Williams and Scobey's equations of unit head loss. In this model, algorithms for the determination of the most unfavorable situation in mobile system with pipes and the maximum length of pipe diameters for fixed rate, with and without use of numerical treatments (use of Newton-Raphson's method as well as use Secantes's), to solve the implicit equations) were also obtained. One high precision mathematic expression adapted from Blasius's formula (errors less than 1,35%) was obtained in order to determine Darcy-Weisbach's friction factor for the most common situations in pressurized irrigation projects (smooth turbulent flow). For the triangular and trapezoidal subunits, the models were designed using the dimensioning method per zone for bypass pipes and multiple output factor for pipes shunts. Another algorithm was created to measure the other pipes that make part of the irrigation systems, as well as to define the assembling of the head control and the selection of the pump-motor set. Due to the several numbers of calculations involved, the proposed models are potentially applied to computer programs.