Relationship between citrus productivity and indicators of uniformity in trickle irrigation system

In trickle irrigation systems, the design is based on the pre-established emission uniformity (EU) which is the combined result of the equipment characteristics and its hydraulic configuration. However, this desired value of the EU may not be confirmed by the final project (in field conditions) and neither by the yield uniformity. The hypotheses of this research were: a) the EU of a trickle irrigation system at field conditions is equal to the emission uniformity pre-established in the its design; b) EU has always the lowest value when compared with other indicators of uniformity; c) the discharge variation coefficient (VC) is not equal to production variation coefficient in the operational unit; d) the difference between the discharge variation coefficient and the productivity variation coefficient depends on the water depth applied. This study aimed to evaluate the relationship between EU used in the irrigation system design and the final yield uniformity. The uniformity indicators evaluated were: EU, distribution uniformity (UD) and the index proposed by Barragan & Wu (2005). They were compared estimating the performance of a trickle irrigation system applied in a citrus orchard with dimensions of 400m x 600m. The design of the irrigation system was optimized by a Linear Programming model. The tree rows were leveled in the larger direction and the spacing adopted in the orchard was 7m x 4m. The manifold line was always operating on a slope condition. The sensitivity analysis involved different slopes, 0, 3, 6, 9 and 12%, and different values of emission uniformity, 60, 70, 75, 80, 85, 90 and 94%. The citrus yield uniformity was evaluated by the variation coefficient. The emission uniformity (EU) after design differed from the EU pre-established, more sharply in the initial values lower than 90%. Comparing the uniformity indexes, the EU always generated lower values when compared with the UD and with the index proposed by Barragan. The emitter variation coefficient was always lower than the productivity variation coefficient. To obtain uniformity of production, it is necessary to consider the irrigation system uniformity and mainly the water depth to be applied.

Distribuição da carga hidráulica em linhas de derivação otimizadas por programação linear

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Optimum design of microirrigation systems in sloping lands

When an area to be irrigated has a high slope gradient in the manifold line direction, an option is to use a tapered pipeline to economize on pipe costs and to keep pressure head variations within desired limits. The objective of this paper is to develop a linear optimization model to design a microirrigation system with tapered, downhill manifold lines, minimizing the equivalent annual cost of the hydraulic network and the annual pumping cost, and maximizing the emission uniformity previously established to the subunit. The input data are irrigation system layout, cost of all hydraulic network components, and electricity price. The output data are equivalent annual cost, pipeline diameter in each line of the system, pressure head in each node, and total operating pressure head. To illustrate its capability, the model is applied in a citrus orchard in Sao, Paulo State, Brazil, considering slopes of 3, 6, and 9%. The model proved to be efficient in the design of the irrigation system in terms of the emission uniformity desired.

Design of microirrigation systems in sloping lands using linear programming

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Análise distribuição da carga hidráulica e vazão na unidade operacional de um sistema de irrigação localizada

The different combination possibilities of emission uniformity and field slope within the operational unities of localized irrigation systems favor the occurence of some configurations in the irrigation system, and consequently different hydraulic head distributions, discharge and system management. After the system has been implanted, it is necessary to verify pressure and discharge distribution in the operational unit. This work objective was to verify pressure and discharge uniformity on derivation line and lateral lines with micro sprinkle in data gotten from operational research. The results allow to check that despite analyzed declivity; the higher the emission uniformity calculated for the line of derivation in the project is, the higher its pressure uniformity is. Previously the results of discharge in the emitters of the operational unit showed a constant variation entering the point of higher discharge and lower discharge, even though differently from the three tested irrigation blades.

Model to increase the lateral line length of drip irrigation systems

Non-pressure compensating drip hose is widely used for irrigation of vegetables and orchards. One limitation is that the lateral line length must be short to maintain uniformity due to head loss and slope. Any procedure to increase the length is appropriate because it represents low initial cost of the irrigation system. The hypothesis of this research is that it is possible to increase the lateral line length combining two points: using a larger spacing between emitters at the beginning of the lateral line and a smaller one after a certain distance; and allowing a higher pressure variation along the lateral line under an acceptable value of distribution uniformity. To evaluate this hypothesis, a nonlinear programming model (NLP) was developed. The input data are: diameter, roughness coefficient, pressure variation, emitter operational pressure, relationship between emitter discharge and pressure. The output data are: line length, discharge and length of the each section with different spacing between drippers, total discharge in the lateral line, multiple outlet adjustment coefficient, head losses, localized head loss, pressure variation, number of emitters, spacing between emitters, discharge in each emitter, and discharge per linear meter. The mathematical model developed was compared with the lateral line length obtained with the algebraic solution generated by the Darcy-Weisbach equation. The NLP model showed the best results since it generated the greater gain in the lateral line length, maintaining the uniformity and the flow variation under acceptable standards. It had also the lower flow variation, so its adoption is feasible and recommended.

Model to design drip hose lateral line using two spacing between emitters

The use of non-pressure compensating drip hose in horticultural and annual cycle fruits is growing in Brazil. In this case, the challenge for designers is getting longer lateral lines with high values of uniformity. The objective of this study was to develop a model to design longer lateral lines using non-pressure compensating drip hose. Using the developed model, the hypotheses to be evaluated were: a) the use of two different spacing between emitters in the same lateral line allows longer length; b) it is possible to get longer lateral lines using high values of pressure variation in the lateral lines since the distribution uniformity stays below allowable limits. A computer program was developed in Delphi based on the model developed and it is able to design lateral lines in level using non-pressure compensating drip hose. The input data are: desired distribution uniformity (DU); initial and final pressure in the lateral line; coefficients of relationship between emitter discharge and pressure head; hose internal diameter; pipe cross-sectional area with the dripper; and roughness coefficient for the Hazen-Williams equation. The program allows calculate the lateral line length with three possibilities: selecting two spacing between emitters and defining the exchange point; using two pre-established spacing between emitters and calculating the length of each section with different spacing; using one emitter spacing. Results showed that the use of two sections with different spacing between drippers in the lateral line didn't allow longer length but got better uniformity when compared with lateral line with one spacing between emitters. The adoption of two spacing increased the flow rate per meter in the final section which represented approximately 80% of the lateral line total length and this justifies their use. The software allowed DU above 90% with pressure head variation of 40% and the use of two spacing between emitters. The developed model/software showed to be accurate, easy to handle and useful for lateral line design using non-pressure compensating drip hose.

Avaliação dos desempenhos hidráulico e econômico de um sistema de irrigação localizada utilizando programação linear

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Relação entre uniformidade da produtividade e indicadores de uniformidade da irrigação em sistema de irrigação por microaspersão em citros

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Dimensionamento da linha lateral utilizando dois espaçamentos entre gotejadores

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Comparação econômica entre critérios de dimensionamento de sistemas de irrigação por microaspersão utilizando modelos de programação linear

Pós-graduação em Agronomia (Irrigação e Drenagem) - FCA

Estudo da uniformidade de emissão de água utilizando diferentes espaçamentos entre gotejadores na linha lateral

Pós-graduação em Agronomia (Irrigação e Drenagem) - FCA

DESIGN OF MICROIRRIGATION SYSTEMS IN SLOPING LANDS USING LINEAR PROGRAMMING

Quando a área a ser irrigada apresenta um elevado gradiente de declive na direção das linhas de derivação, uma opção de dimensionamento é o uso de tubulações com vários diâmetros para economizar no custo e também para manter a variação de pressão dentro dos limites desejados. O objetivo deste trabalho foi desenvolver um modelo de programação linear para dimensionar sistemas de irrigação por microaspersão com linhas de derivação com mais de um diâmetro e operando em declive, visando a minimização do custo anualizado da rede hidráulica e do custo anual com energia elétrica, além de assegurar que a máxima variação de carga hidráulica na linha será respeitada. Os dados de entrada são: configuração da rede hidráulica do sistema de irrigação, custo de todos os componentes da rede hidráulica e custo da energia. Os dados de saída são: custo anual total, diâmetro da tubulação em cada linha do sistema, carga hidráulica em cada ponto de derivação e altura manométrica total. Para ilustrar a potencialidade do modelo desenvolvido, ele foi aplicado em um pomar de citros no Estado de São Paulo, Brasil. O modelo demonstrou ser eficiente no dimensionamento do sistema de irrigação quanto à obtenção da uniformidade de emissão desejada. O custo anual com bombeamento deve ser considerado no dimensionamento de sistemas de irrigação por microaspersão porque ele gera menores valores de custo anual total quando comparado com a mesma alternativa que não considera aquele custo.

Increasing the lateral line length of drip irrigation systems

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Prototype emitter for use in subsurface drip irrigation: Manufacturing, hydraulic evaluation and experimental analyses

The current research aims to analyse theoretically and evaluate a self-manufactured simple design for subsurface drip irrigation (SDI) emitter to avoid root and soil intrusion. It was composed of three concentric cylindrical elements: an elastic silicone membrane; a polyethylene tube with two holes drilled on its wall for water discharge; and a vinyl polychloride protector system to wrap the other elements. The discharge of the emitter depends on the change in the membrane diameter when it is deformed by the water pressure. The study of the operation of this emitter is a new approach that considers mechanical and hydraulic principles. Thus, the estimation on the membrane deformation was based on classical mechanical stress theories in composite cylinders. The hydraulic principles considered the solid deformation due to force based on water pressure and the general Darcy–Weisbach head-loss equation. Twenty emitter units, with the selected design, were handcrafted in a lathe and were used in this study. The measured pressure/discharge relationship for the emitters showed good agreement with that calculated by the theoretical approach. The variation coefficient of the handcrafted emitters was high compared to commercial emitters. Results from field evaluations showed variable values for the relative flow variation, water emission uniformity and relative flow rate coefficients, but no emitter was obstructed. Therefore, the current emitter design could be suitable for SDI following further studies to develop a final prototype.