Increasing the Lateral Line Length of Drip Irrigation Systems.

Aims: The hypothesis of this research is that it is possible to increase the drip irrigation lateral line length by using a larger spacing between emitters at the beginning of the lateral line and a smaller one after a certain distance, which would allow for a higher pressure variation along the lateral line under an acceptable value of distribution uniformity. Study Design: Non-pressure compensating drip hose is widely utilized for vegetables and orchards irrigation. Though there is a limitation, which is 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. Place and Duration of Study: This study was conducted at the College of Agricultural Sciences of Sao Paulo State University in Botucatu, SP, during the year 2011. Methodology: To evaluate this hypothesis, a nonlinear programming model (NLP) was developed. The input data were: diameter, roughness coefficient, pressure variation, emitter operational pressure, relationship between emitter discharge and pressure. The output data were: 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. Results: 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 a greater gain in the lateral line length, maintaining the uniformity and the flow variation under acceptable standards. It also had lower flow variation. Conclusion: NLP model showed the best results when compared with the conventional procedure, generating gain in the lateral line length, keeping the uniformity and flow variation under acceptable standards.

Utilização de modelos de programação não-linear para sistematização de terras para irrigação em áreas regulares / Nonlinear programming models for irrigation of regularly shaped areas

Objetivou-se com este trabalho, desenvolver modelos de programação não-linear para sistematização de terras, aplicáveis para áreas com formato regular e que minimizem a movimentação de terra, utilizando o software GAMS para o cálculo. Esses modelos foram comparados com o Método dos Quadrados Mínimos Generalizado, desenvolvido por Scaloppi & Willardson (1986), sendo o parâmetro de avaliação o volume de terra movimentado. Concluiu-se que, ambos os modelos de programação não-linear desenvolvidos nesta pesquisa mostraram-se adequados para aplicação em áreas regulares e forneceram menores valores de movimentação de terra quando comparados com o método dos quadrados mínimos.

The present investigation aimed at the development of nonlinear programming models applicable to regularly shaped areas, intended to minimize the impact of soil manipulation. Software GAMS was used for calculation and two models were compared to the Method of Generalized Minimum Squares, developed by Scaloppi & Willardson (1986). The evoluation parameter was the volume of soil manipulated. The study concluded that both nonlinear programming models developed during the present investigation have shown to be appropriate to practical use in regulary shaped areas. Moreover, the models presented lower volume of soil manipulated when compared to the Method of Generalized Minimum Squares.