Analytic Representation of the Optimal Flow for Gravity Irrigation

Carlos Fuentes,Carlos Chávez

doi:10.3390/w12102710

Carlos Fuentes, Carlos Chávez

Open Access

https://doi.org/10.3390/w12102710

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Abstract

The aim of this study is the deduction of an analytic representation of the optimal irrigation flow depending on the border length, hydrodynamic properties, and soil moisture constants, with high values of the coefficient of uniformity. In order not to be limited to the simplified models, the linear relationship of the numerical simulation with the hydrodynamic model, formed by the coupled equations of Barré de Saint-Venant and Richards, was established. Sample records for 10 soil types of contrasting texture were used and were applied to three water depths. On the other hand, the analytical representation of the linear relationship using the Parlange theory of infiltration proposed for integrating the differential equation of one-dimensional vertical infiltration was established. The obtained formula for calculating the optimal unitary discharge is a function of the border strip length, the net depth, the characteristic infiltration parameters (capillary forces, sorptivity, and gravitational forces), the saturated hydraulic conductivity, and a shape parameter of the hydrodynamic characteristics. The good accordance between the numerical and analytical results allows us to recommend the formula for the design of gravity irrigation.

Highlights

Gravity irrigation is the water supply at the head of a channel or inclined ditch built on a plot, as a border or a furrow, in order to take advantage of the gravitational field to provide the necessary amount of water for optimal development of cultivated plants
The optimal flow should be determined for a border length, and its value should be updated in proportion to the new length, which was verified by Rendón et al [39]
A linear relationship has been validated between the length of the border and the optimal irrigation flow, defined as the inflow rate that has to be applied to obtain a maximum value of Christiansen’s uniformity coefficient with high values of application efficiency and irrigation requirement efficiency

Summary

Introduction

Gravity irrigation is the water supply at the head of a channel or inclined ditch built on a plot, as a border or a furrow, in order to take advantage of the gravitational field to provide the necessary amount of water for optimal development of cultivated plants. Three phases are distinguished in the surface water movement [1,2]. The first begins when water flow is provided on the dry border until the water wave reaches the end part of the same; it is known as the advance phase. The second starts from the arrival of the wave at the end of the border until the water supply is cut off, known as the storage phase.

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