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 Barre 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.

中文翻译：

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重力灌溉最佳流量的解析表示

本研究的目的是根据边界长度、水动力特性和土壤水分常数，推导出最佳灌溉流量的分析表示，具有较高的均匀系数值。为了不局限于简化模型，建立了数值模拟与水动力模型的线性关系，由Barre de Saint-Venant 和Richards 的耦合方程组成。使用了 10 种不同质地的土壤类型的样本记录，并应用于三个水深。另一方面，利用Parlange渗透理论建立了线性关系的解析表示，用于对一维垂直渗透的微分方程进行积分。获得的最佳单一流量计算公式是边界带长度、净深度、特征渗透参数（毛细管力、吸附力和重力）、饱和导水率和水动力特征形状参数的函数. 数值和分析结果之间的良好一致性使我们能够推荐重力灌溉的设计公式。