*2.3. Analytical Representation to Calculate Optimal Flow*

According to Fuentes and Chávez [12], the analytical representation of the optimal irrigation expenditure is a function of the border length, the hydrodynamic properties, and the soil moisture constants, maintaining a maximum value of the uniformity coefficient. In this way,

$$\mathbf{q}\_{\rm o} = \alpha\_{\rm u} \,\mathrm{K}\_{\rm s} \mathrm{L} \,\mathrm{a}\_{\rm u} = \frac{\ell\_{\rm n}}{\ell\_{\rm n} - \frac{\rm S^2}{2\mathcal{K}\_{\rm s}} \ln\left(1 + \frac{2\mathcal{K}\_{\rm u}}{\rm S^2} \ell\_{\rm n}\right)}\tag{4}$$

in which it should be noted that Ks L = qm represents the minimal unit flux necessary for the water to reach the final part of the border; S is the sorptivity of the medium expressed by S2 <sup>=</sup> 2 Ks hf (θ<sup>s</sup> <sup>−</sup> <sup>θ</sup>o); and <sup>n</sup> is the net irrigation depth. The optimal flow per row is calculated as Qo = b qo, where b is the width of the furrow. This analytical formula has been applied in field experiments with good results [2,3].

#### *2.4. Case Study*

Irrigation District 023 is located between the municipalities of San Juan del Río and Pedro Escobedo in the state of Querétaro, México (Figure 1), and has an area of 11,048 ha. The water for irrigation is obtained from the San Ildefonso, Constitución de 1917, La Llave and La Venta dams, and from 54 deep wells. It is legally constituted by three irrigation modules and the RIGRAT program was carried out in modules II and III on an area of 5021 ha. Its predominant climate is semiarid with summer rains, with an annual precipitation average of 599 mm and annual average temperature of 21 ◦C [1]. The water is conducted through open channels. The main channels are lined with concrete, but all the laterals channels that carry water to the plots are unlined. The separation of the plots in some cases are by trees, unlined channels, drains, or roads.

**Figure 1.** Location map of the Irrigation District 023 San Juan del Río Querétaro.
