# Wetting Body Characteristics and Infiltration Model of Film Hole Irrigation

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Laboratory Experiments

^{3}. The soil box was weighed layer by layer and filled based on 5 cm. When filling the soil, attention was paid so that the soil was closely attached to the side wall of the soil box in order to prevent the side wall from generating preferential flow. During our laboratory experiments, in order to minimize the influence of side-wall flow, the soil was filled carefully. At the end of the experiments, we took the soil samples out of the soil boxes to check whether obvious side-wall flow appeared. In order to determine whether side-wall flow occurred, we compared the wetted soil in the boxes and the wetting front which had observed outside the box. If they are not consistent, it indicates that the side-wall flow occurred. The results of this experiment would be discarded and replaced by a new experiment until the requirements are met.

#### 2.2. Numerical Simulation Experiments

^{3}/cm

^{3}); $h$ is negative pressure water head (cm); $t$ is the infiltration time (min); $K$ is hydraulic conductivity (cm/min); ${B}_{r}$ and ${B}_{z}$ are the width and height of the soil box (cm); ${h}_{0}$ is the initial negative pressure water head (cm); ${H}_{0}$ is the water depth in the film hole (cm); $R$ is the radius of the film hole (cm).

^{3}/cm

^{3}); ${\theta}_{s}$ is saturated water content (cm

^{3}/cm

^{3}); ${K}_{s}$ is saturated hydraulic conductivity (cm/min); $\alpha $ is the parameter related to air-entry value (cm

^{−1}); $n$ and $m$ are the shape coefficients, $=1-\frac{1}{n}$; $D\left(h\right)$ presents soil diffusivity (cm

^{2}/min). The soil parameters used in this study are shown in Table 1.

## 3. Results and Discussion

#### 3.1. Verification for Numerical Simulation Experiment

^{2}> 0.99. Figure 3b shows the comparison between simulated and measured values of the migration distance of the wetting front, and its determination coefficients of horizontal and vertical directions are greater than 0.99. The coefficients are all close to 1, which proved that it was accurate to simulate the infiltration process of film hole irrigation using HYDRUS. Therefore, HYDRUS could be used in order to simulate the infiltration process of film hole irrigation in different soils.

#### 3.2. Wetting Front Shape

^{2}of five tests at different times ranges from 0.94 to 1.00, which is close to 1, indicating that it fitted well, so the shape of the wetting front could be expressed using the elliptic equation.

#### 3.3. Distribution Characteristics of Water Content in the Wetting Body

^{2}ranges from 0.99 to 1.00, all of which are close to 1, indicating that the water content distribution is well fitted to the elliptic curve. As shown in Figure 7 and Table 3, with different soil types and irrigation durations, the water content distribution of the wetting body radius is well fitted to the elliptic curve. Wang et al. [31] showed that the distribution of soil water content under one-dimensional vertical infiltration can be represented by elliptic curve, and we discovered that the water content distribution of film hole irrigation has similar properties.

^{3}/cm

^{−3}); $x$ is the distance between this point and the center of the film hole (cm); $l$ is the radius of the wetting body (cm); and function image of Equation (4) is shown in Figure 8b. If the ${F}_{r}$ and ${F}_{z}$ of the wetting front are known, the equivalent radius can be expressed as the geometric mean value:

#### 3.4. The Relationship between Cumulative Infiltration and Migration Distance of the Wetting Front

^{3}); $dI$ is the water content change in the element (cm

^{3}). The cumulative infiltration can be obtained by integrating Equation (6):

^{2}are all close to 1, which indicates that the cumulative infiltration of film hole irrigation can be accurately calculated using Equation (9) under the condition of experiment.

#### 3.5. Irrigation Requirement for Crops

## 4. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 3.**Comparison of simulated and experimental results: (

**a**) Cumulative infiltration (

**b**) Migration distance of the wetting front.

**Figure 4.**Fitting diagram of wetting front and elliptic curve: (

**a**) Experimental results of Xi’an silt loam; (

**b**) Simulated results of Xi’an silt loam; (

**c**) Simulated results of silt; (

**d**) Simulated results of silt loam; (

**e**) Simulated results of loam.

**Figure 6.**Water content distribution of the wetting body radius of Xi’an silt loam after irrigation for 360 min: (

**a**) β = 0°; (

**b**) β = 45°; (

**c**) β = 90°.

**Figure 7.**Water content distribution of the wetting body radius at different durations simulated by HYDRUS: (

**a**) Xi’an silt loam; (

**b**) Silt; (

**c**) Silt loam; (

**d**) Loam.

**Figure 8.**(

**a**) Film hole irrigation profile; (

**b**) Water content distribution curve of wetting body radius; (

**c**) Root distribution of crops.

**Figure 9.**Comparison of cumulative infiltration calculated using Equation (9) and of the Experiments: (

**a**) Xi’an silt loam; (

**b**) Silt; (

**c**) Silt loam; (

**d**) Loam.

Treatment | Soil Type | Hole Radius (cm) | Water Depth (cm) | ${\mathit{\theta}}_{\mathit{i}}$ | ${\mathit{\theta}}_{\mathit{s}}$ | ${\mathit{\theta}}_{\mathit{r}}$ | α (m ^{−1}) | m | n | K_{s}(cm/min) |
---|---|---|---|---|---|---|---|---|---|---|

1 | Xi’an Silt loam | 3 | 5 | 0.10 | 0.45 | 0.09 | 0.009 | 0.33 | 1.49 | 0.006 |

2 | Silt | 3 | 5 | 0.10 | 0.46 | 0.03 | 0.016 | 0.27 | 1.37 | 0.004 |

3 | Silt loam | 3 | 5 | 0.10 | 0.45 | 0.07 | 0.020 | 0.29 | 1.41 | 0.008 |

4 | Loam | 3 | 5 | 0.10 | 0.43 | 0.08 | 0.036 | 0.36 | 1.56 | 0.017 |

Experiment Type | Soil Type | 10 min | 30 min | 60 min | 120 min | 240 min | 360 min |
---|---|---|---|---|---|---|---|

Laboratory experiment | Xi’an silt loam | 0.97 | 0.99 | 0.99 | 0.99 | 0.99 | 0.99 |

Numerical simulation experiment | Xi’an silt loam | 0.96 | 0.98 | 0.99 | 0.99 | 1.00 | 1.00 |

silt | 0.94 | 0.98 | 0.97 | 0.99 | 0.99 | 0.99 | |

silt loam | 0.98 | 0.99 | 1.00 | 1.00 | 1.00 | 1.00 | |

loam | 0.99 | 1.00 | 1.00 | 1.00 | 0.99 | 0.99 |

Soil Type | Duration (min) | Fitting Curve Equations of Water Content $\frac{{\left(\mathit{\theta}-{\mathit{\theta}}_{\mathit{i}}\right)}^{2}}{{\left({\mathit{\theta}}_{\mathit{s}}-{\mathit{\theta}}_{\mathit{i}}\right)}^{2}}+\frac{{\mathit{x}}^{2}}{{\mathit{l}}^{2}}=1$ | Coefficient of Determination R^{2} |
---|---|---|---|

Xi’an Silt loam | 30 | $\frac{{\left(\theta -0.1\right)}^{2}}{{0.35}^{2}}+\frac{{x}^{2}}{{6.94}^{2}}=1$ | 0.97 |

120 | $\frac{{\left(\theta -0.1\right)}^{2}}{{0.35}^{2}}+\frac{{x}^{2}}{{10.08}^{2}}=1$ | 0.99 | |

360 | $\frac{{\left(\theta -0.1\right)}^{2}}{{0.35}^{2}}+\frac{{x}^{2}}{{13.80}^{2}}=1$ | 1.00 | |

Silt | 30 | $\frac{{\left(\theta -0.1\right)}^{2}}{{0.36}^{2}}+\frac{{x}^{2}}{{4.95}^{2}}=1$ | 0.94 |

120 | $\frac{{\left(\theta -0.1\right)}^{2}}{{0.36}^{2}}+\frac{{x}^{2}}{{6.79}^{2}}=1$ | 0.97 | |

360 | $\frac{{\left(\theta -0.1\right)}^{2}}{{0.36}^{2}}+\frac{{x}^{2}}{{8.92}^{2}}=1$ | 0.99 | |

Silt loam | 30 | $\frac{{\left(\theta -0.1\right)}^{2}}{{0.35}^{2}}+\frac{{x}^{2}}{{5.50}^{2}}=1$ | 0.95 |

120 | $\frac{{\left(\theta -0.1\right)}^{2}}{{0.35}^{2}}+\frac{{x}^{2}}{{7.59}^{2}}=1$ | 0.98 | |

360 | $\frac{{\left(\theta -0.1\right)}^{2}}{{0.35}^{2}}+\frac{{x}^{2}}{{10.20}^{2}}=1$ | 1.00 | |

Loam | 30 | $\frac{{\left(\theta -0.1\right)}^{2}}{{0.33}^{2}}+\frac{{x}^{2}}{{6.22}^{2}}=1$ | 0.97 |

120 | $\frac{{\left(\theta -0.1\right)}^{2}}{{0.33}^{2}}+\frac{{x}^{2}}{{9.00}^{2}}=1$ | 0.99 | |

360 | $\frac{{\left(\theta -0.1\right)}^{2}}{{0.33}^{2}}+\frac{{x}^{2}}{{12.40}^{2}}=1$ | 0.99 |

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**MDPI and ACS Style**

Jie, F.-l.; Fei, L.-j.; Zhong, Y.; Liu, L.-h.; Kang, S.-x.
Wetting Body Characteristics and Infiltration Model of Film Hole Irrigation. *Water* **2020**, *12*, 1226.
https://doi.org/10.3390/w12051226

**AMA Style**

Jie F-l, Fei L-j, Zhong Y, Liu L-h, Kang S-x.
Wetting Body Characteristics and Infiltration Model of Film Hole Irrigation. *Water*. 2020; 12(5):1226.
https://doi.org/10.3390/w12051226

**Chicago/Turabian Style**

Jie, Fei-long, Liang-jun Fei, Yun Zhong, Li-hua Liu, and Shou-xuan Kang.
2020. "Wetting Body Characteristics and Infiltration Model of Film Hole Irrigation" *Water* 12, no. 5: 1226.
https://doi.org/10.3390/w12051226