# The Effect of Plug Height and Inflow Rate on Water Flow Characteristics in Furrow Irrigation

^{1}

^{2}

^{3}

^{4}

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. FLOW-3D Simulation

#### 2.1.1. Governing Equations

#### 2.1.2. Grid Division

#### 2.1.3. Boundary Conditions

#### 2.1.4. Working Conditions

^{3}(Table 1).

#### 2.2. HYDRUS-2D Simulation

#### 2.2.1. Governing Equations

_{e}is the relative saturation; K

_{s}is the saturated hydraulic conductivity; ${\mathsf{\theta}}_{\mathrm{r}}$ and ${\mathsf{\theta}}_{\mathrm{s}}$ are the residual and saturated water contents, respectively; $\mathsf{\alpha}$ is an empirical parameter inversely related to the air entry value; and n and m are van Genuchten–Mualem shape parameters.

#### 2.2.2. Boundary Conditions and Initial Conditions

^{−1}. Daily variations in the evaporation rate were not considered.

#### 2.3. Irrigation Uniformity

_{i}is the ith cumulative infiltration of the observed point in the furrow and $\overline{\mathrm{Z}}$ is the average cumulative infiltration of the total n observed points.

#### 2.4. Cumulative Infiltration

_{s}is saturated hydraulic conductivity; z

_{f}is the generalized wetting front depth; s

_{f}is the water suction at the wetting front; and H is the water level.

## 3. Results and Discussion

#### 3.1. Water Advancement in the Furrow and Plug Operating Speed

#### 3.2. Water Levels

#### 3.3. Cumulative Infiltration

^{2}. Adding a plug dramatically affected the furrow-long infiltration. The changes in cumulative infiltration are similar to the plugging treatments. The longer time required for the irrigation water to reach the end of the furrow and the large infiltration rate results in a small difference in the cumulative infiltration at each point in the furrow. The cumulative infiltration is observed to be higher for the large inflow rate treatments and increases with plug height. For example, the cumulative infiltration of B2 is 1.08 times that of A2 at the 30 m position.

#### 3.4. Uniformity Coefficient

## 4. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 1.**Overview of the furrow and plug. (

**a**) Photo from the field. (

**b**) Longitudinal section of the furrow. (

**c**) Cross section of the furrow.

**Figure 2.**General view of the furrow and plug for the simulated furrow irrigation scenario. (

**a**) Simulated furrow. (

**b**) Plug. (

**c**) Cross-sectional size of furrow. (

**d**) Cross-sectional size of plug.

**Figure 6.**Water level for initial irrigation water positions of 6 m, 18 m, and 30 m in the furrow of different treatments. (

**a**) B1; (

**b**) A1; (

**c**) B2; (

**d**) A2; (

**e**) B3; (

**f**) A3; (

**g**) B4; (

**h**) A4.

**Figure 7.**Cumulative infiltration curve for all treatments. (

**a**) B1; (

**b**) A1; (

**c**) B2; (

**d**) A2; (

**e**) B3; (

**f**) A3; (

**g**) B4; (

**h**) A4.

Treatments | Flow Rate (L/s) | Field Slope | Height of Plug (cm) |
---|---|---|---|

A1 | 2.8 | 0.002 | 15 |

A2 | 2.8 | 0.002 | 18 |

A3 | 2.8 | 0.002 | 21 |

A4 | 2.8 | 0.002 | 0 (no plug) |

B1 | 3.0 | 0.002 | 15 |

B2 | 3.0 | 0.002 | 18 |

B3 | 3.0 | 0.002 | 21 |

B4 | 3.0 | 0.002 | 0 (no plug) |

Soil | θ_{r} | θ_{s} | α | n | Ks |
---|---|---|---|---|---|

(cm^{3} cm^{−3}) | (cm^{3} cm^{−3}) | (m^{−1}) | (-) | (cm h^{−1}) | |

Sandy loam | 0.065 | 0.41 | 0.075 | 1.89 | 4.42 |

Loam | 0.078 | 0.43 | 0.036 | 1.56 | 1.04 |

Soil Texture | Irrigation Uniformity | |||||||
---|---|---|---|---|---|---|---|---|

A1 | A2 | A3 | A4 | B1 | B2 | B3 | B4 | |

Sandy loam | 97.30% | 98.60% | 99.22% | 88.72% | 95.81% | 97.49% | 98.36% | 88.84% |

Loam | 90.18% | 96.02% | 96.01% | 89.44% | 93.11% | 94.97% | 96.72% | 89.58% |

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**MDPI and ACS Style**

Yu, J.; Liu, K.; Li, A.; Yang, M.; Gao, X.; Zhao, X.; Cai, Y.
The Effect of Plug Height and Inflow Rate on Water Flow Characteristics in Furrow Irrigation. *Agronomy* **2022**, *12*, 2225.
https://doi.org/10.3390/agronomy12092225

**AMA Style**

Yu J, Liu K, Li A, Yang M, Gao X, Zhao X, Cai Y.
The Effect of Plug Height and Inflow Rate on Water Flow Characteristics in Furrow Irrigation. *Agronomy*. 2022; 12(9):2225.
https://doi.org/10.3390/agronomy12092225

**Chicago/Turabian Style**

Yu, Juan, Keyao Liu, Anbin Li, Mingfei Yang, Xiaodong Gao, Xining Zhao, and Yaohui Cai.
2022. "The Effect of Plug Height and Inflow Rate on Water Flow Characteristics in Furrow Irrigation" *Agronomy* 12, no. 9: 2225.
https://doi.org/10.3390/agronomy12092225