# Improving Water Distribution Uniformity by Optimizing the Structural Size of the Drive Spoon Blades for a Vertical Impact Sprinkler

^{*}

## Abstract

**:**

_{1}), the width of curved blades (h

_{2}) and number of blades (s) were chosen as the experiential variables. The suitable ranges of three variables for response surface method were determined initially by one-factor experimental design method, and 17 different drive spoons were designed according to response surface methodology. The results showed that in the one-factor experimental condition, the CU (Christiansen’s uniformity coefficient) values first increased and decreased slightly when h

_{1}exceeded 3 mm with the increase of h

_{1}within the variation range of the experimental factor. The CU values firstly increased and then decreased with the increase of h

_{2}. The CU values decreased rapidly when s was less than 3 or greater than 6. The relationship between CU values and h

_{1}, h

_{2}and s was established using response surface methodology. The p-values for h

_{1}, h

_{2}and s were 0.0359, 0.0092, 0.0212, and all of the selected factors were significant on CU. The order of parameters affecting CU were h

_{2}, h

_{1}and s. The ideal parameters for the drive spoon blades were h

_{1}= 6 mm, h

_{2}= 4 mm, and s = 3. CU was greatly improved after the optimization of structure for the drive spoon blades, which increased to 87.96% from 73.12%. After optimization, the application rates within 1 to 5 m were improved and increased from 10% to 15% with an average of 10.7% under different operating pressures. The maximum application rates decreased from 9.3, 9.3, 9.4 and 8.4 mm·h

^{−1}to 8.5, 8.4, 8.5 and 7.9 mm·h

^{−1}with operating pressures of 300, 400, 500 and 600 kPa, respectively. The maximum application rates in the overlap area were decreased from 18, 16, 16 and 15 mm·h

^{−1}to 16, 14, 14 and 12 mm·h

^{−1}with operating pressures of 300, 400, 500 and 600 kPa, respectively.

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Structure of the Drive Spoon

_{1}), the width of curved blades (h

_{2}), outlet angle of water jet on curved blades (α

_{2}), number of blades (s) and blade thickness (b).

_{2}) is the outlet angle when the water flow passes through the drive spoon; the size of which has influence on the magnitude of the vertical impact force obtained by the drive spoon from the water jet. The angle is generally 45°, and the curved blades can achieve preferable impact force to drive the sprinkler and attain desirable dispersion of water flow as well.

#### 2.2. Experiment Set-Up

#### 2.3. Evaluation Index

_{i}is measured depth (volume or mass) of water in equally spaced catch cans on a grid; x

_{m}is mean depth (volume or mass) of water of the catch in all cans.

## 3. Results and Discussion

#### 3.1. Analysis of Single Factor Experiment Results

_{1}and CU values. The graph shows that the CU values initially increased and then decreased slightly when h

_{1}exceeded 3 mm with the increase of h

_{1}within the variation range of the experimental factor. When h

_{1}was 4 mm, CU achieved a maximum value of 75.06%.

_{2}and CU values. It can be observed that the CU values firstly increased and then decreased with the increase of h

_{2}within the variation range of experimental factor. When h

_{2}was 7 mm, CU achieved a maximum value of 78.65%. Tang et al. [18] stated that the frequency of a drive spoon break water jet presented normal distribution with h

_{2}, which indicated that larger or smaller size of h

_{2}has influence on the water distribution.

#### 3.2. Response Surface Analysis

_{2}+ 32.67h

_{1}− 63.095s + 0.41h

_{1}·h

_{2}+ 1.575h

_{2}·s − 1.735h

_{1}·s + 1.52h

_{2}

^{2}− 3.725h

_{1}

^{2}+ 7.205s

^{2}

#### 3.3. Optimization and Validation

_{1}≤ 5, 6 ≤ h

_{2}≤ 8, 3 ≤ s ≤ 5.

#### 3.4. Comparison of Hydraulic Performance before and after Optimization

^{−1}to 8.5, 8.4, 8.5 and 7.9 mm·h

^{−1}with operating pressures of 300, 400, 500 and 600 kPa, respectively. Li et al. [30] indicated that the triangular shape of the water distribution curve was beneficial to reduce the peak water application rate. It can be observed by the shapes at the end of the water distribution curves that the sprinkler is more suitable for combining application after optimization.

^{−1}to 16, 14, 14 and 12 mm·h

^{−1}with operating pressures of 300, 400, 500 and 600 kPa, respectively. This is effective for reducing the risk of disrupting crops [31]. On the other hand, King [32] developed a soil-independent, quantitative potential runoff index based on application rates to facilitate selection of sprinklers for irrigation systems, and indicated that low sprinkler application rates facilitated soil infiltration and reduced the risk of surface runoff. Al-Kayssi and Mustafa [33] also indicated that the soil infiltration rate was significantly decreased with increasing sprinkler application rate. Hence, the vertical impact sprinkler after optimizing the drive spoon blades was more conducive to the application to deal with different soil and crops.

## 4. Conclusions

^{−1}to 8.5, 8.4, 8.5 and 7.9 mm·h

^{−1}, respectively. The maximum application rates in the overlap area were decreased from 18, 16, 16 and 15 mm·h

^{−1}to 16, 14, 14 and 12 mm·h

^{−1}, and this is effective for reducing the risk of disrupting crops and surface runoff.

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

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**Figure 1.**General arrangement diagram of vertical impact sprinkler: 1. lower bearing assembly, 2. stop shifter, 3. shift lever, 4. Counterweight, 5. drive arm, 6. shift lever shaft, 7. drive arm shaft, 8. spray tube, 9. nozzle and 10. drive spoon.

**Figure 2.**Structural diagram of the drive spoon: (

**a**) Top view of drive spoon; (

**b**) View from direction A of drive. α is the angle between straight blades and the centerline of jet (°); α

_{1}is the angle of straight blades into water jet (°); α

_{2}is the outlet angle of water jet on curved blades (°); h

_{1}is the width of straight blade (mm); h

_{2}is the width of curved blade (mm); b is blade thickness (mm).

**Figure 4.**Schematic diagram of sprinkler under square combination: l is overlapping distance of two sprinklers; R is radius of throw.

**Figure 5.**Relationships between three design variables and CU (Christiansen’s uniformity coefficient) values: (

**a**) The width of straight blades; (

**b**) The width of curved blades; (

**c**) Number of blades.

**Figure 6.**Water distribution comparison diagram before and after optimization: (

**a**) 300 kPa; (

**b**) 400 kPa; (

**c**) 500 kPa; (

**d**) 600 kPa.

**Figure 7.**Comparison of spatial water distribution (mm·h

^{−1}) before and after optimization: (

**a**) Before optimization with 300 kPa; (

**b**) After optimization with 300 kPa; (

**c**) Before optimization with 400 kPa; (

**d**) After optimization with 400 kPa; (

**e**) Before optimization with 500 kPa; (

**f**) After optimization with 500 kPa; (

**g**) Before optimization with 600 kPa; (

**h**) After optimization with 600 kPa.

No. | The Width of Straight Blades (h_{1}, mm) | The Width of Curved Blades (h_{2}, mm) | Number of Blades (s) |
---|---|---|---|

1 | 2, 3, 4, 5, 6 | 10 | 6 |

2 | 6 | 6, 7, 8, 9, 10 | 6 |

3 | 6 | 10 | 2, 3, 4, 5, 6, 7 |

Code | Factor | ||
---|---|---|---|

h_{1} (mm) | h_{2} (mm) | s | |

1 | 3 | 6 | 3 |

0 | 4 | 7 | 4 |

−1 | 5 | 8 | 5 |

No. | h_{1} (mm) | h_{2} (mm) | n | CU/% |
---|---|---|---|---|

1 | 0 | 0 | 0 | 69.65 |

2 | 1 | −1 | 0 | 68.31 |

3 | −1 | 1 | 0 | 69.28 |

4 | 0 | −1 | 1 | 76.10 |

5 | 0 | 1 | −1 | 81.02 |

6 | 1 | 0 | −1 | 76.34 |

7 | 1 | 1 | 0 | 67.87 |

8 | 0 | 0 | 0 | 72.31 |

9 | 0 | 1 | 1 | 80.69 |

10 | 0 | 0 | 0 | 70.64 |

11 | −1 | 0 | −1 | 75.44 |

12 | 0 | 0 | 0 | 71.39 |

13 | −1 | −1 | 0 | 71.36 |

14 | 0 | 0 | 0 | 73.06 |

15 | −1 | 0 | 1 | 76.91 |

16 | 1 | 0 | 1 | 70.87 |

17 | 0 | −1 | −1 | 82.73 |

Std. Dev. | CV/% | R-Squared | Pred R-Squared | Adj R-Squared | Adeq Precision |
---|---|---|---|---|---|

1.31 | 1.78 | 0.9646 | 0.7406 | 0.9191 | 15.407 |

**Table 5.**Comparison of the values of design variables and performance before and after optimization.

Scheme | h_{1} (mm) | h_{2} (mm) | s | CU (%) |
---|---|---|---|---|

Initial values | 6 | 10 | 6 | 73 |

Solving results | 4 | 6 | 3 | 83 |

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## Share and Cite

**MDPI and ACS Style**

Tang, P.; Chen, C.; Li, H.
Improving Water Distribution Uniformity by Optimizing the Structural Size of the Drive Spoon Blades for a Vertical Impact Sprinkler. *Sustainability* **2020**, *12*, 7574.
https://doi.org/10.3390/su12187574

**AMA Style**

Tang P, Chen C, Li H.
Improving Water Distribution Uniformity by Optimizing the Structural Size of the Drive Spoon Blades for a Vertical Impact Sprinkler. *Sustainability*. 2020; 12(18):7574.
https://doi.org/10.3390/su12187574

**Chicago/Turabian Style**

Tang, Pan, Chao Chen, and Hong Li.
2020. "Improving Water Distribution Uniformity by Optimizing the Structural Size of the Drive Spoon Blades for a Vertical Impact Sprinkler" *Sustainability* 12, no. 18: 7574.
https://doi.org/10.3390/su12187574