# Comparison of Water Distribution Characteristics for Two Kinds of Sprinklers Used for Center Pivot Irrigation Systems

^{*}

## Abstract

**:**

## 1. Introduction

^{2}[18].

## 2. Materials and Methods

#### 2.1. Sprinkler Parameters

#### 2.2. Experimental Set-Up

^{3}·h

^{−1}. The polyvinyl chloride (PVC) pipes used for the water supply were 25 mm in diameter. A sand and gravel filter was installed in the pipes to avoid nozzle clogging. We used a pressure gauge and a pressure-regulating valve installed in the upper reaches of the sprinkler to adjust the working pressure of the sprinkler. The wind speed was recorded with an automatic weather station (WatchDog 2900ET, Spectrum Technologies, Inc., Aurora, Israel), which was set 60 m outside the experimental plots in an upwind direction.

#### 2.3. Water Distribution Measurements

_{D}, y

_{D}). P

_{1}, P

_{2}, P

_{3}, and P

_{4}are the four nearest points to point D on the two adjacent radial lines, and their coordinates are (x

_{1}, y

_{1}), (x

_{2}, y

_{2}), (x

_{3}, y

_{3}), and (x

_{4}, y

_{4}), respectively. The water depths in those measured points are h

_{1}, h

_{2}, h

_{3}, and h

_{4}, respectively. Thus, their distance away from point D is as follows:

_{i}is the distance from point D to P

_{i}. The water depth of point D (h

_{D}) can be expressed as following:

_{1}, C

_{2}, C

_{3}, and C

_{4}are calculated as following:

_{m}is the average water depth of all observations, and h is the water depth of the i-th observation.

#### 2.4. Nozzle Configuration for the Center Pivot

_{ZN}, mm) is defined as follows:

_{N}is the actual flow rate of the ending sprinkler (m

^{3}·s

^{−1}); H

_{N}is the pressure of the ending sprinklers (m); R

_{N}is the distance from the pivot to the ending sprinkler (m); and g is gravitational acceleration (m·s

^{−2}). The pressure of the other sprinklers is decided by the head losses, which is calculated as follows:

_{i}and H

_{i+1}is the pressure of the i-th and (i + 1)-th sprinklers (m); H

_{w}

_{(i,i+1)}is the head losses between the i-th and (i + 1)-th sprinklers (m); h

_{j}

_{(i,i+1)}is the local head losses between the i-th and (i+1)-th sprinklers (m); f is friction coefficient; d is internal diameter of water pipe (mm); b is coefficient of pipe diameter; m is flow index; N is number of sprinklers; and $\sum _{k=k+1}^{N}{q}_{k}$ is flow rate in the section between i-th and (i + 1)-th sprinklers (m

^{3}·s

^{−1}). Then, the nozzle diameters of the other sprinklers are defined as following:

_{Zi}is nominal diameter of selected nozzles (mm); and q

_{ie}is expected flow rate of the i-th sprinkler (m

^{3}·s

^{−1}). In addition, the expected flow rate of the i-th sprinkler (q

_{ie}) is calculated as following:

_{i}is the distance from the pivot to the i-th sprinkler (m); ω is angular velocity of the operating center pivot (°·s

^{−1}); and p is water application depth per unit time (mm·h

^{−1}).

#### 2.5. Simulation on Same-Nozzle-Sprinkler Pipe Sections

#### 2.6. Simulation on Full Circular Irrigated Area

^{−3}·s

^{−1}), A is the opening area of the nozzle (m

^{2}), g is gravitational acceleration (m·s

^{−2}), H is the pressure head (m) and c is the discharge coefficient. Thus, the water distributions of those sprinkler of unmeasured nozzles in this experiments (except the 2.78-, 4.76-, and 6.75-mm nozzle) could be estimated by means of weighted average based on the three measured ones. The weights were decided by the opening area of the nozzle. Let A

_{x}be the opening area of unmeasured nozzle, for which the subscript x indicates its nozzle diameter. Then the sprinkling intensity of any point of the unmeasured nozzles could be estimated as:

_{x,ij}is sprinkling intensity at point (i, j) when the nozzle diameter is x, and A

_{2.77}, A

_{4.76}and A

_{6.75}are the opening areas of 2.78-, 4.76- and 6.75-mm nozzles respectively. Following the above procedures, the estimated average radial application patterns for the unmeasured nozzles are shown in Figure 4.

#### 2.7. General Characteristics of the Experiments

## 3. Results and Discussion

#### 3.1. Individual Sprinklers

#### 3.2. Same-nozzle-sprinkler Pipe Sections

#### 3.3. Full Circular Irrigated Area

## 4. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

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**Figure 1.**Schematic of the experimental system for measuring water distribution of rotating and fixed spray plate sprinklers.

**Figure 2.**Catch can arrangements for measurements of water distribution with rotating (

**a**) and fixed (

**b**) spray plate sprinklers. Asterisks indicate the locations of sprinklers.

**Figure 3.**Nozzle configuration for the simulated center pivot irrigation system with different sprinkler intervals: 1.5, 3.0, and 4.5 m.

**Figure 4.**The estimated average radial application patterns for the unmeasured nozzles equipped in RSPSs (

**a**) and FSPSs (

**b**). The three solid lines in each figure indicated the three actual measured nozzles: 6.75, 4.76 and 2.78 mm, appearing from top to bottom respectively.

**Figure 5.**Water distribution characteristics of individual rotating spray plate sprinklers (RSPSs) and fixed spray plate sprinklers (FSPSs). The figures in different columns and rows indicate different sprinkler types (RSPS and FSPS) and nozzle diameters (2.78, 4.76, and 6.75 mm): RSPS—2.78 (

**a**), RSPS—4.76 (

**b**), RSPS—6.75 (

**c**), FSPS—2.78 (

**d**), FSPS—4.76 (

**e**) and FSPS—6.75 (

**f**).

**Figure 6.**Application intensity in radii of individual rotating spray plate sprinklers (RSPSs) (

**a**), and fixed spray plate sprinklers (FSPSs) (

**b**).

**Figure 7.**Water distribution characteristics of same-nozzle-sprinkler pipe sections with rotating spray plate sprinklers (RSPSs). The figures in different columns and rows indicate different nozzle diameters (2.78, 4.76, and 6.75 mm) and sprinkler intervals (1.5, 3.0, and 4.5 m): RSPS—2.78—1.5 (

**a**), RSPS—4.76—1.5 (

**b**), RSPS—6.75—1.5 (

**c**), RSPS—2.78—3.0 (

**d**), RSPS—4.76—3.0 (

**e**), RSPS—6.75—3.0 (

**f**), RSPS—2.78—4.5 (

**g**), RSPS—4.76—4.5 (

**h**) and RSPS—6.75—4.5 (

**i**).

**Figure 8.**Water distribution characteristics of same-nozzle-sprinkler pipe sections with fixed spray plate sprinklers (FSPSs). The figures in different columns and rows indicate different nozzle diameters (2.78, 4.76, and 6.75 mm) and sprinkler intervals (1.5, 3.0, and 4.5 m): FSPS—2.78—1.5 (

**a**), FSPS—4.76—1.5 (

**b**), FSPS—6.75—1.5 (

**c**), FSPS—2.78—3.0 (

**d**), FSPS—4.76—3.0 (

**e**), FSPS—6.75—3.0 (

**f**), FSPS—2.78—4.5 (

**g**), FSPS—4.76—4.5 (

**h**) and FSPS—6.75—4.5 (

**i**).

**Table 1.**Basic performance parameters of rotating and fixed spray plate sprinklers (RSPSs and FSPSs).

Sprinkler | Nozzle Diameter (mm) | Pressure Range (kPa) | Flow Range (m^{3}·h^{−1}) | Wetted Radius ^{1} (m) |
---|---|---|---|---|

RSPS (Nelson R3000) ^{2} | 2.78–9.92 mm | 98–196 | 0.293–5.470 | 5–9 |

FSPS (Nelson D3000) ^{2} | 1.79–9.92 mm | 40–274 | 0.077–5.470 | 4–6 |

**for the case when the height of sprinkler is 80 cm;**

^{1}^{2}R3000 and D3000 are types of RSPSs and FSPSs respectively.

Sprinkler | Type | Spray Plate | Elevation Angle and Trajectory | Sprinkler Height (cm) | Nozzle Size (mm) | Number of Grooves on Spray Plate |
---|---|---|---|---|---|---|

RSPS ^{1} | R3000 | Brown | Medium and multi-trajectory | 80 | 2.78 | 12 |

4.76 | 12 | |||||

6.75 | 12 | |||||

FSPS ^{2} | D3000 | Blue | Slight and uniform trajectory | 80 | 2.78 | 36 |

4.76 | 36 | |||||

6.75 | 36 |

^{1}RSPS, rotating spray plate sprinkler;

^{2}FSPS, fixed spray plate sprinkler.

Configurations | Configuration Parameters | Operating Parameters | ||||||
---|---|---|---|---|---|---|---|---|

Sprinkling Radius | Pressure of End Sprinkler | End Gun | Pipe Diameter | Sprinkler Intervals | Sprinkling Volumes | Sprinkling Intensity | Cycle Length | |

Parameters | 300 m | 103 kPa | None | 165 mm | 4.5 m | 10 mm | 10 mm/h | 36 h |

Sprinklers and Nozzles ^{1} | Number of Measurements | Average Wind Speed (m/s) |
---|---|---|

RSPS—2.78 | 4 | 0.7 |

RSPS—4.76 | 8 | 0.8 |

RSPS—6.75 | 4 | 0.6 |

FSPS—2.78 | 6 | 0.4 |

FSPS—4.76 | 12 | 0.7 |

FSPS—6.75 | 7 | 0.4 |

^{1}RSPS, rotating spray plate sprinkler; FSPS, fixed spray plate sprinkler; 2.78, 4.76 and 6.75 indicate the nozzle diameters of 2.78 mm, 4.76 mm and 6.75 mm respectively.

**Table 5.**Wetted radii of rotating spray plate sprinklers (RSPSs) and fixed spray plate sprinklers (FSPSs) with nozzles of differing diameters installed.

Sprinkler | Wetted Radius (m) | ||
---|---|---|---|

2.78-mm-Diameter Nozzle | 4.76-mm-Diameter Nozzle | 6.75-mm-Diameter Nozzle | |

RSPS | 4.88 ± 0.22a | 6.40 ± 0.11b | 7.05 ± 0.09c |

FSPS | 5.02 ± 0.06a | 6.33 ± 0.07b | 6.85 ± 0.15c |

**Table 6.**Christiansen coefficients of uniformities (CUCs) of same-nozzle-sprinkler pipe sections (PSs) of rotating spray plate sprinklers (RSPSs) and fixed spray plate sprinklers (FSPSs) with differing nozzle diameters and sprinkler intervals.

Nozzle Diameter | Sprinkler Interval | CUC of PSs with the Same Nozzle Diameter | |
---|---|---|---|

RSPS | FSPS | ||

2.78 mm | 1.5 m | 47.3% | 40.4% |

3.0 m | 46.1% | 40.3% | |

4.5 m | 51.0% | 41.3% | |

4.76 mm | 1.5 m | 48.3% | 43.9% |

3.0 m | 48.0% | 44.0% | |

4.5 m | 48.0% | 41.6% | |

6.75 mm | 1.5 m | 45.1% | 58.0% |

3.0 m | 44.7% | 58.0% | |

4.5 m | 45.1% | 50.9% |

**Table 7.**Christiansen coefficients of uniformities (CUCs) for the full circular irrigated area for the simulated center pivot irrigation system.

Sprinkler Types | Sprinkler Intervals and Required Sprinkler Quantities | ||
---|---|---|---|

1.5 m/191 | 3.0 m/96 | 4.5 m/64 | |

RSPS | 85.8% | 89.3% | 91.7% |

FSPS | 85.8% | 86.2% | 85.8% |

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## Share and Cite

**MDPI and ACS Style**

Jiao, J.; Wang, Y.; Han, L.; Su, D.
Comparison of Water Distribution Characteristics for Two Kinds of Sprinklers Used for Center Pivot Irrigation Systems. *Appl. Sci.* **2017**, *7*, 421.
https://doi.org/10.3390/app7040421

**AMA Style**

Jiao J, Wang Y, Han L, Su D.
Comparison of Water Distribution Characteristics for Two Kinds of Sprinklers Used for Center Pivot Irrigation Systems. *Applied Sciences*. 2017; 7(4):421.
https://doi.org/10.3390/app7040421

**Chicago/Turabian Style**

Jiao, Jian, Yadong Wang, Liliang Han, and Derong Su.
2017. "Comparison of Water Distribution Characteristics for Two Kinds of Sprinklers Used for Center Pivot Irrigation Systems" *Applied Sciences* 7, no. 4: 421.
https://doi.org/10.3390/app7040421