# Atomization Characteristics of a Hollow Cone Nozzle for Air-Assisted Variable-Rate Spraying

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## Abstract

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_{v}0.5), the relative span of the droplet spectrum, and droplet velocity at different spray pressures, were studied at distances ranging from 0.4 to 2.4 m from the nozzle orifice with an air velocity of 10 m/s at the nozzle orifice position. The effects of longitudinal distance, transverse distance, and spray pressure on D

_{v}0.5, relative span, and droplet velocity were analysed by multiple linear regression analysis, and the regression model was established. The experimental results show that at a longitudinal distance of 1.8 m, D

_{v}0.5 ranges from 120 to 150 μm, meeting the requirements for optimal droplet size for controlling crawling pests and plant diseases on crop leaves; and the relative span is 1.2, indicating a wide droplet spectrum. At different pressure conditions, D

_{v}0.5 decreases as pressure increases. Through multiple linear regression analysis, the longitudinal distance, the transverse distance, and the spray pressure have high significance for D

_{v}0.5 and the droplet velocity. The longitudinal distance and the transverse distance have a highly significant effect on the relative span. In this study, the mathematical relational model of droplet characteristics at different spatial positions and different pressures was established, providing an agricultural reference for predicting the droplet characteristics at different spatial positions to achieve the best application effect. This model is conducive to the effective use of pesticides and reduces environmental pollution.

## 1. Introduction

_{v}0.5 was 250 μm and the deposition density was 50 droplets ${\mathrm{c}\mathrm{m}}^{-2}$, or when D

_{v}0.5 was 602 μm and the deposition density was 10 droplets ${\mathrm{c}\mathrm{m}}^{-2}$. Thus, the droplet size and droplet deposition density have a significant impact on the prevention and control of pests and diseases.

_{v}0.5 did not change significantly in the vertical direction of the nozzle centre but increased gradually in the horizontal direction with an increasing distance. At the same position, the droplet size decreased as pressure increased, and the droplet velocity increased. This experiment can provide a basis for the selection of adjuvants and nozzles in pesticide applications. It also provides a data basis for studying the distribution of droplets on the target. Nuyttens et al. [23] studied the velocity characteristics of droplet sizes measured at 0.5 m below the nozzle by using a droplet measuring device according to 13 combinations, such as the spray pressure, nozzle type, and nozzle size. The experimental results show that the size of the droplets and the velocity of the droplets were affected by the above three factors. The droplet velocity is related to the droplet size and spray speed; the larger the droplet size is, the higher the droplet velocity, and the smaller the droplet size is, the smaller the droplet velocity. Aiming at the problems of less mathematical description of flat-fan nozzle atomization characteristics and insufficient pesticide application theories, Li et al. [24] analysed relevant spray parameters and studied the influences of the spray angle, spray pressure, nozzle equivalent hole diameter, and spatial atomization position on the atomization characteristics of the nozzle. The droplet size is positively correlated with the nozzle equivalent hole diameter at a certain spray pressure and spray angle. The spray angle and spray distance are negatively correlated with the droplet velocity, which has a great influence on the droplet velocity and particle size in the horizontal direction of the X-axis, and the spray distance has no effect on the droplet size in the axial direction of the spray.

## 2. Materials and Methods

#### 2.1. Overall Design of the Test Bench

#### 2.1.1. System Hardware Structure

_{v}0.5 and the droplet spectrum are measured. For the measurement of the droplet velocity, the relative moving position of the droplet in the measurement area is obtained by setting the emission time interval of the laser beam before and after, and then the droplet velocity is calculated.

#### 2.1.2. System Software

#### 2.2. Measurement Method

_{v}0.5, relative span of the droplet spectrum, and droplet velocity were studied. To ensure the reliability of the experimental data, each measurement was repeated three times, and at least 10,000 droplet data points were measured each time [28,29,30]. The droplet measurement range was 0$~$5000 μm, and the droplet velocity measurement range was 0$~$50 m/s.

#### 2.3. Droplet-Related Parameters

- D
_{v}0.1: 10% of the total volume is carried by droplets lower than D_{v}0.1. - D
_{v}0.5: 50% of the total volume is carried by droplets lower than D_{v}0.5. - D
_{v}0.9: 90% of the total volume is carried by droplets lower than D_{v}0.9.

#### 2.4. Data Processing and Analysis

## 3. Results

#### 3.1. The Characteristics of Volume Median Diameter and Multiple Linear Regression Significance Analysis

#### 3.1.1. The Characteristics of Volume Median Diameter

_{v}0.5 distributions along the X-axis and Y-axis directions on each axis are shown in Figure 4. Figure 4a shows that D

_{v}0.5 at three measurement points at a close distance of X = 0.4 m increases with an increasing Y-value. At the other X distances, D

_{v}0.5 increases first and then decreases. When the distance from the nozzle orifice is X = 1.8 m and X = 2.4 m, D

_{v}0.5 is 120 μm$~$140 μm in the Y-axis direction. The D

_{v}0.5 fluctuation is more stable. The peak value of D

_{v}0.5 is less than the peak diameter at X = 0.6 m, X = 0.8 m, and X = 1.2 m. When Y = 0.4 m, D

_{v}0.5 at X = 1.8 m is larger than that at X = 2.4 m.

_{v}0.5 change trend. At the centreline of the nozzle Y = 0 m, as the X value increases, D

_{v}0.5 increases, but it is smaller than D

_{v}0.5 at each point on Y = 0.1 m, Y = 0.2 m, and Y = 0.3 m. D

_{v}0.5 at the positions of Y = 0.1 m, Y = 0.2 m, and Y = 0.3 m first increases, then decreases, and finally increases along the X-axis direction. At Y = 0.4 m, D

_{v}0.5 first increases and then decreases. The change in D

_{v}0.5 at the two measurement points at Y = 0.5 m is not obvious.

_{v}0.5 at different pressures is shown in Figure 5. To compare and analyse as much as possible with more data, the cross-section of the position X = 1.8 m from the nozzle orifice is selected. The distance of X = 1.8 m is also closer to the position of the unilateral sprayer to the centreline of the tree row in the orchard (Figure 5a). The longitudinal section at the centreline of the nozzle at Y = 0 was selected to analyse the change in D

_{v}0.5 at different pressures (Figure 5b). From the analysis of Figure 5a, it can be seen that D

_{v}0.5 decreases as spray pressure increases. With an increasing Y-value, D

_{v}0.5 first increases and then decreases. The distance from the centreline of the nozzle is Y $\ge $ 0.4 m, and D

_{v}0.5 at different pressure conditions does not change significantly.

_{v}0.5 increases with an increasing distance from the nozzle orifice. When X = 0.4 m and X = 0.6 m, the growth rate of D

_{v}0.5 is the largest at various pressure conditions. When the pressure is 0.7 MPa, 0.8 MPa, and 0.9 MPa, the effect of increasing D

_{v}0.5 at the position of X = 0.6 m to X = 0.8 m is not obvious.

#### 3.1.2. Multiple Linear Regression Significance Analysis of Volume Median Diameter

_{v}0.5 of each point in the space at different pressures of 0.6 MPa, 0.7 MPa, 0.8 MPa, 0.9 MPa, and 1.0 MPa were carried out using MATLAB software. To determine whether the factors influencing longitudinal distance X, transverse distance Y, and spray pressure P have a significant influence on D

_{v}0.5 and the response law, it is assumed that the relationship between the dependent variable D

_{v}0.5 and the independent variables longitudinal distance, transverse distance, and spray pressure is a ternary quadratic polynomial.

_{v}0.5 is shown in Table 2. In the analysis of D

_{v}0.5, the interaction of spray pressure P

^{2}, longitudinal distance X, spray pressure P, transverse distance Y, and spray pressure P have no significant effect on D

_{v}0.5. In order to determine the significance of each factor on the evaluation index, stepwise regression and backward elimination approach were used to analyse the data, and analysis of variance (ANOVA) was performed at a significant level of p = 0.05 [36]. p < 0.001 is used as the probability p-value obtained by the statistical test to be less than the significance level. The model can accurately represent the relationship between the longitudinal distance X, the transverse distance Y, the spray pressure P, and D

_{v}0.5. In the subsequent table, the insignificant items are no longer displayed.

_{v}0.5. Therefore, the volume median diameter is changed by changing three factors. The D

_{v}0.5 significance test of the whole model has a highly significant impact, and the determination coefficient R

^{2}= 0.7769. The regression model is:

_{v}0.5 = 112.8672 + 32.9753X + 204.8911Y − 29.2415P − 5.556X

^{2}− 366.3529Y

^{2}− 30.3372XY

_{v}0.5 (mm) is the volume mean diameter; X (m) is the longitudinal distance; Y (m) is the transverse distance; and P (MPa) is the spray pressure.

#### 3.2. The Characteristics of Relative Span and Multiple Linear Regression Significance Analysis

#### 3.2.1. The Characteristics of Relative Span

#### 3.2.2. Multiple Linear Regression Significance Analysis of Relative Span

^{2}= 0.9409, and the fitting degree is high. It is assumed that the relationship between the relative span of the dependent variable and the longitudinal distance X, transverse distance Y, and spray pressure P of the independent variable is a ternary quadratic polynomial. According to the McLaughlin expansion, the multiple regression model is as follows:

^{2}− 1.3516Y

^{2}− 0.4884YP

#### 3.3. The Characteristics of Droplet Velocity and Multiple Linear Regression Significance Analysis

#### 3.3.1. The Characteristics of Droplet Velocity

#### 3.3.2. Multiple Linear Regression Significance Analysis of Droplet Velocity

^{2}= 0.8779. The regression model is:

^{2}+ 6.2268XY + 1.0590XP

## 4. Discussion

- 1.
- Through the analysis of the multiple linear regression equation and Figure 4a, it can be seen that when the pressure is 1 MPa, along the Y-axis direction, farther away from the centreline of the nozzle, D
_{v}0.5 first increases and then decreases rapidly. The main reason is that the spray field of the nozzle is a hollow cone, and the centre position entrains small droplets. With the increase in the distance from the centreline of the nozzle, D_{v}0.5 gradually increases until the maximum peak of the axis (the fog-shaped edge of the cone spray), and D_{v}0.5 far away from the fog-shaped edge drops sharply. This part is mainly due to the influence of the air at the edge of the droplet field, which has a certain amount of small droplets outside the edge of the drifting spray field. In Figure 4b, when Y = 0.1 m, Y = 0.2 m, Y = 0.3 m, and Y = 0.4 m, D_{v}0.5 increases first, then decreases and then increases with an increasing longitudinal X-axis distance. The main reason is that in the measurement process, the first measurement is the drift of small droplets outside the edge of the hollow cone spray field. As the distance increases, D_{v}0.5 gradually increases. There are small droplets in the interior of the hollow cone spray field, all of which are small droplets. D_{v}0.5 drops sharply. When the X value is further increased, the hollow effect of the droplets affected by their own gravity is no longer obvious. The large droplets above the same horizontal plane of the nozzle gradually fall to the measurement point, resulting in D_{v}0.5 gradually increasing with an increasing X distance. When X = 1.8 m and X = 2.4 m, D_{v}0.5 along the Y direction is in the range of 120~140 μm. Compared with D_{v}0.5 at distances of X = 0.6 m, X = 0.8 m, and X = 1.2 m, the peak value is small, and the fluctuation of D_{v}0.5 at each point is relatively stable. The main reason is that the peak measuring point of D_{v}0.5 is located at the edge of the spray field at X = 0.6 m, X = 0.8 m, and X = 1.2 m. Through the analysis of Hu et al. [37], it can be seen that droplets with large particle sizes have a short propagation distance, uneven distribution, and poor spray effect. Due to the influence of the droplet’s own gravity, as the distance from the nozzle orifice increases, the air speed effect at the edge position is no longer obvious, resulting in droplets with larger values of D_{v}0.5 that cannot be measured at the next point. Therefore, the peak value of the D_{v}0.5 falling at a close distance is greater than the peak value of D_{v}0.5 falling at a long distance. The optimal biological particle size for flying insects is 10~50 μm. According to the linear regression equation, even if the longitudinal distance X, the transverse distance Y, and the spray pressure P reach the best state, the droplet size cannot be satisfied in the range of 10~50 μm. The spray pressure is negatively correlated with droplet size. If the system continues to increase the pressure to reduce the volume medium diameter, the hardware requirements of the system will be enhanced. Nuyttens et al. [23] found that the nozzle type, equivalent hole diameter, and other factors can reduce the droplet size. The droplet size under the influence of other factors can continue to be improved in the future.At different pressure conditions, D_{v}0.5 decreases as spray pressure increases at the same measurement position. D_{v}0.5 increases with an increasing X value and the variation law along the Y-axis is the same as that at a pressure of 1 MPa. Since the standardized orchard row spacing is 4~5 m, the median diameter of the volume gradually increases along the centreline of the nozzle. When the distance is greater than 2.5 m, the air force has little effect on the droplets, and it can be ignored. D_{v}0.5 gradually decreases with an increasing X value. When the farthest distance from the centreline of the nozzle is Y = 0.5 m, D_{v}0.5 does not change significantly with an increasing X value. The main reason is that small-volume droplets with stable drift are measured outside the spray field. - 2.
- Through the analysis of the multiple linear regression equation, it can be seen that when the pressure is 1 MPa, as the X value increases, the relative span increases gradually. By comparing and analysing the relationship between the relative span and D
_{v}0.5, Hewitt [38] found that the laws of relative span and D_{v}0.5 are similar. The relative span gradually increases when D_{v}0.5 increases. Through D_{v}0.5 in Figure 4b and the relative span in Figure 6b, when Y = 0.1, Y = 0.2, Y = 0.3, and Y = 0.4 m, with an increasing distance in the X direction, D_{v}0.5 varies greatly from outside the edge of the spray field to the edge of the spray field and into the spray field, resulting in the relative span not changing positively with the change in D_{v}0.5. However, under relatively stable conditions inside the spray field, the relative span still satisfies the above law. At distances of X = 0.4 m, X = 0.6 m, X = 0.8 m, and X = 1.2 m, due to the hollow effect of the close-range conical spray field, the range of the droplet size near the edge of the spray field gradually increases. The relative span gradually increases in the Y direction. The relative span outside the edge of the spray field continues to increase, but D_{v}0.5 decreases. The main reason is that the air at the edge of the spray field is unstable, so the fluctuation range of the measured droplet size is large, resulting in a large relative span of the actual measurement. With an increasing X value, the relative span increases because the hollow effect of the cone spray gradually decreases. Different from the variation trend of the relative span at distances of X = 0.4 m, X = 0.6 m, X = 0.8 m, and X = 1.2 m, the relative span first increases and then decreases with an increasing Y-value when X = 1.8 m and X = 2.4 m. The main reason for this result is that as the X value increases, the Y-value from the centreline of the nozzle is at the edge of the spray field, and the large droplets are less affected by the air field. When it has not yet reached X = 1.8 m, it falls below the measurement point, resulting in a decrease in the relative span.At different pressure conditions, the relative span at X = 1.8 m does not change significantly at each measurement position, and the size fluctuates by approximately 1.2. Hewitt [32] proposed some reasonable suggestions on how to reduce the relative span of the droplet spectrum. For example, using a rotating disk and studying the shear viscosity of the liquid can change the relative span of the droplet. At the centreline of the nozzle, Y = 0 m, the relative span gradually increases with an increasing X distance. The main reason for this result is that as X increases, the hollow effect gradually decreases, the larger droplet size gradually falls to the measurement point, and the droplet size range increases. Through the study of Maciel et al. [39], it is found that the relative span decreases with the increase in air speed, and a small relative span can better show a narrow droplet spectrum. In the future, the optimal effective particle size range can be determined by studying the variation of spatial droplet size and relative span under different air speed conditions and combining it with the needs of pest control. - 3.
- Through the analysis of the multiple linear regression equation, it can be seen that when the pressure is 1 MPa, with the distance from the nozzle orifice being farther, the droplet velocity value decreases with the Y-axis, and its change rate is also smaller. The main reason for this result is that the X value is small. The cross-section of the spray field is small. The droplet velocity at the centre position is high and varies greatly at each measurement point position. The droplet velocity at the edge of the spray field decreases more obviously. When X = 1.8 m and X = 2.4 m, the droplet velocity fluctuates less at each measurement point. The droplet velocity increases first and then decreases from the centre of the spray field to the edge, which is inconsistent with the gradual decrease in the droplet velocity from the centre to the edge studied by Li et al. [24]. The main reason is that in the actual spraying process, the axial flow fan will produce a certain amount of air direction offset after a certain distance from the outlet of the fan, which leads to the maximum air speed position not being on the centreline of the nozzle X = 1.8 m and X = 1.2 m. The change in the droplet velocity at the positions of Y = 0.2 m, Y = 0.3 m, and Y = 0.4 m from the centreline of the nozzle first increases and then decreases with an increasing X value. The main reason for this result is that when the X value is small, the three measurement points are at the edge of the air field and the velocity is small. As the X value increases, the air field section gradually increases, approaching the centre of the air field. The droplet velocity gradually increases. When the X value continues to increase, the droplet velocity gradually decreases due to the influence of air resistance.Under different pressure conditions, the droplet velocity does not change significantly at each measurement position under the condition of an external air field. The variation trend of the droplet velocity is similar to the droplet velocity at the X = 1.8 m transverse position and Y = 0 m longitudinal position at a pressure of 1 MPa.

## 5. Conclusions

- 1.
- At the position of X = 1.8 m, D
_{v}0.5 at different pressure conditions is in the range of 120$~$150 μm, which is within the range of the best droplet size of 30$~$150 μm for the control of crop leaf reptile larvae and plant diseases. The significance analysis of multiple linear regression showed that the longitudinal distance, transverse distance, and spray pressure had significant effects on droplet size. The multiple linear regression model of the volume median diameter was established. The determination coefficient R^{2}of the model fitting degree is 0.7769. - 2.
- The significance analysis of multiple linear regression shows that the spatial position has a significant effect on the relative span. When the spray pressure P and the lateral distance Y interact with each other, the relative span has a significant effect. The multiple linear regression model of the relative span was established. The model fitting degree determination coefficient R
^{2}is 0.9409, and the fitting degree is high. According to the analysis of the experimental results, as the distance from the nozzle orifice increases, the hollow effect of the spray field gradually decreases, resulting in a gradual increase in the relative span. For different types of pest control requirements, it is necessary to more accurately control the droplet size and study how to reduce the relative span at a long distance from the nozzle orifice. - 3.
- The significance analysis of multiple linear regression shows that the longitudinal distance X, the transverse distance Y, and the spray pressure have a significant effect on the droplet velocity. The multiple linear regression model of the droplet velocity was established. The model fitting coefficient R
^{2}is 0.8779. To determine the spraying effect at each position, the droplet deposition effect under the same conditions can be carried out in the orchard. The optimal speed of droplets can be determined by measuring the deposition characteristics and the control effect of pests and diseases. According to the multiple linear regression equation of speed, the reference is provided for the subsequent adjustment of fan speed to improve the droplet speed. - 4.
- The phenomenon of droplet evaporation will exist in the process of movement, and the evaporation rate is affected by the physical properties of the liquid, the initial droplet size, and the ambient temperature, humidity, air speed, and other conditions during spray release. In the future, the evaporation law of droplets will be studied for different agents under different vapour pressure deficits and air speed conditions. Considering various experimental factors, the atomization characteristics of droplets will be explored, the variation law of droplet characteristics at different positions in space will be analysed, and a mathematical relationship model will be established to provide a theoretical basis for reducing droplet drift and evaporation.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Data Availability Statement

## Conflicts of Interest

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**Figure 1.**Variable-rate spraying control system composition. 1. anemometer, 2. fan, 3. three-phase asynchronous motor, 4. frequency converter, 5. notebook computer, 6. C37 controller, 7. solenoid valve, 8. nozzle, 9. flow sensor, 10. pressure sensor, 11. pressure-regulating valve, 12. plunger pump and 13. water tank.

**Figure 2.**Experimental platform of the droplet size measuring instrument: 1. variable-rate spraying control system test bench, 2. droplet particle size measurement area, 3. droplet particle size measuring instrument, 4. lifting platform, 5. position calibration plate, and 6. grid line.

**Figure 4.**Change in D

_{v}0.5 at a pressure of 1 MPa. (

**a**) D

_{v}0.5 change in the transverse direction; (

**b**) D

_{v}0.5 change in the longitudinal direction.

**Figure 5.**Change in D

_{v}0.5 at different pressures: (

**a**) X = 1.8 m transverse D

_{v}0.5 change; (

**b**) Y = 0 m longitudinal droplet D

_{v}0.5 change.

**Figure 6.**Change in the relative span at a pressure of 1 MPa. (

**a**) Relative span change in the transverse direction; (

**b**) relative span change in the longitudinal direction.

**Figure 7.**Change in the relative span at different pressures. (

**a**) X = 1.8 m transverse relative span change; (

**b**) Y = 0 m longitudinal relative span change.

**Figure 8.**Change in droplet velocity at a pressure of 1 MPa. (

**a**) Droplet velocity change in the transverse direction; (

**b**) droplet velocity change in the longitudinal direction.

**Figure 9.**Change in the droplet velocity at different pressures. (

**a**) X = 1.8 m transverse droplet velocity change; (

**b**) Y = 0 m longitudinal droplet velocity change.

Subsystem | Category | Model | Main Parameters | Company |
---|---|---|---|---|

Air speed control module | Frequency converter | 2.2G1-220 V | Power supply: single-phase power | Xuzhou Xinshengda |

supply of AC 220 V~240 V; | Automation Equipment | |||

Power: 2.2 kW; Current: 9.5 A. | Co., Ltd., Xuzhou, China | |||

Three-phase asynchronous motor | YE3- 100L1-4 | Power: 2.2 kW; Current: 5.05 A; | Taizhou Pusi | |

Power supply: AC 220 V; | Electromechanical | |||

Rated speed: 24 rad/s. | Co., Ltd., Taizhou, China | |||

Fan | AY-S-500 | Maximum speed: 24 rad/s; | Tianjin Chengen Technology Co., Ltd., Tianjin, China | |

Air volume: 10,000 m^{3}/h; | ||||

Full pressure: 200 Pa. | ||||

Anemometer | 8455- CR1000X | Measuring range: 0.127~50.8 m/s; | Beijing Bolun Jingwei | |

Accuracy: ±2% of the reading value; | Technology Development | |||

Input voltage: DC 11 V~30 V. | Co., Ltd., Beijing, China | |||

Host computer | Notebook computer | HP DESKTOP- B0FOTJI | Input voltage: AC 100 V~240 V; | China Hewlett-Packard Co., Ltd., Beijing, China |

Current: 1.6 A. | ||||

Spray pressure control module | Frequency converter | 2.2G1-220 V | Power supply: single-phase power supply of AC 220 V~240 V; Power: 2.2 kW; Current: 9.5 A. | Xuzhou Xinshengda Automation Equipment Co., Ltd., Xuzhou, China |

Three-phase asynchronous motor | YE3-100L1-4 | Power: 2.2 kW; Current: 5.05 A; Power supply: AC 220 V. | Taizhou Pusi Electromechanical Co., Ltd., Taizhou, China | |

Plunger pump | 3WZB-80 | Working pressure: 1~3.5 MPa; Theoretical flow: 46~60 L/min. | Taizhou Huali Machinery Co., Ltd., Taizhou, China | |

Water tank | 300 | Capacity: 200 L. | Yutian Cangsheng Plastic Products Co., Ltd., Tangshan, China | |

Pressure sensor | AS-131 | Pressure range: 0~2.5 MPa; Output voltage: DC 0~5 V; Full-scale accuracy level: 1%. | Beijing Aosheng Automation Technology Co., Ltd., Beijing, China | |

Pressure regulating valve | FT100 | Input voltage: DC ± 12 V voltage to adjust the valve opening direction. | Ningbo Licheng Agricultural Spray Technology Co., Ltd., Ningbo, China | |

Controller | HSC37 | 12 PWM outputs; 4 pulse inputs; 6 analogue inputs; The field-programmable controller is developed based on the CoDeSys V2.3 software platform. | Suzhou Hesheng Microelectronics Tech_x0002_nology Co., Ltd., Suzhou, China | |

Spray module | Flow sensor | SK-4040- HZ60 | Flow range: 1~30 L/min; 1 L flow corresponds to 596 pulses. | Zhongshan Qingong Sensor Co., Ltd., Zhongshan, China |

Solenoid valve | ZG1000 | Input voltage: DC 12 V; Pressure range: 0.03~1.6 MPa. | Dongguan City Zhonggu Fluid Technology Co., Ltd., Dongguan, China | |

Nozzle | QY82.317.22 | 360° rotatable adjustive hollow cone nozzle. | Zhejiang Qiangyu Machinery Co., Ltd., Zhuji, China |

**Table 2.**A significance test of the influence of each factor and the whole model on the volume median diameter was carried out.

Source of Variance | SS | df | MS | F | p | Significance |
---|---|---|---|---|---|---|

X^{2} | 517.0747 | 1 | 517.0747 | 4.3431 | 0.0391 | * |

Y^{2} | 6.97 × 10^{3} | 1 | 6.97 × 10^{3} | 58.5544 | p < 0.001 | ** |

X | 2.38 × 10^{3} | 1 | 2.38 × 10^{3} | 19.9664 | p < 0.001 | ** |

Y | 1.07 × 10^{3} | 1 | 1.07 × 10^{4} | 89.9598 | p < 0.001 | ** |

P | 2.31 × 10^{3} | 1 | 2.31 × 10^{3} | 19.3916 | p < 0.001 | ** |

XY | 717.205 | 1 | 717.205 | 6.0241 | 0.0155 | * |

Model | 2.32 × 10^{4} | 6 | 3.87 × 10^{3} | 32.4884 | p < 0.001 | ** |

Residual | 1.52 × 10^{4} | 128 | 119.0554 | 2.946 | ||

Total | 3.84 × 10^{4} | 134 | R^{2} = 0.7769 |

**Table 3.**A significance test of the influence of various factors and the whole model on the relative span was carried out.

Source of Variance | SS | df | MS | F | p | Significance |
---|---|---|---|---|---|---|

X^{2} | 0.0768 | 1 | 0.0768 | 11.1868 | 0.0011 | ** |

Y^{2} | 0.1304 | 1 | 0.1304 | 18.9942 | p < 0.001 | ** |

X | 0.4388 | 1 | 0.4388 | 63.9266 | p < 0.001 | ** |

Y | 0.3148 | 1 | 0.3148 | 45.8542 | p < 0.001 | ** |

YP | 0.0391 | 1 | 0.0391 | 5.6995 | 0.0184 | * |

Model | 6.8324 | 6 | 1.3665 | 199.0739 | p < 0.001 | ** |

Residual | 0.8855 | 128 | 0.0069 | 3.1624 | ||

Total | 7.7179 | 134 | R^{2} = 0.9409 |

**Table 4.**A significance test of the influence of various factors and the whole model on droplet velocity was carried out.

Source of Variance | SS | df | MS | F | p | Significance |
---|---|---|---|---|---|---|

X^{2} | 1.9968 | 1 | 1.9968 | 5.2371 | 0.0237 | * |

X | 14.6971 | 1 | 14.6971 | 38.547 | p < 0.001 | ** |

Y | 58.2808 | 1 | 58.2808 | 152.8568 | p < 0.001 | ** |

P | 1.5562 | 1 | 1.5562 | 4.0816 | 0.0454 | * |

XY | 41.515 | 1 | 41.515 | 108.884 | p < 0.001 | ** |

XP | 1.5155 | 1 | 1.5155 | 3.9748 | 0.0483 | * |

Model | 164.0794 | 6 | 27.3466 | 71.7236 | p < 0.001 | ** |

Residual | 48.8035 | 128 | 0.3813 | 2.946 | ||

Total | 212.8829 | 134 | R^{2} = 0.8779 |

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## Share and Cite

**MDPI and ACS Style**

Yuan, F.; Gu, C.; Yi, K.; Dou, H.; Li, S.; Yang, S.; Zou, W.; Zhai, C.
Atomization Characteristics of a Hollow Cone Nozzle for Air-Assisted Variable-Rate Spraying. *Agriculture* **2023**, *13*, 1992.
https://doi.org/10.3390/agriculture13101992

**AMA Style**

Yuan F, Gu C, Yi K, Dou H, Li S, Yang S, Zou W, Zhai C.
Atomization Characteristics of a Hollow Cone Nozzle for Air-Assisted Variable-Rate Spraying. *Agriculture*. 2023; 13(10):1992.
https://doi.org/10.3390/agriculture13101992

**Chicago/Turabian Style**

Yuan, Feixiang, Chenchen Gu, Kechuan Yi, Hanjie Dou, Si Li, Shuo Yang, Wei Zou, and Changyuan Zhai.
2023. "Atomization Characteristics of a Hollow Cone Nozzle for Air-Assisted Variable-Rate Spraying" *Agriculture* 13, no. 10: 1992.
https://doi.org/10.3390/agriculture13101992