# Effects of Flow Path Geometrical Parameters on the Hydraulic Performance of Variable Flow Emitters at the Conventional Water Supply Stage

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## Abstract

**:**

_{I}) of 1–2 L/h for crop irrigation. At working stage II (H > 0.1 MPa; exceeding the design pressure), VFE delivered a larger flow rate (q

_{II}). The larger q

_{II}facilitated water movement upward from the underground to the surface seedbed during the crop planting, thus ameliorating crop germination issues under SDI. We focused on the impacts of four structural parameters of the flow channel: tooth height (E), tooth spacing (B), tooth angle (A), and flow channel depth (D) on the q

_{I}and VFE-flow index (x) at working stage I. Computational fluid dynamic (CFD) simulations were conducted along with a physical laboratory test to develop VFE using computerized numerical control (CNC) technology (accuracy = 0.05 mm). Nine VFEs were designed using an L9(3

^{4}) orthogonal test. The combination of tetrahedral meshing with a six-layer boundary layer and the realizable k–ε turbulence model was found suitable for CFD simulations. The standard root-mean-square error (nRMSE) of the measured and simulated q

_{Is}was a minimum of 7.4%. The four parameters influenced q

_{Is}as D > B > E > A, and the four factors influenced the x

_{s}as B > E > D > A. Based on the numerical simulation data, multiple linear regression models were constructed for the q

_{Is}and x

_{s}with four parameters when H = 0.1 MPa. Aiming for the minimum x, the optimal combination of the flow channel structural parameters corresponding to different q

_{Is}was determined by the ergodic optimization algorithm. When q

_{I}was 1.5 L/h, the optimal structural combinations were E = 1.2 mm, B = 1.8 mm, A = 42°, and D = 1 mm. The VFE with a q

_{I}of 1.5 L/h was created by CNC technology. The relative errors of the measured and predicted q

_{Is}using the regression model were −0.19–6.31%, and their nRMSE was 6.76%. Thus, optimizing the flow channel structural parameters based on a multiple linear regression model and the ergodic optimization algorithm is a highly precise theoretical base for VFE development.

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Structural Design and Working Principles of Variable Flow Emitters

_{I}) of VFE was 1–2 L/h, which was typical for SDI. When H was greater than the design working pressure, the pressure in the flow channel could cause the cylindrical elastomer to expand and deform in the cavity body. The cylindrical elastomer would exit the groove, and the increase in the section of the flow channel would result in a higher flow rate (q

_{II}), which realized a step change in the flow rate of the VFE. At this instance, the VFE shifted to working stage II. At this time, the self-cleaning function of VFE was also started, and the sediment that accumulated in the flow channel could be flushed out due to the expansion of the flow section so as to improve the anti-clogging performance of the emitter.

_{I}and the flow index (x) in working stage I with the structural parameters of the flow channel and elucidating the appropriate combination of structural parameters corresponding to different q

_{I}was an important prerequisite for the development of VFE. Consequently, this study focused solely on working stage I.

#### 2.2. Analysis of Flow Channel Structural Parameter Affecting Hydraulic Performance of VFE in the Working Stage I

_{I}and x to H for VFE in the working stage I (Figure 4).

#### 2.2.1. Experiment Design

^{4}), was used for the experimental design. The flow channel structural parameters of nine VFEs designed by orthogonal experiment are shown in Table 1, No. 1–9. The VFE of serial number 10 is used to adjust the parameters of the Fluent model for the simulation of the flow of VFE under different H.

#### 2.2.2. Hydraulic Performance Test Method and Test Index

_{I}(L/h) values corresponding to different H (MPa) values, Equation (1) can be used to determine the flow coefficient (k) and x of the VFE in working stage I.

_{I}= k × H

^{x}

#### 2.3. The Numerical Simulation

#### 2.3.1. Determination of the Meshing and Turbulence Model Using Fluent Software

_{i}and E

_{i}represented the measured and simulated values, respectively; n was the number of measured data; and E

_{ave}, the mean of the measured data. The model evaluation criteria were as follows: nRMSE ≤ 10%, excellent agreement between the simulated and measured rates; 10% < nRMSE < 20%, good; 20% ≤ nRMSE ≤ 30%, fair; and nRMSE > 30%, poor.

#### 2.3.2. Influence of the Flow Channel Structural Parameters on the Hydraulic Performance of VFE

## 3. Results

#### 3.1. Establishment of the Meshing and Turbulence Model

_{Im}) and simulated flow rate (q

_{Is}) of the variable flow emitter (VFE)in working stage I for different meshing and turbulence models when H was 0.05–0.15 MPa. When the turbulence model was standard k-ε, the difference between q

_{Im}and q

_{Is}using tetrahedral meshing with a six-layer boundary layer (TBL) was the smallest, with an nRMSE = 8.4%, indicating that the simulation result is in excellent agreement. When the meshing model was TBL, the nRMSE corresponding to the other four turbulence models was less than 10%, except for the kω turbulence model, and the simulated value using the realizable k–ε turbulence model came the closest to the measured value (nRMSE = 7.4%). Therefore, a combination of the TBL meshing model and realizable k–ε turbulence model should be adopted in the simulation of q

_{Is}of VFE using the Fluent software.

#### 3.2. Simulation Results of the Emitter Flow Rate and Flow Index of Variable Flow Emitters

_{Is}with respect to H following the numerical simulation of the nine VFEs in Table 1 using the TBL meshing model and the realizable k–ε turbulence model. When H = 0.1 MPa, the simulated flow rate (q

_{Is0.1}) of VFE was 1.05–2.21 L/h, which was close to the desired range of 1–2 L/h. After fitting q

_{Is}and H to the power function, the simulated flow indexes (x

_{s}) of these nine VFEs were between 0.4870 and 0.5148, all of which were within the range of the flow index of the most widely used non-pressure compensated emitters currently on the market [52,62] (Table 3).

#### 3.3. Range Analysis of Hydraulic Performance of Variable Flow Emitter

_{1}, q

_{2}, q

_{3}, and x

_{1}, x

_{2}, and x

_{3}are the respective mean values of q

_{Is0.1}and x

_{s}corresponding to levels 1, 2, and 3 (which can be calculated from Table 3), and R is the range of corresponding factors. The higher the value of R, the greater the influence of that factor on the test index. Within the level range of this experimental factor study, the order of the influence of each experimental factor on q

_{Is0.1}was D > B > E > A, whereas the order of the influence of each experimental factor on x

_{s}was B > E > D > A.

_{Is0.1}was negatively correlated with E, positively correlated with B and D, and had a modest variation with A. x

_{s}was positively correlated with B, negatively correlated with E and A, and variable (an initial increased and subsequent decreased) correlation with D (Figure 9). Within the flow rate range of 1–2 L/h, the optimal combination of the flow channel structural parameters was E

_{3}B

_{1}A

_{3}D

_{3}with E = 1.2 mm, B = 1.8 mm, A = 42°, and D = 1 mm, using the minimum value of x

_{s}as the preference principle [64,65,66].

#### 3.4. Linear Regression Model for Hydraulic Performance of the Variable Flow Emitter

_{Is}0.1) and flow index (x

_{s}) with E, B, A, and D were developed based on simulation data. The constant term and regression coefficients of E, B, and D had a significant effect on the multi-linear regression equation of q

_{Is}0.1 (p < 0.05); however, A did not have a significant effect on the linear regression equation of q

_{Is}0.1 (p > 0.1). The constant terms E and B had a significant influence on the linear regression equation of x

_{s}at p < 0.1 and p < 0.05, respectively. However, the influence of A and D on the linear regression equation of x

_{s}did not reach the significance level (p > 0.1) (Table 5). To simplify the regression model, factor A was removed from the q

_{Is}0.1 regression model. In order to determine A in the optimal flow channel structure, only factor D was removed from the regression model of x

_{s}. After optimization, the coefficient of determination (R

^{2}) of the multiple linear regression equation for q

_{Is}0.1 and x

_{s}were 0.99 and 0.80, respectively (Table 6). Both coefficients reached significance (p < 0.05) (Table 7), which indicated a strong match.

#### 3.5. Optimization and Verification of the Flow Channel Structural Parameters Using the Ergodic Optimization Algorithm

_{I0.1}values of 1.03, 1.5, and 2.0 L/h to meet the minimum x aim (Table 8). The relative errors between x using the multiple linear regression model and x

_{s}using the Fluent model were −0.7–0.3% for the three VFEs.

_{I0.1}of 1.5 L/h (VFE-1.5) were measured with a 2.5-dimension image size measuring instrument (Table 9). After three measurements, it was found that the difference between the design size and the actual size was modest, and the relative error was 0.24–6.33%, indicating that CNC processing accuracy was high.

_{Im}) of VFE-1.5 was measured at H = 0.02–0.16 MPa, and compared with the q

_{I}predicted by the q

_{I}-H formula in Table 8 revealed that when H < 0.06 MPa, q

_{Im}was slightly smaller than q

_{I}, with a relative error of -6.31%–0.19%. When H ≥ 0.06 MPa, q

_{Im}was slightly larger than q

_{I}, and the relative error was 1.13%–4.40% (Table 10). For H = 0.02–0.16 Mpa, the nRMSE of q

_{Im}and q

_{I}was 6.76%, showing excellent agreement between them.

## 4. Discussion

#### 4.1. Influence of Meshing and Turbulence Model on the Accuracy of Fluent Simulation on Flow Rate

#### 4.2. Analysis of the Influence of Flow Channel Structural Parameters on the Hydraulic Performance of Variable Flow Emitters

#### 4.3. Construction of Regression Model for the Hydraulic Performance of a Variable Flow Emitter and Flow Channel Structure Optimization

_{I0.1}), x, and flow channel structural parameters using the Fluent simulation results. To simplify the model, it was necessary to exclude factors that have an insignificant influence. Specifically, A (p = 0.76595) in the q

_{I0.1}regression model and D (p = 0.96564) and A (p = 0.24303) in the x regression model. However, considering that A is one of the four structural parameters of the flow channel and that factor p = 0.32 was retained in the regression model in the work by Yang et al. [47], factor A was retained in the x regression model in the current study.

_{I0.1}. For the VFE with q

_{I0.1}= 1.5 L/h, the measured flow rate (q

_{Im}) in working stage I was initially slightly lower than the formula-based calculated flow rate (q

_{I}) and subsequently raised to a value slightly higher than q

_{I}with an increase in H. In order to ensure the tightness of the flow channel of the VFE in working stage I, the inner diameter of the cylindrical elastomer with small elasticity was kept slightly smaller than the outer diameter of the core body, and the elastomer would embed a small part of the flow channel, resulting in the actual size of the flow channel depth (D

_{a}) being less than that of design value (D), giving rise to the actual water flow channel section less than the designed section. q

_{I}was calculated using the Fluent simulation based on D, while q

_{Im}was obtained using the test based on D

_{a}causing q

_{Im}< q

_{I}when H < 0.6 MPa. When H ≥ 0.6 MPa, the D

_{a}would be larger than D owing to the small elasticity of the cylindrical elastomer; therefore, q

_{Im}> q

_{I}. When H was 0.02–0.16 MPa, the nRMSE of q

_{Im}and q

_{I}was less than 10%, indicating excellent agreement between them. Therefore, the accuracy of the method based on the regression model and EOA to determine the optimal combination of flow channel structural parameters with the minimum flow index was greater. This method can shorten the development time of new emitters.

## 5. Conclusions

- The combination of tetrahedral meshing with six-layer boundary layer TBL and the realizable k-ε turbulence model was suitable for the flow rate simulation of VFE using Fluent software.
- The results of the range analysis show that the order of influence of the flow channel structure factors on the flow rate was D > B > E > A, while the primary order of influence of the flow index was B > E > D > A.
- With the aim of minimizing the flow index, the optimal combination of the structural parameters of the flow channel corresponding to different flow rates was obtained on the basis of multiple linear regression modeling of the flow rate, flow index, and flow channel structural parameters, in conjunction with the EOA.
- A VFE with a flow rate of 1.5 L/h at H = 0.1 MPa was developed using CNC processing technology, and its hydraulic performance was tested. The nRMSE value of the measured flow rate and calculated flow rate using the formula was 6.76%, and the prediction accuracy of the model was high.

## 6. Patents

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Nomenclature

SDI | Subsurface drip irrigation |

VFE | Variable flow emitter |

EOA | Ergodic optimization algorithm |

x | Flow index |

q_{I} | Flow rate at working stage I, (L·h^{−1}) |

q_{II} | Flow rate at working stage II, (L·h^{−1}) |

k | Flow coefficient |

H | Water pressure, (MPa) |

H_{I} | Water pressure at working stage I, (MPa) |

H_{II} | Water pressure at working stage II, (MPa) |

P_{I} | The pressure in the flow channel at working stage I |

P_{II} | The pressure in the flow channel at working stage II |

E | Tooth height |

B | Tooth spacing |

A | Tooth Angle |

D | Flow channel depth |

D_{a} | The actual size of the flow channel depth |

TWBL | Tetrahedros meshing without boundary layer |

TBL | Tetrahedros meshing with six-layer boundary layer |

HEX | Hexahedral meshing |

nRSME | Normalized root-mean-square error |

S_{i} | Observation value |

E_{i} | Estimation value |

n | The number of observed data |

E_{ave} | Average of the observed data |

R^{2} | Coefficient of determination |

q_{Im} | Measured value of emitter flow rate |

q_{Is} | Simulation value of emitter flow rate based on ergodic optimization algorithm, (L·h^{−1}) |

q_{Is0.1} | Simulation value of emitter flow rate based on ergodic optimization algorithm under the pressure of 0.1MPa, (L·h^{−1}) |

x_{s} | Simulation value of emitter flow index based on ergodic optimization algorithm |

q_{I0.1} | Flow rate at working stage I when the flow index is minimum under the pressure of 0.1MPa, (L·h^{−1}) |

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**Figure 1.**Schematic illustration of variable flow emitter structure. Note: 1. Shell body; 2. Cylindrical elastomer; 3. Core body; 4. Base part; 5. Flow channel; 6. Cavity body.

**Figure 2.**Axonometric diagram of the movement route of the water in the flow channel (the red arrow).

**Figure 3.**A sectional view of the variable flow emitter in the working stage I (

**a**) and stage II (

**b**). Note: P

_{I}and q

_{I}are the pressure of the internal flow of the flow channel on the elastomer and the outflow flow rate in the conventional flow supply stage I, respectively. P

_{II}and q

_{II}are the pressure of the internal water flow of the flow channel on the elastomer and the outflow flow rate in the larger flow supply stage II, respectively.

**Figure 5.**The flow channel on the core body of a variable flow emitter is carved using computerized numerical control technology.

**Figure 6.**Schematic diagram of the variable flow emitter and testing device made by the computerized numerical control technology. Note: 1. Teflon elastomer; 2. Core body; 3. Special test equipment; 4. Screw; 5. Nut.

**Figure 7.**Hydraulic performance test platform for variable flow emitter. Note: 1. Water storage tank; 2. Centrifugal pump; 3. Filter; 4. Ball valve; 5. Pressure gauge; 6. Valve; 7. Special testing device; and 8. Bucket.

**Figure 8.**Simulated flow rates (q

_{Is}) of the nine variable flow emitters in working stage I and the working pressure (H).

**Figure 9.**Effect of flow channel structural parameters on (

**a**) the simulated flow rate (q

_{Is0.1}) and (

**b**) flow index (x

_{s}) of the variable flow emitter in working stage I.

Serial Number | Experimental Treatment | Tooth Height (E)/mm | Tooth Spacing (B)/mm | Tooth Angle (A)/° | Flow Channel Depth (D)/mm |
---|---|---|---|---|---|

1 | E_{1}B_{1}A_{1}D_{1} | 0.8 | 1.8 | 34 | 0.6 |

2 | E_{1}B_{2}A_{3}D_{2} | 0.8 | 2.0 | 42 | 0.8 |

3 | E_{1}B_{3}A_{2}D_{3} | 0.8 | 2.2 | 38 | 1.0 |

4 | E_{2}B_{1}A_{3}D_{3} | 1.0 | 1.8 | 42 | 1.0 |

5 | E_{2}B_{2}A_{2}D_{1} | 1.0 | 2.0 | 38 | 0.6 |

6 | E_{2}B_{3}A_{1}D_{2} | 1.0 | 2.2 | 34 | 0.8 |

7 | E_{3}B_{1}A_{2}D_{2} | 1.2 | 1.8 | 38 | 0.8 |

8 | E_{3}B_{2}A_{1}D_{3} | 1.2 | 2.0 | 34 | 1.0 |

9 | E_{3}B_{3}A_{3}D_{1} | 1.2 | 2.2 | 42 | 0.6 |

10 | CK | 1.0 | 2.2 | 42 | 0.8 |

The Inlet Pressure of VFE (H)/MPa | The Measured Flow Rate (q _{Im})/L·h^{−1} | The Simulated Flow Rate (q_{I}_{s})/(L·h^{−1}) | |||||||
---|---|---|---|---|---|---|---|---|---|

Meshing Model (The Turbulence Model is Standard k-ε) | Turbulence Model (The Meshing Model is TBL) | ||||||||

TWBL | TBL | HEX | Standard k-ε | RNG k-ε | Realizable k-ε | kω | RSM | ||

0.05 | 1.38 | 1.65 | 1.48 | 1.56 | 1.48 | 1.50 | 1.47 | 1.52 | 1.45 |

0.06 | 1.52 | 1.82 | 1.64 | 1.71 | 1.64 | 1.66 | 1.62 | 1.66 | 1.61 |

0.07 | 1.64 | 1.97 | 1.78 | 1.85 | 1.78 | 1.79 | 1.76 | 1.82 | 1.76 |

0.08 | 1.76 | 2.12 | 1.91 | 1.98 | 1.91 | 1.92 | 1.89 | 1.98 | 1.89 |

0.09 | 1.87 | 2.26 | 2.03 | 2.11 | 2.03 | 2.04 | 2.01 | 2.08 | 2.02 |

0.10 | 1.97 | 2.39 | 2.14 | 2.22 | 2.14 | 2.15 | 2.13 | 2.18 | 2.15 |

0.11 | 2.06 | 2.52 | 2.26 | 2.33 | 2.26 | 2.26 | 2.23 | 2.30 | 2.24 |

0.12 | 2.16 | 2.64 | 2.36 | 2.44 | 2.36 | 2.36 | 2.34 | 2.41 | 2.37 |

0.15 | 2.42 | 2.97 | 2.66 | 2.72 | 2.66 | 2.65 | 2.62 | 2.76 | 2.68 |

nRMSE (%) | 17.9 | 8.4 | 11.5 | 8.4 | 8.8 | 7.4 | 10.6 | 8.3 |

**Table 3.**The simulated flow rates at H = 0.1 MPa (q

_{Is0.1}) and the simulated flow indexes (x

_{s}) of the variable flow emitter in working stage I.

Experimental Treatment | q_{I}_{s0.1}/(L·h^{−1}) | x_{s} |
---|---|---|

E_{1}B_{1}A_{1}D_{1} | 1.05 | 0.4980 |

E_{1}B_{2}A_{3}D_{2} | 1.63 | 0.5001 |

E_{1}B_{3}A_{2}D_{3} | 2.21 | 0.5084 |

E_{2}B_{1}A_{3}D_{3} | 1.81 | 0.4869 |

E_{2}B_{2}A_{2}D_{1} | 1.11 | 0.4931 |

E_{2}B_{3}A_{1}D_{2} | 1.69 | 0.5148 |

E_{3}B_{1}A_{2}D_{2} | 1.39 | 0.4887 |

E_{3}B_{2}A_{1}D_{3} | 1.86 | 0.4870 |

E_{3}B_{3}A_{3}D_{1} | 1.18 | 0.4919 |

Experimental Factor | Tooth Height (E)/mm | Tooth Spacing (B)/mm | Tooth Angle (A)/° | Flow Channel Depth (D)/mm | |
---|---|---|---|---|---|

q_{I}_{s0.1} | q_{1} | 1.63 | 1.42 | 1.53 | 1.12 |

q_{2} | 1.54 | 1.54 | 1.57 | 1.57 | |

q_{3} | 1.48 | 1.70 | 1.54 | 1.96 | |

R | 0.16 | 0.28 | 0.04 | 0.85 | |

x_{s} | x_{1} | 0.5022 | 0.4912 | 0.4999 | 0.4943 |

x_{2} | 0.4983 | 0.4934 | 0.4967 | 0.5012 | |

x_{3} | 0.4892 | 0.5050 | 0.4930 | 0.4941 | |

R | 0.0130 | 0.0138 | 0.0070 | 0.0071 |

**Table 5.**Significance analysis of multiple linear regression coefficients for the hydraulic performance of flow rate at H = 0.1 MPa (q

_{Is0.1}) and flow index (x

_{s}) with structural parameters.

Hydraulic Pe | Regression Coefficient | Unstandardized Coefficient | Standardized Coefficient | t-Value | p-Value | Significance | |
---|---|---|---|---|---|---|---|

B | Standard Error | Beta | |||||

q_{Is0.1} | Constant term | −1.17828 | 0.23150 | −5.08973 | 0.00703 | ** | |

Tooth height (E)/mm | −0.39174 | 0.07601 | −0.17297 | −5.15403 | 0.00673 | ** | |

Tooth spacing (B)/mm | 0.69102 | 0.07601 | 0.30511 | 9.09146 | 0.00081 | ** | |

Tooth angle (A)/° | 0.00121 | 0.00380 | 0.01069 | 0.31863 | 0.76595 | NS | |

Flow channel depth (D)/mm | 2.11538 | 0.07601 | 0.93401 | 27.83128 | 0.00001 | ** | |

x_{s} | Constant term | 0.49335 | 0.03877 | 12.72572 | 0.00022 | ** | |

Tooth height (E)/mm | −0.03242 | 0.01273 | −0.57318 | −2.54677 | 0.06352 | * | |

Tooth spacing (B)/mm | 0.03458 | 0.01273 | 0.61149 | 2.71699 | 0.05315 | * | |

Tooth angle (A)/° | −0.00087 | 0.00064 | −0.30795 | −1.36831 | 0.24303 | NS | |

Flow channel depth (D)/mm | −0.00058 | 0.01273 | −0.01031 | −0.04583 | 0.96564 | NS |

**Table 6.**Multiple linear regression model for the hydraulic performance of flow rate at H = 0.1 MPa (q

_{Is0.1}) and flow index (x

_{s}) with structural parameters.

The Regression Model | Coefficient of Determination (R^{2}) |
---|---|

q_{Is0.1}= 1.132 − 0.392E + 0.691B + 2.115D | 0.99 |

x_{s}= 0.493 − 0.032E + 0.035B − 0.00087A | 0.80 |

Hydraulic Performance | Quadratic Sum | Degree of Freedom | Mean Square | F Value | p-Value | Significance |
---|---|---|---|---|---|---|

q_{Is0.1} | 1.225 | 3 | 0.408 | 359.134 | 0.000003 | ** |

x_{s} | 0.001 | 2 | 0.00027 | 6.555 | 0.026 | ** |

**Table 8.**Optimal combination of flow channel structural parameters for different flow rates at H = 0.1 MPa (q

_{I0.1}).

q_{I0.1}/(L·h^{−1}) | Tooth Height (E)/mm | Tooth Spacing (B)/mm | Tooth Angle (A)/° | Flow Channel Depth (D)/mm | The Formula of q_{I} with H | The Flow Index (x) | The Simulated Flow Index (x _{s}) | Relative Error of x and x _{s}/% |
---|---|---|---|---|---|---|---|---|

1.03 | 0.9 | 1.8 | 42 | 0.6 | q_{I} = 3.18 × H^{0.4895} | 0.4895 | 0.4930 | −0.7 |

1.5 | 0.8 | 1.8 | 42 | 0.8 | q_{I} = 4.67 × H^{0.4927} | 0.4927 | 0.4910 | 0.3 |

2.0 | 0.6 | 2.1 | 42 | 0.9 | q_{I} = 6.46 × H^{0.5095} | 0.5095 | 0.5126 | −0.6 |

**Table 9.**Comparison of the actual and design size of the flow channel structure of the processed variable flow emitter when the flow rate (q

_{I0.1}) was 1.5 L/h.

Flow Channel Structural Parameters | Design Size | Actual Size | Relative Error/% | |||
---|---|---|---|---|---|---|

First Measurement | Second Measurement | Third Measurement | Average | |||

Tooth height (E)/mm | 0.8 | 0.85 | 0.85 | 0.86 | 0.85 | 6.33 |

Tooth spacing (B)/mm | 1.8 | 1.82 | 1.82 | 1.80 | 1.81 | 0.63 |

Tooth Angle (A)/° | 42 | 41.9 | 42.5 | 41.9 | 42.1 | 0.24 |

Flow channel depth (D)/mm | 0.8 | 0.80 | 0.79 | 0.78 | 0.79 | 1.29 |

**Table 10.**Relative error between the measured flow rate (q

_{Im}) and the predicted flow rate (q

_{I}) when q

_{I0.1}was 1.5 L/h based on the formula in Table 8.

H/MPa | q_{Im}/(L·h^{−}^{1}) | q_{I}/(L·h^{−}^{1}) | Relative Error/% |
---|---|---|---|

0.02 | 0.64 | 0.68 | −6.31 |

0.04 | 0.94 | 0.96 | −2.00 |

0.06 | 1.16 | 1.17 | −0.19 |

0.08 | 1.36 | 1.34 | 1.13 |

0.10 | 1.53 | 1.5 | 2.20 |

0.12 | 1.69 | 1.64 | 2.74 |

0.14 | 1.84 | 1.77 | 3.70 |

0.16 | 1. 97 | 1.83 | 4.40 |

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## Share and Cite

**MDPI and ACS Style**

Gao, N.; Mo, Y.; Wang, J.; Yang, L.; Gong, S. Effects of Flow Path Geometrical Parameters on the Hydraulic Performance of Variable Flow Emitters at the Conventional Water Supply Stage. *Agriculture* **2022**, *12*, 1531.
https://doi.org/10.3390/agriculture12101531

**AMA Style**

Gao N, Mo Y, Wang J, Yang L, Gong S. Effects of Flow Path Geometrical Parameters on the Hydraulic Performance of Variable Flow Emitters at the Conventional Water Supply Stage. *Agriculture*. 2022; 12(10):1531.
https://doi.org/10.3390/agriculture12101531

**Chicago/Turabian Style**

Gao, Ni, Yan Mo, Jiandong Wang, Luhua Yang, and Shihong Gong. 2022. "Effects of Flow Path Geometrical Parameters on the Hydraulic Performance of Variable Flow Emitters at the Conventional Water Supply Stage" *Agriculture* 12, no. 10: 1531.
https://doi.org/10.3390/agriculture12101531