# Impact of Elastic Diaphragm Hardness and Structural Parameters on the Hydraulic Performance of Automatic Flushing Valve

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

_{amin}) required for automatic closing and the maximum flushing duration (FD

_{max}) are two important performance indexes of AFV. The existing AFV products have the problem of larger H

_{amin}and smaller FD

_{max}, which result higher investment and operating cost, and poor flushing efficiency. Based on the mechanical analysis of the AFV elastic diaphragm and the derivation of the FD, elastic diaphragm hardness (E), ascending channel offset distance (D), and drain hole width (W) were selected as the experimental factors, and nine AFVs were designed by L

_{9}(3

^{3}) orthogonal test method to investigate the influence of elastic diaphragm hardness and structural parameters on the hydraulic performance of AFVs. The hydraulic performance test results showed that the H

_{amin}of the nine AFVs ranged from 0.026 to 0.082 MPa and FD

_{max}ranged from 36.3 to 95.7 s. H

_{amin}was positively correlated with E and D and negatively correlated with W. FD

_{max}was negatively correlated with E and W and tended to increase and then decrease with D. All elastic diaphragm hardness and structural parameters had a significant effect on H

_{amin}, and E and W had a significant effect on FD

_{max}. Based on the range analysis, two new combinations of AFV elastic diaphragm hardness and structural parameters with minimum H

_{amin}(E = 40 HA, D = 0 mm, W = 2 mm) and maximum FD

_{max}(E = 40 HA, D = 2 mm, W = 1.68 mm) were determined, and the corresponding H

_{amin}was 0.022 MPa, 63.3% lower than that of the existing product, and FD

_{max}was 116.4 s, 71.2% higher than that of the existing product. In this study, two ternary nonlinear mathematical regression models of H

_{amin}and FD

_{max}with elastic diaphragm hardness and structural parameters was constructed. The simulation accuracy of the models is good and can be used to quickly predict the optimal combination of AFV parameters to satisfy the actual engineering-required H

_{amin}and FD

_{max}.

## 1. Introduction

^{2+}, Mg

^{2+}, K

^{+}and SO

_{4}

^{2-}in fertilizers form large sediment particle agglomerates with sulfate and other precipitates, which accelerate the formation of clogging silt in the flow channel [5,6,7,8], which in turn reduces the turbulence of water flow and makes sediment particles prone to siltation in the dripline and flow channels [9,10].

_{a}) is 0.06–0.1 MPa, the FD of both AFVs produced by Naandanjain (NaanDanJain Irrigation, Ltd., Post Naan, Israel) and Netafim (Netafim Ltd., Tel Aviv, Israel) is less than 10 s, which is much less than the FD requirement of 3–6 min proposed by scholars [11,13,25,26,27,28]. Zhao developed an AFV with a FD of 53 s by improving the delay channel structure [29], Mo et al. increased the water storage volume by adding an exhaust device to the upper cavity of the AFV, and the FD could be increased to 68 s [24]. After 400 h of continuous operation with a water source of 1 kg/m³ sand content, the average relative flow rate of the emitter on a 12 m long dripline with an AFV was 16.6% higher than that without an AFV [29]; the average relative flow rate of the emitter on a 48 m long dripline with an AFV was increased by 4.0% compared to that without an AFV [30]. The installation of an AFV can substantially improve the dripline blockage resistance, but the effect decreases with increasing dripline length. The FD of the existing AFV may still be short for the common dripline length of 60~80 m in actual projects, which cannot meet the flushing demand. In addition, there has been a lack of in-depth research on the intrinsic mechanisms to improve the FD by optimizing the AFV elastic diaphragm hardness and structural parameters.

_{amin}. When the drip irrigation system is equipped with AFVs, the water supply pressure of the pump not only needs to meet the design pressure value (e.g., 0.1 MPa) of the emitter farthest from the pump but also the H

_{amin}of the AFV farthest from the pump. In addition, the increased water velocity in the pipeline during flushing can substantially increase the head loss along the pipeline network, which in turn increases the pump water supply pressure demand. Then, reducing H

_{amin}can reduce the pump input cost and operation cost of an automatic flushing drip irrigation system and promote the application of automatic flushing technology, but no research related to H

_{amin}of the AFV has been reported.

_{amin}and FD

_{max}were studied, and the mechanism of structural parameter optimization on the hydraulic performance of AFV was investigated. The mathematical model of quantitative characterization of H

_{amin}and FD

_{max}with the change of elastic diaphragm hardness and structural parameters was constructed. This provides a theoretical basis for AFV update iteration and technical support for alleviating the problem of drip irrigation water and fertilizer integration clogging.

## 2. Materials and Methods

#### 2.1. The Working Principle of the Automatic Flushing Valve

_{y}) (Equation (4)). F

_{y}is composed of the upper cavity water pressure (F1y) (Equation (1)), the lower cavity water pressure (F2y) (Equation (2)), and the elastic force of the elastic diaphragm (F3y) (Equation (3)). Since the F

_{y}is greater than zero, the H

_{a}(inlet pressure at the beginning of flushing for the AFV to automatically close) can be calculated in Equation (5).

_{1y}is the downwards vertical force (N) exerted by water in the upper cavity on the elastic diaphragm. F

_{2y}is the vertical upwards force of water in the lower cavity on the elastic diaphragm (N). F

_{3y}is the vertical elastic force of the elastic diaphragm (N); E is the hardness of the elastic diaphragm (HA); F

_{y}is the vertical downwards resultant force of the elastic diaphragm (N); a and b are the primary term coefficient and constant term, respectively, a > 0 [31]; H

_{a}is the AFV inlet pressure (MPa); h

_{f}

_{1}is the water loss generated in the water inlet (MPa) in Figure 1b; h

_{f}

_{2}is the water loss generated in the ascending channel in Figure 1b and delay channel (MPa) in Figure 1a; S

_{x}is the projection area of the elastic diaphragm on the horizontal plane (m

^{2}); and S

_{drain x}is the projection area of the drain hole on the horizontal plane (m

^{2}).

_{w}, mL) and the average flow rate of water entering the upper cavity from the end of the delay channel (q, mL/s) (Equation (6)). According to the result from Mo et al. [24], C

_{w}is approximately equal to the volume added by the downwards movement of the elastic diaphragm (C

_{b}, mL) based on the initial volume of the upper cavity (C

_{a}, mL).

#### 2.2. Analysis of Parameters Affecting the Hydraulic Performance of AFVs

_{a}and FD are the key design parameters for automatic flushing drip irrigation system (AFDS). From Equation (5), it can be seen that H

_{a}increases with the decrease in S

_{drainx}and the increase in E. Furthermore, this can be achieved by setting different drain hole widths (W) and elastic diaphragm materials. From Equation (6), FD can increase with the increase in C

_{b}and decrease in q. When H

_{a}is the same, C

_{b}may be influenced by E. In addition, this paper intends to increase h

_{f}

_{2}by setting a different ascending channel offset distance (D) to reduce the delay channel inlet pressure and thus reduce q.

#### 2.2.1. Experimental Design

^{3}), and the experimental design is shown in Table 1. The elastic diaphragm hardness test is carried out using a Shore durometer on the “A” scale. The range of Shore durometer (Yueqing Handpi Instrument Co., Ltd., Zhejiang, China) is 0–100 HA with an accuracy of 0.5 grade.

#### 2.2.2. Experimental Method and Measurement Index

_{a}, and the AFVs discharged water into the bucket. When the AFV was closed and no water flowed out, the timing stopped, the timer time was the FD. At this point, the pressure gauge reading returned to H. Each experiment was repeated three times. During the experiment, the minimum H

_{a}to control the AFV automatic closure was H

_{amin}, and the corresponding flushing duration was FD

_{max}.

#### 2.3. Data Analysis

_{i}and E

_{i}were the simulated and measured values, respectively; i was the number of the measured value, n was the total number of measured values; and E

_{ave}was the average of all measured values. 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.

## 3. Results and Analysis

#### 3.1. Hydraulic Performance Experimental Results

#### 3.2. Analysis of the Hydraulic Performance Range of AFVs

_{amin1}, H

_{amin2}, and H

_{amin3}and FD

_{max1}, FD

_{max2}, and FD

_{max3}are the average values of H

_{amin}and FD

_{max}, respectively, when each experimental factor is taken at the 1, 2 and 3 levels, such that H

_{amin1}= (0.026 + 0.031 + 0.041)/3= 0.033 MPa, where 0.026, 0.031 and 0.041 MPa are the H

_{amin}values at E = 40 HA (Table 2), respectively. R is the range of the corresponding factor; a larger R indicates that the experimental factor in the design range of the change leads to greater changes in the value of the experimental index and a greater degree of influence of the factor on the hydraulic performance of the AFV. The range analysis results show that the main order of the effect of each experimental factor on H

_{amin}and FD

_{max}is D, E, and W, and E, W, and D, respectively.

_{amin}is positively correlated with E and D and negatively correlated with W. FD

_{max}is negatively correlated with E and W and shows a trend of increasing and then decreasing with D. When E is reduced from 60 HA to 40 HA, the reduction of H

_{amin}is 42.1% and the increase of FD

_{max}is 91.4%; when D is reduced from 4 mm to 0 mm, the reduction of H

_{amin}is 47.6% and the increase of FD

_{max}is 3.5%; and when W is increased from 1 mm to 2 mm, the reduction of H

_{amin}is 16.3%, at which time FD

_{max}decreases by 18.7%.

_{1}D

_{1}W

_{3}when the smaller H

_{amin}is the optimal principle and E

_{1}D

_{2}W

_{1}when the larger FD

_{max}is the optimal principle, and these two AFVs are not in Table 2.

#### 3.3. Variance Analysis of the Hydraulic Performance of the Automatic Flushing Valve

_{amin}. E and W have a significant effect on FD

_{max}, while D has no significant effect on FD

_{max}.

#### 3.4. Construction and Verification of a Mathematical Regression Model for Hydraulic Performance of AFV

_{amin}, m, etc. The smaller H

_{amin}is, the less pressure is required for the pump of the drip irrigation system, and the lower the system investment and freight cost. When the T is certain, the m increases with increasing FD; thus, the number of AFVs required for the system decreases, and the investment is reduced. Therefore, it is necessary to determine the appropriate H

_{amin}and FD

_{max}according to the actual project requirements and then determine the AFV elastic diaphragm hardness and structural parameters. In this study, the multivariate nonlinear regression models of H

_{amin}and FD

_{max}with E, D, and W are constructed with the help of SPSS 26.0 statistical software, and the coefficients of determination (R

^{2}) of H

_{amin}and FD

_{max}regression models are 0.953 and 0.829, respectively, which means well fitted.

_{amin}and FD

_{max}are −12.2% to 19.0% and −18.4% to 18.3%, respectively, with a small root mean square error (RMSE) of 0.003 MPa and 10.2 s, respectively, and the normalized root mean square error (nRMSE) is 8.0% and 14.5%, respectively, both less than 20%. The range analysis results show that the combination with the smallest H

_{amin}result is E

_{1}D

_{1}W

_{3}and the combination with the largest FD

_{max}is E

_{1}D

_{2}W

_{1}. As shown in Table 5, the measured H

_{amin}of E

_{1}D

_{1}W

_{3}is 0.022 MPa, and the measured FD

_{max}of E

_{1}D

_{2}W

_{1}is 116.4 s, which are lower and larger than the values in Table 2, respectively. The regression Equations (9) and (10) can be used to predict the combination of AFV elastic diaphragm hardness and structural parameters corresponding to H

_{amin}and FD

_{max}required for the actual project and can shorten the development time.

## 4. Discussion

_{max}for the AFV without considering the decrease in H

_{amin}[23,24]. Compared with the conventional drip irrigation system without AFVs, the AFV in the flushing process, the water flow in the pipe network system increases significantly, resulting in a significant increase in the head loss (h

_{f}) between the pump and the AFVs inlet. To meet the H

_{amin}of the farthest AFV from the pump, the pump water supply pressure of AFDS (H) should be greater than (H

_{amin}+ h

_{f}). It is necessary to reduce the H

_{amin}and then reduce the pump input and operating costs.

_{amin}decreases with the decrease in h

_{f}

_{1}, h

_{f}

_{2}, S

_{x}and E and decreases with the increase in S

_{drainx}. When E decreases from 60 HA to 40 HA, H

_{amin}decreases by 42.1% on average; D decreases from 4 mm to 0 mm leading to the decrease of h

_{f}

_{2}, and thus H

_{amin}decreases by 47.6% on average; W increases from 1 mm to 2 mm leading to an increase in S

_{drainx}and an average decrease in H

_{amin}of 16.3%; and the effects of H

_{amin}by E, D and W all reach significance levels.

_{b}and q (Equation (7)). When H

_{a}is the same, the AFV flushing is over, and the elastic diaphragm is in close contact with the outlet and the expansion of the elastic diaphragm on the horizontal plane increases as E decreases, which in turn increases C

_{b}(Figure 1d); therefore, when E decreases from 60 HA to 40 HA, FD

_{max}increases significantly by 91.2% on average. When W decreases from 2 mm to 1 mm, FD

_{max}increases by 22.9% on average, probably because the elastic diaphragm moves downwards under the action of F

_{y}(Figure 1c,d), and F

_{y}decreases with the increase of F

_{2y}(Equation (4)); therefore, when the AFV is guaranteed to close automatically, increasing F

_{2y}within a certain range can slow down the process of downwards movement of the elastic diaphragm and increase the FD. F

_{2y}increases as W decreases (Equation (2)), F

_{2y}increases as the force F

_{y}on the elastic diaphragm decreases, and the AFV automatically closes the longer the flushing duration is needed; therefore, FD

_{max}increases as W decreases. h

_{f2}increases as D increases. When H

_{a}is the same, q decreases as D increases, resulting in FD increases as D increases. When D increases from 1 mm to 2 mm, FD

_{max}increases by 13.8%; however, when D increases from 2 mm to 4 mm, h

_{f}

_{2}increases, and H

_{amin}increases from 0.040 MPa to 0.063 MPa before the AFV can close automatically (Table 3), and the increase in q causes the FD to decrease.

_{amin}and FD

_{max}: E

_{1}D

_{1}W

_{3}and E

_{1}D

_{2}W

_{1}, respectively. The measured H

_{amin}of the E

_{1}D

_{1}W

_{3}AFV is 0.022 MPa, which is 15.4% lower than the lowest value of H

_{amin}in Table 2 and 63.3% lower than the existing AFV [29]. The measured FD

_{max}of E

_{1}D

_{2}W

_{1}is 116.4 s, which is 21.6% higher than the maximum value of FD

_{max}in Table 2 and 71.2% higher than the existing AFV [24].

_{amin}needs to be determined according to the scale of the pipe network system and parameters such as length and diameter of pipes at all levels, and the appropriate FD

_{max}needs to be determined by considering the system investment and operation cost. The appropriate FD

_{max}also needs to be determined by considering the water quality conditions of water sources, fertilizer types, clog formation characteristics, system investment, and other factors through a large number of experiments [13,25,26,28]. The quantitative regression model of H

_{amin}, FD

_{max}and AFV elastic diaphragm hardness and structural parameters constructed in this study has a good prediction accuracy [34,35,36], which can help manufacturers to produce AFVs for practical engineering needs at low cost and quickly by providing a theoretical basis and prediction guidance. In future research, it is necessary to construct a hydraulic calculation model of AFDS to study the dynamic balance relationship of water supply pressure and flow rate required by pumps and H

_{amin}under different engineering conditions.

## 5. Conclusions

_{amin}and FD

_{max}were examined, and the main conclusions were drawn as follows:

- The physical relationship model between H
_{amin}and FD_{max}and the elastic diaphragm hardness and structural parameters and the measured results of hydraulic performance show that H_{amin}increases with increasing E and D and decreases with increasing W, FD_{max}decreases with increasing E and W, and E, D and W have a significant effect on H_{amin}. E and W have significant effects on FD_{max}(p < 0.05); - Based on range analysis, the minimum H
_{amin}is 0.022 MPa, which is lower than the H_{amin}of the existing AFV by 63.3%. And the maximum FD_{max}is 116.4 s, which is higher than that of the existing AFV by 71.2%. - The ternary nonlinear regression equation of hydraulic performance and elastic diaphragm hardness and structural parameters of the AFV has a good prediction accuracy, which can quickly give the structural parameter combination of the AFV required by the actual project and shorten the research and development time.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Nomenclature

AFV | Automatic flushing valve |

H_{a} | The inlet pressure, (MPa) |

H_{amin} | The minimum inlet pressure, (MPa) |

FD | The flushing duration, (s) |

FD_{max} | The maximum flushing duration, (s) |

E | Elastic diaphragm hardness, (HA) |

D | Ascending channel offset distance, (mm) |

W | Drain hole width, (mm) |

AFDS | Automatic flushing drip irrigation system |

F_{1y} | The downwards vertical force exerted by water in the upper cavity on the elastic diaphragm, (N) |

F_{2y} | The vertical upwards force of water in the lower cavity on the elastic diaphragm, (N) |

F_{3y} | The vertical elastic force of the elastic diaphragm, (N) |

F_{y} | The vertical downwards resultant force of the elastic diaphragm, (N) |

h_{f1} | The water loss generated in the water inlet, (MPa) |

h_{f2} | The water loss generated in the ascending channel and delay channel, (MPa) |

S_{x} | The projection area of the elastic diaphragm on the horizontal plane, (m^{2}) |

S_{drain x} | The projection area of the drain hole on the horizontal plane, (m^{2}) |

C_{w} | The water storage volume of the AFV body, (mL) |

C_{a} | The initial volume of the upper cavity, (mL) |

C_{b} | The volume added by the downwards movement of the elastic diaphragm, (mL) |

C_{air} | The volume of air in the upper cavity, (mL) |

q | The average flow rate of water entering the upper cavity from the end of the delay channel, (mL/s) |

m | The number of driplines controlled by one AFV |

T | The flushing duration per unit length of dripline, (s/m) |

H | The pump water supply pressure of AFDS, (MPa) |

RMSE | Root mean square error |

nRMSE | The normalized root mean square error |

h_{f} | The head loss between the pump and the AFVs inlet, (MPa) |

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**Figure 1.**Schematic diagram of the automatic flushing valve (AFV) structure. 1. Valve body; 2. Elastic diaphragm; 3. Valve cover; 4. Threaded ring; 5. Raised edge of the elastic diaphragm; 6. Water inlet; 7. Ascending channel; 8. Delay channel; 9. Upper cavity; 10. Outlet; 11. Drain hole; and 12. Lower cavity. Note: C

_{a}is the initial volume of the upper cavity, mL; C

_{b}is the volume added by the downwards movement of the elastic diaphragm, mL; F

_{1y}is the downwards vertical force exerted by water in the upper cavity on the elastic diaphragm, N; F

_{2y}is the vertical upwards force of water in the lower cavity on the elastic diaphragm, N; F

_{3y}is the vertical elastic force of the elastic diaphragm, N; and the blue arrow is the direction of water movement.

**Figure 2.**Schematic diagram of the variation in different ascending channel offset distances (

**D**) (D

_{1}, D

_{2}and D

_{3}) and different drain hole widths (

**W**) (W

_{1}, W

_{2}and W

_{3}) of the AFV.

**Figure 3.**Schematic diagram of the hydraulic experimental platform of the AFV. 1. Automatic flushing valve; 2. PE pipe; 3. ball valve; 4. bucket; 5. centrifugal pump; and 6. pressure gauge.

**Figure 4.**Automatic flushing valve minimum closing pressure (H

_{amin}) (

**a**) and maximum flushing duration (FD

_{max}) (

**b**), three-dimensional distribution of experimental results. Note: The diameter of the sphere or circle is proportional to the value of H

_{amin}(

**a**) or FD

_{max}(

**b**); the red sphere represents H

_{amin}; the magenta sphere represents FD

_{max}; the blue, yellow and green circles represent the projections of H

_{amin}(

**a**) or FD

_{max}(

**b**) on the three faces of D-W, E-D and E-W, respectively.

**Figure 5.**Effect of different factor levels on the minimum closing pressure (H

_{amin}) (

**a**) and maximum flushing duration (FD

_{max}) (

**b**) of the automatic flushing valve (AFV).

**Figure 6.**Comparison of measured and predicted values by the regression model for the automatic flushing valve.

Order | Treatments | Experimental Factors | ||
---|---|---|---|---|

E (HA) | D (mm) | W (mm) | ||

1 | E_{1}D_{1}W_{1} | 40 | 0 | 1.00 |

2 | E_{1}D_{2}W_{2} | 40 | 2 | 1.68 |

3 | E_{1}D_{3}W_{3} | 40 | 4 | 2.00 |

4 | E_{2}D_{1}W_{3} | 55 | 0 | 2.00 |

5 | E_{2}D_{2}W_{1} | 55 | 2 | 1.00 |

6 | E_{2}D_{3}W_{2} | 55 | 4 | 1.68 |

7 | E_{3}D_{1}W_{2} | 60 | 0 | 1.68 |

8 | E_{3}D_{2}W_{3} | 60 | 2 | 2.00 |

9 | E_{3}D_{3}W_{1} | 60 | 4 | 1.00 |

Treatments | H_{amin} (MPa) | FD_{max} (s) |
---|---|---|

E_{1}D_{1}W_{1} | 0.026 | 95.7 |

E_{1}D_{2}W_{2} | 0.031 | 83.3 |

E_{1}D_{3}W_{3} | 0.041 | 87.3 |

E_{2}D_{1}W_{3} | 0.033 | 38.7 |

E_{2}D_{2}W_{1} | 0.040 | 82.7 |

E_{2}D_{3}W_{2} | 0.065 | 58.7 |

E_{3}D_{1}W_{2} | 0.040 | 54.3 |

E_{3}D_{2}W_{3} | 0.048 | 48.7 |

E_{3}D_{3}W_{1} | 0.082 | 36.3 |

**Table 3.**Minimum closing pressure (H

_{amin}) and maximum flushing duration (FD

_{max}) range analysis of the automatic flushing valve.

Experimental Indexes | Experimental Factors | |||
---|---|---|---|---|

E (HA) | D (mm) | W (mm) | ||

H_{amin} | H_{amin1} | 0.033 | 0.033 | 0.049 |

H_{amin2} | 0.046 | 0.040 | 0.045 | |

H_{amin3} | 0.057 | 0.063 | 0.041 | |

R | 0.024 | 0.030 | 0.008 | |

FD_{max} | FD_{max1} | 88.8 | 62.9 | 71.6 |

FD_{max2} | 60.0 | 71.6 | 65.4 | |

FD_{max3} | 46.4 | 60.8 | 58.2 | |

R | 42.4 | 10.8 | 13.4 |

**Table 4.**Variance analysis of the influence of experimental factors on minimum closing pressure (H

_{amin}) and maximum flushing duration (FD

_{max}).

Experimental Indexes | E | D | W |
---|---|---|---|

H_{amin} | 78.236 ** | 131.082 ** | 10.180 ** |

FD_{max} | 33.773 ** | 2.357 | 3.219 * |

Treatments | E (HA) | D (mm) | W (mm) | H_{amin} | FD_{max} | ||||
---|---|---|---|---|---|---|---|---|---|

Predicted Value (MPa) | Measured Value (MPa) | Relative Error (%) | Predicted Value (s) | Measured Value (s) | Relative Error (%) | ||||

E_{1}D_{1}W_{2} | 40 | 0 | 1.68 | 0.024 | 0.026 | −9.3 | 86.4 | 73.0 | 18.3 |

E_{1}D_{1}W_{3} | 40 | 0 | 2.00 | 0.021 | 0.022 | −2.7 | 77.0 | 94.3 | −18.4 |

E_{1}D_{2}W_{1} | 40 | 2 | 1.00 | 0.033 | 0.028 | 19.0 | 97.7 | 116.4 | −16.1 |

E_{1}D_{3}W_{2} | 40 | 4 | 1.68 | 0.051 | 0.047 | 9.3 | 79.6 | 90.3 | −11.9 |

E_{2}D_{1}W_{1} | 55 | 0 | 1.00 | 0.036 | 0.036 | −0.4 | 68.6 | 80.4 | −14.6 |

E_{2}D_{1}W_{2} | 55 | 0 | 1.68 | 0.037 | 0.036 | 3.3 | 56.6 | 58.7 | −3.5 |

E_{2}D_{2}W_{2} | 55 | 2 | 1.68 | 0.043 | 0.040 | 7.3 | 68.0 | 73.3 | −7.3 |

E_{2}D_{2}W_{3} | 55 | 2 | 2.00 | 0.038 | 0.039 | −1.9 | 62.6 | 55.3 | 13.3 |

E_{2}D_{3}W_{3} | 55 | 4 | 2.00 | 0.058 | 0.053 | 9.1 | 60.0 | 65.5 | −8.4 |

E_{3}D_{1}W_{1} | 60 | 0 | 1.00 | 0.040 | 0.046 | −12.2 | 55.0 | 62.7 | −12.2 |

E_{3}D_{1}W_{3} | 60 | 0 | 2.00 | 0.040 | 0.039 | 1.4 | 33.7 | 33.9 | −0.4 |

E_{3}D_{2}W_{1} | 60 | 2 | 1.00 | 0.051 | 0.047 | 9.5 | 59.0 | 67.8 | −13.1 |

E_{3}D_{2}W_{2} | 60 | 2 | 1.68 | 0.047 | 0.044 | 7.8 | 56.3 | 67.6 | −16.7 |

E_{3}D_{3}W_{2} | 60 | 4 | 1.68 | 0.070 | 0.065 | 6.9 | 51.6 | 58.0 | −11.0 |

E_{3}D_{3}W_{3} | 60 | 4 | 2.00 | 0.062 | 0.061 | 2.2 | 51.0 | 57.8 | −11.8 |

RMSE | 0.003 MPa | 10.2 s | |||||||

nRMSE (%) | 8.0 | 14.5 |

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© 2023 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Gao, H.; Mo, Y.; Wu, F.; Wang, J.; Gong, S.
Impact of Elastic Diaphragm Hardness and Structural Parameters on the Hydraulic Performance of Automatic Flushing Valve. *Water* **2023**, *15*, 287.
https://doi.org/10.3390/w15020287

**AMA Style**

Gao H, Mo Y, Wu F, Wang J, Gong S.
Impact of Elastic Diaphragm Hardness and Structural Parameters on the Hydraulic Performance of Automatic Flushing Valve. *Water*. 2023; 15(2):287.
https://doi.org/10.3390/w15020287

**Chicago/Turabian Style**

Gao, Hao, Yan Mo, Feng Wu, Jiandong Wang, and Shihong Gong.
2023. "Impact of Elastic Diaphragm Hardness and Structural Parameters on the Hydraulic Performance of Automatic Flushing Valve" *Water* 15, no. 2: 287.
https://doi.org/10.3390/w15020287