# Impact of Orifice-to-Pipe Diameter Ratio on Leakage Flow: An Experimental Study

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## Abstract

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## 1. Introduction

## 2. Experimental Study

#### 2.1. Experimental Apparatus

#### 2.2. Experimental Procedures

#### 2.3. Experimental Results

#### 2.3.1. Discharge Coefficient for the Experiments with Water as External Medium

#### 2.3.2. Discharge Coefficient for the Experiments with Air as External Medium

#### 2.3.3. Effect of Reynolds Number

#### 2.3.4. Synthesis of the Experimental Results

## 3. Conclusions

- The dimensionless parameter λ (the orifice-to-pipe diameter radio) indeed affected the pipe leakage with the same size of orifice. With constant orifice pressure and main pipe flow velocity, λ increased (i.e., with the decrease of the pipe diameter, with the increase of pipe wall curvature), and the outflow discharge coefficient increased. The conclusion in the experimental results was true under three molds of opening leakage, namely, round hole, longitudinal crack, and circumferential crack. ${C}_{d}$ was more sensitive to λ when the pipe was around the water under low pressure.
- The discharge coefficient slightly increased with orifice diameter (3 and 6 mm), which also suggests that a general relationship between ${C}_{d}$ and the dimensionless parameter λ (the orifice-to-pipe diameter ratio) may exist. Further experimental and numerical studies will be carried out to investigate this potential relationship.
- The water around the orifice favored the outflow. With similar main pipe velocity and constant orifice pressure, the value of ${C}_{d}$ in the orifice discharging into water was larger than that outflowing into air. ${C}_{d}$ also dropped faster with pressure in the case of air.
- The experiments provided values of ${C}_{d}$ ranging from about 0.60 to 0.85, which presented some deviations from the classical range of 0.61–0.67 reported in the literature. This may have a relevant impact on real pipeline systems.

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 2.**Photos of leakage openings with different areas and shapes in pipes with different diameters: (

**a**) 3 mm circular orifice, (

**b**) 6 mm circular orifice, (

**c**) longitudinal orifice (7 mm length and 1 mm width), and (

**d**) circumferential orifice (7 mm length and 1 mm width).

**Figure 4.**Variation of outflow discharge coefficient of round orifices discharging into water as a function of α and pipe diameter: (

**a**) 3 mm orifice; (

**b**) 6 mm orifice.

**Figure 5.**Variation of outflow discharge coefficient of round orifices discharging into air as a function of leakage pressure and pipe diameter: (

**a**) 3 mm orifice; (

**b**) 6 mm orifice.

**Figure 6.**Variation of outflow discharge coefficient of orifices with different shapes discharging into air as a function of α and pipe diameter: (

**a**) longitudinal crack; (

**b**) circumferential crack.

**Figure 7.**Variation of outflow discharge coefficient for the 3 mm circular hole discharging into air as a function of Reynolds number.

**Figure 8.**Leakage conditions with different pipe wall curvatures (and angle θ): (

**a**) outflow in a pipe with small diameter (with angle θ > 0); (

**b**) outflow in a pipe with large diameter (or a rectangular pipe, where θ = 0); (

**c**) inflow to a pipe of small diameter (with angle θ > 0)

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**MDPI and ACS Style**

Yu, T.; Zhang, X.; E. Lima Neto, I.; Zhang, T.; Shao, Y.; Ye, M. Impact of Orifice-to-Pipe Diameter Ratio on Leakage Flow: An Experimental Study. *Water* **2019**, *11*, 2189.
https://doi.org/10.3390/w11102189

**AMA Style**

Yu T, Zhang X, E. Lima Neto I, Zhang T, Shao Y, Ye M. Impact of Orifice-to-Pipe Diameter Ratio on Leakage Flow: An Experimental Study. *Water*. 2019; 11(10):2189.
https://doi.org/10.3390/w11102189

**Chicago/Turabian Style**

Yu, Tingchao, Xiangqiu Zhang, Iran E. Lima Neto, Tuqiao Zhang, Yu Shao, and Miaomiao Ye. 2019. "Impact of Orifice-to-Pipe Diameter Ratio on Leakage Flow: An Experimental Study" *Water* 11, no. 10: 2189.
https://doi.org/10.3390/w11102189