# Discharge Coefficient of a Round-Crested Weir

^{*}

## Abstract

**:**

## 1. Introduction

_{d}is the discharge coefficient in connection with the upstream head, assuming that the velocity head and surface tension are not taken into consideration.

_{max}was increased up to 0.11, where R is the rounded upstream corner and H

_{max}is the maximum value of the upstream total head, and stated that the discharge coefficient did not increase distinctly when R/H

_{max}was increased beyond 0.11.

## 2. Experimental Setup

## 3. Analysis of Data

#### 3.1. Discharge Characteristic

^{3}/s (R3.0-R10), 0.023 m

^{3}/s (R5.0-R10), and 0.029 m

^{3}/s (R10-R10), the detachment point does not change. The detachment point will move downstream when the discharge rate is greater than 0.065 m

^{3}/s. For the convenience of calculation, the height of the weir plate is equal to 0.25 m, not the position of the detachment point.

^{3}/s, two nappes of R10-R10 and R10-SQ were separated from the crest at the downstream corner, and the discharge capability of the second one was relatively small because the squared downstream corner of the weir raised the water level. The weir, namely SQ-SQ, was equivalent to a short-crested weir for a small head, Q < 0.012 m

^{3}/s, and the nappe left the downstream corner and did not jump, as shown in Figure 6 and Figure 7, so the flow coefficient of SQ-SQ was larger than SQ-R10. When the discharge rate over the weir reached a certain value, 0.015 m

^{3}/s, the downstream angle of the crest did not affect the nappe, and the weir of the same upstream corner had the same discharge capability.

^{3}/s, the weir plate, namely SQ-R10 or SQ-SQ, had the same flow capacity as the sharp-crested weir, meaning the flow rate could also be measured by this weir plate instead of a sharp-crested weir in a laboratory or irrigation setting.

#### 3.2. Formulation for Discharge Coefficient

_{1}and k

_{2}are parameters that are calculated by r/b. It can be seen from Figure 8 that when r/b increases from 0.30 to 0.75, k

_{1}increases and k

_{2}decreases. b is the half width of the round weir, and the half width of the weir near the downstream was not in contact with the flow and did not affect the nappe. The equations for k

_{1}and k

_{2}can be written as follows:

_{d}and the calculated C

_{d}matched well. All data points were within ±2% of the total error. The error of the calculated value was within an acceptable range. It is clear from the above discussions that Equation (8) derived by empirical fit can be used for calculating the discharge coefficient for a round-crested weir.

## 4. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 3.**Variation of the detachment point for the round-crested weir: (

**a**) Definition sketch of the distance (L) between the detachment point and upstream surface of the weir; (

**b**) variation of L with h for weirs of different upstream corners.

**Figure 6.**Definition sketch of flow over the weir of SQ-R10: (

**a**) Q = 0.006 m

^{3}/s; (

**b**) Q = 0.012 m

^{3}/s.

**Figure 7.**Definition sketch of flow over the weir of SQ-SQ: (

**a**) Q = 0.006 m

^{3}/s; (

**b**) Q = 0.012 m

^{3}/s.

**Figure 8.**Variation of C

_{d}with h/P for the round-crested weir: five lines are drawn by the power function with different parameters for different radii of rounded upstream corners.

Body Name | Radian of Round Upstream Corner (mm) | Radian of Round Downstream Corner (mm) | Round Radio (r/b) |
---|---|---|---|

R10-R10 | 10.0 | 10.0 | 1.00 |

SQ-R10 | 0.0 | 10.0 | 0.00 |

R10-SQ | 10.0 | 0.0 | \ |

SQ-SQ | 0.0 | 0.0 | \ |

R1.0-R10 | 1.0 | 10.0 | 0.10 |

R3.0-R10 | 3.0 | 10.0 | 0.30 |

R4.0-R10 | 4.0 | 10.0 | 0.40 |

R5.0-R10 | 5.0 | 10.0 | 0.50 |

R6.5-R10 | 6.5 | 10.0 | 0.65 |

R7.5-R10 | 7.5 | 10.0 | 0.75 |

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**MDPI and ACS Style**

Gong, J.; Deng, J.; Wei, W. Discharge Coefficient of a Round-Crested Weir. *Water* **2019**, *11*, 1206.
https://doi.org/10.3390/w11061206

**AMA Style**

Gong J, Deng J, Wei W. Discharge Coefficient of a Round-Crested Weir. *Water*. 2019; 11(6):1206.
https://doi.org/10.3390/w11061206

**Chicago/Turabian Style**

Gong, Jing, Jun Deng, and Wangru Wei. 2019. "Discharge Coefficient of a Round-Crested Weir" *Water* 11, no. 6: 1206.
https://doi.org/10.3390/w11061206