# Investigating the Pressure Fluctuations of Hydraulic Jump in an Abrupt Expanding Stilling Basin with Roughened Bed

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Experimental Setup

#### 2.2. Theoretical Expression

#### 2.3. Dimensional Analysis

## 3. Results and Discussions

#### 3.1. Sequent Depth Ratio

#### 3.2. ${C}_{P}{}^{\prime}$ Parameter

- Without expansion ($\beta =1$)

- With abrupt expansion jump

#### 3.3. Maximum Non-Dimensional Pressure Fluctuations Parameter (${C}_{P}{{}^{\prime}}_{max}$)

#### 3.4. Positive and Negative Pressure Coefficients (${C}^{+}p$ ,${C}^{-}p$)

## 4. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 1.**Different kinds of hydraulic jumps in a channel with sudden expansion [6] (Bremen 1990).

**Figure 10.**Positive and negative pressure fluctuations versus dimensional distance from jump toe and range of the Froude numbers.

${\mathit{B}}_{1}$ (cm) | ${\mathit{B}}_{2}$ (cm) | Expansion Ratio (β) | bed | ${\mathit{Y}}_{1}$ (cm) | $\mathit{R}\mathit{e}$ | $\mathit{F}{\mathit{r}}_{1}$ | $\mathit{Q}\left(\frac{\mathit{l}}{\mathit{s}}\right)$ |
---|---|---|---|---|---|---|---|

80 | 80 | 1 | 60,000–132,000 | 2–6.9 | 40–90 | ||

53 | 80 | 0.67 | smooth | 3–6 | 82,000–161,000 | 2.2–8.5 | 45–102 |

40 | 80 | 0.5 | 53,000–172,000 | 2.3–9.5 | 22–73 | ||

27 | 80 | 0.33 | 91,000–192,000 | 2.5–10.5 | 25–60 | ||

80 | 80 | 1 | 52,000–141,000 | 2–6.5 | 31–96 | ||

53 | 80 | 0.67 | rough | 3–6 | 65,000–156,000 | 2.3–8 | 32–90 |

40 | 80 | 0.5 | 62,000–153,000 | 2.4–9.1 | 26–70 | ||

27 | 80 | 0.33 | 74,000–242,000 | 3–9.5 | 20-70 |

**Table 2.**Comparison of reduction percentage of ${C}_{P}{{}^{\prime}}_{max}$ in respect to smooth prismatic jump.

Type of Jump | Reduction (%) of ${\mathit{C}}_{\mathit{P}}{{}^{\prime}}_{\mathit{m}\mathit{a}\mathit{x}}$ |
---|---|

smooth bed and sudden expansion; β = 0.67 | 18 |

smooth bed and sudden expansion; β = 0.5 | 23 |

smooth bed and sudden expansion; β = 0.33 | 30 |

rough bed and prismatic jump; β = 1 | 20 |

rough bed and sudden expansion; β = 0.67 | 27 |

rough bed and sudden expansion; β = 0.5 | 46 |

rough bed and sudden expansion; β = 0.33 | 58 |

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**MDPI and ACS Style**

Hasani, M.N.; Nekoufar, K.; Biklarian, M.; Jamshidi, M.; Pham, Q.B.; Anh, D.T. Investigating the Pressure Fluctuations of Hydraulic Jump in an Abrupt Expanding Stilling Basin with Roughened Bed. *Water* **2023**, *15*, 80.
https://doi.org/10.3390/w15010080

**AMA Style**

Hasani MN, Nekoufar K, Biklarian M, Jamshidi M, Pham QB, Anh DT. Investigating the Pressure Fluctuations of Hydraulic Jump in an Abrupt Expanding Stilling Basin with Roughened Bed. *Water*. 2023; 15(1):80.
https://doi.org/10.3390/w15010080

**Chicago/Turabian Style**

Hasani, Marzieh Naem, Kouros Nekoufar, Morteza Biklarian, Morteza Jamshidi, Quoc Bao Pham, and Duong Tran Anh. 2023. "Investigating the Pressure Fluctuations of Hydraulic Jump in an Abrupt Expanding Stilling Basin with Roughened Bed" *Water* 15, no. 1: 80.
https://doi.org/10.3390/w15010080