Modeling of Type B hydraulic jump characteristics and comparative analysis focusing on sequent depth ratio, energy loss, and effect of sill installation under laboratory conditions

Document Type : Research Paper

Authors

Department of Irrigation and Reclamation Engineering, University of Tehran, Tehran, Iran.

10.22059/ijswr.2025.402484.670008

Abstract

This study analyzes Type B hydraulic jumps in rectangular channels with and without downstream sills, proposing improved formulas for sequent depth and energy loss. Experiments were conducted under controlled tailwater depth conditions. Experimental results demonstrated that previous models based on the momentum principle had a Mean Absolute Percentage Error (MAPE) between 20% and 30%, whereas the empirical relationship proposed by Carollo et al. (2011) performed better, with a MAPE of less than 5%. A new relationship with a MAPE of about 4% was introduced for predicting the sequent depth ratio. As the Froude number increased from 7.8 to 13, the sequent depth ratio increased from 12 to 23.5. The energy loss of the jump varied between 60% and 80% with the increase in the Froude number. The new model demonstrated a MAPE of 1.7% in predicting energy loss, performing better than previous established models such as Hager (1992). The installation of a sill near the slope change area increased turbulence and the sequent depth ratio; however, the energy dissipation in this range was low and the performance was not optimal. With the sill located at 1.4 to 3 channel widths, the flow achieved hydrostatic conditions, resulting in the target energy loss of 65% to 80%. The optimal sill height was determined to be approximately 10 cm. Installing the sill at the relative position of 1.4 times the channel width resulted in the formation of an optimal stilling basin, suitable energy loss, and optimization of the structure's dimensions.

Keywords

Main Subjects

Introduction

A novel momentum-based model is introduced for the prediction of B-type hydraulic jumps occurring on positive slopes in the presence of submerged downstream obstacles. Experimental data confirm that the model enhances predictive accuracy for both the sequent depth ratio and energy dissipation, overcoming key shortcomings of prior empirical methods.

Method

This study experimentally investigated B-type hydraulic jumps in a rectangular flume with a 45° inclined plate (choute) and downstream gate, measuring key flow parameters under varying conditions. A momentum balance method with a sill correction factor was employed to predict sequent depth ratios, integrating experimental and theoretical analyses to assess the impact of geometry and control structures on B-type jumps.

Results

This study evaluates models for Type B hydraulic jumps without sills. Traditional momentum-based models were inaccurate, with a 20–30% MAPE for sequent depth ratio. While Carollo et al.'s empirical model reduced this error to 5%, our proposed Traditional momentum-based formula, featuring an empirical coefficient (K=1), achieves a further improvement to 4.5% MAPE. Additionally, it precisely predicts energy dissipation rates of 60–80% with a MAPE of 1.7%. A secondary finding demonstrates that sill installation at specific heights and locations optimizes dissipation and stabilizes flow conditions.

Conclusions

This research developed a new momentum-based equation that accurately predicts both the sequent depth ratio and energy dissipation for Type B hydraulic jumps under varying tailwater and sill configurations, achieving MAPEs of approximately 4.5% and 1.7%, respectively. Findings indicate that higher initial Froude numbers raise the sequent depth ratio and energy dissipation, while optimal sill placement-between 1.4 and 2.2 from the slope change area-improves energy dissipation and reduces the size of stilling basins, promoting more efficient hydraulic design.

Author Contributions

All authors contributed equally to the conceptualization of the article and writing of the original and subsequent drafts.

Data Availability Statement

Data available on request from the authors.

Acknowledgements

The authors would like to thank all participants of the present study.

Ethical considerations

The authors avoided data fabrication, falsification, plagiarism, and misconduct.

 

Conflict of interest

The author declares no conflict of interest.

 

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Iranian Journal of Soil and Water Research
Volume 56, Issue 11
January 2026
Pages 2951-2967

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