Hydraulic Jump and Resultant Flow Choking in a Circular Sewer Pipe of Steep Slope
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Bibliographic record
Abstract
Urban flood caused by storm-water runoff has been problematic for many regions. There is a need to improve the design and hydraulic performance of storm sewer-pipes, which will help reduce the impact of urban flood. Such a need has motivated the current study. This paper investigates the flow behaviour in a circular pipe of steep slope, in which supercritical flow descends the steep terrain and forms a hydraulic jump under control acting downstream. So far, the jump behaviour and resultant flow choking in a circular pipe are poorly understood. This paper formulates the problem of the hydraulic jump in a circular pipe of slope on the basis of the momentum principle and solves it by using iterative methods. The solutions include the filling ratio and flow field downstream of an undular jump and a direct jump. For the first time, the Froude number’s dependence on the pipe slope has been quantified. For a given slope, it is possible to have two different filling ratios (or equivalently discharges) that associate with the same Froude number value. This paper reports detailed results of the initial versus sequent depth of the hydraulic jumps and quantitatively delineates the slope-filling ratio space between flow-choking and choking-free zones. For the design of storm sewers in a hilly area, it is necessary to correct the current design guidelines, which rely mostly on the uniform flow theory and suggest filling ratios as high as 85%. The corrections are either decreasing the filling ratio or increasing the pipe diameter to achieve choking-free flow in a circular pipe.
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Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from it