New Compound Open Channel Section with Polynomial Sides: Improving Cost and Aesthetics
Bibliographic record
Abstract
Previous research on compound trapezoidal cross sections has mainly focused on improving the prediction of the discharge (flow rate) because of its inherent challenges. This paper focuses on two other important aspects: Section shape and optimal construction cost. First, the paper proposes a new compound section with third-degree polynomial sides of main channel with horizontal bottom (HB) that allows its top corners to be smooth, called herein compound polynomial section. The special cases of this versatile section include the simple polynomial section, polygonal section, trapezoidal-rectangular section, two-segment linear-side section, and parabolic bottom-trapezoidal section. The simple polynomial section, which is the bank-full part of the compound polynomial section, can further produce parabolic (with or without HB), trapezoidal, rectangular, and triangular sections. Second, an optimization model that minimizes construction cost (excavation and lining) of the compound (or simple) polynomial section is developed. The model includes discharge and physical constraints. Theoretical and empirical methods of discharge prediction were used in the model. The results show that the simple polynomial section was more economical than the popular parabolic section by up to 8.6% when the side slopes were restricted. The new polynomial-based sections not only reduced construction cost, but also improved maintenance and aesthetics. As such, the new sections should be of interest to researchers and practitioners in hydraulic engineering.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.001 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.003 | 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 itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".