Discussion of "Explicit solutions of the Manning equation for partially filled circular pipes"
Notice bibliographique
Résumé
The discusser has read with interest the work on sewer design based on the Manning equation. Two distinctly different conditions have to be considered, namely the “full-flowing” and the “partially filled” sewer flows. According to European standards, a sewer should be designed based on the Colebrook and White equation for the full-flowing condition. The Manning equation is currently in use, however, for predicting the flow characteristics in the partially filled sewer flow regime. Stable flow in partially filled sewers The discusser conducted a study on the historical development and currently accepted design guidelines of the partially filled sewer flow (Hager 1991a, 1991b). Curves for relative discharge in terms of sewer filling have been in use since the 1880s, before Robert Manning (1816–1897) presented his equation. A large number of experimental studies on the flow of water in partially filled pipes were conducted in the 20th century based on deviations between the measurements in existing sewers and the results furnished by the Manning equation. Notable works were presented by Ackers (1961a, 1961b) and Sauerbrey (1969). The following conclusions were drawn by Hager (1991a, 1991b): The full-flowing condition in sewers is an important notion in sewer design, although it may not occur in nature. The characteristics of full-flowing sewers should be computed with the Colebrook and White equation, thereby accounting for the effects of Reynolds number and relative roughness. The Manning equation approximates the previous relation in the turbulent rough flow regime; it may be useful for designing partially filled sewers. The air flow close to the sewer top has a small effect on the water flow in a sewer. Filling diagrams are limited towards the sewer top; flow above the filling limit is hydraulically unstable. The transition from free surface to pressurized sewer flow is abrupt; the stable upper limit corresponds to the maximum free surface discharge condition. The findings of Sauerbrey (1969) appear to account in the best way for the effective flow characteristics in circular, partially filled sewers. The author did not account for observations made with sewers; instead, he accepted the relations furnished by the Manning equation without recourse to previous investigations. When plotting the relative discharge Q/Qv versus the relative filling y = h/D (where Q is the discharge, Qv is the discharge for the full-flowing condition, h is the uniform flow depth, and D is the sewer diameter), the condition Q/Qv is attained twice, namely for y = 1 as required from the scalings and for y ≅ 0.85; the latter condition was identified as the full-flowing condition in practice because it furnishes a discharge identical to that of the condition y = 1, in the stable flow pattern. A sewer flow is unstable in the upper filling region, typically for 0.85 ≤ y ≤ 1. Therefore, this region was excluded in sewer design. Circular profile computations
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Comment cette classification a été obtenuedéplier
Prédiction machine sur la base complète
Imitation des enseignantsNi prévalence calibrée, ni vérité terrain. Validation humaine à venir. Le volet Gemma est une étiquette directe du modèle pour chaque travail de la base, lue sur la notice réduite au titre. Le volet Codex est un classifieur appris des 10 348 étiquettes directes de Codex et calibré sur les taux pondérés de l'échantillon; les champs sans appui suffisant ne portent aucun appel Codex. Le mode candidate est l'union des deux volets; le consensus est leur intersection. Ces sorties portent le statut machine_predicted_unvalidated et ne sont pas des étiquettes humaines.
Scores du classifieur distillé par catégorie (deux têtes)
| Catégorie | Codex | Gemma |
|---|---|---|
| Métarecherche | 0,001 | 0,004 |
| Méta-épidémiologie (sens strict) | 0,001 | 0,000 |
| Méta-épidémiologie (sens large) | 0,001 | 0,001 |
| Bibliométrie | 0,001 | 0,001 |
| Études des sciences et des technologies | 0,001 | 0,002 |
| Communication savante | 0,001 | 0,003 |
| Science ouverte | 0,002 | 0,002 |
| Intégrité de la recherche | 0,004 | 0,003 |
| Charge utile insuffisante (le modèle a refusé de juger) | 0,010 | 0,002 |
Scores machine (provisoires)
Les deux têtes enseignantes du modèle étudiant, lues sur ce travail. Un score ordonne la base pour la relecture; il n'affirme jamais une catégorie, et le statut de validation accompagne chaque rangée tel quel.
Scores de référence d'un modèle non mature (critères de maturité non atteints, 7 itérations). Un score ordonne; il n'affirme jamais une catégorie.
score_only:v0-immature-baseline · tel quel depuis la passe de notation : score_only signifie que le nombre peut ordonner les travaux, et qu'aucune étiquette de catégorie n'en découleClassification
machine, non validéePrédiction automatique; un appel candidat d’une seule source (Gemma direct ou Codex distillé), pas un consensus.
Le détail, modèle par modèle et score par score, se trouve en fin de page sous « Comment cette classification a été obtenue ».