Explicit solutions of the Manning equation for partially filled circular pipes

Abstract

The application of the Manning equation to partly filled circular channels is considered. The four types of problem that require iterative calculations are elucidated, and explicit solutions proposed in the literature are reviewed. New and improved equations are presented for one type of problem. Explicit analytical equations are developed for the two types of problem for which no explicit solutions could be found in the literature. For each type of problem, two cases are considered: (i) constant Manning roughness coefficient, and (ii) variable Manning roughness coefficient that depends on the depth of flow. Separate equations are presented for each case. The accuracy of each equation is demonstrated by calculating and reporting its maximum deviation from the exact solution within its range of applicability. In addition to obviating the need for iterative calculations, these equations facilitate the calculation of both solutions when the problem at hand has two distinct solutions (two possible flow depths). The proposed equations are accurate enough to be used in computer calculations and sufficiently simple to be used with a hand-held calculator.Résumé : Cet article considère l'application de la formule de Manning à des canaux circulaires partiellement remplis. Les quatre types de problèmes demandant des calculs interactifs sont éclaircis. Des solutions explicites proposées dans la littérature sont examinées. De nouvelles équations améliorées sont proposées pour l'un de ces types de problème. Des équations analytiques explicites sont développées pour les deux types de problème pour lesquels aucune solution explicite n'a été trouvée dans la littérature. Deux cas ont été considérés pour chaque type de problème : (i) le coefficient de rugosité constant de Manning et (ii) le coefficient de rugosité variable de Manning qui dépend de la profondeur de l'écoulement. Des équations séparées sont présentées pour chaque cas. L'exactitude de chaque équation est démontrée en calculant et en rapportant sa déviation maximale de la solution exacte dans sa plage d'application. En plus d'enlever le besoin de faire des calculs itératifs, ces équations facilitent le calcul des deux solutions lorsque le problème possède deux solutions distinctes (deux profondeurs d'écoulement possibles). Les équations proposées sont suffisamment exactes pour être utilisées dans les calculs informatiques et suffisamment simples pour être calculées à l'aide d'une calculatrice de poche.Mots clés : solution explicite, hydraulique, formule de Manning, écoulement à surface libre, coefficient de rugosité, conception des égouts.[Traduit par la Rédaction]

Coupling distributed stormwater collection and managed aquifer recharge: Field application and implications

“…We calculated the volume of runoff routed into the infiltration basin by relating water depth in the inflow culvert to flow rate using the Manning equation (Akgiray, 2005) (see SI). Calculations during WY14 suggested that the corrugated culvert with a 46-cm inner diameter was a flow bottleneck that could cause flooding.…”

Analytical solution for the flow velocity and water surface angle in drainage and sewer networks: case of pipes arranged in series

“…Many authors consider that Manning equation (Manning, 1889) is the best model to describe free surface flow (Chow, 1959;Saatçi, 1990;Carlier, 1980;Akgiray, 2004Akgiray, , 2005Swamee, 1994;Swamee and Rathie, 2004). Manning equation can be expressed as follow (Agouridis, 2014):…”

“…Other authors such as Saatçi (1990), Giroud et al (2000) and Akgiray (2004Akgiray ( , 2005 have developed approximate methods for the case where the water surface angle ranges from 0 to 302.41°.…”

Optimization Technique for Design of Gravity Sewers and Related Aspects

“…The conduit is required to be designed to convey this flow and it is the usual situation that any sewerage and drainage engineer has to deal with. Recent works by Akgiray (2004Akgiray ( , 2005 put forward explicit formulas for partial flow in conduits over the entire range of flow depth taking into account any variation in the "n" value over depth of flow. In line with this, it was suggested that hydraulic design of sewers should preferably be done using maximum "d/D" ratio of 0.88 considering Manning's n as variable over depth and adopting a maximum q actual /Q full ratio of 1.0 (Dey, 2013).…”