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Article

Flow at an Ogee Crest Axis for a Wide Range of Head Ratios: Theoretical Model

1
Hydraulics in Environmental and Civil Engineering (HECE), Research Unit Urban & Environmental Engineering (UEE), University of Liège, 4000 Liège, Belgium
2
Artelia, BU Villes & Territoires, Agence des Hauts-de-France, 59520 Marquette-lez-Lille, France
*
Author to whom correspondence should be addressed.
Academic Editor: Wencheng Guo
Water 2022, 14(15), 2337; https://doi.org/10.3390/w14152337
Received: 18 June 2022 / Revised: 18 July 2022 / Accepted: 22 July 2022 / Published: 28 July 2022
(This article belongs to the Special Issue Advances in Spillway Hydraulics: From Theory to Practice)
The discharge coefficient of an ogee crest is a function of the ratio of the effective head to the design head. The purpose of the present study is to derive a theoretical model of this relation, which does not depend on empirical coefficients and whose predictions over a wide range of head ratios are accurate enough for practical use. The developments consider unsubmerged ogee crests without approach flow or lateral contraction effects, heads large enough to enable surface tensions to be neglected, and heads small enough to avoid flow separation. The method is based on potential flow theory, depth integration in a curvilinear reference frame, and critical flow theory. The characteristics of the crest shape are defined by the trajectory of a free jet passing over the crest at the design head. The dimensionless equations show that the position of the critical section is not at the apex of the crest. Nevertheless, they also suggest an approximate equation at the apex of the crest from which the discharge coefficient is derived, together with the local water depth, velocity, and pressure distribution. The results compare well with experimental data for head ratios between 0 and 5, which validates the underlying assumptions of the theoretical model. View Full-Text
Keywords: ogee spillway; discharge coefficient; curvilinear flow; critical section ogee spillway; discharge coefficient; curvilinear flow; critical section
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MDPI and ACS Style

Stilmant, F.; Erpicum, S.; Peltier, Y.; Archambeau, P.; Dewals, B.; Pirotton, M. Flow at an Ogee Crest Axis for a Wide Range of Head Ratios: Theoretical Model. Water 2022, 14, 2337. https://doi.org/10.3390/w14152337

AMA Style

Stilmant F, Erpicum S, Peltier Y, Archambeau P, Dewals B, Pirotton M. Flow at an Ogee Crest Axis for a Wide Range of Head Ratios: Theoretical Model. Water. 2022; 14(15):2337. https://doi.org/10.3390/w14152337

Chicago/Turabian Style

Stilmant, Frédéric, Sebastien Erpicum, Yann Peltier, Pierre Archambeau, Benjamin Dewals, and Michel Pirotton. 2022. "Flow at an Ogee Crest Axis for a Wide Range of Head Ratios: Theoretical Model" Water 14, no. 15: 2337. https://doi.org/10.3390/w14152337

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