Description
In open channel flows, the flow conditions such as the specific energy (of the mean flow) is minimum are called the critical flow conditions. With commonly used Froude number definitions, the critical flow conditions occur for Fr = 1. If the flow is critical, small changes in specific energy cause large changes in flow depth, and critical flows over a long reach of channel are unstable. Basically, the critical flow conditions constitute a singularity of the depth-averaged Bernoulli principle for open channel flow.
The concept of critical flow conditions was first developed by J.B. Bélanger (1828), in relation to the singularity of the backwater equation It was first associated with the idea of minimum specific energy by Boris Bakhmeteff (1912, 1932).
When the flow is critical, there is an unique relationship between the water depth and the discharge, including in critical flow situations with nonhydrostatic pressure distribution and nonuniform velocity distribution (Chanson 2006,2008), as well as unsteady flows (Castro-Orgaz and Chanson 2016).
Hubert Chanson.
Author
Hubert Chanson
Date
2021
Copyright
Hubert Chanson
References
BÉLANGER, J.B. (1828). "Essai sur la Solution Numérique de quelques Problèmes Relatifs au Mouvement Permanent des Eaux Courantes." ('Essay on the Numerical Solution of Some Problems relative to Steady Flow of Water.') Carilian-Goeury, Paris, France, 38 pages & 5 tables (in French).
BAKHMETEFF, B.A. (1912). "O Neravnomernom Dwijenii Jidkosti v Otkrytom Rusle." ('Varied Flow in Open Channel.') St Petersburg, Russia (in Russian).
BAKHMETEFF, B.A. (1932). "Hydraulics of Open Channels." McGraw-Hill, New York, USA, 1st ed., 329 pages.
LIGGETT, J.A. (1993). "Critical Depth, Velocity Profiles and Averaging." Journal of Irrigation and Drainage Engineering, ASCE, Vol. 119, No. 2, pp. 416-422.
CHANSON, H. (2006). "Minimum Specific Energy and Critical Flow Conditions in Open Channels." Journal of Irrigation and Drainage Engineering., ASCE, Vol. 132, No. 5, pp. 498-502 (DOI: 10.1061/(ASCE)0733-9437(2006)132:5(498)).
CHANSON, H. (2008). "Minimum Specific Energy and Critical Flow Conditions in Open Channels - Closure." Journal of Irrigation and Drainage Engineering, ASCE, Vol. 134, No. 6, pp. 883-887 (DOI: 10.1061/(ASCE)0733-9437(2008)134:6(883)).
FELDER, S, and CHANSON, H. (2012). "Free-surface Profiles, Velocity and Pressure Distributions on a Broad-Crested Weir: a Physical study." Journal of Irrigation and Drainage Engineering, ASCE, Vol. 138, No. 12, pp. 1068–1074 (DOI: 10.1061/(ASCE)IR.1943-4774.0000515)
CASTRO-ORGAZ, O., and CHANSON, H. (2016). "Minimum Specific Energy and Transcritical Flow in Unsteady Open-Channel Flow." Journal of Irrigation and Drainage Engineering, ASCE, Vol. 142, No. 1, Paper 04015030, 12 pages (DOI: 10.1061/(ASCE)IR.1943-4774.0000926).
IAHR Media Library
This web site was launched by Prof. Michele Mossa of the Polytechnic University of Bari (Italy) with the initial support of Fondazione Caripuglia, Bari, Italy for the Research Project LIC-MON of 2003 and of the Project IMCA (Integrated Monitoring of Coastal Areas) financed by MIUR PON D.M. 593/00. Later, the initiative was supported with other Prof. Michele Mossa’s funds, most recently provided by the RITMARE Project.
