Critical flow in open channel hydraulics

In open channel flows, critical flow conditions correspond to a singularity of the flow motion. At critical flow, the water depth dc and the cross-sectional averaged velocity Vc are solely functions of the water discharge and cross-sectional shape.
Historically, the notion of critical flow was introduced as a singularity of the backwater equation (Bélanger 1828).
The modern approach follows the definition of Boris Bakhmeteff (1912, 1932). That is, critical flow occurs when the specific energy is minimum, with the specific energy E defined as: E = H - zo, with H the total head and zo the local bed elevation.
Examples of flow situations leading to minimum specific energy include:
a spillway crest;
an overflow gate; and
a channel contraction leading to choking, e.g. culvert barrel at design flow.
The concept of critical flow in open channels is one of the most important concept in hydraulic engineering, with many practical applications. In open channel flows, the critical flow conditions correspond to a singularity of the flow motion. At critical flow, the water depth dc and the cross‐sectional averaged velocity Vc are solely functions of the water discharge and cross‐sectional shape.
A basic understanding of open channel hydraulic engineering is most relevant in many real-word applications related to water security and flood protection. These are discussed in a number of relevant UA-cam video movies in the same Playlist at:
{ / @hubert_chanson }
Fluid mechanics and hydraulics in Hubert Chanson UA-cam channel { / @hubert_chanson }
Fundamentals of open channel hydraulics [Playlist]
Environmental hydraulics of open channel flows [Playlist]
Advanced hydraulics of open channel flows [Playlist]
Specific energy in open channel flow { • Specific energy in ope... }
Critical flow conditions in open channels {www.youtube.co...}
Critical flow calculations in open channels of irregular cross‐sections { • Critical flow calculat... }
Hydraulic control in open channels: upstream and downstream controls { • Hydraulic control in o... }
Acknowledgements
Professor Colin J. APELT
References
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. (2004). "The Hydraulics of Open Channel Flow: An Introduction." Butterworth-Heinemann, 2nd edition, Oxford, UK, 630 pages (ISBN 978 0 7506 5978 9).
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)).
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).