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Critical flow calculations in open channels of irregular cross-sections

In open channel flows, the critical flow conditions occurred when the specific energy (of the mean flow) is minimum. The critical flow conditions constitute a singularity of the depth-averaged Bernoulli principle for open channel flow. While there is a direct solution of critical flow calculations for rectangular channels, the complete calculations for channels of irregular cross-sections are more complicated.
The calculations of critical flow are conducted iteratively or graphically. In the former, the calculations are typically conducted by trial and error.
Hubert Chanson.

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Hubert Chanson
Hubert Chanson
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).
HENDERSON, F.M. (1966). "Open Channel Flow." MacMillan Company, New York, USA.
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. (2004). "The Hydraulics of Open Channel Flow: An Introduction." Butterworth-Heinemann, 2nd edition, Oxford, UK, 630 pages (ISBN 978 0 7506 5978 9).

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