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Oct 1, 2006

Minimum Specific Energy and Critical Flow Conditions in Open Channels

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Publication: Journal of Irrigation and Drainage Engineering
Volume 132, Issue 5

Abstract

In open channels, the relationship between the specific energy and the flow depth exhibits a minimum, and the corresponding flow conditions are called critical flow conditions. Herein they are reanalyzed on the basis of the depth-averaged Bernoulli equation. At critical flow, there is only one possible flow depth, and a new analytical expression of that characteristic depth is developed for ideal-fluid flow situations with nonhydrostatic pressure distribution and nonuniform velocity distribution. The results are applied to relevant critical flow conditions: e.g., at the crest of a spillway. The finding may be applied to predict more accurately the discharge on weir and spillway crests.

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Acknowledgments

The writer thanks Dr. Sergio Montes (The University of Tasmania) for many helpful exchanges and discussion. He thanks further Professor A. S. Ramamurthy (Concordia University, Canada) for providing the original data of his former Ph.D. student (Vo 1992) and Professor C. J. Apelt (The University of Queensland) for helpful comments.

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, 1st Ed., McGraw–Hill, New York.
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 (in French).
Chanson, H. (1999). The hydraulics of open channel flows: An introduction, 1st Ed., Edward Arnold, London.
Chanson, H. (2004). The hydraulics of open channel flows: An introduction, 2nd Ed., Butterworth-Heinemann, Oxford, U.K.
Chanson, H., and Montes, J. S. (1998). “Overflow characteristics of circular weirs: Effects of inflow conditions.” J. Irrig. Drain. Eng., 124(3), 152–162.
Fawer, C. (1937). “Etude de quelques ecoulements permanents à filets courbes.” (‘Study of some steady flows with curved streamlines.’) Thesis, Imprimerie La Concorde, Lausanne, Switzerland (in French).
Henderson, F. M. (1966). Open channel flow, MacMillan, New York.
Jaeger, C. (1956). Engineering fluid mechanics, Blackie & Son, Glascow, U.K.
Liggett, J. A. (1993). “Critical depth, velocity profiles and averaging.” J. Irrig. Drain. Eng., 119(2), 416–422.
Ramamurthy, A. S., Vo, N.-D., and Vera, G. (1992). “Momentum model of flow past weir.” J. Irrig. Drain. Eng., 118(6), 988–994.
Rouse, H. (1946). Elementary mechanics of fluids, Wiley, New York.
Vallentine, H. R. (1969). Applied hydrodynamics, SI Ed., Butterworths, London.
Vo, N. D. (1992). “Characteristics of curvilinear flow past circular-crested weirs.” Ph.D. thesis, Concordia Univ., Canada.

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Go to Journal of Irrigation and Drainage Engineering
Journal of Irrigation and Drainage Engineering
Volume 132Issue 5October 2006
Pages: 498 - 502

History

Received: Jun 2, 2005
Accepted: Dec 9, 2005
Published online: Oct 1, 2006
Published in print: Oct 2006

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Reader, Environmental Fluid Mechanics, Dept. of Civil Engineering, The Univ. of Queensland, Brisbane QLD 4072, Australia. E-mail: [email protected]

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