Abstract
Critical flow occurs when a set of conditions are fulfilled. These are enumerated in this chapter. Along with these, the critical flow is hydraulically described and the requirements for critical flow are explained in detail. Critical flow is then computed for the three standard cross-sections, namely, the circular, the egg-shaped and the horseshoe sections. The critical energy head and the critical slope are also determined in terms of basic flow parameters.
As an application of the critical flow principle, the transition from a mild to a steep sewer reach is described. This relevant problem can, for all practical purposes, be presented with the aid of simplified relations.
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References
Castro-Orgaz, O., Hager, W.H. (2009). Curved-streamline transitional flow from mild to steep slopes. Journal of Hydraulic Research 47(5): 574–584.
Chadwick, A., Morfett, J. (1996). Hydraulics in civil and environmental engineering. Spon: London.
Chow, V.T. (1959). Open channel hydraulics. McGraw-Hill: New York.
Hager, W.H. (1985). Critical flow condition in open channel hydraulics. Acta Mechanica 54: 157–179.
Hager, W.H. (1987). Übergang von Flach- auf Steilstrecke in Kanalisationen (Transition from mild to steep sewer). Gas-Wasser-Abwasser 67(7): 420–426 [in German].
Hager, W.H. (1990). Froudezahl im Kreisprofil (Froude number in circular conduit). Korrespondenz Abwasser 37(7): 789–791 [in German].
Hager, W.H. (1995). Übergang von Flach- auf Steilstrecken (Transition from mild to steep channels). Wasser und Boden 47(9): 20–24.
Henderson, F.M. (1966). Open channel flow. MacMillan: New York.
Ivicsics, L. (1975). Hydraulic models. Research Institute for Water Resources Development: Budapest.
Kobus, H. (1980). Hydraulic modelling. Pitman: Boston.
Kobus, H., ed. (1984). Symposium on Scale effects in modelling hydraulic structures. Technische Akademie: Esslingen, Germany.
Miller, D., ed. (1994). Discharge measurement structures. IAHR Hydraulic Structures Design Manual 8. Balkema: Rotterdam, The Netherlands.
Naudascher, E. (1987). Hydraulik der Gerinne und Gerinnebauwerke (Hydraulics of channels and channel structures). Springer: Wien, New York [in German].
Novak, P., Cabelka, J. (1981). Models in hydraulic engineering. Pitman: Boston.
Sharp, J.J. (1981). Hydraulic modelling. Butterworths: London.
Westernacher, A. (1965). Abflussbestimmung an ausgerundeten Abstürzen mit Fliesswechsel (Discharge determination at rounded drops involving transcritical flow). Dissertation. TU Karlsruhe, Germany [in German].
Weyermuller, R.G., Mostapha, M.G. (1976). Flow at grade-break from mild to steep slopes. Journal of the Hydraulics Division ASCE 102(HY10): 1439–1448; 103(HY8): 946–947; 103(HY9): 1110–1111; 104(HY2): 307–308.
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Hager, W.H. (2010). Critical Flow. In: Wastewater Hydraulics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-11383-3_6
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DOI: https://doi.org/10.1007/978-3-642-11383-3_6
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