Acta Mechanica

, Volume 54, Issue 3–4, pp 157–179 | Cite as

Critical flow condition in open channel hydraulics

  • W. H. Hager
Contributed Papers


Transition between sub- and supercritical flows in open channel occurs at the so-called critical point, for which critical flow conditions appear. This particular flow state has been originally introduced for flows with parallel streamlines. However, as streamlines are considerably sloped and inclined in the vicinity of the critical point, these effects have to be accounted for. The present investigation explores in detail these effects. In particular, present investigations include i) first order analysis expressing discharge in terms of upstream head and channel geometry (calibration of discharge measurement structures) and ii) determination of surface profiles for transitional flow states by accounting for the effective pressure and velocity distributions. Analysis is based on a first order model with restriction to typical channel bottom and sidewall geometry. Results are compared with observations, and a fair agreement between the two is noted.


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  1. [1]
    Ali, K. H. M.: Flow over rounded spillways. Proc. ASCE, J. Hydraulics Division98, HY 2, 365–379 (1972).Google Scholar
  2. [2]
    Blau, E.: Die modellmäßige Untersuchung von Venturikanälen verschiedener Größe und Form. (Veröffentlichungen Forschungsanstalt Schiffahrt, Wasser- und Grundbau, Nr. 8). Berlin: Akademie-Verlag 1960.Google Scholar
  3. [3]
    Bos, M. G.: Discharge measurement structures. Laboratorium voor Hydraulica en Afvoerhydrologie, Nr. 4. Nederland: Wageningen 1976.Google Scholar
  4. [4]
    Chow, V. T.: Open channel hydraulics. Tokyo: McGraw-Hill 1959.Google Scholar
  5. [5]
    Diersch, H.-J., Schirmer, A., Busch, K.-F.: Analysis of flow with initially unknown discharge. Proc. ASCE, J. Hydraulics Division103, HY 3, 213–232 (1977).Google Scholar
  6. [6]
    Hager, W. H.: Stau- und Senkungskurven im Kanalbau. Gas-Wasser-Abwasser61, 157–167 (1981).Google Scholar
  7. [7]
    Hager, W. H.: Die Hydraulik von Verteilkanälen. Thesis presented at the Federal Institute of Technology, ETH, Zürich, for the requirements of Doctor of Sciences. Vol. 6948, Parts I & II, Zürich, 1981.Google Scholar
  8. [8]
    Hager, W. H., Hutter, K.: Approximate treatment of hydraulic jump with separation zone above the flow zone. J. Hydraulic Research21, 195–204 (1983).Google Scholar
  9. [9]
    Hager, W. H., Hutter, K.: Approximate treatment of two-dimensional channel, flow. Acta Mechanica51, 31–48 (1984).Google Scholar
  10. [10]
    Hager, W. H., Hutter, K.: On pseudo-uniform flow in open channel hydraulics. Acta Mechanica53, 183–200 (1984).Google Scholar
  11. [11]
    Hager, W. H.: Abflußerscheinungen in offenen Kanälen. Schweizer Ingenieur und Architekt (to be published).Google Scholar
  12. [12]
    Jaeger, C.: Technische Hydraulik. Basel: Birkhäuser 1949.Google Scholar
  13. [13]
    Khafagi, A.: Der Venturikanal. Mittl. Versuchsanstalt Wasserbau, ETH Zürich, Vol. I. Zürich-Leipzig: Leemann & Co. 1942.Google Scholar
  14. [14]
    Khafagi, A., Hammad, S. Z.: Velocity and pressure distributions in curved streamline flow. Water and Water Engineering9, 106–115, 436–445 (1954).Google Scholar
  15. [15]
    Marchi, G., de: Dispositivi per la misura delle portata dei canali con minime perdite di quota. L'Energia Elettrica14, 189–216 (1937).Google Scholar
  16. [16]
    Matthew, G. D.: Discussion to: Potential flow over spillways at low heads, by Lenau, C. W., Proc. ASCE, J. Engineering Mechanics94, EM 1, 354–359 (1968).Google Scholar

Copyright information

© Springer-Verlag 1985

Authors and Affiliations

  • W. H. Hager
    • 1
  1. 1.CCH Institut de Travaux HydrauliquesITH, EPFLLausanneSwitzerland

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