Computation of Steady Gradually-Varied Flows

  • Oscar Castro-OrgazEmail author
  • Willi H. Hager


Steady open channel flow is generally non-uniform. In gradually-varied flows, the changes of depth and velocity in space are small, so that streamline curvature effects can be neglected. If the channel bottom slope is small, then the hydrostatic vertical pressure distribution prevails.


  1. Apelt, C. J. (1971). Numerical integration of the equation of gradually varied and spatially varied flow. In: Proceedings of 4th Australasian Conference on Hydraulics and Fluid Mechanics, Monash University, Melbourne, Australia (pp. 146–153).Google Scholar
  2. Bakhmeteff, B. A. (1912). O нepaвнoмepнoм движeнии жидкocти в oткpытoм pycлe [Varied flow of liquids in open channels]. St Petersburg, Russia (in Russian).Google Scholar
  3. Bakhmeteff, B. A. (1932). Hydraulics of open channels. New York: McGraw-Hill.Google Scholar
  4. Bélanger, J. B. (1828). Essai sur la solution numérique de quelques problèmes relatifs au mouvement permanent des eaux courantes [On the numerical solution of some steady water flow problems]. Carilian-Goeury, Paris (in French).Google Scholar
  5. Bresse, J. (1860). Cours de mécanique appliquée, 2ème partie: Hydraulique [Lecture notes on applied mechanics, Part 2, Hydraulics]. Paris: Mallet-Bachelier (in French).Google Scholar
  6. Brunner, G. W. (2016). HEC-RAS River Analysis System Hydraulic Reference Manual. Report CPD69, Version 5.0, US Army Corps of Engineers, Hydrologic Engineering Center (HEC), Davis, CA.Google Scholar
  7. Chanson, H. (2004). The hydraulics of open channel flows: An introduction. Oxford, UK: Butterworth-Heinemann.Google Scholar
  8. Chapra, S. C., & Canale, R. P. (2010). Numerical methods for engineers (6th ed.). New York: McGraw-Hill.Google Scholar
  9. Chaudhry, M. H. (2008). Open-channel flow (2nd ed.). New York: Springer.CrossRefGoogle Scholar
  10. Chow, V. T. (1959). Open channel hydraulics. New York: McGraw-Hill.Google Scholar
  11. Fenton, J. D. (2010). Calculating resistance to flow in open channels. Technical Report, Alternative Hydraulics Paper 2, Vienna University of Technology, Vienna, Austria.Google Scholar
  12. Fread, D. L., & Harbaugh, T. E. (1971). Open-channel profiles by Newton’s iteration technique. Journal of Hydrology, 13, 78–80.CrossRefGoogle Scholar
  13. Hager, W. H. (2010). Wastewater hydraulics: Theory and practice (2nd ed.). Berlin: Springer.CrossRefGoogle Scholar
  14. Hasumi, M. (1931). Untersuchungen über die Verteilung der hydrostatischen Drücke an Wehrkronen und -Rücken von Überfallwehren infolge des abstürzenden Wassers [Studies on the distribution of hydrostatic pressure distributions at overflows due to water flow]. Journal of the Department of Agriculture, Kyushu Imperial University 3(4), 1–97 (in German).Google Scholar
  15. Henderson, F. M. (1966). Open channel flow. New York: MacMillan Co.Google Scholar
  16. Hoffman, J. D. (2001). Numerical methods for engineers and scientists (2nd ed.). New York: Marcel Dekker.zbMATHGoogle Scholar
  17. Jaeger, C. (1956). Engineering fluid mechanics. Edinburgh: Blackie and Son.Google Scholar
  18. Jain, S. C. (2001). Open channel flow. New York: Wiley.Google Scholar
  19. Jan, C.-D. (2014). Gradually-varied flow profiles in open channels: Analytical solutions by using Gaussian hypergeometric function. Advances in Geophysical and Environmental Mechanics and Mathematics. Berlin: Springer.CrossRefGoogle Scholar
  20. Jeppson, R. (2011). Open channel flow: Numerical methods and computer applications. Boca Raton: CRC Press.Google Scholar
  21. Katopodes, N. D. (2019). Free surface flow: Shallow-water dynamics. Oxford, UK: Butterworth-Heinemann.Google Scholar
  22. Lee, M. T., Babbitt, H. E., & Baumann, E. R. (1952). Gradually varied flow in uniform channels on mild slopes. Engineering Experiment Station Bulletin Nº 404, University of Illinois at Urbana Champaign, College of Engineering, Engineering Experiment Station.Google Scholar
  23. Montes, J. S. (1998). Hydraulics of open channel flow. Reston, VA: ASCE.Google Scholar
  24. Puertas, J., & Sánchez, M. (2001). Apuntes de Hidráulica de canales [Open channel hydraulics lecture notes]. Civil Engineering School, University da Coruña, Spain (in Spanish).Google Scholar
  25. Rouse, H. (1938). Fluid mechanics for hydraulic engineers. New York: McGraw-Hill.Google Scholar
  26. Rouse, H. (1950). Engineering hydraulics. New York: Wiley.Google Scholar
  27. Rouse, H. (1965). Critical analysis of open-channel resistance. Journal of the Hydraulics Division, ASCE, 91(HY4), 1–25.Google Scholar
  28. Sturm, T. W. (2001). Open channel hydraulics. New York: McGraw-Hill.Google Scholar
  29. Subramanya, K. (1986). Flow in open channels. New Delhi: Tata McGraw-Hill.Google Scholar
  30. White, F. M. (1991). Viscous fluid flow. New York: McGraw-Hill.Google Scholar
  31. White, F. M. (2003). Fluid mechanics. New York: McGraw-Hill.Google Scholar
  32. Woodward, S. M., & Posey, C. J. (1941). Hydraulics of steady flow in open channels. New York: Wiley.zbMATHGoogle Scholar
  33. Yen, B. C. (1973). Open-channel flow equations revisited. Journal of the Engineering Mechanics Division, ASCE, 99(EM5), 979–1009.Google Scholar
  34. Yen, B. C. (1991). Hydraulic resistance in open channels. In B. C. Yen (Ed.), Channel flow resistance: Centennial of Manning’s formula (pp. 1–135). Highlands Ranch, USA: Water Resources Publications.Google Scholar
  35. Yen, B. C. (2002). Open channel flow resistance. Journal of Hydraulic Engineering, 128(1), 20–39.CrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.University of CórdobaCórdobaSpain
  2. 2.VAW, ETH ZürichZürichSwitzerland

Personalised recommendations