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Hydrology and Earth System Sciences An interactive open-access journal of the European Geosciences Union
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Volume 17, issue 3
Hydrol. Earth Syst. Sci., 17, 973–987, 2013
https://doi.org/10.5194/hess-17-973-2013
© Author(s) 2013. This work is distributed under
the Creative Commons Attribution 3.0 License.
Hydrol. Earth Syst. Sci., 17, 973–987, 2013
https://doi.org/10.5194/hess-17-973-2013
© Author(s) 2013. This work is distributed under
the Creative Commons Attribution 3.0 License.

Research article 05 Mar 2013

Research article | 05 Mar 2013

Gradually varied open-channel flow profiles normalized by critical depth and analytically solved by using Gaussian hypergeometric functions

C.-D. Jan1 and C.-L. Chen2,† C.-D. Jan and C.-L. Chen
  • 1Department of Hydraulic and Ocean Engineering, National Cheng Kung University, Tainan 70101, Taiwan
  • 2Consulting Hydrologist, Cupertino, California, USA
  • Deceased

Abstract. The equation of one-dimensional gradually varied flow (GVF) in sustaining and non-sustaining open channels is normalized using the critical depth, yc, and then analytically solved by the direct integration method with the use of the Gaussian hypergeometric function (GHF). The GHF-based solution so obtained from the yc-based dimensionless GVF equation is more useful and versatile than its counterpart from the GVF equation normalized by the normal depth, yn, because the GHF-based solutions of the yc-based dimensionless GVF equation for the mild (M) and adverse (A) profiles can asymptotically reduce to the yc-based dimensionless horizontal (H) profiles as yc/yn → 0. An in-depth analysis of the yc-based dimensionless profiles expressed in terms of the GHF for GVF in sustaining and adverse wide channels has been conducted to discuss the effects of yc/yn and the hydraulic exponent N on the profiles. This paper has laid the foundation to compute at one sweep the yc-based dimensionless GVF profiles in a series of sustaining and adverse channels, which have horizontal slopes sandwiched in between them, by using the GHF-based solutions.

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