Abstract
Abstract. The equation of one-dimensional gradually-varied flow (GVF) in sustaining and non-sustaining open channels is normalized using the critical depth, hc, 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 hc-based dimensionless GVF equation is more useful and versatile than its counterpart from the GVF equation normalized by the normal depth, hn, because the GHF-based solutions of the hc-based dimensionless GVF equation for the mild (M) and adverse (A) profiles can asymptotically reduce to the hc-based dimensionless horizontal (H) profiles as hc/hn → 0. An in-depth analysis of the hc-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 hc/hn and the hydraulic exponent N on the profiles This paper has laid the foundation to compute at one sweep the hc-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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