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