By Chyan-Deng Jan
Gradually-varied move (GVF) is a gradual non-uniform movement in an open channel with sluggish alterations in its water floor elevation. The overview of GVF profiles below a particular circulate discharge is essential in hydraulic engineering. This booklet proposes a singular method of analytically clear up the GVF profiles by utilizing the direct integration and Gaussian hypergeometric functionality. either normal-depth- and critical-depth-based dimensionless GVF profiles are offered. the radical strategy has laid the root to compute at one sweep the GVF profiles in a chain of maintaining and hostile channels, which can have horizontal slopes sandwiched in among them.
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Extra info for Gradually-varied Flow Profiles in Open Channels: Analytical Solutions by Using Gaussian Hypergeometric Function
18) is not necessary. 2. More ETF-based solutions of the two indefinite integrals having M = 3 and five different N -values obtained from the Mathematica software are displayed in Appendix D. It is obvious that these ETF-based analytical solutions, as shown in Appendix D, are lengthy and disorgannized, except Bresse’s solution for the case of M = N = 3. As for the second way to express the solutions of the two integrals using an infinite series, one can also readily obtain the GHF-based solutions of the two integrals from the Mathematica software, as will be elaborated later in Chap.
7 The Equation for GVF in Non-Prismatic Channels A channel that has constant bottom slope and cross-section is termed as a prismatic channel. Most of artificial channels are prismatic channels over long stretches. All natural channels are non-prismatic channels, having varying cross-sections. The GVF equations discussed in previous sections are all in the form of differential equations. This kind of differential GVF equations is suitable for GVF in prismatic channels. However, in a natural channel, the cross-sectional shape and size are likely to vary from section to section, and the cross-sectional information is known only a few locations along the channel.
An alternative practice of accounting for eddy losses is to increase the Mannings roughness coefficient by a suitable small amount. This procedure simplifies calculations in some cases, as pointed out by Subramanya (2009). The problem of computation of the GVF profile in a non-prismatic channel can be stated as: Given the discharge and stage at one section and the cross-sectional information at two adjacent sections, it is required to determine the stage at the other section. The sequential determination of the stage as a solution of the assigned problem will lead to the GVF profile, as mentioned by Chow (1959) and Subramanya (2009).