Application of the Gaussian Hypergeometric Function to Analytically Solve Water Surface Profiles of Gradually-Varied Flows in Circular Channels

• Main Authors: Wan-LingKo, 柯宛伶
• Other Authors: Chyan-Deng Jan
• Format: Others
• Language: zh-TW
• Published: 2013
• Online Access: http://ndltd.ncl.edu.tw/handle/91241986800888747556

碩士 === 國立成功大學 === 水利及海洋工程學系碩博士班 === 101 === Abstract Many hydraulic engineering works involve the computation of surface profiles of one-dimensional gradually-varied flow (GVF) that is a steady non-uniform flow in an open channel with gradual changes in its water surface elevation. Rectangular channels and trapezoidal channels are general in open channel, but circular channels in urban drainage systems are common. Such GVF equation can be analytically integrated by the use of the Gaussian hypergeometric function (GHF) without recourse to the so-called varied-flow function, as done by Jan and Chen (2012). However, their solution is treated with the GVF profile problems of wide rectangular channels, but does not involve the GVF profiles problems of circular channels yet. The characteristics of the analytical solutions of GHF-based GVF profiles in circular channels are discussed in this paper. This paper uses Jan and Chen’s (2012) method to slove circular channels GVF profiles.There are two main focus in this study：1. Based on the simplified, empirical GVF equation (hydraulic exponents are constant M=N=4) presented by Hager (1991), we improve the transformation parameter β (fix the axial distance). 2. Then we compare with Vatankhah and Easa (2013) semi-analytical solution and find the suitable hydraulic exponents (denoted as and ). The results reveal the GHF can appropriately slove circular channels GVF profiles via the validation of case study. Furthermore, compare our method with the Standard Fourth Order Runge-Kutta (SFORK) to discuss their discrepancy and the calculation of time. Key words：Gaussian hypergeometric function, circular channels, gradually-varied flow water profiles, hydraulic exponents