Hydraulic analysis of a 2-D water flow down a slope

• Main Authors: Pei-Yuan Hsu, 徐培原
• Other Authors: Ping-Cheng Hsieh
• Format: Others
• Language: zh-TW
• Published: 2015
• Online Access: http://ndltd.ncl.edu.tw/handle/86587545632846223599

碩士 === 國立中興大學 === 水土保持學系所 === 103 === In this study, the flow field is divided into two regions (the water layer and soil layer). By additionally considering the vertical velocity and the inertia force, we were aimed at having a deeper discussion on the water flow down a slope. Considering the vertical velocity of the flow, we searched for a new way to derive horizontal and vertical velocity distribution both in the water and soil layers. In this article, the soil layer is regarded as a porous media so that the nonzero velocity at the ground surface could be expected. In the water layer, we adopt the Navier-Stokes equation to describe the motion of the water flow, while in the soil layer, Song’s (1993) laminar model based on Biot’s poroelastic theory (1956b) is chosen. With the velocity type set by Desseaux (1999), we derive a couple of nonlinear ordinary differential equations which are solved by taking the Differential Transform Method (DTM) proposed by Arikoglu & Ozkol (2006). Finally, we derive the horizontal and vertical velocity distributions and some other physical quantities. After the analytical solution is obtained, we select the relevant parameters and then the velocity, shear stress, and normal stress distributions can be discussed. We find that the vertical velocity is actually far less than the horizontal velocity, and is about 0.1% of the horizontal one. Besides, we also find that at x=0 , the horizontal velocity considering inertia force is 0.3 time more than neglecting the inertial force. In this research, we focus on the distribution of horizontal and vertical velocity, and the results compared with the previous research are acceptable. Because we don’t neglect the vertical velocity of flow, as a result, not only the difficulty is more than ever, but also we have to search more relevant methods and theories in the literature. The results of this study are inspiring and show a new way of the future research on the overland flow.