Shapes of canal cross sections affect their discharge capacity, water depth and construction cost. Researches have shown that the curve-shaped canal such as quadratic parabolic and semi-cubic parabolic shape has good hydraulic property. However, the less smooth base of the quadratic parabolic and semi-cubic parabolic shape canal can affect the discharge capacity. To improve the hydraulic property and increase the discharge of the quadratic parabolic sections of canals, a section with two and a half parabola shape was proposed in this paper. Formulas for flow area, shape factor and water surface width for this new section were derived. The theoretical formula for the wetted perimeter was deduced using Gauss super-geometric functions. A model of the optimum hydraulic section that minimized the flow area for a given discharge was developed based on the Manning formula. The partial differential equation for the optimum hydraulic section was deduced using Lagrange's multiplier method. After substituting the derivatives of wetted perimeter and flow area with respect to water depth and water surface width into this partial differential equation, the optimum model was successfully converted into an equation about the water surface width-depth ratio. Various explicit formulas to compute the characteristic's parameters such as wetted perimeter, shape factor, flow area, normal water depth and critical water depth for the best hydraulic section were obtained. Using these formulas, the hydraulic design could be achieved easily. The results showed that the best ratio of water surface width-depth ratio for the optimum hydraulic section of the two and a half parabola-shaped canal was a constant (2.0883). The two and a half parabola-shaped canal had better hydraulic properties than that with quadratic or semi-cubic parabolic sections. Comparisons with quadratic and semi-cubic parabolic sections showed that the flow discharge of the two and a half parabola-shaped section was the largest under the same water depth, which means it is an economical section. Under the same discharge, the water depth of the two and a half parabola-shaped section was smaller than the quadratic parabolic and semi-cubic parabolic sections. The flow area, wetted perimeter and water surface width of the two and a half parabola-shaped section was the least under the same discharge among the three sections. Minimum wetted perimeter and flow area implied that the cost of construction (excavation and lining cost) was minimized. In theory, the comparisons with quadratic and semi-cubic parabolic sections also showed that the construction cost of the proposed best hydraulic section was the lowest under the same discharge. To aid practical use, the 3- point and 4-point method of Gauss-Legendre approximate algorithm were presented for the wetted perimeter calculation. The application example with the water depth of 1.0-3.5 m showed that the approximate algorithm was highly accurate. The 3-point approximate format formula could meet the practical use and design with the maximum absolute error of 0.00401 m. The results from the 4-point format formula almost equaled to those of the theoretical results with the maximum absolute error of 0.00097 m. This research provides a theoretical basis for the design of the two and a half parabola-shaped canals with improved hydraulic properties.%为提高抛物线形断面的水力特性,增加输水能力,该文提出了一种二分之五次(以下简称2.5次)方抛物线形渠道断面,推导其水力断面特性.将湿周用高斯超几何函数表示后,将水力最优断面的最优化模型转换为关于宽深比的一元方程,得到2.5次方抛物线形渠道水力最优断面的解析解,其最优宽深比为2.0883.比较结果表明,2.5次方抛物线形断面较常规抛物线形断面具有更好的水力学特性.与平方、半立方抛物线形断面比较,在相同水深条件下,2.5次方抛物线形水力最优断面的过流能力更大.相反,在相同流量下,2.5次方抛物线形水力最优断面的过流面积、湿周、水深更小.2.5次方抛物线形水力最优断面的建造成本与其他2种断面相比是最小的.进一步地,为便于工程应用,基于高斯勒让德算法,提出2.5次方抛物线形断面的三点和四点格式近似湿周算法.结果表明,四点格式近似算法具有较高精度.研究可为明渠设计提供理论依据.
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