平底抛物线形复合渠道水力最佳断面及实用经济断面统一设计方法

大中型渠道常采用平底抛物线形复合渠道断面形式进行设计,但任意幂律指数的平底抛物线形复合渠道的湿周计算理论上无解析解,致使任意幂律指数的平底抛物线形复合渠道的水力最佳断面及实用经济断面无统一设计方法。现有的文献,仅研究了给定幂律指数情况下的平底抛物线形复合渠道断面,并没进行全局范围内的研究。本文首先采用高斯超几何函数给出了任意幂律指数的平底抛物线形复合渠道湿周的解析计算式,再以水面宽度与水深的比率、渠部底宽与水深的比率及水深为变量,利用拉格朗日乘数法建立了平底抛物线形复合渠道的水力最佳断面求解方程;进一步根据实用经济断面与水力最佳断面的关系建立了平底抛物线形复合渠道的实用经济断面求解方程。本文不仅给出了全范围内连续变化的任意幂律指数的平底抛物线形复合渠道的水力最佳断面及实用经济断面统一设计方法,直接计算公式及数据表格,而且得到了平底抛物线形复合渠道的水力最佳断面中的最优幂律指数为3,从而取得全局水力最佳断面。本文结果可供大中型渠道规划设计参考应用。

Design method for optimal hydraulic cross-section and practically economic cross-section of horizontal-bottomed power-law shaped canals with general exponent parameter

As to large and medium-sized canals, they are often designed in the form of horizontal-bot-tomed Power-Law shaped canals. But there is no analytical solution for all of the wetted-perimeter of hori-zontal-bottomed power-law shaped canals with general exponent parameter. Therefore, its optimal hydraulic cross-section and practically economic cross-section with general exponent parameter is very complicated. In addition,in the literature the optimum hydraulic horizontal-bottomed power-law shaped canals has been de-veloped for only specific exponent m of the power-law formula. In this article,by using Gauss-hypergeomet-ric function, an analytical solution for the integral formula of the wetted-perimeter of horizontal-bottomed power-law section with general exponent parameter is obtained. Taking ratio of water surface width of pow-er-law shaped side to water depth, and ratio of bed width to water depth as variables, hydraulic optimal section parameter can be obtained by using Lagrange multiplier method. The parameter equation of optimal hydraulic cross-section is obtained. According to the relationship between optimal hydraulic cross-section and practically economic cross-section, the parameter equation of practically economic cross-section of any horizontal-bottomed power-law section with general exponent parameter is also obtained. This article not on-ly presents the uniform design method of optimal hydraulic cross-section and practically economic cross-sec-tion about these shaped canals with general exponent parameter, but also gives a super-optimal hydraulic horizontal-bottomed power-law shaped canals''s exponent parameter m=3, where the discharge is largest. This super-optimal hydraulic section presents a new discovery as it provides the global maximum discharge among all possible section shapes. It can be used as reference in the planning and design of large and me-dium-sized canals.