抛物线类渠道水力最佳及实用经济断面统一设计方法  

Optimal Design of Hydraulic and Practical Cross-section of Parabolic Canals

作　　者：陈柏儒 王羿[1,2] 赵延风[1,2] 王正中[1,2,3] CHEN Bairu;WANG Yi;ZHAO Yanfeng;WANG Zhengzhong(College of Water Resources and Architectural Engineering,Northwest A ＆ F University,Yangling 712100,China;Cold and Arid Regions Water Engineering Safety Research Center,Northwest A ＆ F University,Yangling 712100,China;State Key Laboratory of Frozen Soils Engineering,Cold and Arid Region Environmental and Engineering Research Institute,CAS,Lanzhou 730000,China)

机构地区：[1]西北农林科技大学水利与建筑工程学院,陕西杨凌712100 [2]西北农林科技大学旱区寒区水工程安全研究中心,陕西杨凌712100 [3]中国科学院寒区旱区环境与工程研究所冻土工程国家重点实验室,兰州730000

出　　处：《灌溉排水学报》2018年第9期91-99,共9页Journal of Irrigation and Drainage

基　　金：国家"十三五"重点研发计划重点专项(2017YFC0405103);国家自然科学基金项目(51279168)

摘　　要：【目的】解决任意次抛物线形渠道湿周积分公式为不可积分而导致水力最佳及实用经济断面无解析解的问题。【方法】采用高斯超几何函数给出了任意次抛物线形渠道湿周的解析计算式,以水深、水面宽度为变量,用拉格朗日乘数法对该类渠道的水力最佳断面参数进行求解。【结果】得到了任意次抛物线类渠道的水力最佳断面参数求解方程,再根据实用经济断面与水力最佳断面的关系得到了任意次抛物线类渠道的实用经济断面参数求解方程。最后给出抛物线类渠道实用经济断面水面宽度与水深的比值的关系表。【结论】该方法易于设计任意次抛物线类水力最佳及实用经济断面,可供渠道规划设计参考应用,也为规范修订提供理论依据。【Objective】There are no analytical solutions to calculate the wetted perimeter in parabolic canals and this paper is to present an alternative method to calculate the hydraulic and practical cross section of the parabolic canals.【Method】The proposed method was based on the Gauss-hypergeometric function, from which the exact solutions for the wetted-perimeter of the canals with parabolic cross section was obtained. Taking water depth and width of the water surface as variables, the optimal hydraulic cross-section can be obtained by using the Lagrange multiplier method.【Result】Based on the relationship between the practically economic cross section and the optimal hydraulic cross-section, the practically economic cross-section parametric equation for the parabolic canal was obtained. The datum table of the ratio between the water width and the water depth of the practically economic cross-section of parabolic canals was provided.【Conclusion】The proposed method is easy to be used to design the optimal hydraulic cross-section and practically economic cross-section of any parabolic canals. It can also be used as a tool in channel planning and design, and provided a theoretical basis for revising standards.

关 键 词：抛物线类渠道 高斯超几何函数 水力最佳断面 实用经济断面 明渠水力学 统一设计方法 

分 类 号：S277[农业科学—农业水土工程] TV131.4[农业科学—农业工程]