| 引用本文: | 李 刚,何武全,翟东汉.基于拉格朗日法的抛物线形复合渠道的水力最佳断面[J].灌溉排水学报,2017,36(11):51-55. |
| LI Gang,HE Wuquan,ZHAI Donghan.基于拉格朗日法的抛物线形复合渠道的水力最佳断面[J].灌溉排水学报,2017,36(11):51-55. |
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| 摘要: |
| 针对标准抛物线形渠道渠口宽、深度大、难以适应大中型渠道等问题，提出了一种新型平方抛物线形渠坡和水平渠底的抛物线形复合渠道，同时推导出了抛物线复合渠道水力要素计算公式，并以水深、水面宽度和水平渠底宽度为变量，利用拉格朗日乘数法建立求最优解的迭代方程，借助Mathcad数学软件进行计算，推导出了抛物线复合渠道水力最佳断面情况下流量和水深的关系式以及水深、水面宽度、过水断面面积和湿周的计算公式。通过实例计算，当流量Q为12 m3/s时，在水力最佳断面情况下抛物线复合渠道的水深H0为2.263 m，水面宽度B0为4.538 m，过水断面面积A0为7.463 m2。结果表明，相同流量下抛物线复合渠道的过水断面面积比梯形渠道减小了1.67%，比弧脚梯形渠道减小了0.84%，比抛物线形渠道减小了1.05%，表明抛物线形复合渠道是更为优越的渠道断面形式。 |
| 关键词: 水力最佳断面； 拉格朗日乘数法； 水力计算 |
| DOI：10.13522/j.cnki.ggps.2017.11.010 |
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| Calculating Optimal Channel Cross Section with Parabolic Slope and Flat Bed Using the Lagrangian Method |
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LI Gang, HE Wuquan, ZHAI Donghan
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College of Water Resources and Architectural Engineering , Northwest A &F University, Yangling 712100, China: The Ministry of Education Key Laboratory of Agricultural Water and Soil Engineering, Yangling 712100, China
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| Abstract: |
| Channels with parabolic cross section are deep and widely open, not suitable for use in medium-large canals. In this paper, we present a channel with parabolic slopes and flat bed and then calculated its hydraulic parameters. Taking water depth and widths of water surface and channel bed as variables, we calculated the relationship between flow rate and water depth after optimizing the channel cross section using the Lagrangianiterative method and the Mathcad software. The dependence of wetting perimeter of the channel on water depth and widths of water surface and channel bed was also analyzed. Numerical calculations showed that when the optimal flow rate was 12 m3/s, the associated water depth was 2.263 m, the width of water surface was 4.538 m, and the cross-section area for water flow was 7.463 m2. This means a reduction in water-flow cross section by 1.67% compared to trapezoidal cross section, 0.84% compared to cross section with trapezoidal slopes and parabolic bed, and 1.05% compared toparabolic cross section. |
| Key words: channel; optimal hydraulic section; Lagrange multiplier method; hydraulic calculation |
