| 简单管水力系统水击的级数解析解 |
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| 引用本文： | 朱永忠,索丽生,张 健.简单管水力系统水击的级数解析解[J].河海大学学报(自然科学版),2007,35(5):577-580. |
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| 作者姓名： | 朱永忠 索丽生 张 健 |
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| 作者单位： | 1. 河海大学理学院,江苏,南京,210098
2. 河海大学水利水电工程学院,江苏,南京,210098 |
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| 基金项目： | 武汉大学水资源与水电工程科学国家重点实验室开放基金资助项目(2006B030) |
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| 摘 要： | 针对简单水力系统的基本方程,考虑阀门按线性关闭历时规律的初始条件和边界条件,利用该偏微分方程组的形式解,推导出时间关于系统末端水击的一阶线性微分方程,从而求解了系统末端水击的隐式解析解.进一步从数学上将水击分解成均具有级数解的两部分,利用三角级数展开的方法分别求解其级数解,最后给出了水击级数解析解的表达式.
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| 关 键 词： | 水击 水力系统 级数解析解 偏微分方程 |
| 文章编号： | 1000-1980（2007）05-0577-04 |
| 修稿时间： | 2006-08-01 |
Series solution to waterhammer of simple pipe hydraulic system |
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| ZHU Yong-zhong,SUO Li-sheng,ZHANG Jian.Series solution to waterhammer of simple pipe hydraulic system[J].Journal of Hohai University (Natural Sciences ),2007,35(5):577-580. |
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| Authors: | ZHU Yong-zhong SUO Li-sheng ZHANG Jian |
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| Institution: | 1. College of Sciences, Hohai University, Nanjing 210098, China; 2. College of Water Conservancy and Hydropower Engineering, Hohai University, Nanjing 210098, China |
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| Abstract: | In consideration of the initial condition and boundary condition for the basic equation of a simple hydraulic system with valves closed linearly,a one-order linear differential equation of time with respect to waterhammer at the end of the system was derived by use of the form solution to the partial differential equations,and the implicit analytical solution to waterhammer was obtained.Furthermore,the waterhammer was divided into two parts with series solutions,and the series solutions were obtained by expansion of trigonometric series.Finally,the series formula for the solution to waterhammer was given. |
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| Keywords: | waterhammer hydraulic system series solution partial differential equation |
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