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.
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.
出处
《河海大学学报（自然科学版）》
CAS
CSCD
北大核心
2007年第5期577-580,共4页
Journal of Hohai University(Natural Sciences)
基金
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)
关键词
水击
水力系统
级数解析解
偏微分方程
waterhammer
hydraulic system
series solution
partial differential equation
