欧拉法01：自相交曲线 交点处存在两类不同的切矢量01 切点处的两个芽空间01 同一时刻的不同流线互不相交。因为根据流线定义，在

自相交曲线 交点处存在两类不同的切矢量

[PDF]

第3 章流体运动基本原理

new.hep.com.cn/datastar/getresource?objectid=B3E92AB0-7B8A-11DF...

得其曲线方程

 

 

 

 

。

1

 

．流线

流线

 

（ｓｔｒｅａｍｌｉｎｅ）是表示某一瞬时流体各点流动趋势的曲线，位于曲线上的

任一质点在该时刻的速度矢量

 

，都与曲线相切（图３ －６）。它描述了流场中不同

质点在同一时刻的运动状况

 

。若在水流中撒上与水同密度的荧光粉，然后曝光

摄影

 

，每一微粒的影像是一条短线，据此绘出曲线，且满足曲线上的每一短线都

与之相切

 

，则此曲线便是流线。当流速矢量随时间变化时，不同时刻的流线各不

相同

 

。流线是欧拉法分析流动的重要概念。

（１）

 

流线的绘制方法可参见图３ －６。在流场中任取一点，绘出某时刻通过

该点的流体质点的流速矢量

 

u，再画出距１ 点很近的２ 点在同一时刻通过该处

的流体质点的流速矢量

 

u２ ，如此继续下去，得一折线１２３４…，若各点无限接近，

其极限就是某时刻的流线

 

。

（２）

 

流线的性质：

①

 

同一时刻的不同流线互不相交。因为根据流线定义，在交点的流体质点

的流速矢量应同时与这两条流线相切

 

，而一个质点不可能同时有两个速度矢量

（

 

图３ －７）。

 

 

图３ －６ 某时刻流线图图３ －７ 流线不能相交

②

 

流线不能是折线，而是一条光滑的曲线。这是因为流体是连续介质，各

运动要素是空间的连续函数

 

。

③

 

对不可压缩流体，流线簇的疏密反映了速度的大小。流线密集的地方流

速大

 

，稀疏的地方流速小。

 

所有跟帖： 

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• eurobank01 www.voxeu.org The debt fears reach the core -marketreflections- ♂ (8787 bytes) () 08/11/2011 postreply 12:07:55

• economist01 Stephen King Mike Dolan macro01 Bretton Woods II. -marketreflections- ♂ (7375 bytes) () 08/11/2011 postreply 05:29:19

• fx01 Robert Sinche The volatility will move on to the equities -marketreflections- ♂ (23798 bytes) () 08/11/2011 postreply 06:11:55

• fx01 Adarsh Sinha When the slowdown spreads to the rest of the w -marketreflections- ♂ (14248 bytes) () 08/11/2011 postreply 06:22:07

• 掌控华尔街交易的计算机算法 -marketreflections- ♂ (11995 bytes) () 08/01/2011 postreply 21:57:25