关于不可压缩流体概念的讨论

httpftp

不可压缩流体的定义：流场中各点的密度在运动过程中保持不变的流体称为不可压缩流体。在课堂上大家对这个概念争执的很激烈，在运动过程究竟是流体质点的密度不变还是空间点上（坐标对应的点）的密度不变。希望高手在这里给出不可压缩流体更具体，更容易理解的解释！谢谢！

onesupeng

严格来说，不可压条件满足$d\rho/dt=0$或者$\nabla \cdot \bf{u}=0$，我们从前面一个式子可以看出，不可压的含义是所有流体微团在运动过程中密度不变。举个不太贴切例子，我们所有人在校园里走动，每个人在近似条件下密度体重不变化，这是不可压。但是假如我们体型大小变化了，那么密度就变化了，这是可压。

ycchen100

Read the attached article, and you get a COMPLETE understanding of the issue of incompressible/compressible flow.
The original article has several errors and I have taken the liberty to correct as much as I can. In any case, I take the responsibility, not the original author.
If you still have trouble in understanding this issue and you are in Shanghai, you can come to the "Advanced Fluid Mechanics" course at our uni. We are teaching this part next week.
Below is the mathematical explanation to the original question raised by httpftp:

according to mass conservation:
\nabla \cdot {\bar u} = -\frac{1}{\rho}\frac{D \rho}{D t}
so, if \nabla \cdot {\bar u} = 0, \frac{D \rho}{D t} = 0.
Therefore the answer of onesupeng is correct.[br][br][以下内容由 ycchen100 在 2007年10月26日 07:25pm 时添加] [br]

ycchen100

feigofly

下载看了，谢谢

niuxiying

LBSALE[2]LBSALE我认为，流体的可压与不可压，不应该看流体的密度是否为常数，而应该看密度是否随压力的变化而变化。如果是密度不随压力的变化而变化，则是不可压；反之，则是可压。