Hello, all. Now I am reading the book Computational fluid dynamics the basics with applications. And a querry about normal stress appears in page 62.

As mentioned in the book,"normal stress(related to the time rate of charge(should be change)of volume)" and "In most viscous flows, normal stress(such as \tau_{xx})are much smaller than shera streses and many times are neglected". As to the first sentance, for incompressible fluid, I think the normal stress should be zero, because of the constant density \rho. As to the second one, I think the normal stress can be neglected in N-S equation for most viscous flow.

Based on the two points above, I think for imcompressible fluid, the normal stress must be zero and neglected. But in fact, I find it does exist in the equations for imcompressible fluid.(I don't know how to display the equations here)

I want to know more detail about it.

Thank you for your explanation.

While in most viscous flows the normal stress is much smaller than tangential stress, it is not zero. You must have confused the normal stress with the divergence of the velocity field, which is indeed zero for incompressible flows. As an example of the flow for which normall stresses are dominant, consider the flow in the pipe with a rapidly (but smoothly) reducing cross-section. Such flows are called extensional. You can find more info in any introductory Fluid Mechanics book.