# Principal Stresses in a Shear Flow

• Kushwoho44
In summary, the conversation discussed principal stresses, which are present when there are no shear stresses and only normal stresses in a 2D system. This can be seen in a solid under external forces. However, in a laminar viscous flow, it can be confusing to understand how there can be principal stresses and strains due to the presence of shear between the lamina of the material. The suggestion was made to consider the analogous case for a Hookean solid or to look at the simple shear deformation of a solid between two infinite parallel plates.

#### Kushwoho44

Hi,

I was thinking about principal stresses and unfortunately this is a bit of a dark spot for me in my education.

I understand principal stresses as the stresses that are present when the co-ordinate system is oriented such that there are no shear stresses, and only normal stresses. As such, for a 2D system, there will two principal axis, which are orthogonal and one of these axis will contain the maximum stress and the other the minima. In the case of a solid under external forces, I can understand this situation.

However, I am a bit confused in even a simple laminar viscous flow, say 2D in a pipe for simpilcity. I cannot visualise a co-ordinate system here where there will be no shear, as there is shear between the lamina of the material, so how can there be principal stresses and strains?

Kind regards.

Joe591
Why not consider the analogous case for a Hookean solid and see how it works out? Or better yet, just look at the simple shear deformation of a solid between two infinite parallel plates. For such a case, what are the components of the strain tensor and the stress tensor in terms of the displacement V of the upper plate?

Lnewqban