Principal Stresses in a Shear Flow

[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.

 

[Chestermiller]

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?