Why fluids cannot maintain a shear stress? Why only perpendicular force component is considered?

Question

In the definition of pressure, force/area, force is required to be the magnitude of force component perpendicular to the area element. Why here, the parallel component does not play any role? The book says "fluid cannot maintain a shear stress" where shear stress is produced by tangential (parallel) force. Why is that?

Answer 1

Fluids flow!

Shear stress is the kind of force which makes one part of a body slide past another part. In the case of solids, the internal forces oppose such relative motion, so any shear stress applied at the outside of the body is opposed inside the body by an equal and opposite shear stress (in the static case).

In the case of a fluid, the response to a shear stress applied to the fluid is that one part of the fluid flows past another part. Real fluids have viscosity, which means there is an internal shear stress opposing this relative motion, but not so much as to prevent it completely. But in the limit where the viscosity is negligible, we have what is called a 'perfect fluid,' and then there are no viscous forces. In this case, a shear stress applied from outside causes relative acceleration between one layer of fluid and another. This is perfectly possible. It means there is no internal stress, but there is this acceleration.

In static conditions, or in conditions of laminar flow without acceleration of one layer relative to another, we have, by definition, no acceleration of that kind, so then it must be that in the case of a perfect fluid, no shear stress is being applied.