Why are shear stresses zero in a fluid that is at rest?

In fluid mechanics, fluids are defined by their inability to resist deformation; they yield to shear stress regardless of how small that stress may be. This resistance to deformation is characterized by the fluid's viscosity, which represents the internal friction that arises when adjacent layers of fluid slip over one another.1

Because shear stress is directly related to the rate at which these layers slip—or the rate of deformation—it follows that in a fluid at rest, there is no relative motion between adjacent layers. Since there is no slip and no rate of deformation, the shear stresses are everywhere zero. Consequently, a fluid in equilibrium is characterized by hydrostatics, where the only stress acting on the fluid is pressure, which acts equally in all directions regardless of orientation, as described by Pascal’s law.213