Doubt & Answer Explanation

Answer Explanation

In general, in any flow, layers move at different velocities
and the fluid's viscosity arises from the shear stress between the
layers that ultimately opposes any applied force. The relationship
between the shear stress and the velocity gradient can be obtained by
considering two plates closely spaced at a distance y, and separated by a homogeneous substance. Assuming that the plates are very large, with a large area A, such that edge effects may be ignored, and that the lower plate is fixed, let a force F
be applied to the upper plate. If this force causes the substance
between the plates to undergo shear flow with a velocity gradient u/y (as opposed to just shearing elastically until the shear stress in the substance balances the applied force), the substance is called a fluid.

The applied force is proportional to the area and velocity gradient in the fluid:

,

where ? is the proportionality factor called dynamic viscosity.

This equation can be expressed in terms of shear stress . Thus as expressed in differential form by Isaac Newton for straight, parallel and uniform flow, the shear stress between layers is proportional to the velocity gradient in the direction perpendicular to the layers:

Hence, through this method, the relation between the shear stress and the velocity gradient can be obtained.

Note that the rate of shear deformation is which can be also written as a shear velocity, .