In a laminar flow between two parallel plates, where one plate is stationary and the other moves at a constant velocity, how does Newton's Law of Viscosity describe the velocity gradient in the fluid?

Explanation:

Viscosity:

Viscosity is the physical property that characterizes the flow resistance of simple fluids.

Newton’s law of viscosity defines, the shear stress between adjacent fluid layers is proportional to the velocity gradients between the two layers.

The ratio of shear stress to shear rate is a constant, for a given temperature and pressure, and is defined as the viscosity or coefficient of viscosity.

Shear stress between two layers of fluid is directly proportional to the rate of change of velocity with respect to perpendicular distance from the fixed point (Velocity Gradient)

\({\rm{\tau \;\propto \;}}\frac{{{\rm{du}}}}{{{\rm{dy}}}}\)

\({\rm{\tau }} = {\rm{\mu \;}}\frac{{{\rm{du}}}}{{{\rm{dy}}}}\)

\({\rm{\mu }} = \frac{{\rm{\tau }}}{{\frac{{{\rm{du}}}}{{{\rm{dy}}}}}}{\rm{\;}}\)

where, τ = Shear stress and \(\frac{{{\rm{du}}}}{{{\rm{dy}}}}\) = Velocity gradient.