Viscosity is defined as the property of fluid which offers resistance to the movement of one layer of fluid over another adjacent layer of the fluid.
When two layers of a fluid, apart by a distance ‘dy’ , move one over the other at different velocities, say u and u+du as shown in figure, the viscosity together with relative velocity cause a shear stress acting between the fluid layers.
The top layer causes a shear stress on the adjacent lower layer while the lower layer causes a shear stress on the adjacent top layer. This shear stress is proportional to the rate of change of velocity with respect to y. It is denoted by τ (Tau)
Mathematically, τ ∝ (du/dy) or τ = μ (du/dy) where μ (mu) is the constant of proportionality and is known as the co-efficient of dynamic viscosity or only viscosity. (du/dy) represents the rate of shear strain or rate of shear deformation or velocity gradient.
We have, μ=[τ/(du/dy)]
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