Viscosity

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.

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.

Figure

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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