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Coefficient of Viscosity

•    The property by virtue of which, a fluid offers resistance to deformation under the action of a shear is called as viscosity or dynamic viscosity.

•    Consider the behavior of two layers of fluid moving one over other at a distance ‘dy’ apart and having velocities (u + du) and u respectively as shown.

•    As the upper layer moves with higher velocity relative to the lower one, the upper later will also try to move the lower layer with the same velocity. But lower layer, which move with smaller velocity, will appose the motion of upper layer.

•    Thus the relative velocity (du) between two adjacent layers together with viscosity cases shear stress acting between the fluid layers.

•    It means that upper layer which is moving relative faster cases a shear stress on the lower layer in the direction of flow whereas the lower layer causes a shear stress in apposite direction to the upper layer.

•    This tangential stress between two adjoining layers is proportional to velocity gradient (the rate at which velocity changes with the distance across the flow) in a direction perpendicular to the layers. This is known as Newton’s law of viscosity. It is denoted by ζ (Tau).

ζ  ∝ du / dy

ζ  = μ du / dy

Where μ = Coefficient of dynamic viscosity

du / dy = Velocity gradient or rate of shear strain

μ = ζ / (du / dy)

• Thus viscosity is also define, as the shear stress is requried to produce unit rate of shear strain.

S.I. unit of viscosity:

μ = shear stress / (change of velocity / Change of distance) = N / m2 / m/s / m

= N-s / m2 = Newton sec / m2

• The unit of viscosity in CGS is called as poise, which is equal to dyne.sec / cm2

1 poise = 1N-s / 10 m2  or  N-s / m2 = 10 poise

1 centi poise = 1/ 100 poise

• The viscosity of water at 200C is 0.01 poise or 1 centipoise

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