Viscosity

 Viscosity

Introduction :  In our daily life we observe certain liquid in motion and experience some difference in their motion. We have seen a water flowing through any surface, flows smoothly  without any friction and on the other hand , a honey do not flow easily. This is because there exist a friction between layer of fluid itself as well as layer of fluid and surface which are in contact. This friction between the layer of fluid is called as Viscosity. Let us understand this topic in detail.

If we observe a river, the water near the bank of river flow with less velocity but as we move in middle of the river the velocity is more. This is due to viscosity which brings relative motion between the layer.

Viscosity : Viscosity is the property of a fluid due to which the relative motion between layer experience a drag force. 

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The viscous flow of different type has been shown in figure below.

Viscous flow : The flow during which layer of the fluid experience frictional force between their layers is called as viscous flow.

Viscous Flow

Non-viscous flow : The flow during which layer of the fluid do not experience any frictional force between their layers is called as non-viscous flow.

Non-Viscous Flow

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 When the fluid flows, the layer which is in contact with the surface in which the fluid is flowing moves with negligible (V=0) velocity .As we move certain distance away from surface the velocity of the layer goes on increasing because the viscous force goes on decreasing. Thus we can say a velocity gradient is developed in the flow. This can be very well understood by the diagram below.

Velocity Gradient

Velocity gradient : The rate of change of velocity(dv) with respect to length(dx) measured from surface is called as Velocity gradient.

Mathematically, 

Velocity gradient = dv/dx

Newton's Law of viscosity

The Viscous force acting on a layer is directly proportional to the area  of the layer and velocity gradient.

F_v  ∝ A ---(1)

The Viscous force acting on a layer is directly proportional to the area  of the layer and velocity gradient.

F_v ∝ dv/dx ---(2)

From (1) and (2)

F_v  ∝ A dv/dx

F_v = ղ A dv/dx ---(3)

Equation (3) gives expression for coefficient of viscosity

where, 

F_v =  Viscous force

ղ = coefficient of viscosity

A = area of the layer

 dv/dx = velocity gradient

│<<< Fluid in motion││ Stoke's law>>>│

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