# Viscosity | Newton’s Law of Viscosity, Coefficient of Viscosity | Physics Grade 11 Notes

### Fluid Mechanics

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#### Kinematics

Introduction to Kinematics

# Viscosity | Newton’s Law of Viscosity, Coefficient of Viscosity

Viscosity: The property of a fluid by virtue of which an internal friction comes into play when the fluid is in motion and opposes the relative motion of its different layers is called viscosity.

Newton’s Law of Viscosity, Coefficient of Viscosity

P + 1/2 . ϱv2 = constant Consider a liquid flowing steadily over a fixed solid horizontal surface as shown in the figure. Every layer of liquid moves parallel to the fixed surface. The layer in contact with the fixed surface is at rest while the velocity of other layers increases uniformly upwards. Consider two layers AB and CD moving with velocity v and v + dv at a distance x and x + dx respectively from the fixed solid surface.

The change of velocity divided by the distance, dv/dx, in a direction perpendicular to the velocity is called the velocity gradient.

According to newton, the viscous force F depends upon the following factors:

• It is directly proportional to area A or the layers in contact. i.e; F α A
• It is directly proportional to the velocity gradient between the layers. i.e; F α dv/ dx
Combining these two factors, we have
F α A dv/ dx
F = - η A dv/ dx …... (i)
Where η is the constant of proportionality called coefficient of viscosity. Its value depends upon the nature of the liquid. If A = 1 and dv/ dx = 1.

Then, from equation (i), we have
η = -F

Hence, the coefficient of viscosity of a liquid is defined as the viscous drag or viscous force acting per unit area of the layer having unit velocity gradient perpendicular to the direction of the flow of the liquid.

Units of coefficient of viscosity is dyne. S. cm-2 or poise in CGS system and N s m-2 or decapoise for SI system. Dimensional formula of η is [M L-1 T-1]

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