Viscosity

Introduction - we always see that our sandal is worn out, our bicycle tires are worn. This is because of frictions. Similar friction occurs in liquid’s different layers. In case of liquid; this friction is termed as viscosity.

Concept of viscosity

Consider two plates, Plate-1 is fixed & plate-2 is free to move. If some oil is present between two plates; then plate-2 moves with certain velocity. Now if oil is replaced by "honey" then greater force is required to move plate-2. This shows that honey is more viscous than oil.

Now let us consider Layer L₁, L₂ & L₃ moving with velocities V-dv, V & V+dv respectively. Layer L₃, forces layer L₂ to move with its velocity at the same time layer L₁, pulls L2 in backward direction. As a result of which there is the opposition to relative motion between them. Hence friction is created between two liquid layers; which is called viscous force.

Viscous force - The force that opposes relative motion between two layers of liquid is called viscous force or viscous drag.

Viscosity - It is a property of fluid to which liquid layers tend to oppose the relative motion between them.

Velocity gradient

Velocity gradient is defined as change in velocity; per unit Change in distance between two adjacent layers.

from figure above

change in velocity = V + dv – V = dv

distance bet two adjacent layer = dx 

Newton's law of viscosity 

This law states that the viscous force “F” is

1. Directly proportional to surface area in contact (A) of liquid layer.
2. Directly proportional to velocity gradient.
   
3. Also depend upon; nature & temperature of liquid.
   

where η = co-efficient of viscosity.

Negative sign indicates that viscous force is backward dragging force.

        therefore; co-efficient of viscosity is defined as viscous force per unit area having velocity gradient equal to unity.