Viscosity

When liquid taken in a beaker is stirred with a glass rod in the middle, the motion of the liquid near the walls and in the middle is not same. In the flow of two liquids (glycerin and water) through identical pipes, water flows rapidly out of the vessel whereas glycerin flows slowly.

These observations indicate a characteristic property of the liquid that determines their motion. This property is known as viscosity.

Whenever a fluid flows, two adjacent layers of the fluid exert a tangential force on each other. This force acts as a drag and opposes the relative motion between them. The property of a fluid by virtue of which it opposes the relative motion in its adjacent layers is known as viscosity.

The viscous force F between two layers of the fluid is proportional to

• area (A) of the layer in contact: F ∝ A
• velocity gradient (dv/dx) in a direction perpendicular to the flow of liquid: F ∝ dv/dx

On combining these,

F ∝ A dv/dx

F = – η A (dv/dx)

where η is constant of proportionality and is called coefficient of viscosity. The negative sign indicates that force is frictional in nature and opposes motion. 

The SI unit of coefficient of viscosity is Nsm^–2. In cgs system, the unit of viscosity is poise.

1 poise = 0.1 Nsm^–2

Dimensions of coefficient of viscosity are [ML^–1T^–1]