Let’s take an example. Take a bucket filled with water and stir it with glass rod, the the water rotates in cylindrical layers. Place some pieces of paper on the rotating water. You will observe that the speed of the pieces of paper is maximum on the innermost cylindrical layer and the speed decreases as you approach the wall of the bucket.

And, when you stop stirring, the water rotates for sometime and then stops. Since no external force is applied, the opposing force must be internal. This opposing force is viscous force and this property of the liquid is known as viscosity.

A liquid flows in the form of different layers. When these layers are moving with different velocities, due to he Vanderwaal force of attraction, *every fast moving layer retards the adjoining slow moving layer and every slow moving layer tries to retard the adjoining fast moving layer. *Because of this, viscous force arises.

*Viscosity is the property of a fluid by virtue of which an internal force arises in the fluid which opposes the relative motion of its different layers.*

Let us consider a liquid flowing steadily over a fixed horizontal surface. The layer in contact with the surface moves with minimum velocity due to the adhesive force between the liquid and the surface. And, the topmost layer moves with maximum velocity.

Consider two adjoining layers $P$ and $Q$. $Q$ tries to accelerate $P$ and $P$ tries to retard $Q$. So, a backward tangential force $(F)$ acts between the two layers. Let the two layers be moving with velocity $dv$ with respect to each other, and are separated by distance $dx$.

Newton observed that, \[F∝A\] $A=$ Area of each layer \[F∝\frac{dv}{dx}\] \[\frac{dv}{dx}=\text{velocity gradient between the layers}\] combining, we get, \[F∝A\frac{dv}{dx}\] \[F=-ηA\frac{dv}{dx}\] where, $η$ is a constant known as coefficient of viscosity of the liquid. There is negative sign because the diection of force is opposite to the direction of velocity.

\[\text{if } A=1\text{ and }\frac{dv}{dx}=1\text{ then,}\] \[η=-F\] Thus, coefficient of viscosity of a fluid can be defined as the viscous force required to maintain unit velocity gradient between two layers of unit area.

The SI system of $η$ is $\text{Nsm}^{-2}$ or Pas (Pascal second).

In CGS, the unit of $η$ is $\text{dyne cm}^{-2}$ or Poise.

**More on Fluid Dynamics**

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