The flow of fluid from one place to another is a very natural phenomenon.

We have also observed water coming out of a pipe.

If petrol comes out of the same pipe, it will not come out with the same speed.

We observe the same thing when we pour water from a container to a bowl or glass. The process of pouring is faster.

And when we pour mango juice or honey to the glasses, the process is comparatively slower.

The variation in the speed of pouring actually depends upon the viscosity of the fluid. So this is important to understand the concept of viscosity.

Let's discuss viscosity.

The viscosity of a fluid is a measure of its resistance to deformation at a given rate. It is defined by the 'concept of the thickness of fluid layers' for liquid.

Consider a block of liquid is acted upon by the force $F$ and moving with velocity $v$.

If the upper plate in this block is moving with velocity $v$ then adjacent layers will move with some velocity gradient.

The liquid is flowing in $x$-direction and velocity gradient in $y$-direction.

The force will be proportional to the area of layers in contact.

The force will also be proportional to velocity gradient.

So the viscous force is proportional to both velocity gradient and area of the layers in contact.

The constant of proportionality in force equation is known as the coefficient of viscosity.

The SI unit of viscosity is $Pascal−second$ and it is represented by $μ$ or $η$.

The dimensional formula of the viscosity can be calculated with the dimensional formula of force, velocity and area.

The dimensional formula of the viscosity becomes,

If we divide the viscosity by the density of the fluid then we obtain kinematic viscosity.

The kinematic viscosity is represented by $ν$ and its SI unit is $m_{2}/sec$. The CGS unit of kinematic viscosity, $cm_{2}/sec$ or stokes is very common.

Now let's discuss the effect of some factors on the viscosity.

The temperature has immense effect on the viscosity. The viscosity of the liquid decreases with temperature.

On the other hand, the viscosity of the gases increases with the increase in the temperature.

This is how we can define the viscosity of the fluid and how the viscosity of liquid and gases vary with temperature.

Revision

The viscosity of a fluid is a measure of its resistance to deformation at a given rate. It is defined by the 'concept of the thickness of fluid layers' for liquid.

The viscosity of a fluid can be defined by force and velocity gradient relation.

The SI unit of viscosity is $Pascal−second$ and it is represented by $μ$ or $η$.

If we divide the viscosity by the density of the fluid then we obtain kinematic viscosity. It is represented by $ν$.