1.5 Viscosity

Viscosity is the measure of the fluid resistance to flow.

Video:
This video also contains about the kinematic viscosity which we are going to cover in the next post. If you want to watch it you can watch it.


It can be said that the resistance is due to the intermolecular forces between the fluid layers. Thus in the figure the top fluid layer only has force on it by the fluid layer under it. But for the fluid layer under it has forces above it and layer under it.


To understand this properly let us consider an example.

Let us consider a fluid moving in x direction as shown in the figure. 

Let us assume that the lines represents the fluid layers and they are dy distance apart. And also assume that the top layer of the fluid is moving at a velocity of u. Now the viscosity is that the layer 2 pulls back the layer 1 for its movement. Thus the velocity of the second layer will be u-du. Therefore the shear stress on the first layer will be towards the left hand side and on the second layer will be towards the right hand side for this example. And we know that the shear stress is defined as the force acting on the given object per unit area. Therefore shear stress can be given as 

Here the proportionality constant becomes the coefficient of viscosity. and is denoted by μ.

Thus the equation can be represented as 

where,

τ is the shear stress 

μ is the coefficient of dynamic viscosity or viscosity.

and du/dy is the rate of shear strain or velocity gradient.

Thus we can write the equation of viscosity can be given as 

Units of viscosity can be given as

and in CGS system can be given as

Where 1 Newton is equal to 100000 dynes and it should be noted that dyne.s/cm² is also called as poise

in MKS system the units can be given as 

and the relation between the MKS system and the SI system can be given as 

Note:

1. All Real fluids have viscosity.
2. Only in ideal fluids viscosity is assumed to be zero.
3. Viscosity is also called as dynamic viscosity. 
4. The More the viscosity the slower the motion of the liquid.