Lecture - 4 ( properties of fluids (part 3) - viscosity)

Viscosity 

Viscosity represents the internal resistance offered by one layer of fluid to the adjacent layer. S.I unit of viscosity is kilogram per metre second. Basically it is fluid friction. More the viscosity means more fluid friction and vice versa. This is also called dynamic viscosity and absolute viscosity. This is absolute quantity because it is a direct measurement of internal resistance between the layers of fluids. We can differentiate between fluids just by observing that which fluid has more viscosity and which one has less viscosity.

In case of liquids the main reason of viscosity is intermolecular bonding (cohesion). Whereas in case of gases the main reason of viscosity is molecular collision.

In below figure fluid is there which moves from its initial position due to the action of shear force. We consider a very small elemental thickness of fluid and study it separately. Let us consider this elemental thickness to be so small that it includes only two layers of fluid, flowing one over another. Let the fluid is flowing with the velocity 'u' and 't' represents time. 'dy' be the small distance between two layers of fluid. 

Here 'dθ/dt' represents the rate of deformation and 'du/dy' represents the velocity gradient. 

In case of fluids shear stress (τ) is directly proportional to rate of shear strain or we can say rate of angular deformation (dθ/dt)

Here 'μ' represent viscosity or dynamic viscosity or coefficient of viscosity. 

( For the fluid whose viscosity is high, its rate of shear strain is less and resistance is high which makes the flow difficult. For the fluid whose viscosity is less, it's rate of Shear Strain is high and resistance is low which makes the flow easy.)

VARIATION OF VISCOSITY WITH TEMPERATURE 

As we know in case of liquids the reason of viscosity is molecular bonding, so when we increase the temperature of liquid these molecular bonds break due to which viscosity decreases. Whereas in case of gases the reason of viscosity is molecular collision, so when we increase the temperature of gas collision between molecules increases and hence the viscosity increases.

Kinematic viscosity (υ)

It signifies the net transfer of fluid momentum from one point to other point that's why it is also called as momentum diffusivity. Kinematic viscosity shows resistance to molecular Momentum transfer (molecular collision). Remember kinematic viscosity is not absolute. Mathematically it is the ratio of dynamic viscosity to density of fluid. It's S.I unit is metre square per second.

υ = μ/ρ
Conduction is basically the ability to transfer the things from one place to other place. It signifies how much material or medium is supporting in transferring things.
Just opposite to this property conduction we have one more property called diffusion. It's basically a storage capacity or we can say absorbing ability of material.
For particular material diffusivity is defined as, how much conducting property is dominating over storage property. So from here we can conclude that net transfer is not represented by conduction it represented by diffusion.
Kinematics viscosity shows net transfer of molecular movement that's why it's called momentum diffusivity not Momentum conductivity.

VARIATION OF KINEMATIC VISCOSITY WITH TEMPERATURE 

In case of liquids as we increase the temperature its dynamic viscosity decreases and as liquids are incompressible their density will remain same, due to which kinematic viscosity decreases. Now for gas if we increase the temperature than its dynamic viscosity increases and also it's density decreases, so we see a significant rise in kinematic viscosity.
Remember for increase in temperature of gasses both dynamic and kinematic viscosity increases but rise in kinematic viscosity is much more than dynamic viscosity.