What is Viscosity?
The property of a fluid due to which it opposes the relative motion between its adjacent layers is called viscosity.
And the force between the layers opposing the relative motion is known as the Viscous Force.
The microscopic cause for viscosity is intermolecular electromagnetic forces. It is also observed that different fluids will have different levels of viscous effect. For example, water flows more rapidly than honey; this is because honey is more viscous than water. and in general viscosity in liquids is much larger than that in gases.
CAUSE OF VISCOSITY
Consider a liquid flowing at a steady rate on a horizontal surface. The liquid may be assumed to consist of different horizontal layers.If a specific layer of a liquid is considered, the layer below it tries to decrease the velocity of the upper layer due to cohesive forces between the molecules of the adjacent layers. In turn, the upper layer (moving with greater velocity) tries to increase the velocity of the lower layer. Thus an opposing force comes into play tending to decrease the relative velocity between the adjacent layers (like frictional force between two solids). This force is called viscous drag.
It appears as if a tangential shearing force is acting between the layers. To overcome these shearing forces and to maintain constant velocity between the adjacent layers, an external force is to be applied. If there is no external force, the velocity of flow decreases and becomes zero.
Coefficient of Viscosity:
The coefficient of viscosity is defined as the tangential force per unit area of the layer, required to maintain unit velocity gradient. (or)
The coefficient of viscosity for a fluid is defined as the ratio of shearing stress to the strain rate.
Consider a fluid moving slowly and steadily over a horizontal surface, where every layer of the fluid moves parallel to the fixed surface. The layer in contact with the fixed surface is at rest and velocity of every other layer increases uniformly as we move upwards.
Let us consider two layers, P and Q having equal areas and separated by a distance Δx in a liquid flow as shown. Let the velocity of the layer P is v + Δv and that of the layer Q is v. The relative velocity is Δv between the layers. The quantity Δv/Δx is called velocity gradient, normal to the direction of flow (or) strain rate.
The upper layer P moving faster than layer Q tends to increase the velocity of lower layer Q. While the lower layer Q tends to decrease the velocity of the upper layer P. The two layers P and Q, thus tend to destroy their relative motion, as if there is a backward dragging tangential force. This tangential force that tend to destroy the relative motion is the viscous force.
According to Newton, the viscous force (F) is directly proportional to
(i) area A of the layer and
Then, we have
From the above two expressions, we have
The negative sign shows that viscous force on a fluid layer acts in a direction opposite to the relative velocity of flow of the fluid.
η is the constant of proportionality called coefficient of viscosity.
Now η = F, when A = 1 unit and
Δv/Δx = 1 unit
While the motion of the fluid, a portion of fluid, which has the shape ABCD at some instant changes into the shape AEFD after short interval of time (Δt). During this time interval the liquid has undergone a shear strain of Δx/ℓ
Since the strain in a flowing fluid increases with time continuously unlike a solid, here the stress is found experimentally to depend on ‘rate of change of strain’ or ‘strain rate’ i.e. Δxℓ(Δt) or (v/ℓ)instead of strain itself.
The coefficient of viscosity for a fluid is defined as the ratio of shearing stress to the strain rate.
This is the formula for coefficient of viscosity.
The SI unit of coefficient of viscosity is Nm⁻²s or Pa s.
It’s unit in C.G.S system is ‘poise’ after the name of the scientist poiseuille.
1 Pa s = 10 poise
The dimensional formula is: ML⁻¹T⁻¹