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Viscosity

Introduction:

All fluids, i.e., all liquids and gases, exhibit viscosity to some degree. Viscosity may be thought

of as fluid friction. Just as the force of friction tries to oppose the relative motion between two

solids in contact, there exists a force which tries to oppose relative motion between two adjacentlayers of any fluid. This force is called viscous force and the property possessed by a fluid, on

account of which it tries to prevent relative motion between its adjacent layers, is called

viscosity. Low viscosity fluids flow easily (water, alcohol etc.); High viscosity fluids flow slowly

(Glycerin, cold honey, etc).

Viscosity is a major factor in determining the forces that must be overcome when fluids are used

in lubrication or transported in pipelines. It also determines the liquid flow in spraying, injection

molding, and surface coating. The knowledge of viscosity helps in studying the circulation of

blood through arteries and veins. The charge on the electron was determined by Millikan from

the knowledge of viscosity.Viscosity of organic liquids such as proteins and cellulose helps us tocalculate their molecular weight and determine their shape.

We shall consider more about the viscosity of fluids in this unit.

Velocity Gradient and Coefficient of Viscosity:

Consider a streamline flow of liquid over a solid horizontal surface AB. Let the liquid can be

supposed to be divided into thin horizontal layers parallel to the surface AB as shown in Fig. 5.1.

Fig. 5.1

These layers have been numbered from 1 to n. The bottom layer numbered 1 which is in

contact of solid surface is at rest i.e. V1 = 0. .As the number of the layer increases its distance andvelocity from AB; measured vertically upwards, increases. Let the velocity changes by an

amount dv over a distance dx. The rate of change of velocity with distance measured from the

fixed horizontal surface is called velocity gradient.

Velocity Gradient =dx

dv

Due to the relative motion between adjacent layers say 2, 3 and 4, viscous force comes into

existence between them. The faster moving layer 4 exerts a tangential force F on the layer 3,

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trying to accelerate it and thus trying to destroy the relative motion between them. At the same

time, the slower moving layer 2 exerts an equal and opposite force on the layer 3, trying to retard

it and thus trying to destroy relative motion between them.

Each layer thus exerts a force on the adjacent layer, in a direction parallel to the layer, tending to

destroy motion between the two layers. Newton found that this force, called viscous force, is

directly proportional to the area of the layer and the velocity gradient. If A is the area of the layer

and

dx

dvis the velocity gradient, the viscous force is given by

dx

dvAF

dx

dvAF = . 6.1

where is a constant depending on the nature of the fluid. It is called coefficient of viscosity

of the fluid. Equation 6.1 is known as Newtons formula for viscosity of fluids. We can write

dxdvA

F =

.. 6.2

Thus coefficient of viscosity of a fluid is defined as the tangential or viscous force per unit area

of a layer, per unit velocity gradient.

The C.G.S. unit of the coefficient of viscosity is dyne-second per square centimeter (dyne

sec/cm2) and is called Poise in the memory of the physicist Poiseuille for his remarkable

contribution to our knowledge of viscosity. It follows that coefficient of viscosity of one poise

means that one dyne of tangential force is required to maintain a velocity difference of one

cm/sec between two surfaces each of area one cm2 and one cm apart. The SI unit of the

coefficient of viscosity is Newton-second per square meter (Ns/m2).

The dimensions of coefficient of viscosity are [ M1 L-1 T-1].

The values of the coefficient of viscosity of some liquids are given in the following table

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Table 6.1. Coefficient of viscosity of liquids at 20C.

Sr. No. Liquid

Coefficient of viscosity

Poise Ns/m2

1

2

3

4

5

Water

Mercury

Alcohol

Turpentin

e

Glycerin

0.01006

0.0156

0.0119

0.0149

8.5

0.1006

0.156

0.119

0.149

85