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# Viscosity

We see that all liquids do not flow with same speed or their rate of flow is not same. Some liquids flow rapidly like water, alcohol etc. while some liquids flow slowly with some resistance, for example glycerine, castor oil etc

That indicates that every liquid has some internal resistance to flow. This internal resistance is viscosity. Those which have low internal resistance flow rapidly while those with more internal resistance flow quite slowly.

## Viscosity Definition

The internal resistance to flow possessed by a liquid is called its viscosity. Viscosity may be defined as the force of friction between two layers of a liquid moving past one another with different velocities. It is the resistance that one part of a liquid flowing with one velocity offers to another part of the liquid flowing with different velocities.

The liquids which flow slowly due to high internal resistance are said to more viscous or having high viscosity. On the other hand, liquids which flow rapidly due to low are said to be less viscous or having less viscosity.

The units of viscosity:
The units of viscosity in c.g.s system are dynes $cm^{-2}$ sec or poises. Still more convenient units are centipoises and millipoises.

## Viscosity of Water

Water is said to be least viscous .The internal resistance in water is very minimal, therefore it has low viscosity. At $25^{0}C$ the dynamic viscosity of water is 8.90 $\times$ $10^{-4}$ Pa. s or 8.90 x $10^{-3}$ dynes cm or 0.910 cP or 0.0091 poise.

## Viscosity of Air

The viscosity of air varies with temperature. The viscosity of air at $25^{0}C$ is 18.6 $\eta$ Pa.s and the kinematic viscosity of air at $25^{0}C$ 15.7 cSt.

## Coefficient of Viscosity Definition

Consider a liquid flowing through a narrow tube. Imagine the liquid is made up of large number of thin cylindrical coaxial layers. The layer which is in contact with the walls of the tube is almost stationary. As we move from the walls towards the centre of the tube, the viscosity of the cylindrical layers keeps on increasing. It is maximum at the centre.

When a molecule moves from the faster layer to the slower layer, it transports momentum to the latter layer, thereby speeding it up. In other words, when a molecule, moves from a slower layer to faster layer, it slows down the latter layer.

Or as we move from the centre of the tube to the wall of the tube, the velocity of layers keeps on decreasing. If V is the velocity of one layer then the velocity of other layer is V + v, where ‘v‘ is the small increase in the velocity.

Force of friction (f) between two cylindrical layers is directly proportional to the area and the velocity gradient.
Therefore force of friction (f) between the two cylindrical layers each having area ‘A’ sq. cm, separated by a distance dy cm, and having a velocity difference v cm/sec, is given by

f $\infty$ A $\frac{dc}{dy}$

Or,

f =  $\eta$ A $\frac{dc}{dy}$   ----------(1)

The equation is known for Newton’s law of viscosity.

Where ‘$\eta$' is a constant known as coefficient of viscosity.

If dy = 1 m , A = 1 sq. cm and dc = 1 cm/sec, then f =  $\eta$

Thus, coefficient of viscosity may be defined as the force of friction (in dynes) required to maintain a  velocity difference of 1 cm/sec between two parallel layers, 1 cm away from each other and each having an area of 1 sq. cm.

The above equation is applied for streamlined or laminar flow. The equation does not apply to turbulent flow. The liquids which obey the equation are called Newtonian fluids and those which do not obey the equation are called non – Newtonian fluids.

## Kinematic Viscosity

ν = $\frac{\mu}{\rho}$
µ = dynamic viscosity of the fluid in Ns/m$^2$,
$\rho$ = density of the fluid in Kg/m$^3$,
ν = kinematic viscosity of the fluid in m$^2$/s.