Let us pour equal amounts of water and castor oil in two identical
funnels. It is observed that water flows out of the funnel very quickly whereas
the flow of castor oil is very slow. This is because of the frictional force
acting within the liquid. This force offered by the adjacent liquid layers is
known as viscous force and the phenomenon is called viscosity.
is the property of the fluid by virtue of which it opposes relative motion
between its different layers. Both liquids and gases exhibit viscosity but
liquids are much more viscous than gases.
Co-efficient of viscosity
Consider a liquid to flow
steadily through a pipe as shown in the Fig. The layers of the liquid which are
in contact with the walls of the pipe have zero velocity. As we move towards
the axis, the velocity of the liquid layer increases and the centre layer has
the maximum velocity v. Consider any two layers P and Q separated by a distance
dx. Let dv be the difference in velocity between the two layers.
The viscous force F acting
tangentially between the two layers of the liquid is proportional to (i) area A
of the layers in contact
(ii) velocity gradient dv/dx
perpendicular to the flow of liquid.
F α A dv/dx
F = η A dv/dx
where η is the coefficient of
viscosity of the liquid.
This is known as Newton's law
of viscous flow in fluids.
If A = 1m2 and
dv/dx = 1s-1
then F= η
coefficient of viscosity of a liquid is numerically equal to the viscous force
acting tangentially between two layers of liquid having unit area of contact
and unit velocity gradient normal to the direction of flow of liquid.
The unit of η is N s m-2. Its dimensional
formula is ML-1T-1.