VISCOSITY
- The property of fluid in motion by virtue of which, there is
an internal friction between different layers of fluid in
contact, which opposes the relative motion between
different layers is called viscosity.
- The cause of viscous force is intermolecular force between
the molecule of different layers.
State and Explain Newton’s law of Viscosity.
Also mention different units of viscosity.
Fig: Solid Surface
From Newton's formula for viscous force
𝐹
𝜂=−
𝑑𝑣
𝐴
𝑑𝑥
The coefficient of viscosity is defined as the viscous force acting
per unit area per unit velocity gradient.
Here,−2
1Nm s = 105 dyne x s x10 −4
cm −2
= 10 dyne scm −2
1 decapoise = 10 dyne scm−2
1 decapoise = 10 poise
On what factors does coefficient of viscosity depends upon?
Temperature:
If the temperature is less then the molecule would be more at rest
so the viscosity would increase.
The velocity of liquid depends upon temperature .As the
temperature increases, the kinetic energy of the molecule increases
and hence the force of cohesion between them decreases.
However in case of gases the velocity is due to diffusion of gas
molecules when temperature increases the rate of diffusion of gas
increases as a result the viscosity of gas increases with rise in
temperature.
Effect of pressure:
The velocity of liquid increases with the increase in pressure.
However the velocity of gas is partially independent of pressure
in case of water the viscosity decreases with increase in
pressure
Effect of density:
The viscosity of liquid depends on the density of liquid. The
viscosity of liquid increases with the increase in density. The
viscosity of thick liquid like Honey is more than thin liquid like
water. The viscosity of gases decreases with increase in density.
Q. A flat plate of area 0.1 m2 is placed on a flat surface and is
separated from it by a film of oil 10-5 cm thick whose coefficient
of viscosity is 1.5 Nsm-2. Calculate the force required to cause
the plate to slide on the surface at a constant speed of 1mms-1.
State and Explain different types of flows:
Stream-Line Flow
When the flow of liquid is such that the velocity, v of every particle at any point
of the fluid is constant, then the flow is said to be steady or streamline flow.
Fig: Streamline flow
Laminar flow
If a liquid is flowing over a horizontal surface with a
steady flow and moves in the form of layers of different
velocities which do not mix with each other, then the flow
of liquid is called laminar flow. In general, laminar flow is
a stream line flow.
Turbulent flow
When a liquid moves with a velocity greater than its critical velocity, the motion
of the particles of liquid becomes irregular, such flow is called turbulent flow.
In a turbulent flow, the path and the velocity of the particles of the liquid change
continuously and haphazardly with time from point to point.
Fig: Figure Turbulent flow of a fluid.
Define Critical Velocity. Derive its relation with
density and viscosity of fluid.
Critical velocity is defined as The limiting velocity below which motion of the fluid is
stream line and
above which it is turbulent.
The critical velocity vc depends on (i) coefficient of viscosity of fluid
(ii) density ρ of the fluid and
(iii) lateral dimensions r of the tube in which liquid is flowing.
The expression is easily obtained by method dimensions
Let vc = k na ρb rc
For a laminar flow of fluid, its value lies between 0 to
about 2000.
For values above 3000, the flow is turbulent.
Between 2000 and 3000 the flow is unstable and may
change from one type to another.
State and Explain Poiseuille's Formula:
Poiseuille studied the stream line flow of a liquid in
capillary tubes as shown in Fig. He concluded that the volume,
V of the liquid flowing per second through a capillary tube is:
Derive Poiseuille's Formula by Dimensional Analysis:
Poiseuille found that the volume of a liquid flowing through a
capillary tube per second depends upon:
𝑃
(i) the pressure gradient
𝑙
(iii)radius of the capillary tube r
(iii) coefficient of viscosity of the liquid, ŋ.
𝑃 a b
That is, volume of liquid flowing per second V α ( ) r ƞc
𝑙
where a, b and c are constants to be determined.
𝑃
V = k ( )a rb ƞc
𝑙
where k is the proportionality constant.
Q. A hose pipe of diameter 1.0cm is 20m long. The pressure
difference between the ends of the pipe is 6.5 x 104 N/m2. Calculate
the mass of water flowing through the pipe in 1 hr.
[Viscosity of water = 10 x 10-3 poise] [2869.2 kg]
