Course: Diploma

Subject: Applied Science Physics

Unit: II

Chapter: III

The liquid like water, kerosene flow easily.

But honey, castor oil can’t flow easily.

For constant speed of flow we have to apply pressure

difference.

So, we note that is some force opposing speed of

flow.

It is due to viscosity. moving plate

fluid

velocity

gradient

static plate

v

F

l

x

In flow any two consecutive layers of fluid have

relative velocities.

The fraction force between two layers.

Velocity gradient is velocity difference of two layers

per unit distance between two layers.

SI unit S-1

This law is for streamline flow of fluid.

2 1V V

d

According to Newton’s experiment,

F α A &

F α

Where η = coefficient of viscosity depends on type of liquid &temperature.

If η is more F is more, η decreases with increasing temperature.

In gas it increases with increasing temperature.

If A=1,&

Then η=F

2 1V V

d

2 1V VF A

d

2 1 1V V

d

coefficient of viscosity: In case of

steady flow if there is unit velocity gradient

between two consecutive layers of unit surface

area the viscous force is called coefficient of

viscosity.

Unit is Nsm-2

1

2

Consider a liquid passing through a glass

tube.

If all particles have same motion at particular point all

time the flow is…………

Path of the particles at a point is same.

If the liquid is pushed in the tube at a rapid rate, flow

is……….

The velocity of different particles passing through same

may be different & change with time. e.g. motion of

water in river

At low velocity fluid flows in steady.

Velocity Increases at certain limit it converts as

turbulent flow.

The velocity below which flow will be stream line &

Above which flow will be turbulent.

Liquid passing through a glass tube

Flow will be any of both

For determination of coefficient of velocity it should be

streamline flow

The factors on which modes of flow depends.

1. η

2. ρ

3. ν

4. D

So, Reynolds’s number is:

Mode of flow depends on NR

1. If NR<2000,streamline

2. IF NR>3000,turbulent

3. If 2000<NR<3000,flow will changes in both.

NR at critical velocity is critical Reynolds’s number.

R

DN

Spherical body ρ & Viscosity of liquid ρ0, ρ> ρ0

Stream line force & flow

Up thrust force: The force opposes motion of

spherical body is……..

Terminal velocity:

When body starts motion with const. velocity the

velocity is called…….

2

0

2( )

9t

r gV

STOKE’S LAW:

When a spherical object, moves through a viscous

liquid there is a viscous drag force upon it:

Fv = 6r

where r = radius of sphere, = viscosity and =

velocity of sphere.

Absolute (or Dynamic) Viscosity,

Units:

1 Poise = 1 g/(cm sec)

1 Pa sec = 1 kg/(m sec) = 1 N sec/m2

1 Poise = 100 cP = 0.1 Pa sec

Kinematic Viscosity: = /ρ

Units:

1 stoke = 1 cm2/sec = 0.0001 m2/sec

Capillary Viscometers

Rotary Viscometers

Falling “Object” Viscometers

And many others….

Temperature: LIQUIDS AND GASES REACT OPPOSITELY TO

CHANGES IN TEMPERATURE.

In liquids, when the temperature increases the particles

move faster and begin to move away from each other.

Because the particles are moving around more they can

flow more; their viscosity is lower.

In gases, the particles are far apart so when energy is

added the particles move faster and collide with each

other more often causing an increase in viscosity.

Concentration:

Concentration is the amount of substance that is

dissolved in a specific volume.

An increase in concentration will usually result in an

increase in viscosity.

Attractive Force:

Particles of the same substance have an attractive force

on one another.

Some substances have a strong attraction while some

substances have a weaker attraction.

The stronger the attraction of particles, the

higher the viscosity.

Particle Size:

The size of the particles of a substance will greatly

affect its viscosity.

Small particles can move more easily past each other

and can therefore flow faster, meaning they have a

lower viscosity.

Large particles would mean a higher viscosity.

2

0

2 g( )

9 t

r

V

REFERENCE BOOKS AUTHOR/PUBLICATION

ENGINEERING PHYSICS S S PATEL (ATUL PRAKASHAN)

MODERN ENGINEERING

PHYSICSA S VASUDEVA

ENGINEERING PHYSICS K. RAJGOPALAN

1. http://theboard.byu.edu/media/attached_files/r_97030

/cylindricalpipeflow.gif

2. http://www.cora.nwra.com/~werne/eos/images/turbul

ent.jpg