This document discusses viscosity and fluid flow. It defines viscosity as a measure of a fluid's resistance to flow, and explains that liquids with higher viscosity, like honey, resist flowing more than low-viscosity liquids like water. It also describes laminar versus turbulent flow, and introduces Reynolds number as a measure of whether flow will be laminar or turbulent based on viscosity, density, velocity, and pipe diameter. Formulas are given for viscosity, drag force, and terminal velocity of objects in fluids. Factors that influence viscosity like temperature, concentration, particle size, and attractive forces are also summarized.

1. Course: Diploma
Subject: Applied Science Physics
Unit: II
Chapter: III

2.  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

3.  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


4.  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 V
F A
d



2 1
1
V V
d



5.  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

6. 1
2

7.  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.

8.  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

9.  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.

10.  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

11.  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
D
N




12.  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
( )
9
t
r g
V  

 

13.  STOKE’S LAW:
 When a spherical object, moves through a viscous
liquid there is a viscous drag force upon it:
 Fv = 6r
 where r = radius of sphere,  = viscosity and  =
velocity of sphere.

14. 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

15.  Capillary Viscometers
 Rotary Viscometers
 Falling “Object” Viscometers
 And many others….

16. 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.

17.  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.

18.  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.

20. 2
0
2 g
( )
9 t
r
V
   

21. REFERENCE BOOKS AUTHOR/PUBLICATION
ENGINEERING PHYSICS S S PATEL (ATUL PRAKASHAN)
MODERN ENGINEERING
PHYSICS
A S VASUDEVA
ENGINEERING PHYSICS K. RAJGOPALAN

22. 1. http://theboard.byu.edu/media/attached_files/r_97030
/cylindricalpipeflow.gif
2. http://www.cora.nwra.com/~werne/eos/images/turbul
ent.jpg