PROGRAM OF “PHYSICS”
Lecturer
:
Dr. DO Xuan Hoi
Room 413
E

mail :
dxhoi@hcmiu.edu.vn
PHYSICS 2
(FLUID MECHANICS AND THERMAL PHYSICS)
02 credits (30 periods)
Chapter 1 Fluid Mechanics
Chapter 2 Heat, Temperature and the Zero
th
Law of Thermodynamics
Chapter 3 Heat, Work and the First Law of
Thermodynamics
Chapter 4 The Kinetic Theory of Gases
Chapter 5 Entropy and the Second Law of
Thermodynamics
References :
Halliday D., Resnick R. and Walker, J. (2005),
Fundamentals of Physics, Extended seventh edition.
John Willey and Sons, Inc.
Alonso M. and Finn E.J. (1992). Physics, Addison

Wesley
Publishing Company
Hecht, E. (2000). Physics. Calculus, Second Edition.
Brooks/Cole.
Faughn/Serway (2006), Serway’s College Physics,
Brooks/Cole.
Roger Muncaster (1994), A

Level Physics, Stanley
Thornes.
http://ocw.mit.edu/OcwWeb/Physics/index.htm
http://www.opensourcephysics.org/index.html
http://hyperphysics.phy

astr.gsu.edu/hbase/HFrame.html
http://www.practicalphysics.org/go/Default.ht
ml
http://www.msm.cam.ac.uk/
http://www.iop.org/index.html
.
.
.
Chapter 1 Fluid Mechanics
1. Variation of Pressure with Depth
2. Fluid Dynamics
3. Bernoulli’s Equation
Question
What is a fluid?
1. A liquid
2. A gas
3. Anything that flows
4. Anything that can be made to
change shape.
States of matter: Phase Transitions
ICE
WATER
STEAM
Add
heat
Add
heat
These are three states of matter
(plasma is another one)
States of Matter
►
Solid
►
Liquid
►
Gas
►
Plasma
States of Matter
►
Solid
►
Liquid
►
Gas
►
Plasma
Has definite volume
Has definite shape
Molecules are held in specific
location by electrical forces and
vibrate about equilibrium positions
Can be modeled as springs
connecting molecules
►
Solid
►
Liquid
►
Gas
►
Plasma
Crystalline solid
Atoms have an ordered structure
Example is salt (red spheres are
Na
+
ions, blue spheres represent Cl

ions)
Amorphous Solid
Atoms are arranged randomly
Examples include glass
States of Matter
States of Matter
►
Solid
►
Liquid
►
Gas
►
Plasma
Has a definite volume
No definite shape
Exist at a higher temperature than solids
The molecules “wander” through the liquid in a
random fashion
The intermolecular forces are not strong
enough to keep the molecules in a fixed
position
Random motion
States of Matter
►
Solid
►
Liquid
►
Gas
►
Plasma
Has no definite volume
Has no definite shape
Molecules are in constant random motion
The molecules exert only weak forces on each
other
Average distance between molecules is large
compared to the size of the molecules
States of Matter
►
Solid
►
Liquid
►
Gas
►
Plasma
Matter heated to a very high temperature
Many of the electrons are freed from the nucleus
Result is a collection of free, electrically charged ions
Plasmas exist inside stars or experimental reactors or
fluorescent light bulbs!
For more information:
http://fusedweb.pppl.gov/CPEP/Chart_Pages/4.CreatingConditions.html
Is there a concept that helps to distinguish between
those states of matter?
Density
►
The density of a substance of uniform composition is defined as its
mass per unit volume
:
some examples:
►
Object is denser
Density is greater
►
The densities of most liquids and solids vary
slightly
with changes
in temperature and pressure
►
Densities of gases vary
greatly
with changes in temperature and
pressure (and generally 1000 smaller)
Units
SI
kg/m
3
CGS
g/cm
3
(
1 g/cm
3
=1000
kg/m
3
)
Pressure
►
Pressure of fluid is the
ratio of the force exerted
by a fluid on a submerged
object to area
Units
SI
Pascal (Pa=N/m
2
)
Example:
100 N over 1 m
2
is P=(100 N)/(1 m
2
)=100 N/m
2
=100 Pa.
1.1 Pressure and Depth
►
If a fluid is at rest in a container,
all portions of the fluid must be in
static equilibrium
►
All points at the same depth must
be at the same pressure
(otherwise, the fluid would not be
in equilibrium)
►
Three external forces act on the
region of a cross

sectional area A
External forces: atmospheric, weight, normal
1. Variation of Pressure with Depth
Test 1
You are measuring the pressure at the depth of 10 cm
in three different containers. Rank the values of
pressure from the greatest to the smallest:
1. 1

2

3
2. 2

1

3
3. 3

2

1
4. It’s the same in all three
10 cm
1
2
3
Pressure and Depth equation
►
P
o
is normal atmospheric
pressure
1.013 x 10
5
Pa = 14.7
lb/in
2
►
The pressure does not
depend upon the shape of
the container
Other units of pressure:
76.0 cm of mercury
One atmosphere 1 atm =
1.013 x 10
5
Pa
14.7 lb/in
2
Example 1:
Find pressure at 100 m below
ocean surface.
1.2
Absolute Pressure and Gauge Pressure
►
The excess pressure above atmospheric pressure is
usually called
gauge pressure (
gh
)
, and the total
pressure is called
absolute pressure
.
A storage tank 12.0 m deep is filled with water. The top of
the tank is open to the air. What is the absolute pressure at
the bottom of the tank? The gauge pressure?
The absolute pressure :
The gauge pressure :
PROBLEM 1
SOLUTION
The U

tube in Fig. 1 contains two liquids in static
equilibrium: Water of density p
w
= 998 kg/m
3
is in the right
arm, and oil of unknown density p
x
is in the left.
Measurement gives
l
= 135 mm and
d
= 12.3 mm.
What is the density of the oil?
In the right arm:
In the left arm:
PROBLEM 2
SOLUTION
1.3 Pascal’s Principle
►
A change in pressure applied to
an enclosed fluid is transmitted
undiminished to every point of
the fluid and to the walls of the
container.
►
The hydraulic press is an
important application of
Pascal’s Principle
►
Also used in hydraulic brakes,
forklifts, car lifts, etc.
Since A
2
> A
1
, then F
2
> F
1
!!!
1.4 Measuring Pressure
►
The spring is calibrated by a
known force
►
The force the fluid exerts on
the piston is then measured
One end of the U

shaped tube
is open to the atmosphere
The other end is connected to
the pressure to be measured
Pressure at B is P
o
+
ρgh
A long closed tube is
filled with mercury and
inverted in a dish of
mercury
Measures atmospheric
pressure as
ρgh
Question
Suppose that you placed an extended
object in the water. How does the
pressure at the top of this object
relate to the pressure at the
bottom?
1. It’s the same.
2. The pressure is greater at the top.
3. The pressure is greater at the
bottom.
4. Whatever…
1.5 Buoyant Force
This force is called the buoyant force.
What is the magnitude of that force?
P
1
A
P
2
A
= mg
Buoyant Force
►
The magnitude of the buoyant force always equals
the
weight of the displaced fluid
►
The buoyant force is the same for a totally
submerged object of any size, shape, or density
►
The buoyant force is exerted by the fluid
►
Whether an object sinks or floats depends on the
relationship between the buoyant force and the
weight
Archimedes' Principle
Any object completely or partially submerged in a
fluid is buoyed up by a force whose magnitude is
equal to the
weight of the fluid displaced by
the object
.
This force is
buoyant force.
Physical cause:
pressure difference between the top and
the bottom of the object
Archimedes’ Principle:
Totally Submerged Object
►
The upward buoyant force is
B =
ρ
fluid
gV
obj
►
The downward gravitational force is
w = mg = ρ
obj
g V
obj
►
The net force is
B
–
w = (ρ
fluid

ρ
obj
) g V
obj
Depending on the direction
of the net force, the object
will either float up or sink!
►
The object is
less dense
than the fluid
ρ
fluid
< ρ
obj
►
The object experiences a
net
upward
force
The net force is
B

w=(ρ
fluid

ρ
obj
) g V
obj
The object is
more dense
than the fluid
ρ
fluid
> ρ
obj
The net force is downward,
so the object accelerates
downward
Test 2
Two identical glasses are filled to the same level
with water. One of the two glasses has ice cubes
floating in it.Which weighs more?
1. The glass without ice cubes.
2. The glass with ice cubes.
3. The two weigh the same.
NOTE :
Ice cubes displace exactly their own
weight in water.
An iceberg floating in seawater, as shown in figure, is extremely
dangerous because much of the ice is below the surface. This
hidden ice can damage a ship that is still a considerable distance
from the visible ice. What fraction of the iceberg lies below the
water level ? The densities of seawater and of iceberg are
W
= 1030 kg/m
3
and
I
= 917 kg/m
3
Weight of the whole iceberg :
Buoyant force :
(V
W
: volume of the displaced water = volume of the ice beneath the water)
The fraction of ice beneath the water’s surface:
PROBLEM 3
SOLUTION
Chapter 8 Fluid Mechanics
1. Variation of Pressure with Depth
2. Fluid Dynamics
2.1 Fluids in Motion: Streamline Flow
►
Streamline flow (also called
laminar flow)
every particle that passes a
particular point moves exactly
along the smooth path
followed by particles that
passed the point earlier
►
Streamline is the path
different streamlines cannot
cross each other
the streamline at any point
coincides with the direction of
fluid velocity at that point
Laminar flow around an
automobile in a test
wind tunnel.
2.1 Fluids in Motion: Turbulent Flow
►
The flow becomes irregular
exceeds a certain velocity
any condition that causes abrupt changes in
velocity
►
Eddy currents are a characteristic of turbulent flow
Hot gases from a
cigarette made visible by smoke
particles. The smoke first moves in
laminar flow at the bottom and
then in turbulent flow above
Fluid Flow: Viscosity
►
Viscosity is the degree of internal friction in the
fluid
►
The internal friction is associated with the
resistance between two adjacent layers of the fluid
moving relative to each other
2.2 Characteristics of an Ideal Fluid
►
The fluid is nonviscous
There is no internal friction between adjacent layers
►
The fluid is incompressible
Its density is constant
►
The fluid is steady
Its velocity, density and pressure do not change in time
►
The fluid moves without turbulence
No eddy currents are present
2.3 Equation of Continuity
►
The product of the cross

sectional area of a pipe
and the fluid speed is a
constant
Speed is high where
the pipe is narrow and
speed is low where
the pipe has a large
diameter
►
Av is called the
volume
flow rate
The mass is
conserved :
Equation of Continuity :
(a) The speed of the oil:
The
mass
flow rate:
(b)
PROBLEM 4
SOLUTION
As part of a lubricating system for heavy machinery, oil of density
850 kg/m
3
is pumped through a cylindrical pipe of diameter 8.0 cm
at a rate of 9.5 liters per second. The oil is incompressible.
(a)
What is the speed of the oil? What is the mass flow rate?
(b)
If the pipe diameter is reduced to 4.0 cm, what are the new
values of the speed and volume flow rate?
Oil incompressible: volume flow rate has the same value:
3. Bernoulli’s Equation
Magnitude of the force
exerted by the fluid in
section 1:
P
1
A
1
( V: volume of section 1)
The work done by this
force
W
1
=
F
1
x
1
=
P
1
A
1
x
1
=
P
1
V
The work done by by the fluid in section 2:
W
2
=

F
2
x
2
=

P
2
A
2
x
1
=

P
2
V
(W
2
< 0 : the fluid force opposes the displacement)
The net work done by two forces:
W =
(
P
1

P
2
)
V
Theorem of the variation of kinetic energy :
Bernoulli’s equation applied to an ideal fluid :
Bernoulli’s Equation
►
Relates pressure to fluid speed and elevation
►
Bernoulli’s equation is a consequence of Conservation
of Energy applied to an ideal fluid
►
Assumes the fluid is incompressible and nonviscous,
and flows in a nonturbulent, steady

state manner
►
States that the sum of the pressure, kinetic energy
per unit volume, and the potential energy per unit
volume has the same value at all points along a
streamline
Measure the speed of the fluid flow: Venturi Meter
►
Shows fluid flowing through a
horizontal constricted pipe
►
Speed changes as diameter
changes
►
Swiftly moving fluids exert less
pressure than do slowly moving
fluids
Application of Bernoulli’s Equation
How to measure the speed
v
2
?
EXAMPLE
Measure the speed of the fluid flow: Venturi Meter
Application of Bernoulli’s Equation
Equation of Continuity :
Rate of flow :
the volume of fluid which passes
through a given surface per unit time (m
3
/s)
4. Poiseuille’s law
Poiseuille's equation :
R
P
1
P
2
v
L
:
viscosity of the fluid
PROBLEM 5
A horizontal pipe of 25

cm
2
cross

section carries water
at a velocity of 3.0 m/s. The pipe feeds into a smaller
pipe with cross section of only 15 cm
2
.
W
=10
3
kg/m
3
(a)
What is the velocity of water in the smaller pipe ?
(b)
Determine the pressure change that occurs from
the larger

diameter pipe to the smaller pipe.
SOLUTION
A
1
v
1
A
2
v
2
(a)
(b)
PROBLEM 6
A large pipe with a cross

sectional area of 1.00 m
2
descends 5.00 m and narrows to 0.500 m
2
, where it
terminates in a valve. If the pressure at point 2 is
atmospheric pressure, and the valve is opened wide
and water allowed to flow freely, find the speed of the
water leaving the pipe.
SOLUTION
h
v
2
v
1
2
P
2
=P
0
P
1
=P
0
SOLUTION
h
v
2
v
1
2
P
2
=P
0
P
1
=P
0
PROBLEM 7
There is a leak in a water tank. The hole is very small
compared to the tank’s cross

sectional area.
(a)
If the top of the tank is open to the atmosphere,
determine the speed at which the water leaves the
hole when the water level is 0.500 above the hole.
SOLUTION
(a)
y
2
y
1
h
A
1
v
1
P
0
P
2
=P
0
A
2
PROBLEM 7
There is a leak in a water tank. The hole is very small
compared to the tank’s cross

sectional area.
(b)
Where does the stream hit the ground if the hole is
3.00 m above the ground ?
SOLUTION
(b)
y
2
y
1
h
A
1
v
1
P
0
P
2
=P
0
A
2
x
y
PROBLEM 8
An airplane has wing, each wing area 4.00 m
2
,
designed so that air flows over the top of the wing at
245 m/s and under the wing at 222 m/s. Find the
mass of the airplane such that the lift on the plane will
support its weight, assuming the force from the
pressure difference across the wings is directed
straight upwards.
SOLUTION
The lift on the plane supports the plane’s weight :
PROBLEM 9
BLOOD PRESSURE WITH DEPTH:
Human blood has a density of approximately
1.05 x 10
3
kg/m
3
.
(a)
Use this information to estimate the difference in
blood pressure between the brain and the feet in a
person who is approximately 1.6 m tall.
SOLUTION
The difference in pressure is given by:
(a)
PROBLEM 9
BLOOD PRESSURE WITH DEPTH:
Human blood has a density of approximately
1.05 x 10
3
kg/m
3
.
(b)
Estimate the volume flow rate of blood from the
head to the feet of this person. Assume an effective
radius of 24 cm.
The viscosity of blood is 0.0027 N.s/m
2
.
SOLUTION
(b)
Poiseuille's equation :
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