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Pertemuan 01 - 02
Introduction
INTRODUCTION TO FLUID MECHANICS
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Definition of a Fluid
A fluid is a substance that flows under the action of shearing
forces. If a fluid is at rest, we know that the forces on it are in
balance.
A gas is a fluid that is easily compressed. It fills any vessel in
which it is contained.
A liquid is a fluid which is hard to compress. A given mass of
liquid will occupy a fixed volume, irrespective of the size of
the container.
A free surface is formed as a boundary between a liquid and a
gas above it.
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Density
• Regardless of form (solid, liquid, gas) we can define how much mass
is squeezed into a particular space
mass
density 
volume
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Pressure
• A measure of the amount of force exerted on a surface area
force
pressure 
area
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Pressure in a Fluid
• The pressure is just the weight of all the fluid above you
• Atmospheric pressure is just the weight of all the air above on area
on the surface of the earth
• In a swimming pool the pressure on your body surface is just the
weight of the water above you (plus the air pressure above the
water)
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Pressure in a Fluid
• So, the only thing that counts in fluid pressure is the gravitational
force acting on the mass ABOVE you
• The deeper you go, the more weight above you and the more
pressure
• Go to a mountaintop and the air pressure is lower
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Pressure in a Fluid
Pressure acts
perpendicular
to the surface
and increases
at greater
depth.
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Pressure in a Fluid
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Buoyancy
Net upward
force is
called the
buoyant
force!!!
Easier to
lift a rock
in water!!
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Displacement of Water
The amount of
water displaced is
equal to the
volume of the
rock.
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Archimedes’ Principle
• An immersed body is buoyed up by a force equal to the weight of
the fluid it displaces.
• If the buoyant force on an object is greater than the force of gravity
acting on the object, the object will float
• The apparent weight of an object in a liquid is gravitational force
(weight) minus the buoyant force
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Flotation
• A floating object displaces a weight of fluid equal to its own weight.
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Flotation
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Fluids:
Statics vs Dynamics
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Density
The density of a fluid is defined as its mass per unit
volume. It is denoted by the Greek symbol, .
= m
kgm-3
V
kg
m3
 water= 998 kgm-3
air =1.2kgm-3
If the density is constant (most liquids), the flow is
incompressible.
If the density varies significantly (eg some gas
flows), the flow is compressible.
(Although gases are easy to compress, the flow may be treated as
incompressible if there are no large pressure fluctuations)
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Density
• Regardless of form (solid, liquid, gas) we can define how much mass
is squeezed into a particular space
mass
density 
volume
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Pressure
Pressure is the force per unit area, where the force is
perpendicular to the area.
Nm-2
(Pa)
p=
F
A
N
m2
pa= 105 Nm-2
1psi =6895Pa
This is the Absolute pressure, the pressure compared to
a vacuum.
The pressure measured in your tyres is the gauge pressure,
p-pa.
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Pressure
• A measure of the amount of force exerted on a surface area
force
pressure 
area
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Pressure
Pressure in a fluid acts equally in all directions
Pressure in a static liquid increases linearly with depth
p= g  h
pressure
increase
increase in
depth (m)
The pressure at a given depth in a continuous, static body of
liquid is constant.
p1
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p2
p3
p1 = p2 = p3
Measuring pressure (1)
Manometers
p1
p2=pa
x
liquid
density 
h
p1 = px
(negligible pressure
change in a gas)
px = py
(since they are at
the same height)
z
pz= p2 = pa
y
py - pz = gh
p1 - pa = gh
So a manometer measures gauge pressure.
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Measuring Pressure (2)
Barometers
A barometer is used to measure
the pressure of the atmosphere.
The simplest type of barometer
consists of a column of fluid.
p2 - p1 = gh
pa = gh
examples
water: h = pa/g =105/(103*9.8) ~10m
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mercury: h = pa/g =105/(13.4*103*9.8)
~800mm
vacuum
p1 = 0
h
p2 = pa
Atmospheric Pressure
Pressure = Force per Unit Area
Atmospheric Pressure is the weight of the
column of air above a unit area. For example, the
atmospheric pressure felt by a man is the weight
of the column of air above his body divided by
the area the air is resting on
P = (Weight of column)/(Area of base)
Standard Atmospheric Pressure:
1 atmosphere (atm)
14.7 lbs/in2 (psi)
760 Torr (mm Hg)
1013.25 millibars = 101.3 kPascals
1kPa = 1Nt/m2
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Fluid Statics
Basic Principles:
 Fluid is at rest : no shear forces
 Pressure is the only force acting
What are the forces acting on the
block?
 Air pressure on the surface neglect
 Weight of the water above the
block
 Pressure only a function of depth
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Units
SI - International System
Length
Time
Mass
Temp
Force
Meter
Sec
Kg
0K = 0C + 273.15
Newton = Nt = 1 kg m / s2
Gravity
9.81 m/s2
Work = Fxd Joule = Nt-m
Power = F/t Watt = Joule/sec
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Units
English
Length in Ft
Time in Sec
lbm (slug) - 1 slug = 32.2 lbm
Force - lb
Gravity - 32.2 ft/sec2
Work = slug-ft/s2
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Properties of Fluids
Density = 
(decreases with rise in T)
 mass per unit volume ( lbs/ft3 or kg/m3 )
for water density = 1.94 slugs/ft3 or 1000 kg/m3
Specific Weight = g
 weight per unit volume
(Heaviness of fluid)
g = g
for water spec wt = 62.4 lbs/ft3 or 9.81 kN/m3
Specific Gravity = SG
 Ratio of the density of a fluid to the density of water
SG = f / w
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SG of Hg = 13.55
Ideal Gas Law relates pressure to Temp for a gas
P = RT
T in 0K units
R = 287 Joule / Kg-0K
Pressure
Force per unit area:
lbs/in2 (psi), N/m2, mm Hg, mbar or atm
1 Nt/m2 = Pascal = Pa
Std Atm P = 14.7 psi = 101.33 kPa = 1013 mb
Viscosity fluid deforms when acted on by shear stress
m = 1.12 x 10-3 N-s/m2
Surface tension - forces between 2 liquids or gas
liquid - droplets on a windshield.
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and
Section 1: Pressure
Pressure at any point in a static fluid not fcn of x,y,or z
Pressure in vertical only depends on g of the fluid
P = g h + Po
Gage pressure: relative to
atmospheric pressure: P = gh
10 ft
Thus for h = 10 ft, P = 10(62.4) =
624 psf
This becomes 624/144 = 4.33 psi
P = 14.7 psi corresponds to 34 ft
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Pressure in a Tank Filled with Gasoline and Water
What is the pressure at point A? At point B?
gG = 42.43 lbs/ft3
SG = 0.68
gW = 62.4 lbs/ft3
PA = gG x hG + PO
At point A:
= 42.43 x 10 + PO
424.3 lbs/ft2 gage
At point B:
PB = PA + gW x hW
= 424.3 + 62.4 x 3
611.5 lbs/ft2 gage
Converting PB to psi:
(611.5 lbs / ft2) / (144 in2/ft2)
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= 4.25 psi
Measurement of Pressure
Barometer (Hg) - Toricelli 1644
Piezometer Tube
U-Tube Manometer - between two points
Aneroid barometer - based on spring
deformation
QuickTime™ and a
TIF
F (LZ W) decompressor
Pressure transducer
- most
advanced
are needed to see this picture.
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Manometers - measure P
Rules of thumb:
 When evaluating, start from the
known pressure end and work
towards the unknown end
 At equal elevations, pressure
is constant in the SAME fluid
 When moving down a
monometer, pressure increases
 When moving up a
monometer, pressure decreases
 Only include atmospheric pressure
on open ends
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Manometers
Simple Example:
P = g x h + PO
Find the pressure at
point A in this open utube monometer with an
atmospheric pressure Po
PD = g W x hE-D + Po
Pc = PD
PB = PC - g Hg x hC-B
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PA = PB
Archimedes’ Principle
• An immersed body is buoyed up by a force equal to the weight of
the fluid it displaces.
• If the buoyant force on an object is greater than the force of gravity
acting on the object, the object will float
• The apparent weight of an object in a liquid is gravitational force
(weight) minus the buoyant force
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Flotation
• A floating object displaces a weight of fluid equal to its own weight.
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Flotation
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Gases
• The primary difference between a liquid and a gas is the distance
between the molecules
• In a gas, the molecules are so widely separated, that there is little
interaction between the individual moledules
• IDEAL GAS
• Independent of what the molecules are
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Boyle’s Law
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Boyle’s Law
• Pressure depends on density of the gas
• Pressure is just the force per unit area exerted by the molecules as
they collide with the walls of the container
• Double the density, double the number of collisions with the wall
and this doubles the pressure
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Boyle’s Law
Density is mass
divided by
volume.
Halve the
volume and you
double the
density and thus
the pressure.
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Boyle’s Law
• At a given temperature for a given quantity of gas, the product of
the pressure and the volume is a constant
P1V1  P2 V2
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Atmospheric Pressure
• Just the weight of the air above you
• Unlike water, the density of the air decreases with altitude since air
is compressible and liquids are only very slightly compressible
• Air pressure at sea level is about 105 newtons/meter2
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Barometers
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Buoyancy in a Gas
• An object surrounded by air is buoyed up by a force equal to the
weight of the air displace.
• Exactly the same concept as buoyancy in water. Just substitute air
for water in the statement
• If the buoyant force is greater than the weight of the object, it will
rise in the air
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Buoyancy in a Gas
Since air gets less
dense with altitude,
the buoyant force
decreases with
altitude. So helium
balloons don’t rise
forever!!!
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Bernoulli’s Principle
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Bernoulli’s Principle
• Flow is faster when the pipe is narrower
• Put your thumb over the end of a garden hose
• Energy conservation requires that the pressure be lower in a gas
that is moving faster
• Has to do with the work necessary to compress a gas (PV is energy,
more later)
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Bernoulli’s Principle
• When the speed of a fluid increases, internal pressure in the fluid
decreases.
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Bernoulli’s Principle
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Bernoulli’s Principle
Why the streamlines are compressed is
quite complicated and relates to the air
boundary layer, friction and turbulence.
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Bernoulli’s Principle
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REVIEW
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Fluid Mechanics
•
•
•
•
•
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Pressure
Pascal’s Law
Archimedes’ Principle
Fluid Dynamics
Bernoulli’s Equation
Pressure
Force per unit area
Fluids apply a compressive
force to submerged objects
from all sides. This means
that the force is spread out
over a surface area.
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Pressure:
F
P
A
(1 Pa = 1 N/m2)
If pressure varies over the area:
dF  PdA
Example – Q14.2
Both dams have the same height and width.
Which needs to be stronger?
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Example
You hold a thumb tack between your index finger and thumb with a force
of 10 N. The needle has a point that is 0.1mm in radius whereas the flat
end has a radius of 5 mm.
(a)What is the force experienced by your finger; what is the force experienced
by your thumb?
(b)Your thumb holds the pointy end. What is the pressure on the thumb; what is
the pressure on your finger?
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Variation of Pressure with Depth
Pressure exerted by a liquid
increases with depth.
P  P0  gh
Pressure at sea level is taken to be
1 atmospheres (atm)
1 atm  1.013 105 Pa
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Example – 14.4
F=?
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Pascal’s Law
• A change in the pressure applied to a fluid is transmitted to every point of the
fluid and to the walls of the container.
P1  P2
F1 F2

A1 A2
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Example 14.2
d1 = 5.00 cm
d2 = 15.0 cm
mgcar = 13300 N
F1 = ?
P=?
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Buoyant Forces – Archimedes’ Principle
Archimedes’ Principle:
The magnitude of the buoyant
force on an object equals the
weight of the fluid displaced by
the object.
B  mf g   fVf g
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Example – 14.5
Weight in air = 7.84 N
Weight in water = 6.84 N
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Totally Submerged Objects
V f  Vobj
B   f V f g   f Vobj g
F  B  M
F   V
f
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obj
g  objVobj g
obj
g  M obja
a is upward if f > obj
a is downward if f < obj
Floating Objects
Fg  B
M obj g   f V f g
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 objVobj g   f V f g
Vf
Vobj
 obj

f
Example
Consider an object that floats in water but sinks
in oil. When the object floats in water, half of it is
submerged. If we slowly pour oil on top of the
water so it completely covers the object, the
object
1. moves up.
2. stays in the same place.
3. moves down.
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Fluid Dynamics
• We now put the fluid in motion (flow).
• Here are several assumptions about the fluid and its flow:
–
–
–
–
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The flow is to be laminar (steady) not turbulent.
The fluid is non-viscous (negligible internal friction). Think water, not honey.
The fluid in incompressible.
The flow irrotational (no angular momentum).
Equation of Continuity
A1v1  A2v2  constant
The product of the
velocity of flow and the
area of the pipe remains
constant.
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Example
A blood platelet drifts along with the flow of blood through an
artery that is partially blocked by deposits. As the platelet moves
from the narrow region to the wider region, its speed
1. increases.
2. remains the same.
3. decreases.
What about the pressure?
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Bernoulli’s Equation
Using conservation of energy:
E  W
P
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1 2
v  gy  constant
2
Example – 14.9
Vout
d1 = 5 cm
d2 = 3 cm
v2 = 15 m/s
Vout in 10 min = ?
v1 = ?
P1 - P2 = ?
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Review
F
P
A
Pressure:
Pascal’s Law: A change in the
pressure applied to a fluid is
transmitted to every point of the
fluid and to the walls of the
container.
F1 A2  F2 A1
P  P0  gh
Archimedes' Law: The
magnitude of the buoyant force
on an object equals the weight
of the fluid displaced by the
object.
Bm g
f
Equation of Continuity: A1v1  A2v2  constant
Fluid Dynamics
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Bernoulli’s Equation: P 
1 2
v  gy  constant
2