Hp08win 1228295929722748-9

Copyright © by Holt, Rinehart and Winston. All rights reserved.
ResourcesChapter menu
Chapter Presentation
Transparencies Sample Problems
Visual Concepts
Standardized Test Prep
Chapter 8 – Fluid Dynamics

Fluid Mechanics
Chapter 8
Table of Contents
Section 1 Fluids and Buoyant Force
Section 2 Fluid Pressure
Section 3 Fluids in Motion

Section 1 Fluids and Buoyant
ForceChapter 8
Objectives
• Define a fluid.
• Distinguish a gas from a liquid.
• Determine the magnitude of the buoyant force
exerted on a floating object or a submerged object.
• Explain why some objects float and some objects
sink.

ForceChapter 8
Defining a Fluid
• A fluid is a nonsolid state of matter in which the
atoms or molecules are free to move past each other
• Both liquids and gases are considered fluids

ForceChapter 8
Density and Buoyant Force
• The concentration of matter of an object is called the
mass density.
ρ =
m
V
mass density =
mass
volume

Chapter 8
Mass Density
Force

ForceChapter 8
Density and Buoyant Force, continued
• The buoyant force is the upward force exerted by a
liquid on an object immersed in or floating on the
liquid.
• Buoyant forces can keep objects afloat.

Chapter 8
Buoyant Force and Archimedes’ Principle
Force

Chapter 8
Displaced Volume of a Fluid
Force

ForceChapter 8
• Archimedes’ principle: Any object completely or
partially submerged in a fluid experiences an upward
buoyant force equal in magnitude to the weight of the
fluid displaced by the object.
FB = Fg (displaced fluid) = mfg
magnitude of buoyant force = weight of fluid displaced

Chapter 8
Buoyant Force on Floating Objects
Force

Chapter 8
Buoyant Force
Force

ForceChapter 8
• For a floating object, the buoyant force equals the
object’s weight.
• For an object with density ρO submerged in a fluid of
density ρf, the buoyant force FB obeys the following
ratio:
Fg
(object)
FB
=
ρO
ρf

ForceChapter 8
Sample Problem
Buoyant Force
A bargain hunter purchases a “gold” crown at a flea
market. After she gets home, she hangs the crown
from a scale and finds its weight to be 7.84 N. She
then weighs the crown while it is immersed in water,
and the scale reads 6.86 N. Is the crown made of
pure gold? Explain.

ForceChapter 8
Sample Problem, continued
Buoyant Force
1. Define
Given:
Fg = 7.84 N
apparent weight = 6.86 N
ρf = pwater = 1.00 × 103
kg/m3
Unknown:
ρO = ?

ForceChapter 8
Diagram:
Buoyant Force
1. Define, continued
TIP: The use of a diagram
can help clarify a problem
and the variables involved.
In this diagram, FT,1 equals
the actual weight of the
crown, and FT,2 is the
apparent weight of the
crown when immersed in
water.

ForceChapter 8
Buoyant Force
2. Plan
Choose an equation or situation: Because the
object is completely submerged, consider the ratio of
the weight to the buoyant force.
ρ
ρ
=
=
– apparent weightg B
g O
B f
F F
F
F

ForceChapter 8
Buoyant Force
2. Plan, continued
Rearrange the equation to isolate the unknown:
( )
ρ ρ
=
=
– apparent weightB g
g
O f
B
F F
F
F

ForceChapter 8
Buoyant Force
3. Calculate
Substitute the values into the equation and solve:
( )ρ ρ
ρ
=
= = ×
= ×
3 3
3 3
7.84 N – 6.86 N = 0.98 N
7.84 N
1.00 10 kg/m
0.98 N
8.0 10 kg/m
B
g
O f
B
O
F
F
F

ForceChapter 8
Buoyant Force
4. Evaluate
From the table, the density of
gold is 19.3 × 103
kg/m3
.
Because 8.0 × 103
kg/m3
< 19.3
× 103
kg/m3
, the crown cannot
be pure gold.

Chapter 8
Objectives
• Calculate the pressure exerted by a fluid.
• Calculate how pressure varies with depth in a fluid.

Chapter 8
Pressure
• Pressure is the magnitude of the force on a surface
per unit area.
• Pascal’s principle states that pressure applied to a
fluid in a closed container is transmitted equally to
every point of the fluid and to the walls of the
container.
P =
F
A
pressure =
force
area

Chapter 8
Pascal’s Principle

Chapter 8
Pascal’s Principle
FF1 = F2
AA1 AA2

Chapter 8
Pressure, continued
• Pressure varies with depth
in a fluid.
• The pressure in a fluid
increases with depth.
( )
ρ= +
× ×
0
absolute pressure =
atmospheric pressure +
density free-fall acceleration depth
P P gh

Chapter 8
Fluid Pressure as a Function of Depth

Chapter 8
Objectives
• Examine the motion of a fluid using the continuity
equation.
• Recognize the effects of Bernoulli’s principle on fluid
motion.

Chapter 8
Fluid Flow
• Moving fluids can exhibit laminar (smooth) flow or
turbulent (irregular) flow.
• An ideal fluid is a fluid that has no internal friction or
viscosity and is incompressible.
• The ideal fluid model simplifies fluid-flow analysis.

Chapter 8
Characteristics of an Ideal Fluid

Chapter 8
Principles of Fluid Flow
• Continuity equation
A1v1 = A2v2
Area × velocity in
region 1 = area ×
velocity in region 2

Chapter 8
Principles of Fluid Flow, continued
• The speed of fluid flow
depends on cross-
sectional area.
• Bernoulli’s principle
states that the pressure
in a fluid decreases as
the fluid’s velocity
increases.

Chapter 8
Bernoulli’s Principle

Multiple Choice
1. Which of the following is the correct equation for the
net force acting on a submerged object?
A. Fnet = 0
B. Fnet = (ρobject – ρfluid)gVobject
C. Fnet = (ρfluid – ρobject)gVobject
D. Fnet = (ρfluid + ρobject)gVobject
Chapter 8

Multiple Choice, continued
2. How many times greater than the lifting force must
the force applied to a hydraulic lift be if the ratio of the
area where pressure is applied to the lifted area is
1/7 ?
F. 1/49
G. 1/7
H. 7
J. 49
Chapter 8

3. A typical silo on a farm has many bands wrapped
around its perimeter, as shown in the figure below.
Why is the spacing between successive bands
smaller toward the bottom?
A. to provide support for the silo’s sides above them
B. to resist the increasing pressure that the grains
exert with increasing depth
C. to resist the increasing pressure that the
atmosphere exerts with increasing depth
D. to make access to smaller quantities of grain near
the ground possible
Chapter 8

4. A fish rests on the bottom of a bucket of water while
the bucket is being weighed. When the fish begins to
swim around in the bucket, how does the reading on
the scale change?
F. The motion of the fish causes the scale reading to
increase.
G. The motion of the fish causes the scale reading to
decrease.
H. The buoyant force on the fish is exerted downward
on the bucket, causing the scale reading to increase.
J. The mass of the system, and so the scale
reading, will remain unchanged.
Chapter 8

Use the passage below
to answer questions 5–6.
A metal block (ρ = 7900
kg/m3
) is connected to a
spring scale by a string 5
cm in length. The block’s
weight in air is recorded. A
second reading is
recorded when the block is
placed in a tank of fluid
and the surface of the fluid
is 3 cm below the scale.
Chapter 8
5. If the fluid is oil (ρ < 1000
kg/m3
), which of the
following must be true?
A. The first scale reading
is larger than the second
reading.
B. The second scale
reading is larger than the
first reading.
C. The two scale
readings are identical.
D. The second scale
reading is zero.

Chapter 8
5. If the fluid is oil (ρ < 1000
kg/m3
), which of the
following must be true?
A. The first scale reading
is larger than the second
reading.
B. The second scale
reading is larger than the
first reading.
C. The two scale
D. The second scale
reading is zero.
kg/m3
) is connected to a
second reading is

Chapter 8
6. If the fluid is mercury (ρ
= 13 600 kg/m3
), which
of the following must be
true?
F. The first scale
reading is larger than
the second reading.
G. The second scale
reading is larger than
the first reading.
H. The two scale
J. The second scale
reading is zero.
kg/m3
) is connected to a
second reading is

Water near the top of a
dam flows down a spillway
to the base of the dam.
Atmospheric pressure is
identical at the top and
bottom of the dam.
Chapter 8
7. If the speed of the water
at the top of the spillway
is nearly 0 m/s, which of
the following equations
correctly describes the
speed of the water at
the bottom of the
spillway?
( )
( )
( )
( )
ρ
ρ
=
=
=
=
. 2 –
. 2 –
. 2 –
. 2 –
bottom water top bottom
bottom top bottom
bottom top bottom
v g h h
v g h h
v g h h
v g h h
A
B
C
D

bottom of the dam.
Chapter 8
7. If the speed of the water
at the top of the spillway
is nearly 0 m/s, which of
the following equations
correctly describes the
speed of the water at
the bottom of the
spillway?
( )
( )
( )
( )
ρ
ρ
=
=
=
=
. 2 –
.
.
2 –
. 2 –
2 –bottom top botto
bottom top bottom
bottom water top bo om
m
tt
v g h
v g h h
v h
v g
h
g h
h h
A
C
D
B

bottom of the dam.
Chapter 8
8. If the cross-sectional
area of the spillway
were half as large, how
many times faster
would the water flow out
of the spillway?
F. 1/4
G. 1/2
H. 2
J. 4

Short Response
9. Will an ice cube float higher in water or in mercury?
Explain your answer.
Chapter 8

Short Response, continued
9. Will an ice cube float higher in water or in mercury?
Explain your answer.
Answer: mercury; because the density of mercury is
greater than that of water
Chapter 8

10. The approximate inside diameter of the aorta is 1.6
cm, and that of a capillary is 1.0 × 10–6
m. The
average flow speed is about 1.0 m/s in the aorta and
1.0 cm/s in the capillaries. If all the blood in the aorta
eventually flows through the capillaries, estimate the
number of capillaries.
Chapter 8

10. The approximate inside diameter of the aorta is 1.6
cm, and that of a capillary is 1.0 × 10–6
m. The
average flow speed is about 1.0 m/s in the aorta and
1.0 cm/s in the capillaries. If all the blood in the aorta
eventually flows through the capillaries, estimate the
number of capillaries.
Answer: 2.5 × 1010
capillaries
Chapter 8

11. A hydraulic brake system is shown below. The area
of the piston in the master cylinder is 6.40 cm2
, and
the area of the piston in the brake cylinder is 1.75
cm2
. The coefficient of friction between the brake
shoe and wheel drum is 0.50. What is the frictional
force between the brake shoe and wheel drum when
a force of 44 N is exerted on the pedal?
Chapter 8

11. A hydraulic brake system is shown below. The area
of the piston in the master cylinder is 6.40 cm2
, and
the area of the piston in the brake cylinder is 1.75
cm2
. The coefficient of friction between the brake
shoe and wheel drum is 0.50. What is the frictional
force between the brake shoe and wheel drum when
a force of 44 N is exerted on the pedal?
Answer: 6.0 N
Chapter 8

Extended Response
Chapter 8
Base your answers to questions 12–14 on the
information below.
Oil, which has a density of 930.0 kg/m3
, floats on water.
A rectangular block of wood with a height, h, of 4.00 cm
and a density of 960.0 kg/m3
floats partly in the water,
and the rest floats under the oil layer.
12. What is the balanced force equation for this
situation?

Extended Response
Chapter 8
information below.
, floats on water.
12. What is the balanced force equation for this
situation?
Answer: FB,oil + FB,water = Fg,block

Extended Response, continued
Chapter 8
information below.
, floats on water.
13. What is the equation that describes y, the thickness
of the part of the block that is submerged in water?

13. What is the equation that describes y, the thickness
of the part of the block that is submerged in water?
Answer:
Chapter 8
( )
( )
ρ ρ
ρ ρ
=
–
–
block oil
water oil
y h
information below.
, floats on water.

Chapter 8
information below.
, floats on water.
14. What is the value for y?

14. What is the value for y?
Answer: 1.71 × 10–2
m
Chapter 8
information below.
, floats on water.

Hp08win 1228295929722748-9

Recommended

Recommended

More Related Content

Similar to Hp08win 1228295929722748-9

Similar to Hp08win 1228295929722748-9 (14)

More from Cleophas Rwemera

More from Cleophas Rwemera (20)

Recently uploaded

Recently uploaded (20)

Hp08win 1228295929722748-9