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Academic PhysicsTRANSCRIPT
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Chapter 8 – Fluid Dynamics
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Fluid MechanicsChapter 8
Table of Contents
Section 1 Fluids and Buoyant Force
Section 2 Fluid Pressure
Section 3 Fluids in Motion
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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.
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Section 1 Fluids and Buoyant 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
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Section 1 Fluids and Buoyant ForceChapter 8
Density and Buoyant Force
• The concentration of matter of an object is called the mass density.
m
V
mass density mass
volume
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Chapter 8
Mass Density
Section 1 Fluids and Buoyant Force
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Section 1 Fluids and Buoyant 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.
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Chapter 8
Buoyant Force and Archimedes’ Principle
Section 1 Fluids and Buoyant Force
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Chapter 8
Displaced Volume of a Fluid
Section 1 Fluids and Buoyant Force
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Section 1 Fluids and Buoyant ForceChapter 8
Density and Buoyant Force, continued
• 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
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Chapter 8
Buoyant Force on Floating Objects
Section 1 Fluids and Buoyant Force
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Chapter 8
Buoyant Force
Section 1 Fluids and Buoyant Force
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Section 1 Fluids and Buoyant ForceChapter 8
Density and Buoyant Force, continued
• For a floating object, the buoyant force equals the object’s weight.
• For an object with density O submerged in a fluid of density f, the buoyant force FB obeys the following ratio:
Fg(object)
FB
O
f
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Section 1 Fluids and Buoyant 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.
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Section 1 Fluids and Buoyant ForceChapter 8
Sample Problem, continued
Buoyant Force1. DefineGiven:
Fg = 7.84 Napparent weight = 6.86 N
f = pwater = 1.00 103 kg/m3
Unknown:
O = ?
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Section 1 Fluids and Buoyant ForceChapter 8
Diagram:
Sample Problem, continued
Buoyant Force1. 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.
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Section 1 Fluids and Buoyant ForceChapter 8
Sample Problem, continued
Buoyant Force2. Plan
Choose an equation or situation: Because the object is completely submerged, consider the ratio of the weight to the buoyant force.
– apparent weightg B
g O
B f
F F
F
F
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Section 1 Fluids and Buoyant ForceChapter 8
Sample Problem, continued
Buoyant Force2. Plan, continued
Rearrange the equation to isolate the unknown:
– apparent weightB g
gO f
B
F F
F
F
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Section 1 Fluids and Buoyant ForceChapter 8
Sample Problem, continued
Buoyant Force3. Calculate
Substitute the values into the equation and solve:
3 3
3 3
7.84 N – 6.86 N = 0.98 N
7.84 N1.00 10 kg/m
0.98 N
8.0 10 kg/m
B
gO f
B
O
F
F
F
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Section 1 Fluids and Buoyant ForceChapter 8
Sample Problem, continued
Buoyant Force4. 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.
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Section 2 Fluid PressureChapter 8
Objectives
• Calculate the pressure exerted by a fluid.
• Calculate how pressure varies with depth in a fluid.
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Section 2 Fluid PressureChapter 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
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Chapter 8
Pascal’s Principle
Section 2 Fluid Pressure
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Chapter 8
Pascal’s Principle
Section 2 Fluid Pressure
FF1 = F2
AA1 AA2
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Section 2 Fluid PressureChapter 8
Pressure, continued
• Pressure varies with depth in a fluid.
• The pressure in a fluid increases with depth.
0
absolute pressure =
atmospheric pressure +
density free-fall acceleration depth
P P gh
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Chapter 8
Fluid Pressure as a Function of Depth
Section 2 Fluid Pressure
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Section 3 Fluids in MotionChapter 8
Objectives
• Examine the motion of a fluid using the continuity equation.
• Recognize the effects of Bernoulli’s principle on fluid motion.
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Section 3 Fluids in MotionChapter 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.
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Chapter 8
Characteristics of an Ideal Fluid
Section 3 Fluids in Motion
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Section 3 Fluids in MotionChapter 8
Principles of Fluid Flow
• Continuity equation
A1v1 = A2v2
Area velocity in region 1 = area velocity in region 2
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Section 3 Fluids in MotionChapter 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.
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Chapter 8
Bernoulli’s Principle
Section 3 Fluids in Motion
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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 = (object – fluid)gVobject
C. Fnet = (fluid – object)gVobject
D. Fnet = (fluid + object)gVobject
Standardized Test PrepChapter 8
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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 = (object – fluid)gVobject
C. Fnet = (fluid – object)gVobject
D. Fnet = (fluid + object)gVobject
Standardized Test PrepChapter 8
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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
Standardized Test PrepChapter 8
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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
Standardized Test PrepChapter 8
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Multiple Choice, continued
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 themB. to resist the increasing pressure that the grains exert with increasing depthC. to resist the increasing pressure that the atmosphere exerts with increasing depthD. to make access to smaller quantities of grain near the ground possible
Standardized Test PrepChapter 8
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Multiple Choice, continued
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 themB. to resist the increasing pressure that the grains exert with increasing depthC. to resist the increasing pressure that the atmosphere exerts with increasing depthD. to make access to smaller quantities of grain near the ground possible
Standardized Test PrepChapter 8
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Multiple Choice, continued
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.
Standardized Test PrepChapter 8
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Multiple Choice, continued
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.
Standardized Test PrepChapter 8
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Multiple Choice, continuedUse the passage below to answer questions 5–6.
A metal block ( = 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.
Standardized Test PrepChapter 8
5. If the fluid is oil ( < 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.
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Multiple Choice, continued
Standardized Test PrepChapter 8
5. If the fluid is oil ( < 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.
Use the passage below to answer questions 5–6.
A metal block ( = 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.
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Multiple Choice, continued
Standardized Test PrepChapter 8
6. If the fluid is mercury ( = 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 readings are identical.J. The second scale reading is zero.
Use the passage below to answer questions 5–6.
A metal block ( = 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.
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Multiple Choice, continued
Standardized Test PrepChapter 8
6. If the fluid is mercury ( = 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 readings are identical.J. The second scale reading is zero.
Use the passage below to answer questions 5–6.
A metal block ( = 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.
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Multiple Choice, continuedUse the passage below to answer questions 7–8.
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.
Standardized Test PrepChapter 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?
. 2 –
. 2 –
. 2 –
. 2 –
bottom water top bottom
bottom top bottom
bottom top bottom
bottom water top bottom
v g h h
v g h h
v g h h
v g h h
A
B
C
D
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Multiple Choice, continuedUse the passage below to answer questions 7–8.
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.
Standardized Test PrepChapter 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?
. 2 –
.
.
2 –
. 2 –
2 –bottom top botto
bottom water top bottom
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
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Multiple Choice, continuedUse the passage below to answer questions 7–8.
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.
Standardized Test PrepChapter 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
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Multiple Choice, continuedUse the passage below to answer questions 7–8.
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.
Standardized Test PrepChapter 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
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Short Response
9. Will an ice cube float higher in water or in mercury? Explain your answer.
Standardized Test PrepChapter 8
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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
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Short Response, continued
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.
Standardized Test PrepChapter 8
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Short Response, continued
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
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Short Response, continued
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?
Standardized Test PrepChapter 8
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Short Response, continued
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
Standardized Test PrepChapter 8
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Extended Response
Standardized Test PrepChapter 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?
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Extended Response
Standardized Test PrepChapter 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?
Answer: FB,oil + FB,water = Fg,block
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Extended Response, continued
Standardized Test PrepChapter 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.
13. What is the equation that describes y, the thickness of the part of the block that is submerged in water?
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Extended Response, continued
13. What is the equation that describes y, the thickness of the part of the block that is submerged in water?Answer:
Standardized Test PrepChapter 8
–
–block oil
water oil
y h
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.
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Extended Response, continued
Standardized Test PrepChapter 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.
14. What is the value for y?
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Extended Response, continued
14. What is the value for y?
Answer: 1.71 10–2 m
Standardized Test PrepChapter 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.