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properly.)
75. Pressure in the spinal fluid is measured as shown
in Figure 11.40. If the pressure in the spinal fluid
is 10.0 mm Hg: (a) What is the reading of the
water manometer in cm water? (b) What is the
reading if the person sits up, placing the top of the
fluid 60 cm above the tap? The fluid density is
1.05 g/mL.
FIGURE 11.40 A water manometer used to measure
pressure in the spinal fluid. The height of the fluid in the
manometer is measured relative to the spinal column, and
the manometer is open to the atmosphere. The measured
pressure will be considerably greater if the person sits up.
76. Calculate the maximum force in newtons exerted
by the blood on an aneurysm, or ballooning, in a
major artery, given the maximum blood pressure
for this person is 150 mm Hg and the effective
area of the aneurysm is . Note that this
force is great enough to cause further
enlargement and subsequently greater force on
the ever-thinner vessel wall.
77. During heavy lifting, a disk between spinal
vertebrae is subjected to a 5000-N compressional
force. (a) What pressure is created, assuming that
the disk has a uniform circular cross section 2.00
cm in radius? (b) What deformation is produced if
the disk is 0.800 cm thick and has a Young’s
modulus of ?
78. When a person sits erect, increasing the vertical
position of their brain by 36.0 cm, the heart must
continue to pump blood to the brain at the same
rate. (a) What is the gain in gravitational potential
energy for 100 mL of blood raised 36.0 cm? (b)
What is the drop in pressure, neglecting any losses
due to friction? (c) Discuss how the gain in
gravitational potential energy and the decrease in
pressure are related.
79. (a) How high will water rise in a glass capillary
tube with a 0.500-mm radius? (b) How much
gravitational potential energy does the water gain?
(c) Discuss possible sources of this energy.
80. A negative pressure of 25.0 atm can sometimes
be achieved with the device in Figure 11.41 before
the water separates. (a) To what height could such
a negative gauge pressure raise water? (b) How
much would a steel wire of the same diameter and
length as this capillary stretch if suspended from
above?
FIGURE 11.41 (a) When the piston is raised, it stretches the
liquid slightly, putting it under tension and creating a
negative absolute pressure (b) The liquid
eventually separates, giving an experimental limit to
negative pressure in this liquid.
81. Suppose you hit a steel nail with a 0.500-kg
hammer, initially moving at and brought
to rest in 2.80 mm. (a) What average force is
exerted on the nail? (b) How much is the nail
compressed if it is 2.50 mm in diameter and
6.00-cm long? (c) What pressure is created on the
1.00-mm-diameter tip of the nail?
82. Calculate the pressure due to the ocean at the
bottom of the Marianas Trench near the
Philippines, given its depth is and
assuming the density of sea water is constant all
the way down. (b) Calculate the percent decrease
in volume of sea water due to such a pressure,
assuming its bulk modulus is the same as water
and is constant. (c) What would be the percent
increase in its density? Is the assumption of
constant density valid? Will the actual pressure be
greater or smaller than that calculated under this
assumption?
83. The hydraulic system of a backhoe is used to lift a
load as shown in Figure 11.42. (a) Calculate the
force the secondary cylinder must exert to
support the 400-kg load and the 150-kg brace and
shovel. (b) What is the pressure in the hydraulic
fluid if the secondary cylinder is 2.50 cm in
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diameter? (c) What force would you have to exert
on a lever with a mechanical advantage of 5.00
acting on a primary cylinder 0.800 cm in diameter
to create this pressure?
FIGURE 11.42 Hydraulic and mechanical lever systems are
used in heavy machinery such as this back hoe.
84. Some miners wish to remove water from a mine
shaft. A pipe is lowered to the water 90 m below,
and a negative pressure is applied to raise the
water. (a) Calculate the pressure needed to raise
the water. (b) What is unreasonable about this
pressure? (c) What is unreasonable about the
premise?
85. You are pumping up a bicycle tire with a hand
pump, the piston of which has a 2.00-cm radius.
(a) What force in newtons must you exert to create
a pressure of (b) What is
unreasonable about this (a) result? (c) Which
premises are unreasonable or inconsistent?
86. Consider a group of people trying to stay afloat
after their boat strikes a log in a lake. Construct a
problem in which you calculate the number of
people that can cling to the log and keep their
heads out of the water. Among the variables to be
considered are the size and density of the log, and
what is needed to keep a person’s head and arms
above water without swimming or treading water.
87. The alveoli in emphysema victims are damaged
and effectively form larger sacs. Construct a
problem in which you calculate the loss of
pressure due to surface tension in the alveoli
because of their larger average diameters. (Part of
the lung’s ability to expel air results from pressure
created by surface tension in the alveoli.) Among
the things to consider are the normal surface
tension of the fluid lining the alveoli, the average
alveolar radius in normal individuals and its
average in emphysema sufferers.
Test Prep for AP® Courses
11.2 Density
1. An under-inflated volleyball is pumped full of air so
that its radius increases by 10%. Ignoring the mass
of the air inserted into the ball, what will happen to
the volleyball's density?
a. The density of the volleyball will increase by
approximately 25%.
b. The density of the volleyball will increase by
approximately 10%.
c. The density of the volleyball will decrease by
approximately 10%.
d. The density of the volleyball will decrease by
approximately 17%.
e. The density of the volleyball will decrease by
approximately 25%.
2. A piece of aluminum foil has a known surface
density of 15 g/cm2. If a 100-gram hollow cube
were constructed using this foil, determine the
approximate side length of this cube.
a. 1.05 cm
b. 1.10 cm
c. 2.6 cm
d. 6.67 cm
e. 15 cm
3. A cube of polystyrene measuring 10 cm per side
lies partially submerged in a large container of
water.
a. If 90% of the polystyrene floats above the
surface of the water, what is the density of the
polystyrene? (Note: The density of water is
1000 kg/m3.)
b. A 0.5 kg mass is placed on the block of
polystyrene. What percentage of the block now
remains above water?
c. The water is poured out of the container and
replaced with ethyl alcohol (density = 790
kg/m3).
i. Will the block be able to remain partially
11 • Test Prep for AP® Courses 519
submerged in this new fluid? Explain.
ii. Will the block be able to remain partially
submerged in this new fluid with the 0.5 kg
mass placed on top? Explain.
d. Without using a container of water, explain how
you could determine the density of the
polystyrene mentioned above if the material
instead were spherical.
4. Four spheres are hung from a variety of different
springs. The table below describes the characteristics
of both the spheres and the springs from which they
are hung. Use this information to rank the density of
each sphere from least to greatest. Show work
supporting your ranking.
Material
Type
Radius of
Sphere
Stretch of
Spring
(from
equilibrium)
Spring
Constant
A 10 cm 5 cm 2 N/m
B 5 cm 8 cm 8 N/m
C 8 cm 10 cm 6 N/m
D 8 cm 12 cm 10 N/m
TABLE 11.6
Rank the densities of the objects listed above, from
greatest to least. Show work supporting your ranking.
11.3 Pressure
5. A cylindrical drum of radius 0.5 m is used to hold
400 liters of petroleum ether (density = .68 g/mL or
680 kg/m3).
(Note: 1 liter = 0.001 m3)
a. Determine the amount of pressure applied to
the walls of the drum if the petroleum ether
fills the drum to its top.
b. Determine the amount of pressure applied to
the floor of the drum if the petroleum ether fills
the drumto its top.
c. If the drum were redesigned to hold 800 liters
of petroleum ether:
i. How would the pressure on the walls
change?
Would it increase, decrease, or stay the
same?
ii. How would the pressure on the floor
change?
Would it increase, decrease, or stay the
same?
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CONNECTION FOR AP® COURSES
CHAPTER 12
Fluid Dynamics and Its Biological and Medical
Applications
12.1 Flow Rate and Its Relation to Velocity
12.2 Bernoulli’s Equation
12.3 The Most General Applications of Bernoulli’s Equation
12.4 Viscosity and Laminar Flow; Poiseuille’s Law
12.5 The Onset of Turbulence
12.6 Motion of an Object in a Viscous Fluid
12.7 Molecular Transport Phenomena: Diffusion, Osmosis, and Related Processes
How do planes fly? How do we model blood flow? How do sprayers work for
paints or aerosols? What is the purpose of a water tower? To answer these questions, we will examine fluid
dynamics. The equations governing fluid dynamics are derived from the same equations that represent energy
conservation. One of the most powerful equations in fluid dynamics is Bernoulli's equation, which governs the
relationship between fluid pressure, kinetic energy, and potential energy (Essential Knowledge 5.B.10). We will see
how Bernoulli's equation explains the pressure difference that provides lift for airplanes and provides the means for
fluids (like water or paint or perfume) to move in useful ways.
The content in this chapter supports:
FIGURE 12.1 Many fluids are flowing in this scene. Water from the hose and smoke from the fire are visible flows. Less visible are the flow
of air and the flow of fluids on the ground and within the people fighting the fire. (credit: Andrew Magill, Flickr)
CHAPTER OUTLINE
• Calculate flow rate.
• Define units of volume.
• Describe incompressible fluids.
• Explain the consequences of the equation of continuity.
Flow rate is defined to be the volume of fluid passing by some location through an area during a period of time, as
seen in Figure 12.2. In symbols, this can be written as
where is the volume and is the elapsed time.
The SI unit for flow rate is , but a number of other units for are in common use. For example, the heart of a
resting adult pumps blood at a rate of 5.00 liters per minute (L/min). Note that a liter (L) is 1/1000 of a cubic meter
or 1000 cubic centimeters ( or ). In this text we shall use whatever metric units are most
convenient for a given situation.
FIGURE 12.2 Flow rate is the volume of fluid per unit time flowing past a point through the area . Here the shaded cylinder of fluid flows
past point in a uniform pipe in time . The volume of the cylinder is and the average velocity is so that the flow rate is
.
EXAMPLE 12.1
Calculating Volume from Flow Rate: The Heart Pumps a Lot of Blood in a Lifetime
How many cubic meters of blood does the heart pump in a 75-year lifetime, assuming the average flow rate is 5.00
L/min?
Strategy
Time and flow rate are given, and so the volume can be calculated from the definition of flow rate.
Solution
Solving for volume gives
12.1
522 12 • Fluid Dynamics and Its Biological and Medical Applications
Big Idea 5 Changes that occur as a result of interactions are constrained by conservation laws.
Enduring Understanding 5.B The energy of a system is conserved.
Essential Knowledge 5.B.10 Bernoulli's equation describes the conservation of energy in a fluid flow.
Enduring Understanding 5.F Classically, the mass of a system is conserved.
Essential Knowledge 5.F.1 The continuity equation describes conservation of mass flow rate in fluids.
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ap-r-courses)
12.1 Flow Rate and Its R elation to Velocity
LEARNING OBJECTIVES
By the end of this section, you will be able to:
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	Chapter 11 Fluid Statics
	Test Prep for AP® Courses
	Chapter 12 Fluid Dynamics and Its Biological and Medical Applications
	Connection for AP® Courses
	12.1 Flow Rate and Its Relation to Velocity