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# Ch 14 v1

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• pg 1
```									Questions
denotes answer available in Student Solutions Manual/Study Guide; O denotes objective question

1. O Figure Q14.1 shows aerial views from directly              8. When an object is immersed in a liquid at rest, why
above two dams. Both dams are equally wide (the                 is the net force on the object in the horizontal direction
vertical dimension in the diagram) and equally high             equal to zero?
(into the page in the diagram). The dam on the left
9. A barge is carrying a load of gravel along a river.
holds back a very large lake, and the dam on the right
The barge approaches a low bridge, and the captain
holds back a narrow river. Which dam has to be built
realizes that the top of the pile of gravel is not going to
more strongly? (a) the dam on the left (b) the dam on
make it under the bridge. The captain orders the crew
the right (c) both the same (d) cannot be predicted
to shovel gravel from the pile into the water. Is that a
good decision?
10. An empty metal soap dish barely floats in water. A
bar of Ivory soap floats in water. When the soap is
stuck in the soap dish, the combination sinks. Explain
why.
11. O A beach ball is made of thin plastic. It has been
inflated with air, but the plastic is not stretched. By
swimming with fins on, you manage to take the ball
from the surface of a pool to the bottom. Once the ball
is completely submerged, what happens to the buoyant
2. Two thin-walled drinking glasses having equal base           force exerted on the beach ball as you take it deeper?
areas but different shapes, with very different cross-          (a) increases (b) remains constant (c) decreases (d) is
sectional areas above the base, are filled to the same          impossible to determine
level with water. According to the expression
P = P0 + gh, the pressure is the same at the bottom of         12. If you release a ball while inside a freely falling
both glasses. In view of this equality, why does one            elevator, the ball remains in front of you rather than
glass weigh more than the other?                                falling to the floor because the ball, the elevator, and
you all experience the same downward gravitational
3. Because atmospheric pressure is about 105 N/m2               acceleration. What happens if you repeat this
and the area of a person’s chest is about 0.13 m2, the          experiment with a helium-filled balloon? (This
force of the atmosphere on one’s chest is around 13             question is tricky.)
000 N. In view of this enormous force, why don’t our
bodies collapse?                                                13. O A small piece of steel is tied to a block of wood.
When the wood is placed in a tub of water with the
4. A fish rests on the bottom of a bucket of water              steel on top, half of the block is submerged. Now the
while the bucket is being weighed on a scale. When              block is inverted so that the steel is under water. (i)
the fish begins to swim around, does the scale reading          Does the amount of the block submerged (a) increase,
change?                                                         (b) decrease, or (c) remain the same? (ii) What
5. You are a passenger on a spacecraft. For your                happens to the water level in the tub when the block is
survival and comfort, the interior contains air just like       inverted? (a) It rises. (b) It falls. (c) It remains the
that at the surface of the Earth. The spacecraft is             same.
coasting through a very empty region of space. That             14. How would you determine the density of an
is, a nearly perfect vacuum exists just outside the wall.       irregularly shaped rock?
Suddenly, a meteoroid pokes a hole, about the size of
a large coin, right through the wall next to your seat.         15. O Rank the buoyant forces exerted on the
What happens? Is there anything you can or should do            following seven objects, from the largest to the
about it?                                                       smallest. Assume the objects have been dropped into a
swimming pool and allowed to come to mechanical
6. Does a ship float higher in the water of an inland           equilibrium. If any buoyant forces are equal, state that
lake or in the ocean? Why?                                      in your ranking. (a) a block of solid oak (b) an
7. O An apple is held completely submerged just                 aluminum block of equal volume to the wood (c) a
below the surface of water in a container. The apple is         beach ball made of thin plastic and inflated with air, of
then moved to a deeper point in the water. Compared             equal volume (d) an iron block of equal volume (e) a
with the force needed to hold the apple just below the          thin-walled, sealed bottle of water equal in volume to
surface, what is the force needed to hold it at the             the wood (f) an aluminum block having the same mass
deeper point? (a) larger (b) the same (c) smaller (d)           as the wood (g) an iron block of equal mass
impossible to determine                                         16. O A person in a boat floating in a small pond
throws an anchor overboard. What happens to the

2 = intermediate 3 = challenging      = SSM/SG          = ThomsonNOW    = symbolic reasoning       =qualitative reasoning
level of the pond? (a) It rises. (b) It falls. (c) It remains     25. Prairie dogs (Fig. Q14.25) ventilate their burrows
the same.                                                         by building a mound around one entrance, which is
open to a stream of air when wind blows from any
17. Is the buoyant force a conservative force? Is a
direction. A second entrance at ground level is open to
potential energy associated with it? Explain your
almost stagnant air. How does this construction create
answers.
an airflow through the burrow?
18. An unopened can of diet cola floats when placed
in a tank of water, whereas a can of regular cola of the
same brand sinks in the tank. What do you suppose
could explain this behavior?
19. O A piece of unpainted porous wood floats in a
container partly filled with water. The container is
sealed and pressurized above atmospheric pressure.
What happens to the wood? (a) It rises. (b) It falls. (c)
It remains at the same level.
20. The water supply for a city is often provided from
reservoirs built on high ground. Water flows from the
reservoir, through pipes, and into your home when you
turn the tap on your faucet. Why is the water flow
26. In Figure Q14.26, an airstream moves from right
more rapid out of a faucet on the first floor of a
to left through a tube that is constricted at the middle.
building than in an apartment on a higher floor?
Three table-tennis balls are levitated in equilibrium
21. If the airstream from a hair dryer is directed over a         above the vertical columns through which the air
table-tennis ball, the ball can be levitated. Explain.            escapes. (a) Why is the ball at the right higher than the
22. When ski jumpers are airborne (Fig. Q14.22), they             one in the middle? (b) Why is the ball at the left lower
bend their bodies forward and keep their hands at their           than the ball at the right even though the horizontal
sides. Why?                                                       tube has the same dimensions at these two points?

23. Why do airplane pilots prefer to take off with the            27. O (i) A glass of water contains floating ice cubes.
airplane facing into the wind?                                    When the ice melts, does the water level in the glass
24. O A water supply maintains a constant rate of flow            (a) go up, (b) go down, or (c) remain the same? (ii)
for water in a hose. You want to change the opening of            One of the predicted problems due to global warming
the nozzle so that water leaving the nozzle reaches a             is that ice in the polar ice caps will melt and raise sea
height that is four times the current maximum height              level everywhere in the world. Is that more of a worry
the water reaches with the nozzle vertical. To do so,             for ice (a) at the north pole, where most of the ice
what should you do? (a) decrease the area of the                  floats on water; (b) at the south pole, where most of
opening by a factor of 16 (b) decrease the area by a              the ice sits on land; (c) both at the north and the south
factor of 8 (c) decrease the area by a factor of 4 (d)            poles equally; or (d) at neither pole?
decrease the area by a factor of 2 (e) give up because it
cannot be done

2 = intermediate 3 = challenging         = SSM/SG         = ThomsonNOW    = symbolic reasoning      =qualitative reasoning
Problems
The Problems from this chapter may be assigned online in WebAssign.
Sign in at www.thomsonedu.com and go to ThomsonNOW to assess your understanding of this
chapter’s topics with additional quizzing and conceptual questions.
1,2,3 denotes straightforward, intermediate, challenging;      denotes full solution available in Student Solutions
Manual/Study Guide;       denotes coached solution with hints available at www.thomsonedu.com;             denotes
developing symbolic reasoning;        denotes asking for qualitative reasoning;     denotes computer useful in solving
problem
rainstorm, drainage from the street fills up the space in
Section 14.1 Pressure                                               front of the concrete wall, but not the basement behind
the wall. The water does not soak into the clay soil.
1. Calculate the mass of a solid iron sphere that has a
Find the force the water causes on the foundation wall.
diameter of 3.00 cm.
For comparison, the gravitational force exerted on the
2. Find the order of magnitude of the density of the                water is
nucleus of an atom. What does this result suggest                   (2.40 m)(9.60 m)(0.183 m)
concerning the structure of matter? Model a nucleus as                              (1 000 kg/m3)(9.80 m/s2) = 41.3 kN
consisting of protons and neutrons closely packed
together. Each has mass 1.67  10–27 kg and radius on               10. (a) A powerful vacuum cleaner has a hose 2.86 cm
the order of 10–15 m.                                               in diameter. With no nozzle on the hose, what is the
weight of the heaviest brick that the cleaner can lift
3. A 50.0-kg woman balances on one heel of a pair of                (Fig. P14.10a)? (b) What If? An octopus uses one
high-heeled shoes. If the heel is circular and has a                sucker of diameter 2.86 cm on each of the two shells
radius of 0.500 cm, what pressure does she exert on                 of a clam in an attempt to pull the shells apart (Fig.
the floor?                                                          P14.10b). Find the greatest force the octopus can exert
4. What is the total mass of the Earth’s atmosphere?                in seawater 32.3 m deep. Caution: Experimental
(The radius of the Earth is 6.37  10 m, and
6                            verification can be interesting, but do not drop a brick
atmospheric pressure at the surface is 1.013  105                  on your foot. Do not overheat the motor of a vacuum
2
N/m .)                                                              cleaner. Do not get an octopus mad at you.

Section 14.2 Variation of Pressure with Depth
5. The spring of the pressure gauge shown in Figure
14.2 has a force constant of 1 000 N/m, and the piston
has a diameter of 2.00 cm. As the gauge is lowered
into water, what change in depth causes the piston to
move in by 0.500 cm?
6. (a) Calculate the absolute pressure at an ocean depth
of 1 000 m. Assume the density of seawater is 1 024
kg/m3 and the air above exerts a pressure of 101.3 kPa.
(b) At this depth, what force must the frame around a              11. A swimming pool has dimensions
circular submarine porthole having a diameter of 30.0
30.0 m  10.0 m and a flat bottom. When the pool is
cm exert to counterbalance the force exerted by the
filled to a depth of 2.00 m with fresh water, what is the
water?
force caused by the water on the bottom? On each
7.    What must be the contact area between a suction              end? On each side?
cup (completely exhausted) and a ceiling if the cup is             12. The tank in Figure P14.12 is filled with water
to support the weight of an 80.0-kg student?                       2.00 m deep. At the bottom of one sidewall is a
8. The small piston of a hydraulic lift has a cross-               rectangular hatch 1.00 m high and 2.00 m wide that is
sectional area of 3.00 cm2 and its large piston has a              hinged at the top of the hatch. (a) Determine the force
cross-sectional area of 200 cm2 (Fig. 14.4a). What                 the water causes on the hatch. (b) Find the torque
force must be applied to the small piston for the lift to          caused by the water about the hinges.
raise a load of 15.0 kN? (In service stations, this force
is usually exerted by compressed air.)
9. For the basement of a new house, a hole is dug in
the ground, with vertical sides going down 2.40 m. A
concrete foundation wall is built across the 9.60-m
width of the excavation. This foundation wall is 0.183
m from the front of the basement hole. During a

2 = intermediate 3 = challenging       = SSM/SG       = ThomsonNOW          = symbolic reasoning     =qualitative reasoning
13. Review problem. The Abbott of Aberbrothock               16. Mercury is poured into a U-tube as shown in
paid for a bell moored to the Inchcape Rock to warn          Figure P14.16a. The left arm of the tube has cross-
sailors away. Assume the bell was 3.00 m in diameter         sectional area A1 of 10.0 cm2, and the right arm has a
and cast from brass with a bulk modulus of 14.0  1010       cross-sectional area A2 of 5.00 cm2. One hundred
N/m2. The pirate Ralph the Rover cut loose the bell          grams of water are then poured into the right arm as
and threw it into the ocean. By how much did the             shown in Figure P14.16b. (a) Determine the length of
diameter of the bell decrease as it sank to a depth of       the water column in the right arm of the U-tube. (b)
10.0 km? Years later, the klutz drowned when his ship        Given that the density of mercury is 13.6 g/cm3, what
collided with the rock. Note: The brass is compressed        distance h does the mercury rise in the left arm?
uniformly, so you may model the bell as a sphere of
diameter 3.00 m.

Section 14.3 Pressure Measurements
14. Figure P14.14 shows Superman attempting to
drink water through a very long straw. With his great
strength he achieves maximum possible suction. The
walls of the tubular straw do not collapse. (a) Find the
maximum height through which he can lift the water.
(b) What If? Still thirsty, the Man of Steel repeats his
attempt on the Moon, which has no atmosphere. Find
17. Normal atmospheric pressure is 1.013  105 Pa.
the difference between the water levels inside and
The approach of a storm causes the height of a
outside the straw.
mercury barometer to drop by 20.0 mm from the
normal height. What is the atmospheric pressure? (The
density of mercury is 13.59 g/cm3.)
18. A tank with a flat bottom of area A and vertical
sides is filled to a depth h with water. The pressure is
1 atm at the top surface. (a) What is the absolute
pressure at the bottom of the tank? (b) Suppose an
object of mass M and density less than the density of
water is placed in the tank and floats. No water
overflows. What is the resulting increase in pressure at
the bottom of the tank? (c) Evaluate your results for a
backyard swimming pool with depth 1.50 m and a
circular base with diameter 6.00 m. Two persons with
combined mass 150 kg enter the pool and float quietly
there. Find the original absolute pressure and the
pressure increase at the bottom of the pool.
15.        Blaise Pascal duplicated Torricelli’s             19. The human brain and spinal cord are immersed
barometer using a red Bordeaux wine, of density 984          in the cerebrospinal fluid. The fluid is normally
kg/m3, as the working liquid (Fig. P14.15). What was         continuous between the cranial and spinal cavities and
the height h of the wine column for normal                   exerts a pressure of 100 to 200 mm of H2O above the
atmospheric pressure? Would you expect the vacuum            prevailing atmospheric pressure. In medical work,
above the column to be as good as for mercury?               pressures are often measured in units of millimeters of
H2O because body fluids, including the cerebrospinal
fluid, typically have the same density as water. The
pressure of the cerebrospinal fluid can be measured by
means of a spinal tap as illustrated in Figure P14.19.

2 = intermediate 3 = challenging      = SSM/SG       = ThomsonNOW    = symbolic reasoning     =qualitative reasoning
23. A 10.0-kg block of metal measuring 12.0 cm 
10.0 cm  10.0 cm is suspended from a scale and
immersed in water as shown in Figure P14.22b. The
12.0-cm dimension is vertical, and the top of the block
is 5.00 cm below the surface of the water. (a) What are
the forces acting on the top and on the bottom of the
block? (Take P0 = 101.30 kPa.) (b) What is the
reading of the spring scale? (c) Show that the buoyant
force equals the difference between the forces at the
top and bottom of the block.
A hollow tube is inserted into the spinal column, and        24. The weight of a rectangular block of low-
the height to which the fluid rises is observed. If the      density material is 15.0 N. With a thin string, the
fluid rises to a height of 160 mm, we write its gauge        center of the horizontal bottom face of the block is tied
pressure as 160 mm H2O. (a) Express this pressure in         to the bottom of a beaker partly filled with water.
pascals, in atmospheres, and in millimeters of               When 25.0% of the block’s volume is submerged, the
mercury. (b) Sometimes it is necessary to determine          tension in the string is 10.0 N. (a) Sketch a free-body
whether an accident victim has suffered a crushed            diagram for the block, showing all forces acting on it.
vertebra that is blocking flow of the cerebrospinal          (b) Find the buoyant force on the block. (c) Oil of
fluid in the spinal column. In other cases, a physician      density 800 kg/m3 is now steadily added to the beaker,
may suspect that a tumor or other growth is blocking         forming a layer above the water and surrounding the
the spinal column and inhibiting flow of cerebrospinal       block. The oil exerts forces on each of the four
fluid. Such conditions can be investigated by means of       sidewalls of the block that the oil touches. What are
Queckenstedt’s test. In this procedure, the veins in the     the directions of these forces? (d) What happens to the
patient’s neck are compressed to make the blood              string tension as the oil is added? Explain how the oil
pressure rise in the brain. The increase in pressure in      has this effect on the string tension. (e) The string
the blood vessels is transmitted to the cerebrospinal        breaks when its tension reaches 60.0 N. At this
fluid. What should be the normal effect on the height        moment, 25.0% of the block’s volume is still below
of the fluid in the spinal tap? (c) Suppose compressing      the waterline. What additional fraction of the block’s
the veins had no effect on the fluid level. What might       volume is below the top surface of the oil? (f) After
account for this result?                                     the string breaks, the block comes to a new
equilibrium position in the beaker. It is now in contact
Section 14.4 Buoyant Forces and Archimedes’s                 only with the oil. What fraction of the block’s volume
Principle                                                    is submerged?
20. (a) A light balloon is filled with 400 m3 of helium.     25. Preparing to anchor a buoy at the edge of a
At 0°C, the balloon can lift a payload of what mass?         swimming area, a worker uses a rope to lower a
(b) What If? In Table 14.1, observe that the density of      cubical concrete block, 0.250 m on each edge, into
hydrogen is nearly one-half the density of helium.           ocean water. The block moves down at a constant
What load can the balloon lift if filled with hydrogen?      speed of 1.90 m/s. You can accurately model the
concrete and the water as incompressible. (a) At what
21. A table-tennis ball has a diameter of 3.80 cm and        rate is the force the water exerts on one face of the
average density of 0.084 0 g/cm3. What force is              block increasing? (b) At what rate is the buoyant force
required to hold it completely submerged under water?        on the block increasing?
22. The gravitational force exerted on a solid object is     26. To an order of magnitude, how many helium-filled
5.00 N. When the object is suspended from a spring           toy balloons would be required to lift you? Because
scale and submerged in water, the scale reads 3.50 N         helium is an irreplaceable resource, develop a
(Fig. P14.22). Find the density of the object.               theoretical answer rather than an experimental answer.
In your solution, state what physical quantities you
take as data and the values you measure or estimate
for them.
27.     A cube of wood having an edge dimension of
20.0 cm and a density of 650 kg/m3 floats on water.
(a) What is the distance from the horizontal top
surface of the cube to the water level? (b) What mass
of lead should be placed on the cube so that the top of
the cube will be just level with the water?
28. A spherical aluminum ball of mass 1.26 kg
contains an empty spherical cavity that is concentric
with the ball. The ball barely floats in water. Calculate

2 = intermediate 3 = challenging      = SSM/SG       = ThomsonNOW    = symbolic reasoning      =qualitative reasoning
(a) the outer radius of the ball and (b) the radius of the     m/s, when the resistive force on it is 1 100 N in the
cavity.                                                        upward direction. The density of seawater is
29. Determination of the density of a fluid has many           1.03  103 kg/m3.
important applications. A car battery contains sulfuric        33. A plastic sphere floats in water with 50.0% of its
acid, for which density is a measure of concentration.         volume submerged. This same sphere floats in
For the battery to function properly, the density must         glycerin with 40.0% of its volume submerged.
be within a range specified by the manufacturer.               Determine the densities of the glycerin and the sphere.
Similarly, the effectiveness of antifreeze in your car’s
engine coolant depends on the density of the mixture           34. The United States possesses the eight largest
(usually ethylene glycol and water). When you donate           warships in the world—aircraft carriers of the Nimitz
blood to a blood bank, its screening includes                  class—and is building two more. Suppose one of the
determination of the density of the blood because              ships bobs up to float 11.0 cm higher in the water
higher density correlates with higher hemoglobin               when 50 fighter planes take off from it in 25 minutes,
content. A hydrometer is an instrument used to                 at a location where the free-fall acceleration is 9.78
determine liquid density. A simple one is sketched in          m/s2. Bristling with bombs and missiles, the planes
Figure P14.29. The bulb of a syringe is squeezed and           have an average mass of 29 000 kg. Find the
released to let the atmosphere lift a sample of the            horizontal area enclosed by the waterline of the \$4-
liquid of interest into a tube containing a calibrated         billion ship. By comparison, its flight deck has area
rod of known density. The rod, of length L and                 18 000 m2. Below decks are passageways hundreds of
meters long, so narrow that two large men cannot pass
average density , floats partially immersed in the          each other.
liquid of density . A length h of the rod protrudes
above the surface of the liquid. Show that the density         Section 14.5 Fluid Dynamics
of the liquid is                                               Section 14.6 Bernoulli’s Equation
0 L
                                      35. A large storage tank, open at the top and filled
Lh                                with water, develops a small hole in its side at a point
16.0 m below the water level. The rate of flow from
the leak is 2.50  10–3 m3/min. Determine (a) the
speed at which the water leaves the hole and (b) the
diameter of the hole.
36. A village maintains a large tank with an open top,
containing water for emergencies. The water can drain
from the tank through a hose of diameter 6.60 cm. The
hose ends with a nozzle of diameter 2.20 cm. A rubber
stopper is inserted into the nozzle. The water level in
the tank is kept 7.50 m above the nozzle. (a) Calculate
the friction force exerted on the stopper by the nozzle.
(b) The stopper is removed. What mass of water flows
30. Refer to Problem 29 and Figure P14.29. A                   from the nozzle in 2.00 h? (c) Calculate the gauge
hydrometer is to be constructed with a cylindrical             pressure of the flowing water in the hose just behind
floating rod. Nine fiduciary marks are to be placed            the nozzle.
along the rod to indicate densities having values of
0.98 g/cm3, 1.00 g/cm3, 1.02 g/cm3, 1.04 g/cm3, …,             37. Water flows through a fire hose of diameter 6.35
1.14 g/cm3. The row of marks is to start 0.200 cm              cm at a rate of 0.012 0 m3/s. The fire hose ends in a
from the top end of the rod and end 1.80 cm from the           nozzle of inner diameter 2.20 cm. What is the speed
top end. (a) What is the required length of the rod? (b)       with which the water exits the nozzle?
What must be its average density? (c) Should the               38. Water moves through a constricted pipe in steady,
marks be equally spaced? Explain your answer.                  ideal flow. At one point as shown in Figure 14.16
31. How many cubic meters of helium are required to            where the pressure is 2.50  104 Pa, the diameter is
lift a balloon with a 400-kg payload to a height of            8.00 cm. At another point 0.500 m higher, the pressure
8 000 m? (Take He = 0.180 kg/m3.) Assume the                  is equal to 1.50  104 Pa and the diameter is 4.00 cm.
balloon maintains a constant volume and the density            Find the speed of flow (a) in the lower section and (b)
of air decreases with the altitude z according to the          in the upper section. (c) Find the volume flow rate
through the pipe.
expression air = 0e–z/8 000, where z is in meters and
0 = 1.25 kg/m3 is the density of air at sea level.            39. Figure P14.39 shows a stream of water in steady
flow from a kitchen faucet. At the faucet, the diameter
32. A bathysphere used for deep-sea exploration has a
of the stream is 0.960 cm. The stream fills a 125-cm3
radius of 1.50 m and a mass of 1.20  104 kg. To dive,         container in 16.3 s. Find the diameter of the stream
this submarine takes on mass in the form of seawater.          13.0 cm below the opening of the faucet.
Determine the amount of mass the submarine must
take on if it is to descend at a constant speed of 1.20

2 = intermediate 3 = challenging       = SSM/SG        = ThomsonNOW    = symbolic reasoning      =qualitative reasoning
44. Old Faithful Geyser in Yellowstone National
Park erupts at approximately 1-h intervals, and the
height of the water column reaches 40.0 m (Fig.
P14.44). (a) Model the rising stream as a series of
separate drops. Analyze the free-fall motion of one of
the drops to determine the speed at which the water
leaves the ground. (b) What If? Model the rising
stream as an ideal fluid in streamline flow. Use
Bernoulli’s equation to determine the speed of the
water as it leaves ground level. (c) How does the
answer from part (a) compare with the answer from
part (b)? (d) What is the pressure (above atmospheric)
40. Water falls over a dam of height h with a mass              in the heated underground chamber if its depth is 175
flow rate of R, in units of kilograms per second. (a)           m? Assume the chamber is large compared with the
Show that the power available from the water is                 geyser’s vent.

= Rgh

where g is the free-fall acceleration. (b) Each
hydroelectric unit at the Grand Coulee Dam takes in
water at a rate of 8.50  105 kg/s from a height of 87.0
m. The power developed by the falling water is
converted to electric power with an efficiency of
85.0%. How much electric power does each
hydroelectric unit produce?
41. A legendary Dutch boy saved Holland by plugging
a 1.20-cm diameter hole in a dike with his finger. If
the hole was 2.00 m below the surface of the North
45. A Venturi tube may be used as a fluid flowmeter
Sea (density 1 030 kg/m3), (a) what was the force on
(see Fig. 14.19). Taking the difference in pressure as
his finger? (b) If he pulled his finger out of the hole,
P1 – P2 = 21.0 kPa, find the fluid flow rate in cubic
during what time interval would the released water fill
meters per second given that the radius of the outlet
1 acre of land to a depth of 1 ft? Assume the hole
tube is 1.00 cm, the radius of the inlet tube is 2.00 cm,
remained constant in size. (A typical U.S. family of
four uses 1 acre-foot of water, 1 234 m3, in 1 year.)           and the fluid is gasoline ( = 700 kg/m3).

42. In ideal flow, a liquid of density 850 kg/m3                Section 14.7 Other Applications of Fluid Dynamics
moves from a horizontal tube of radius 1.00 cm into a
second horizontal tube of radius 0.500 cm. A pressure           46. An airplane has a mass of 1.60  104 kg, and each
wing has an area of 40.0 m2. During level flight, the
difference P exists between the tubes. (a) Find the
pressure on the lower wing surface is 7.00  104 Pa.
volume flow rate as a function of P. Evaluate the
Determine the pressure on the upper wing surface.
volume flow rate (b) for P = 6.00 kPa and (c) for P
= 12.0 kPa. (d) State how the volume flow rate                  47. A siphon of uniform diameter is used to drain
depends on P.                                                  water from a tank as illustrated in Figure P14.47.
Assume steady flow without friction. (a) If h = 1.00 m,
43. Water is pumped up from the Colorado River to               find the speed of outflow at the end of the siphon. (b)
supply Grand Canyon Village, located on the rim of              What If? What is the limitation on the height of the
the canyon. The river is at an elevation of 564 m, and          top of the siphon above the water surface? (For the
the village is at an elevation of 2 096 m. Imagine that         flow of the liquid to be continuous, the pressure must
the water is pumped through a single long pipe 15.0             not drop below the vapor pressure of the liquid.)
cm in diameter, driven by a single pump at the bottom
end. (a) What is the minimum pressure at which the
water must be pumped if it is to arrive at the village?
(b) If 4 500 m3 of water is pumped per day, what is the
speed of the water in the pipe? (c) What additional
pressure is necessary to deliver this flow? Note:
Assume the free-fall acceleration and the density of air
are constant over this range of elevations. The
pressures you calculate are too high for an ordinary
pipe. The water is actually lifted in stages by several
pumps through shorter pipes.

2 = intermediate 3 = challenging      = SSM/SG          = ThomsonNOW    = symbolic reasoning      =qualitative reasoning
48. An airplane is cruising at altitude 10 km. The           52. Figure P14.52 shows a water tank with a valve at
pressure outside the craft is 0.287 atm; within the          the bottom.
passenger compartment, the pressure is 1.00 atm and
the temperature is 20°C. A small leak occurs in one of
the window seals in the passenger compartment.
Model the air as an ideal fluid to find the speed of the
stream of air flowing through the leak.
49. A hypodermic syringe contains a medicine having
the density of water (Fig. P14.49).

If this valve is opened, what is the maximum height
attained by the water stream coming out of the right
side of the tank? Assume h = 10.0 m, L = 2.00 m, and
The barrel of the syringe has a cross-sectional area
 = 30.0° and assume the cross-sectional area at A is
A = 2.50  10–5 m2, and the needle has a cross-
very large compared with that at B.
sectional area a= 1.00  10–8 m2. In the absence of a
force on the plunger, the pressure everywhere is 1 atm.      53. The true weight of an object can be measured in a
A force of F magnitude 2.00 N acts on the plunger,           vacuum, where buoyant forces are absent. An object
making medicine squirt horizontally from the needle.         of volume V is weighed in air on an equal-arm balance
Determine the speed of the medicine as it leaves the         with the use of counterweights of density .
needle’s tip.                                                Representing the density of air as air and the
50. The Bernoulli effect can have important                  balance reading as F’g, show that the true weight
consequences for the design of buildings. For                Fg is
example, wind can blow around a skyscraper at
   F 
remarkably high speed, creating low pressure. The                          Fg  Fg  V  g  air g
higher atmospheric pressure in the still air inside the                                  g 
buildings can cause windows to pop out. As originally
constructed, the John Hancock Building in Boston             54. Water is forced out of a fire extinguisher by air
popped windowpanes that fell many stories to the             pressure as shown in Figure P14.54. How much gauge
sidewalk below. (a) Suppose a horizontal wind blows          air pressure in the tank (above atmospheric) is
with a speed of 11.2 m/s outside a large pane of plate       required for the water jet to have a speed of 30.0 m/s
glass with dimensions 4.00 m  1.50 m. Assume the            when the water level is 0.500 m below the nozzle?
density of the air to be 1.30 kg/m3. The air inside the
building is at atmospheric pressure. What is the total
force exerted by air on the windowpane? (b) What If?
If a second skyscraper is built nearby, the airspeed can
be especially high where wind passes through the
narrow separation between the buildings. Solve part
(a) again with a wind speed of 22.4 m/s, twice as high.

Additional Problems
51. A helium-filled balloon is tied to a 2.00-m-long,        55. A light spring of constant k = 90.0 N/m is attached
0.050 0-kg uniform string. The balloon is spherical          vertically to a table (Fig. P14.55a). A 2.00-g balloon is
with a radius of 0.400 m. When released, it lifts a          filled with helium (density = 0.180 kg/m3) to a volume
length h of string and then remains in equilibrium as        of 5.00 m3 and is then connected to the spring, causing
shown in Figure P14.51. Determine the value of h.            the spring to stretch as shown in Figure P14.55b.
The envelope of the balloon has a mass of 0.250 kg.          Determine the extension distance L when the balloon
is in equilibrium.

2 = intermediate 3 = challenging      = SSM/SG       = ThomsonNOW    = symbolic reasoning     =qualitative reasoning
hemispheres. Two teams of eight horses each could
pull the hemispheres apart only on some trials and
then ―with greatest difficulty,‖ with the resulting
sound likened to a cannon firing (Fig. P14.60). (a)
Show that the force F required to pull the thin-walled
evacuated hemispheres apart is R2(P0 – P), where R
is the radius of the hemispheres and P is the pressure
inside the hemispheres, which is much less than P0.
(b) Determine the force for P = 0.100P0 and
R = 0.300 m.

56. We can’t call it Flubber. Assume a certain
liquid, with density 1 230 kg/m3, exerts no friction
force on spherical objects. A ball of mass 2.10 kg and
radius 9.00 cm is dropped from rest into a deep tank of
this liquid from a height of 3.30 m above the surface.
(a) Find the speed at which the ball enters the liquid.
(b) What two forces are exerted on the ball as it moves
through the liquid? (c) Explain why the ball moves
down only a limited distance into the liquid and
calculate this distance. (d) With what speed does the
ball pop up out of the liquid? (e) How does the time
interval tdown, during which the ball moves from the
surface down to its lowest point, compare with the
time interval tup for the return trip between the same
two points? (f) What If? Now modify the model to
suppose the liquid exerts a small friction force on the
ball, opposite in direction to its motion. In this case,
how do the time intervals tdownand tup compare?
Explain your answer with a conceptual argument
rather than a numerical calculation.
57. As a 950-kg helicopter hovers, its horizontal
rotor pushes a column of air downward at 40.0 m/s.
What can you say about the quantity of this air?
Explain your answer. You may model the air motion
Figure P14.60 The colored engraving, dated 1672, illustrates Otto
as ideal flow.
von Guericke’s demonstration of the force due to air pressure as it
58. Evangelista Torricelli was the first person to              might have been performed before Emperor Ferdinand III.
realize that we live at the bottom of an ocean of air.
He correctly surmised that the pressure of our                61. A 1.00-kg beaker containing 2.00 kg of oil
atmosphere is attributable to the weight of the air. The      (density = 916.0 kg/m3) rests on a scale. A 2.00-kg
density of air at 0°C at the Earth’s surface is 1.29          block of iron suspended from a spring scale is
kg/m3. The density decreases with increasing altitude         completely submerged in the oil as shown in Figure
(as the atmosphere thins). On the other hand, if we           P14.61. Determine the equilibrium readings of both
assume the density is constant at 1.29 kg/m3 up to            scales.
some altitude h and is zero above that altitude, then h
would represent the depth of the ocean of air. Use this
model to determine the value of h that gives a pressure
of 1.00 atm at the surface of the Earth. Would the peak
of Mount Everest rise above the surface of such an
atmosphere?
59.     Review problem. With reference to Figure
14.5, show that the total torque exerted by the water
behind the dam about a horizontal axis through O is
1
6
 gwH 3 . Show that the effective line of action of the
total force exerted by the water is at a distance
1
H above O.                                                 62. A beaker of mass mb containing oil of mass mo and
3
density o rests on a scale. A block of iron of mass mFe
60. In about 1657, Otto von Guericke, inventor of the         suspended from a spring scale is completely
air pump, evacuated a sphere made of two brass

2 = intermediate 3 = challenging       = SSM/SG       = ThomsonNOW    = symbolic reasoning        =qualitative reasoning
submerged in the oil as shown in Figure P14.61.
Determine the equilibrium readings of both scales.

63. In 1983, the United States began coining the cent
piece out of copper-clad zinc rather than pure copper.
The mass of the old copper penny is 3.083 g and that
of the new cent is 2.517 g. Calculate the percent of
zinc (by volume) in the new cent. The density of
copper is 8.960 g/cm3 and that of zinc is 7.133 g/cm3.
The new and old coins have the same volume.
64. Show that the variation of atmospheric pressure
with altitude is given by P = P0 e–y, where
 = 0g/P0, P0 is atmospheric pressure at some                68. The water supply of a building is fed through a
reference level y = 0, and 0 is the atmospheric density      main pipe 6.00 cm in diameter. A 2.00-cm-diameter
at this level. Assume the decrease in atmospheric             faucet tap, located 2.00 m above the main pipe, is
pressure over an infinitesimal change in altitude (so         observed to fill a 25.0-L container in 30.0 s. (a) What
that the density is approximately uniform) is given by        is the speed at which the water leaves the faucet? (b)
dP = –g dy and that the density of air is proportional       What is the gauge pressure in the 6-cm main pipe?
to the pressure.                                              (Assume the faucet is the only ―leak‖ in the building.)
65. Review problem. A uniform disk of mass 10.0 kg            69. A U-tube open at both ends is partially filled with
and radius 0.250 m spins at 300 rev/min on a low-             water (Fig. P14.69a). Oil having a density 750 kg/m3
friction axle. It must be brought to a stop in 1.00 min       is then poured into the right arm and forms a column
by a brake pad that makes contact with the disk at an         L = 5.00 cm high (Fig. P14.69b). (a) Determine the
average distance of 0.220 m from the axis. The                difference h in the heights of the two liquid surfaces.
coefficient of friction between the pad and the disk is       (b) The right arm is then shielded from any air motion
0.500. A piston in a cylinder of diameter 5.00 cm             while air is blown across the top of the left arm until
presses the brake pad against the disk. Find the              the surfaces of the two liquids are at the same height
pressure required for the brake fluid in the cylinder.        (Fig. P14.69c). Determine the speed of the air being
66. A cube of ice whose edges measure 20.0 mm is              blown across the left arm. Take the density of air as
floating in a glass of ice-cold water, and one of the ice     1.29 kg/m3.
cube’s faces is parallel to the water’s surface. (a) How
far below the water surface is the bottom face of the
ice cube? (b) Ice-cold ethyl alcohol is gently poured
onto the water surface to form a layer 5.00 mm thick
above the water. The alcohol does not mix with the
water. When the ice cube again attains hydrostatic
equilibrium, what is the distance from the top of the
water to the bottom face of the block? (c) Additional
cold ethyl alcohol is poured onto the water’s surface
until the top surface of the alcohol coincides with the
top surface of the ice cube (in hydrostatic
equilibrium). How thick is the required layer of ethyl
alcohol?                                                      70. A woman is draining her fish tank by siphoning
67. An incompressible, nonviscous fluid is initially at       the water into an outdoor drain as shown in Figure
rest in the vertical portion of the pipe shown in Figure      P14.70. The rectangular tank has footprint area A and
P14.67a, where L = 2.00 m. When the valve is opened,          depth h. The drain is located a distance d below the
the fluid flows into the horizontal section of the pipe.      surface of the water in the tank, where
What is the speed of the fluid when it is all in the          d >> h. The cross-sectional area of the siphon tube is
horizontal section as shown in Figure P14.67b?                A. Model the water as flowing without friction. (a)
Assume the cross-sectional area of the entire pipe is         Show that the time interval required to empty the tank
constant.                                                     is
Ah
t 
A 2 gd
(b) Evaluate the time interval required to empty the
tank if it is a cube 0.500 m on each edge, taking
A = 2.00 cm2 and d = 10.0 m.

2 = intermediate 3 = challenging       = SSM/SG       = ThomsonNOW   = symbolic reasoning      =qualitative reasoning
that the upward lift force exerted by the water on the
hydrofoil has a magnitude
F  1 (n2  1) v2 A
2            b

(b) The boat has mass M. Show that the liftoff speed is

2Mg
v
(n2  1) A

(c) Assume an 800-kg boat is to lift off at 9.50 m/s.
Evaluate the area A required for the hydrofoil if its
design yields n = 1.05.

71. The hull of an experimental boat is to be lifted
above the water by a hydrofoil mounted below its keel
as shown in Figure P14.71. The hydrofoil is shaped
like an airplane wing. Its area projected onto a
horizontal surface is A. When the boat is towed at
sufficiently high speed, water of density  moves in
streamline flow so that its average speed at the top of
the hydrofoil is n times larger than its speed vb below
the hydrofoil. (a) Ignoring the buoyant force, show

2 = intermediate 3 = challenging     = SSM/SG       = ThomsonNOW    = symbolic reasoning     =qualitative reasoning

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