Physics

James S. Walker

Chapter 15 Fluids - all with Video Answers

Educators

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Chapter Questions

02:36

Problem 1

Estimate the weight of the air in your physics classroom.

Alexander Allen

Numerade Educator

02:57

Problem 2

What weight of water is required to fill a 25 -gallon aquarium?

Alexander Allen

Numerade Educator

03:53

Problem 3

You buy a "gold" ring at a pawn shop. The ring has a mass of
4.7 $\mathrm{g}$ and a volume of 0.55 $\mathrm{cm}^{3} .$ Is the ring solid gold?

Alexander Allen

Numerade Educator

03:22

Problem 4

A cube of metal has a mass of 0.347 $\mathrm{kg}$ and measures 3.21 $\mathrm{cm}$ on
a side. Calculate the density and identify the metal.

Alexander Allen

Numerade Educator

02:03

Problem 5

What is the downward force exerted by the atmosphere on a soccer field whose dimensions are 105 $\mathrm{m}$ by 55 $\mathrm{m}$ ?

Alexander Allen

Numerade Educator

03:18

Some species of dinoflagellate (a type of unicellular plankton) can produce light as the result of biochemical reactions within the cell. This light is an example of bioluminescence. It is found that bioluminescence in dinoflagellates can be triggered by deformation of the cell surface with a pressure as low as one dyne $\left(10^{-5} \mathrm{N}\right)$ per square centimeter. What is this pressure in (a) pascals and (b) atmospheres?

Alexander Allen

Numerade Educator

03:00

Problem 7

A 71-kg person sits on a 3.9-kg chair. Each leg of the chair makes
contact with the floor in a circle that is 1.1 cm in diameter. Find
the pressure exerted on the floor by each leg of the chair, assuming
the weight is evenly distributed

Alexander Allen

Numerade Educator

02:22

Problem 8

To prevent damage to floors (and to increase friction), a crutch
will often have a rubber tip attached to its end. If the end of the
crutch is a circle of radius 0.95 cm without the tip, and the tip is a
circle of radius 2.0 cm, by what factor does the tip reduce the pressure exerted by the crutch?

Alexander Allen

Numerade Educator

04:13

Problem 9

Suppose that when you ride on your 7.85 -kg bike the weight of
you and the bike is supported equally by the two tires. If the gauge
pressure in the tires is 70.2 $\mathrm{lb} / \mathrm{in}^{2}$ and the area of contact between
each tire and the road is $7.03 \mathrm{cm}^{2},$ what is your weight?

Alexander Allen

Numerade Educator

02:17

Problem 10

On February 15, 2013, a 12,000,000-kg asteroid exploded in the atmosphere above Chelyabinsk, Russia,
generating a shock wave with a pressure amplitude of 750 Pa. What
force (in $N )$ would this pressure difference exert on a window with
dimensions of 0.86 $\mathrm{m} \times 1.17 \mathrm{m}$ ? (The shock wave shattered many
glass windows, resulting in a number of injuries.)

Alexander Allen

Numerade Educator

07:10

Problem 11

The weight of your $1420-\mathrm{kg}$ car is supported equally by its four tires, each inflated to a gauge pressure of 35.0 $\mathrm{lb} / \mathrm{in}^{2}$ (a) What is the area of contact each tire makes
with the road? (b) If the gauge pressure is increased, does the area of contact increase, decrease, or stay the same? (c) What gauge pressure is required to give an area of contact of 116 $\mathrm{cm}^{2}$ for each tire?

Alexander Allen

Numerade Educator

03:52

Problem 12

Two drinking glasses, 1 and $2,$ are filled with water to the same depth. Glass 1 has twice the diameter of glass $2 .$ (a) Is the weight of
the water in glass 1 greater than, less than, or equal to the weight of
the water in glass 2$?$ (b) Is the pressure at the bottom of glass 1 greater
than, less than, or equal to the pressure at the bottom of glass 2$?$

Alexander Allen

Numerade Educator

01:32

Problem 13

FIGURE 15-39 shows four containers, each filled with water to the same level. Rank the containers in order of increasing pressure
at the depth $h$ . Indicate ties where appropriate.

Alexander Allen

Numerade Educator

01:11

Problem 14

Water in the lake behind Hoover Dam is 221 $\mathrm{m}$ deep. What is the
water pressure at the base of the dam?

Alexander Allen

Numerade Educator

03:09

Problem 15

In a classroom demonstration, the pressure inside a soft drink
can is suddenly reduced to essentially zero. Assuming the can to
be a cylinder with a height of 12 cm and a diameter of 6.5 cm, find
the net inward force exerted on the vertical sides of the can due to
atmospheric pressure.

Alexander Allen

Numerade Educator

04:15

Problem 16

As a storm front moves in, you notice that the column of mercury in a barometer rises to only 736 mm. (a) What is the air pressure? (b) If the mercury in this barometer is replaced with water, to
what height does the column of water rise? Assume the same air
pressure found in part (a).

Alexander Allen

Numerade Educator

05:54

Problem 17

In the hydraulic system shown in FIGURE 15-40, the piston on the left has a diameter
of 5.1 $\mathrm{cm}$ and a mass of 2.3 $\mathrm{kg}$ . The piston on the right has a diameter of 13 $\mathrm{cm}$ and a mass of 3.6 $\mathrm{kg}$ . If the density of the fluid is $750 \mathrm{kg} / \mathrm{m}^{3},$ what is the height difference $h$ between the two pistons?

Alexander Allen

Numerade Educator

05:05

Problem 18

A circular wine barrel 75 cm in diameter will burst if the net
upward force exerted on the top of the barrel is 643 N. A tube
1.0 cm in diameter extends into the barrel through a hole in the
top, as indicated in Figure 15-38. Initially, the barrel is filled to
the top and the tube is empty above that level. What weight of
water must be poured into the tube in order to burst the barrel?

Alexander Allen

Numerade Educator

05:59

Problem 19

A cylindrical container with a cross-sectional area of 65.2 $\mathrm{cm}^{2}$ holds a fluid of density 806 $\mathrm{kg} / \mathrm{m}^{3} .$ At the bottom of the container
the pressure is 126 $\mathrm{kPa}$ (a) What is the depth of the fluid? (b) Find
the pressure at the bottom of the container after an additional
$2.05 \times 10^{-3} \mathrm{m}^{3}$ of this fluid is added to the container. Assume that
no fluid spills out of the container.

Alexander Allen

Numerade Educator

04:00

Problem 20

A submarine called the Deep View 66 is being developed to take 66 tourists at a time on sight-
seeing trips to tropical coral reefs. According to guidelines of the
American Society of Mechanical Engineers (ASME), to be safe for
human occupancy the Deep View 66 must be able to withstand a
pressure of 10.0 $\mathrm{N}$ per square millimeter. (a) To what depth can the Deep View 66 safely descend in seawater? (b) If the submarine is
used in freshwater instead, is its maximum safe depth greater than,
less than, or the same as in seawater? Explain.

Alexander Allen

Numerade Educator

03:40

Problem 21

A water storage tower is filled with freshwater to a depth of 6.4 $\mathrm{m} .$ What is the pressure at (a) 4.5 $\mathrm{m}$ and (b) 5.5 $\mathrm{m}$
below the surface of the water? (c) Why are the metal bands on such
towers more closely spaced near the base of the tower?

Alexander Allen

Numerade Educator

03:51

Problem 22

You step into an elevator holding a glass of water filled to a depth of 7.9 $\mathrm{cm}$ . After a moment, the elevator moves upward with constant acceleration, increasing its speed
from 0 to 2.4 $\mathrm{m} / \mathrm{s}$ in 2.9 $\mathrm{s}$ (a) During the period of acceleration, is
the pressure exerted on the bottom of the glass greater than, less than, or the same as before the elevator began to move? Explain. (b) Find the change in the pressure exerted on the bottom of the
glass as the elevator accelerates.

Alexander Allen

Numerade Educator

03:26

Problem 23

Suppose you pour water into a container until it reaches a depth
of 14 cm. Next, you carefully pour in a 7.5-cm thickness of olive
oil so that it floats on top of the water. What is the pressure at the
bottom of the container?

Alexander Allen

Numerade Educator

10:25

Problem 24

Referring to Example 15-8, suppose that some vegetable oil has
been added to both sides of the U tube. On the right side of the
tube, the depth of oil is 5.00 cm, as before. On the left side of the
tube, the depth of the oil is 3.00 cm. Find the difference in fluid
level between the two sides of the tube.

Alexander Allen

Numerade Educator

04:19

Problem 25

As a stunt, you want to sip some water
through a very long, vertical straw. (a) First, explain why the liquid
moves upward, against gravity, into your mouth when you sip. (b)
What is the tallest straw that you could, in principle, drink from
in this way?

Alexander Allen

Numerade Educator

02:12

Problem 26

The patient in FIGURE 15-41 is to receive an intravenous injection of medication. In order to work properly, the pressure of fluid containing the medication must be 109 $\mathrm{kPa}$
at the injection point. (a) If the fluid has a density of 1020 $\mathrm{kg} / \mathrm{m}^{3}$ ,
find the height at which the bag of fluid must be suspended above the patient. Assume that the pressure inside the bag is one atmosphere. (b) If a less dense fluid is used instead, must the height of
suspension be increased or decreased? Explain.

Dading Chen

Numerade Educator

06:46

Problem 27

A cylindrical container 1.0 m tall contains mercury to a certain
depth, d. The rest of the cylinder is filled with water. If the pressure at
the bottom of the cylinder is two atmospheres, what is the depth d?

Alexander Allen

Numerade Educator

04:10

Problem 28

On Wednesday, August 15, $1934,$ William Beebe and Otis Barton made history by descending
in the Bathysphere-basically a steel sphere 4.75 $\mathrm{ft}$ in diameter 3028 $\mathrm{ft}$ below the surface of the ocean, deper than anyone had been before. (a) As the Bathysphere was lowered, was the buoyant force exerted on it at a depth of 10 ft greater than, less than,
or equal to the buoyant force exerted on it at a depth of 50 $\mathrm{ft}$ ? (b)
Choose the best explanation from among the following:
\begin{equation}\begin{array}{l}{\text { 1. The buoyant force depends on the density of the water, which }} \\ {\text { is essentially the same at } 10 \text { ft and } 50 \mathrm{ft.}} \\ {\text { II. The pressure increases with depth, and this increases the }} \\ {\text { buoyant force. }} \\ {\text { IIL. The buoyant force decreases as an object sinks below the sur- }} \\ {\text { face of the water. }}\end{array}\end{equation}

Alexander Allen

Numerade Educator

03:55

Problem 29

Lead is more dense than aluminum. (a) Is the buoyant force on a solid lead sphere greater than, less than, or equal to the buoyant force on a solid aluminum sphere of the same diameter?
(b) Does your answer to part (a) depend on the fluid that is causing
the buoyant force?

Alexander Allen

Numerade Educator

03:04

Problem 30

A fish adjusts its buoyancy to hover in one place in a small bowl
as it drops a pebble it was holding in its mouth. When the pebble is
released, does the water level in the bowl rise, fall, or stay the same?

Alexander Allen

Numerade Educator

03:25

Problem 31

A raft is 3.7 m wide and 6.1 m long. When a horse is loaded onto
the raft, it sinks 3.8 cm deeper into the water. What is the weight
of the horse?

Alexander Allen

Numerade Educator

04:05

Problem 32

Many ray-finned fish adjust their buoyancy by changing the volume of gas in a swim
bladder located just below their spine. (a) If the volume of the fish
increases while the mass remains the same, does the buoyant force
on the fish increase, decrease, or remain the same? (b) Calculate the change in the buoyant force on a fish if its volume increases by 11 $\mathrm{cm}^{3},$ assuming it swims in seawater.

Mark J

Numerade Educator

02:35

Problem 33

Submarines adjust their buoyancy by changing the amount of water held in rigid containers called ballast tanks. (a) If the mass of a submerged submarine increases while the volume remains the same, does the buoyant force on the submarine increase, decrease, or remain the same?
(b) Calculate the change in the buoyant force on a submerged submarine if it pumps 0.85 $\mathrm{m}^{3}$ of seawater into its ballast tank.

Krystal K

Numerade Educator

04:45

Problem 34

A 3.2 -kg balloon is filled with helium (density $=0.179 \mathrm{kg} / \mathrm{m}^{3} )$
If the balloon is a sphere with a radius of $4.9 \mathrm{m},$ what is the maxi-
mum weight it can lift?

Alexander Allen

Numerade Educator

02:50

Problem 35

A hot-air balloon plus cargo has a mass of 312 kg and a volume of 2210 $\mathrm{m}^{3}$ on a day when the outside air density is 1.22 $\mathrm{kg} / \mathrm{m}^{3}$ .
The balloon is floating at a constant height of 9.14 $\mathrm{m}$ above the
ground. What is the density of the hot air in the balloon?

Alexander Allen

Numerade Educator

02:58

Problem 36

In the lab you place a beaker that is half full of water (density $\rho_{w} )$ on a scale. You now use a light string to suspenda piece of metal of volume $V$ in the water. The metal is completely submerged, and none of the water spills out of the beaker. Give a symbolic expression for the change in reading of the scale.

Alexander Allen

Numerade Educator

03:38

Problem 37

Predict/Explain A block of wood has a steel ball glued to
one surface. The block can be floated with the ball "high and dry" on its top surface. (a) When the block is inverted, and the ball is immersed in water, does the volume of wood that is submerged increase, decrease, or stay the same? (b) Choose the best explanation from among the following:
1. When the block is inverted the ball pulls it downward, causing more of the block to be submerged.
II. The same amount of mass is supported in either case, therefore the amount of the block that is submerged is the same.
III. When the block is inverted the ball experiences a buoyant
force, which reduces the buoyant force that must be provided
by the wood.

Alexander Allen

Numerade Educator

04:25

Problem 38

In the preceding problem, suppose the block of wood with the ball "high and dry" is floating in a tank
of water. (a) When the block is inverted, does the water level in
the tank increase, decrease, of stay the same? (b) Choose the best
explanation from among the following:
\begin{equation}\begin{array}{l}{\text { I. Inverting the block makes the block float higher in the water, }} \\ {\text { which lowers the water level in the tank. }} \\ {\text { II. The same mass is supported by the water in either case, and }} \\ {\text { therefore the amount of displaced water is the same. }} \\ {\text { III. The inverted block floats lower in the water, which displaces }} \\ {\text { more water and raises the level in the tank. }}\end{array}\end{equation}

Alexander Allen

Numerade Educator

04:55

Problem 39

A hydrometer, a device for measuring fluid density, is constructed as shown in FIGURE $15-42$ . If the hydrometer samples fluid 1 , the small float inside the tube is submerged to level 1. When fluid 2 is sampled, the float is submerged to level $2 .$ Is the density of fluid 1 greater than, less than, or equal to the density of fluid 2$?$ (This is how mechanics test your antifreeze level. Since antifreeze [ethylene glycol] is more dense than water, the higher the density of coolant in your radiator the more anti-freeze protection you have.)

Alexander Allen

Numerade Educator

04:01

Problem 40

Referring to Example 15-12, suppose the flask with the wood tied to the bottom is placed on a scale. At some
point the string breaks and the wood rises to the surface where it
floats. (a) When the wood is floating, is the reading on the scale
greater than, less than, or equal to its previous reading? (b) Choose
the best explanation from among the following:
I. The same mass is supported by the scale before and after the
string breaks, and therefore the reading on the scale remains
the same.
II. When the block is floating the water level drops, and this
reduces the reading on the scale.
III. When the block is floating it no longer pulls upward on the
flask; therefore, the reading on the scale increases

Alexander Allen

Numerade Educator

02:17

Problem 41

On a planet in a different solar system the acceleration of gravity is greater than it is on Earth. If you float in a pool of water on this planet, do you float higher than, lower than, or at the same
level as when you float in water on Earth?

Alexander Allen

Numerade Educator

03:34

Problem 42

An air mattress is 2.3 m long, 0.66 m wide, and 14 cm deep. If the
air mattress itself has a mass of 0.22 kg, what is the maximum mass
it can support in freshwater?

Alexander Allen

Numerade Educator

03:21

Problem 43

A solid block is attached to a spring scale. When the block is
suspended in air, the scale reads 21.2 N; when it is completely
immersed in water, the scale reads 18.2 N. What are (a) the volume
and (b) the density of the block?

Sheh Lit Chang

University of Washington

14:39

Problem 44

As in the previous problem, a solid block is suspended from a spring scale. If the reading on the scale when the block is completely immersed in water is 25.0 $\mathrm{N}$ , and the reading when it is
completely immersed in alcohol of density 806 $\mathrm{kg} / \mathrm{m}^{3}$ is $25.7 \mathrm{N},$
what are (a) the block's volume and (b) its density?

Alexander Allen

Numerade Educator

05:36

Problem 45

A person weighs 756 N in air and has a body-fat percentage of 28.1$\%$ . (a) What is the overall density of this person's body? (b) What is the volume of this person's body? (c) Find the apparent weight of this person when completely submerged in water.

Alexander Allen

Numerade Educator

03:39

Problem 46

A log floats in a river with one-fourth of its volume above the water. (a) What is the density of the log? (b) If the river carries the log into the ocean, does the portion of the log
above the water increase, decrease, or stay the same? Explain.

Alexander Allen

Numerade Educator

07:15

Problem 47

A person with a mass of 78 $\mathrm{kg}$ and a volume of 0.086 $\mathrm{m}^{3}$ floats qui- etly in water. (a) What is the volume of the person that is above water?
(b) If an upward force $F$ is applied to the person by a friend, the volume
of the person above water increases by 0.0032 $\mathrm{m}^{3} .$ Find the force $F .$

Alexander Allen

Numerade Educator

09:28

Problem 48

A block of wood floats on water. A layer of oil is now poured on top of the water to a depth that more than covers the block, as shown in FIGURE 15-43. (a) Is the volume of wood submerged in water greater than, less than, or the same as before? (b) If 90$\%$ of the wood is submerged in water before the oil is added, find the fraction submerged when oil with a density of 875 $\mathrm{kg} / \mathrm{m}^{3}$ covers the block.

Alexander Allen

Numerade Educator

05:15

Problem 49

A piece of lead has the shape of a hockey puck, with a diameter
of 7.5 $\mathrm{cm}$ and a height of 2.5 $\mathrm{cm}$ . If the puck is placed in a mercury
bath, it floats. How deep below the surface of the mercury is the
bottom of the lead puck?

Alexander Allen

Numerade Educator

08:02

Problem 50

A lead weight with a volume of $0.82 \times 10^{-5} \mathrm{m}^{3}$ is lowered on a fishing line into a lake to a depth of 1.0 $\mathrm{m}$ . (a) What tension is required in the fishing line to give the
weight an upward acceleration of 2.1 $\mathrm{m} / \mathrm{s}^{2}$ (b) If the initial depth
of the weight is increased to $2.0 \mathrm{m},$ does the tension found in part (a) increase, decrease, or stay the same? Explain. (c) What acceleration will the weight have if the tension in the fishing line is 1.2 $\mathrm{N}$ ? Give both direction and magnitude.

Alexander Allen

Numerade Educator

03:10

Problem 51

To water the yard, you use a hose with a diameter of 3.6 $\mathrm{cm}$ .
Water flows from the hose with a speed of 1.3 $\mathrm{m} / \mathrm{s} .$ If you partially
block the end of the hose so the effective diameter is now $0.52 \mathrm{cm},$
with what speed does water spray from the hose?

Alexander Allen

Numerade Educator

01:52

Problem 52

Water flows through a pipe with a speed of 2.4 $\mathrm{m} / \mathrm{s}$ . Find the flow
rate in $\mathrm{kg} / \mathrm{s}$ if the diameter of the pipe is 3.1 $\mathrm{cm} .$

Alexander Allen

Numerade Educator

03:36

Problem 53

To fill a child's inflatable wading pool, you use a garden hose
with a diameter of 2.9 $\mathrm{cm}$ . Water flom this hose with a speed
of 1.3 $\mathrm{m} / \mathrm{s}$ . How much time will it take to fill the pool to a depth of
26 $\mathrm{cm}$ if the pool is circular and has a diameter of 2.0 $\mathrm{m} ?$

Alexander Allen

Numerade Educator

02:56

Problem 54

When at rest, your heart pumps blood at the
rate of 5.00 liters per minute $(\mathrm{L} / \mathrm{min}) .$ What are the volume and
mass of blood pumped by your heart in one day?

Alexander Allen

Numerade Educator

04:34

Problem 55

in an Arteriole A typical arteriole has a diameter
of 0.080 $\mathrm{mm}$ and carries blood at the rate of $9.6 \times 10^{-5} \mathrm{cm}^{3} / \mathrm{s}$ . (a) What is the speed of the blood in an arteriole? (b) Suppose an arteriole branches into 8800 capillaries, each with a diameter of $6.0 \times 10^{-6} \mathrm{m} .$ What is the blood speed in the capillaries? (The low speed in capillaries is beneficial; it promotes the diffusion of materials to and from the blood.)

Alexander Allen

Numerade Educator

05:56

Problem 56

Water flows at the rate of 3.11 kg>s through a hose with a diameter of 3.22 $\mathrm{cm}$ (a) What is the speed of water in this hose? (b) If the hose is attached to a nozzle with a diameter of
$0.732 \mathrm{cm},$ what is the speed of water in the nozzle? (c) Is the number of kilograms per second flowing through the nozzle greater than, less than, or equal to 3.11 $\mathrm{kg} / \mathrm{s} ?$ Explain.

Alexander Allen

Numerade Educator

02:17

Problem 57

A river narrows at a rapids from a width of 12 m to a width of only 5.8 $\mathrm{m}$ . The depth of the river before the rapids is 2.7 $\mathrm{m}$ ; the depth in the rapids is 0.85 $\mathrm{m}$ . Find the speed of water flowing in the rapids, given that its speed before the rapids is 1.2 $\mathrm{m} / \mathrm{s}$ . Assume the river has a rectangular cross section.

Alexander Allen

Numerade Educator

03:52

Problem 58

The aorta has an inside diameter of approximately $2.1 \mathrm{cm},$ compared to that of a capillary, which is about $1.0 \times 10^{-5} \mathrm{m}(10 \mu \mathrm{m}) .$ In addition, the average speed of
flow is approximately 1.0 $\mathrm{m} / \mathrm{s}$ in the aorta and 0.30 $\mathrm{mm} / \mathrm{sina}$ capillary. Assuming that all the blood that flows through the aorta
also flows through the capillaries, how many capillaries does the
circulatory system have?

Alexander Allen

Numerade Educator

04:41

Problem 59

The buildup of plaque on the walls of an artery may decrease its diameter from 1.1 cm to 0.75 cm. If the
speed of blood flow was 15 cm>s before reaching the region of
plaque buildup, find (a) the speed of blood flow and (b) the pressure drop within the plaque region.

Mukesh Devi

Numerade Educator

04:43

Problem 60

A horizontal pipe contains water at a pressure of 120 kPa flowing
with a speed of 1.9 m>s. When the pipe narrows to one-half its original diameter, what are (a) the speed and (b) the pressure of the water?

Alexander Allen

Numerade Educator

05:48

Problem 61

Unfiltered olive oil must flow at a minimum speed of 3.0 m>s to
prevent settling of debris in a pipe. The oil leaves a pump at a pressure
of 88 kPa through a pipe of radius 9.5 mm. It then enters a horizontal
pipe at atmospheric pressure. Ignore the effects of viscosity. (a) What
is the speed of the oil as it leaves the pump if it flows at 3.0 m>s in the
horizontal pipe? (b) What is the radius of the horizontal pipe?

Alexander Allen

Numerade Educator

04:29

Problem 62

Tests of lung capacity show that adults are able
to exhale 1.5 liters of air through their mouths in as little as 1.0 second. (a) If a person blows air at this rate through a drinking straw
with a diameter of 0.60 cm, what is the speed of air in the straw?
(b) If the air from the straw in part (a) is directed horizontally
across the upper end of a second straw that is vertical, as shown in
FIGURE 15-44, to what height does water rise in the vertical straw?

Alexander Allen

Numerade Educator

09:13

Problem 63

Water flows through a horizontal tube of
diameter 2.5 cm that is joined to a second horizontal tube of diameter 1.2 cm. The pressure difference between the tubes is 7.3 kPa.
(a) Which tube has the higher pressure? (b) Which tube has the
higher speed of flow? (c) Find the speed of flow in the first tube.

Alexander Allen

Numerade Educator

02:25

Problem 64

A garden hose is attached to a water faucet on one end and a
spray nozzle on the other end. The water faucet is turned on, but
the nozzle is turned off so that no water flows through the hose.
The hose lies horizontally on the ground, and a stream of water
sprays vertically out of a small leak to a height of 0.68 m. What is
the pressure inside the hose?

Alexander Allen

Numerade Educator

01:19

Problem 65

A water tank springs a leak. Find the speed of water emerging
from the hole if the leak is 2.9 m below the surface of the water,
which is open to the atmosphere.

Alexander Allen

Numerade Educator

02:50

Problem 66

(a) Find the pressure difference on an airplane wing if air flows over the upper surface with a speed of $125 \mathrm{m} / \mathrm{s},$ and along the bot-
tom surface with a speed of 109 $\mathrm{m} / \mathrm{s} .$ (b) If the area of the wing is
$32 \mathrm{m}^{2},$ what is the net upward force exerted on the wing?

Alexander Allen

Numerade Educator

03:14

Problem 67

On a vacation flight, you look out the window of the jet and
wonder about the forces exerted on the window. Suppose the air
outside the window moves with a speed of approximately 170 m>s
shortly after takeoff, and that the air inside the plane is at atmospheric pressure. (a) Find the pressure difference between the
inside and outside of the window. (b) If the window is 25 cm by
42 cm, find the force exerted on the window by air pressure.

Alexander Allen

Numerade Educator

02:17

Problem 68

The pitot tube is commonly used to measure the air
speed of an aircraft. Air flows into a small opening at the end of
a tube that is closed at the other end, bringing the air to rest and
allowing the measurement of the pressure difference between air
at rest inside the tube and air moving rapidly just outside the tube. If the high-altitude air density is 0.364 kg/m' $^{3}$ , and the pressure difference between inside and outside the tube is 9460 $\mathrm{Pa}$ , what is the airplane's speed relative to the air?

Alexander Allen

Numerade Educator

03:07

Problem 69

During a thunderstorm, winds with a speed of 47.7 $\mathrm{m} / \mathrm{s}$ blow across a flat roof with an area of 668 $\mathrm{m}^{2}$ . (a) Find
the magnitude of the force exerted on the roof as a result of this
wind. (b) Is the force exerted on the roof in the upward or down-
ward direction? Explain.

Alexander Allen

Numerade Educator

05:29

Problem 70

A garden hose with a diameter of 1.6 cm has water flowing in it
with a speed of 1.3 m>s and a pressure of 1.5 atmospheres. At the
end of the hose is a nozzle with a diameter of 0.64 cm. Find (a) the
speed of water in the nozzle and (b) the pressure in the nozzle.

Alexander Allen

Numerade Educator

07:06

Problem 71

Water flows in a cylindrical, horizontal pipe. As the pipe narrows to half its initial diameter, the pressure in the pipe changes. (a) Is the pressure in the narrow region greater than, less than, or the same as the initial pressure? Explain. (b) Calculate the change in pressure between the wide and narrow regions of the pipe. Give your answer symbolically in terms of the density of the water, $\rho,$ and its initial speed $v .$

Alexander Allen

Numerade Educator

04:45

Problem 72

When the body requires an increased blood
flow rate in a particular organ or muscle, it can accomplish this by
increasing the diameter of arterioles in that area. This is referred
to as vasodilation. What percentage increase in the diameter of an
arteriole is required to double the volume flow rate of blood, all
other factors remaining the same?

Alexander Allen

Numerade Educator

05:22

Problem 73

(a) Find the volume of blood that flows per second through
the pulmonary artery described in Example 15-25. (b) If the radius of the artery is reduced by $18 \%,$ by what factor is the blood flow rate reduced? Assume that all other properties of the artery remain
unchanged.

Alexander Allen

Numerade Educator

02:19

Problem 74

Suppose an occlusion in an artery reduces its diameter by 15$\%$ , but the volume flow rate of blood in
the artery remains the same. By what factor has the pressure drop
across the length of this artery increased?

Alexander Allen

Numerade Educator

04:27

Problem 75

The viscosity of 5W-30 motor oil changes from $6.4 \mathrm{N} \cdot \mathrm{s} / \mathrm{m}^{2} \mathrm{at}-30^{\circ} \mathrm{C}$ to 0.0090\textrm{N} \cdot \mathrm { s } / \mathrm { m } ^ { 2 } \text { at } 1 0 0 ^ { \circ } \mathrm { C } \text { . Model the oil cir- }
culation system of a carengine as a tube of radius 5.0 $\mathrm{mm}$ and length
$2.1 \mathrm{m},$ driven by a pump that produces a pressure difference of
110 $\mathrm{kPa}$ across the ends of the tube. (a) What volume flow rate does the pump produce when the oil is at $-30^{\circ} \mathrm{C} ?$ (b) What is the volume
flow rate when the oil is at the operating temperature of $100^{\circ} \mathrm{C} ?$

Alexander Allen

Numerade Educator

09:31

Problem 76

Water at $20^{\circ} \mathrm{C}$ flows through a horizontal garden hose at the rate of $5.0 \times 10^{-4} \mathrm{m}^{3} / \mathrm{s}$ . The diameter of the
garden hose is 2.5 $\mathrm{cm}$ . (a) What is the water speed in the hose?
(b) What is the pressure drop across a $15-\mathrm{m}$ length of hose? Sup-
pose the cross-sectional area of the hose is halved, but the length
and pressure drop remain the same. (c) By what factor does the water speed change? (d) By what factor does the volume flow rate
change? Explain.

Alexander Allen

Numerade Educator

02:06

Problem 77

A weather glass, as shown in FIGURE $15-45$ , is used to give an indication of a change in the weather. Does the water level in the neck of the weather glass move up or move down when a low-pressure system approaches?

Alexander Allen

Numerade Educator

03:38

Problem 78

A person floats in a boat in a small backyard swimming pool. Inside the boat with the person are some bricks. (a) If the person drops the
bricks overboard to the bottom of the pool, does the water level in
the pool increase, decrease, or stay the same? (b) Choose the best
explanation from among the following:
I. When the bricks sink they displace less water than when they
were floating in the boat; hence, the water level decreases.
II. The same mass (boat + bricks + person) is in the pool in either case, and therefore the water level remains the same.
III. The bricks displace more water when they sink to the bottom
than they did when they were above the water in the boat;
therefore the water level increases.

Alexander Allen

Numerade Educator

02:50

Problem 79

A person floats in a boat in a small backyard swimming pool.
Inside the boat with the person are several blocks of wood. Suppose the person now throws the blocks of wood into the pool,
where they float. (a) Does the boat float higher, lower, or at the
same level relative to the water? (b) Does the water level in the
pool increase, decrease, or stay the same?

Alexander Allen

Numerade Educator

04:38

Problem 80

The three identical containers in FIGURE 15-46 are open to the
air and filled with water to the same level. A block of wood floats
in container A; an identical block of wood floats in container B,
supporting a small lead weight; container C holds only water.
(a) Rank the three containers in order of increasing weight of
water they contain. Indicate ties where appropriate. (b) Rank the
three containers in order of increasing weight of the container
plus its contents. Indicate ties where appropriate.

Alexander Allen

Numerade Educator

01:30

Problem 81

When a person's blood pressure is taken with a device known as a sphygmomanometer, it is measured
on the arm, at approximately the same level as the heart. If the
measurement were to be taken on a standing patient's leg instead,
would the readingon the sphygmomanometer be greater than, less
than, or the same as when the measurement is made on the arm?

Alexander Allen

Numerade Educator

02:06

Problem 82

A water main broke on Lake Shore Drive in Chicago on
November $8,2002,$ shooting water straight upward to a height of
8.0 $\mathrm{ft}$ . What was the pressure in the pipe?

Alexander Allen

Numerade Educator

02:22

Problem 83

A useful instrument for evaluating fibromyalgia and trigger-point tenderness is the doloriometer or algorimeter. This device consists of a force meter attached to a
circular probe that is pressed axperienced. If the circular the diameter of the circular probe is $1.39 \mathrm{cm},$ what is the pressure applied to the skin? Give
your answer in pascals.

Alexander Allen

Numerade Educator

03:45

Problem 84

The power output of the heart is given by the product of the average blood pressure, 1.33 $\mathrm{N} / \mathrm{cm}^{2}$ , and the flow rate, 105 $\mathrm{cm}^{3} / \mathrm{s}$ . (a) Find the power of the heart. Give your answer in watts. (b) How much energy does the heart expend
in a day? (c) suppose the energy found in part (b) is used to lift a
72 -kg person vertically to a height $h .$ Find $h,$ in meters.

Alexander Allen

Numerade Educator

05:51

Problem 85

A solid block is suspended from a spring scale. When the block
is in air, the scale reads 35.0 N, when immersed in water the scale
reads 31.1 N, and when immersed in oil the scale reads 31.8 N. (a)
What is the density of the block? (b) What is the density of the oil?

Alexander Allen

Numerade Educator

05:52

Problem 86

A wooden block with a density of 710 $\mathrm{kg} / \mathrm{m}^{3}$ and a volume of
0.012 $\mathrm{m}^{3}$ is attached to the top of a vertical spring whose force
constant is $k=540 \mathrm{N} / \mathrm{m} .$ Find the amount by which the spring is stretched or compressed if it and the wooden block are (a) in air
or (b) completely immersed in water. [The density of air may be
neglected in part ( $($ a). $]$ .

Alexander Allen

Numerade Educator

07:20

Problem 87

A 1.35-kg wooden block has an iron ball of radius 1.22 $\mathrm{cm}$ glued to one side. (a) If
the block floats in water with the iron ball "high and dry," what
is the volume of wood that is submerged? (b) If the block is now
inverted, so that the iron ball is completely immersed, does the
volume of wood that is submerged in water increase, decrease, or remain the same? Explain.(c) Calculate the volume of wood that
is submerged when the block is in the inverted position.

Alexander Allen

Numerade Educator

04:14

Problem 88

Evangelista Torricelli (1608-1647) was the first to put forward the idea that we live at the bottom of an ocean of air. (a) Given the value of atmospheric pressure at the
surface of the Earth, and the fact that there is zero pressure in the
vacuum of space, determine the depth of the atmosphere, assuming that the density of air and the acceleration of gravity are constant. (b) According to this model, what is the atmospheric pressure at the summit of Mt. Everest, 29,029 ft above sea level. (In fact,
the density of air and the acceleration of gravity decrease with altitude, so the result obtained here is less than the actual depth of the
atmosphere. Still, this is a reasonable first estimate.)

Alexander Allen

Numerade Educator

04:54

Problem 89

Consider the lightweight contain ers shown in FilsuRE $15-47 .$ Both containers have bases of area
$A_{\text { base }}=24 \mathrm{cm}^{2}$ and depths of water equal to 18 $\mathrm{cm} .$ As a result, the downward force on the base of container 1 is equal to the downward force on container $2,$ even though the containers clearly hold different weights of water. This referred to as the hydrostatic
paradox. (a) Given that container 2 has an annular (ring-shaped)
region of area $A_{\text { ting }}=72 \mathrm{cm}^{2},$ determine the net downward force exerted on the container by the water. (b) Show that your result from part (a) is equal to the weight of the water in container $2 .$

Alexander Allen

Numerade Educator

07:50

Problem 90

Consider the two lightweight containers shown in FlGuRE $15-48 .$ As in the previous problem, these containers have equal forces on their bases but contain different weights of water. This is another version of the hydrostatic paradox. (a) Determine the net downward force exerted by the water on container $2 .$ Note that the bases of the containers have an area $A_{\text { buse }}=24 \mathrm{cm}^{2}$ , the annular region has an area $A_{\text { ting }}=18 \mathrm{cm}^{2}$ , and the depth of the water is 18 $\mathrm{cm}$ . (b) Show that your result from
part (a) is equal to the weight of the water in container $2 .$ (c) If a hole is poked in the annular region of container $2,$ how fast will water exit the hole? (d) How high above the hole will the stream of water rise?

Alexander Allen

Numerade Educator

04:12

Problem 91

A backyard swimming pool is circular in shape and contains water to a uniform depth of 42 $\mathrm{cm} .$ It is 2.4 $\mathrm{m}$ in diameter and is not completely filled.(a) What is the pressure at the bottom of the pool? (b) If a person gets into the pool and floats peacefully, does the pressure at the bottom of the pool increase, decrease, or stay the same? (c) Calculate the pressure due to the water and the person at the bottom of the pool if the floating person has a mass of 73 kg.

Alexander Allen

Numerade Educator

06:11

Problem 92

A prospector finds a solid rock composed of granite $\left(\rho=2650 \mathrm{kg} / \mathrm{m}^{3}\right)$ and gold. If the volume of the rock is
$3.84 \times 10^{-4} \mathrm{m}^{3},$ and its mass is $3.40 \mathrm{kg},($ a) what mass of gold is
contained in the rock? What percentage of the rock is gold by
(b) volume and (c) mass?

Alexander Allen

Numerade Educator

08:28

Problem 93

(a) If the tension in the string in Example 15-12 is $0.89 \mathrm{N},$ what is the volume of the wood? Assume that everything else remains the same. (b) If the string breaks and the wood floats
on the surface, does the water level in the flask rise, drop, or stay
the same? Explain. (c) Assuming the flask is cylindrical with a cross-sectional area of $62 \mathrm{cm}^{2},$ find the change in water level after
the string breaks.

Alexander Allen

Numerade Educator

04:10

Problem 94

A siphon is a device that allows water to flow from one level to another. The siphon
shown in FlGURE $15-49$ delivers water from an irrigation canal to a
field of crops. To operate the siphon, water is first drawn through
the length of the tube. After the flow is started in this way it continues on its own. (a) Using points 1 and 3 in Figure $15-49,$ find the speed $v$ of the water leaving the siphon at its lower end. Give
a symbolic answer. (b) Is the speed of the water at point 2 greater
than, less than, or the same as its speed at point 3$?$ Explain.

Alexander Allen

Numerade Educator

04:37

Problem 95

The density of raw milk at body temperature is 1023 $\mathrm{kg} / \mathrm{m}^{3} .$ After being extracted from the cow, the milk is
pumped through a pipe to the bottom of a cooling tank filled to a
depth of $h=1.8 \mathrm{m}$ (FiGuRE $15-50 )$ . (a) If the pressure at location 2 in Figure $15-50$ is atmospheric pressure, what minimum speed $v_{1}$
must the milk have in order to enter the cooling tank? Assume the
milk at location 2 is essentially at rest. (b) What is the pressure at
the bottom of the cooling tank?

Alexander Allen

Numerade Educator

13:00

Problem 96

A tin can is filled with water to a depth of 39 cm. A hole 11 cm above the bottom of the can produces a stream of water that is directed at an angle of $36^{\circ}$ above the horizontal. Find (a) the range
and (b) the maximum height of this stream of water.

Alexander Allen

Numerade Educator

03:55

Problem 97

A person weighs 685 N in air but only 497 N when standing in water up to the hips. Find (a) the volume of each of the person's legs and (b) the mass of each leg, assuming they have a density that is 1.05 times the density of water.

Alexander Allen

Numerade Educator

08:31

Problem 98

Rain-cooled air near the core of a thunder storm sinks and then spreads out in front of the storm in a forward flank downdraft gust front (FIGURE $15-51$ ). These gusts can vary from a cool breeze to a violent and damaging wind. Thunderstorms are
extremely complex, but modeling air as an incompressible fluid
can offer some insight. (a) Suppose 1.0 $\mathrm{m}^{3}$ of rain-cooled air has a
density of $0.835 \mathrm{kg} / \mathrm{m}^{3},$ while the warmer air surrounding it has a density of $0.835 \mathrm{kg} / \mathrm{m}^{3},$ while the warmer air surrounding it has a
density of 0.819 $\mathrm{kg} / \mathrm{m}^{3}$ . Taking into account the buoyant force on
the parcel of air, find its downward acceleration. (b) If the parcel
maintains the same acceleration from rest at an altitude of $4000 \mathrm{m},$ what is its speed when it arrives at the surface? (c) Now model the
air as an incompressible fluid of constant density 1.02 kg/m's that is
at rest and has a pressure of 61.6 $\mathrm{kPa}$ at $h=4000 \mathrm{m}$ altitude, but is
moving and has a pressure of 101.3 $\mathrm{kPa}$ at $h=0 .$ What is the speed
of the air at the surface?

Alexander Allen

Numerade Educator

03:23

Problem 99

A horizontal pipe carries oil whose coefficient of viscosity is 0.00012 $\mathrm{N} \cdot \mathrm{s} / \mathrm{m}^{2} .$ The diameter of the pipe is $5.2 \mathrm{cm},$ and its length
is 55 $\mathrm{m} .$ (a) What pressure difference is required between the ends
of this pipe if the oil is to flow with an averagespeed of 1.2 $\mathrm{m} / \mathrm{s} ?$ (b)
What is the volume flow rate in this case?

Alexander Allen

Numerade Educator

05:20

Problem 100

A patient is given an injection with a hypodermic needle 3.3 cm long and 0.26 $\mathrm{mm}$ in diameter. Assuming the solution
being injected has the same density and viscosity as water at
$20^{\circ} \mathrm{C},$ find the pressure difference needed to inject the solution
at the rate of 1.5 $\mathrm{g} / \mathrm{s}$ .

Alexander Allen

Numerade Educator

06:22

Problem 101

On one episode of Mythbusters, Jamie and Adam try to make a lead balloon that will
float when filled with helium. The balloon they constructed was
approximately cubical in shape, and 10 feet on a side. They used a thin lead foil, which gave the finished balloon a mass of 11 kg.
(a) What was the thickness of the foil? (b) Would the lead balloon float if filled with helium? (c) If the balloon does float, what
would be the most mass it could lift in addition to its own mass?

Alexander Allen

Numerade Educator

07:10

Problem 102

A round wooden log with a diameter of 73 $\mathrm{cm}$ floats with onehalf of its radius out of the water. What is the log's density?

Alexander Allen

Numerade Educator

03:49

Problem 103

The hollow, spherical glass shell shown in FIGURE $15-52$ has an inner radius $R$ and an outer radius 1.2$R .$ The density of the glass is $\rho_{g}$ What fraction of the shell is submerged when it floats in a liquid of density $\rho=1.5 \rho_{g} ?$ (Assume the interior of the shell is a vacuum.)

Alexander Allen

Numerade Educator

03:39

Problem 104

A geode is a hollow rock with a solid shell and an air-filled interior. Suppose a particular geode weighs twice as much in air as it does when completely submerged in water. If the density of the solid part of the geode is $2500 \mathrm{kg} / \mathrm{m}^{3},$ what fraction of the geode's volume is hollow?

Alexander Allen

Numerade Educator

03:19

Problem 105

A tank of water filled to a depth $d$ has a hole in its side a height
$h$ above the table on which it rests. Show that water emerging
from the hole hits the table at a horizontal distance of 2$\sqrt{(d-h) h}$ from the base of the tank.

Alexander Allen

Numerade Educator

04:56

Problem 106

The water tank in FIGURE 15-53 is open to the atmosphere and
has two holes in it, one 0.80 m and one 3.6 m above the floor on
which the tank rests. If the two streams of water strike the floor in
the same place, what is the depth of water in the tank?

Alexander Allen

Numerade Educator

02:54

Problem 107

Assuming the doughnut has a cylindrical shape of height $H$ and
diameter $D,$ and that the height of the white stripe is $0.22 H,$ what
is the density of the doughnut?
\begin{equation}\begin{array}{lll}{\text { A. } 260 \mathrm{kg} / \mathrm{m}^{3}} & {\text { B. } 360 \mathrm{kg} / \mathrm{m}^{3}} \\ {\text { C. } 720 \mathrm{kg} / \mathrm{m}^{3}} & {\text { D. } 820 \mathrm{kg} / \mathrm{m}^{3}}\end{array}\end{equation}

Alexander Allen

Numerade Educator

02:41

Problem 108

Figure $15-57$ has comments where the "height" of the white
stripe is 0.5$H$ and $0 .$ The comment for $-0.5 H$ has been left blank,
however. Which of the following comments is most appropriate
for this case?
\begin{equation}\begin{array}{l}{\text { A. The doughnut sinks. }} \\ {\text { B. The white stripe is still present, but has a negative height. }} \\ {\text { C. Half the doughnut is light brown, half is dark brown. }} \\ {\text { D. The top and bottom of the doughnut are white, the middle }} \\ {\text { one-half is brown. }}\end{array}\end{equation}

Alexander Allen

Numerade Educator

02:13

Problem 109

A new doughnut is being planned whose density will be
330 $\mathrm{kg} / \mathrm{m}^{3} .$ If the height of the doughnut is $H,$ what will be the
height of the white stripe?
\begin{equation}\begin{array}{ll}{\text { A. } 0.14 H} & {\text { B. } 0.24 H} \\ {\text { C. } 0.28 H} & {\text { D. } 0.64 H}\end{array}\end{equation}

Alexander Allen

Numerade Educator

01:32

Problem 110

Suppose the density of a doughnut is 550 $\mathrm{kg} / \mathrm{m}^{3} .$ In terms of
the height of the doughnut, $H,$ what is the height of the portion
of the doughnut that is out of the oil?
\begin{equation}\begin{array}{ll}{\text { A. } 0.20 H} & {\text { B. } 0.40 H} \\ {\text { C. } 0.67 H} & {\text { D. } 0.80 H}\end{array}\end{equation}

Alexander Allen

Numerade Educator

05:34

Problem 111

REFERRING TO EXAMPLE 15-8 Suppose we use a different vegetable oil that has a higher density than the one in Example $15-8 .$ (a) If everything else remains the same, will the
height difference, $h,$ increase, decrease, or remain the same?
Explain. (b) Find the height difference for an oil that has a den-
sity of $9.60 \times 10^{2} \mathrm{kg} / \mathrm{m}^{3} .$

Alexander Allen

Numerade Educator

04:20

Problem 112

REFERRING TO EXAMPLE 15-8 Find the height difference, h, if the
depth of the oil is increased to 7.50 cm. Assume everything else
in the problem remains the same

Alexander Allen

Numerade Educator

05:24

Problem 113

REFERRING TO EXAMPLE 15-24 (a) Find the height H required to make $D=0.655 \mathrm{m} .$ Assume everything else in the problem remains the same. (b) Find the depth $h$ required to make $D=0.455 \mathrm{m} .$ Assume everything else in the problem remains the same.

Alexander Allen

Numerade Educator

03:52

Problem 114

REFERRING TO EXAMPLE 15-24 Suppose both h and H are increased
by a factor of two. By what factor is the distance D increased?

Alexander Allen

Numerade Educator