College Physics

Hugh D. Young

Chapter 13

Fluid Mechanics - all with Video Answers

Educators

Chapter Questions

Problem 1

You purchase a rectangular piece of metal that has dimensions 5.0 $\mathrm{mm} \times 15.0 \mathrm{mm} \times 30.0 \mathrm{mm}$ and mass 0.0158 $\mathrm{kg}$ .
The seller tells you that the metal is gold. To check this, you compute the average density of the piece. What value do you get? Were you cheated?

K B

K B

Numerade Educator

Problem 2

A kidnapper demands a 40.0 $\mathrm{kg}$ cube of platinum as a ransom. What is the length of a side?

Elan Stopnitzky

Elan Stopnitzky

Numerade Educator

Problem 3

Calculate the weight of air at $20^{\circ} \mathrm{C}$ in a room that measures
$5.00 \times 4.50 \times 3.25 \mathrm{m} .$ Give your answer in newtons and in pounds.

K B

Numerade Educator

Problem 4

By how many newtons do you increase the weight of your car when you fill up your 11.5 gal gas tank with gasoline? A gallon is equal to 3.788 $\mathrm{L}$ and the density of gasoline is 737 $\mathrm{kg} / \mathrm{m}^{3}$ .

Elan Stopnitzky

Elan Stopnitzky

Numerade Educator

Problem 5

How big is a million dollars? At the time this problem was written, the price of gold was about $\$ 1239$ per ounce, while that of platinum was about $\$ 1508$ an ounce. The "ounce" in this case is the troy ounce, which is equal to 31.1035 g. The more familiar avoirdupois ounce is equal to 28.35 g.) The density of gold is 19.3 $\mathrm{g} / \mathrm{cm}^{3}$ and that of platinum is 21.4 $\mathrm{g} / \mathrm{cm}^{3} .$ (a) If you find a spherical gold nugget worth 1.00 million dollars,
what would be its diameter? (b) How much would a platinum nugget of this size be worth?

K B

Numerade Educator

Problem 6

A cube 5.0 $\mathrm{cm}$ on each side is made of a metal alloy. After you drill a cylindrical hole 2.0 $\mathrm{cm}$ in diameter all the way through and perpendicular to one face, you find that the cube weighs 7.50 $\mathrm{N}$ (a) What is the density of this metal? (b) What did the cube weigh before you drilled the hole in it?

Elan Stopnitzky

Elan Stopnitzky

Numerade Educator

Problem 7

A cube of compressible material (such as Styrofoam or balsa wood) has a density $\rho$ and sides of length $L .$ (a) If you keep its mass the same, but compress each side to half its length, what will be its new density, in terms of $\rho ?$ (b) If you keep the mass and shape the same, what would the length of each side have to be (in terms of $L )$ so that the density of the cube was three times its original value?

K B

Numerade Educator

Problem 8

A hollow cylindrical copper pipe is 1.50 $\mathrm{m}$ long and has an outside diameter of 3.50 $\mathrm{cm}$ and an inside diameter of 2.50 $\mathrm{cm} .$ How much does it weigh?

Elan Stopnitzky

Elan Stopnitzky

Numerade Educator

Problem 9

A uniform lead sphere and a uniform aluminum sphere have the same mass. What is the ratio of the radius of the aluminum sphere to the radius of the lead sphere?

K B

Numerade Educator

Problem 10

Blood pressure. Systemic blood pressure is defined as the ratio of two pressures, both expressed in millimeters of mercury. Normal blood pressure is about $\frac{120 \mathrm{mm}}{80 \mathrm{mm}},$ which is usually just stated as $\frac{120}{80}$ . (See also Problem $24 . )$ What would normal systemic blood pressure be if, instead of millimeters of mercury, we expressed pressure in each of the following units, but continued to use the same ratio format? (a) atmospheres, (b) torr, (c) Pa, (d) $\mathrm{N} / \mathrm{m}^{2},$ (e) psi.

Elan Stopnitzky

Elan Stopnitzky

Numerade Educator

Problem 11

Blood. (a) Mass of blood. The human body typically contains 5 L of blood of density 1060 $\mathrm{kg} / \mathrm{m}^{3} .$ How many kilograms of blood are in the body? (b) The average blood pressure is $13,000 \mathrm{Pa}$ at the heart. What average force does the blood exert on each square centimeter of the heart? (c) Red blood cells. Red blood cells have a specific gravity of 5.0 and a diameter of about 7.5$\mu \mathrm{m}$ . If they are spherical in shape (which is not quite true), what is the mass of such a cell?

Nathan Silvano

Numerade Educator

Problem 12

Landing on Venus. One of the great difficulties in landing on Venus is dealing with the crushing pressure of the atmosphere, which is 92 times the earth's atmospheric pressure.
(a) If you are designing a lander for Venus in the shape of a hemisphere 2.5 $\mathrm{m}$ in diameter, how many newtons of inward force must it be prepared to withstand due to the Venusian atmosphere? (Don't forget about the bottom!) (b) How much force would the lander have to withstand on the earth?

Elan Stopnitzky

Elan Stopnitzky

Numerade Educator

Problem 13

You are designing a diving bell to withstand the pressure of seawater at a depth of 250 $\mathrm{m}$ (a) What is the gauge pressure at this depth? (You can ignore the small changes in the density of the water with depth.) (b) At the 250 $\mathrm{m}$ depth, what is the net force due to the water outside and the air inside the bell on a circular glass window 30.0 $\mathrm{cm}$ in diameter if the pressure inside the diving bell equals the pressure at the surface of the water? (You may ignore the small variation in pressure over
the surface of the window.)

Nathan Silvano

Numerade Educator

Problem 14

Glaucoma. Under normal circumstances, the vitreous humor, a jelly-like substance in the main part of the eye, exerts a pressure of up to 24 $\mathrm{mm}$ of mercury that maintains the shape of the eye. If blockage of the drainage duct for aqueous humor causes this pressure to increase to about 50 $\mathrm{mm}$ of mercury, the condition is called glaucoma. What is the increase in the total force (in newtons) on the walls of the eye if the pressure increases from 24 $\mathrm{mm}$ to 50 $\mathrm{mm}$ of mercury? We can quite accurately model the eye as a sphere 2.5 $\mathrm{cm}$ in diameter.

Elan Stopnitzky

Elan Stopnitzky

Numerade Educator

Problem 15

By means of physiological adaptations that are still not very well understood, sperm whales are thought to be able to hunt for their food at depths of between 400 $\mathrm{m}$ and 3000 $\mathrm{m.}$ (a) What range of gauge pressures (in Pa and atm) do the whales withstand at these depths? (b) Estimate the total inward force of water pressure on the surface of a sperm whale at a depth of $3000 \mathrm{m},$ modeling the whale as a cylinder 16 $\mathrm{m}$ long and 4 $\mathrm{m}$ in diameter.

Nathan Silvano

Numerade Educator

Problem 16

What gauge pressure must a pump produce to pump water from the bottom of the Grand Canyon (elevation 730 $\mathrm{m} )$ to Indian Gardens (elevation 1370 $\mathrm{m} ) ?$ Express your result in pascals and in atmospheres.

Elan Stopnitzky

Elan Stopnitzky

Numerade Educator

Problem 17

Intravenous feeding. A hospital patient is being fed intravenously with a liquid of density
1060 $\mathrm{kg} / \mathrm{m}^{3}$ . (See Figure $13.40 . )$ The container of liquid is raised 1.20 $\mathrm{m}$ above the patient's arm where the fluid enters his veins.
What is the pressure this fluid exerts on his veins, expressed in millimeters of mercury?

Nathan Silvano

Numerade Educator

Problem 18

A $975-\mathrm{kg}$ car has its tires each Problem 17 inflated to $"32.0$ pounds."
(a) What are the absolute and gauge pressures in these tires in $\mathrm{lb} / \mathrm{in.}^{2}$ , $\mathrm{Pa},$ and atm? (b) If the tires were perfectly round, could the tire pressure exert any force on the pavement? (Assume that the tire walls are flexible so that the pressure exerted by the tire on the pavement equals the air pressure inside the tire.) (c) If you examine a car's tires, it is obvious that there is some flattening at the bottom. What is the total contact area for all four tires of the flattened part of the tires at the pavement?

Elan Stopnitzky

Elan Stopnitzky

Numerade Educator

Problem 19

An electrical short cuts off all power to a submersible diving vehicle when it is 30 m below the surface of the ocean. The crew must push out a hatch of area 0.75 $\mathrm{m}^{2}$ and weight 300 $\mathrm{N}$ on the bottom to escape. If the pressure inside is 1.0 atm, what downward force must the crew exert on the hatch to open it?

Nathan Silvano

Numerade Educator

Problem 20

Standing on your head. (a) When you stand on your head, what is the difference in pressure of the blood in your brain compared with the pressure when you stand on your feet if you
are 1.85 m tall? The density of blood is 1060 $\mathrm{kg} / \mathrm{m}^{3}$ . (b) What
effect does the increased pressure have on the blood vessels in your brain?

Elan Stopnitzky

Elan Stopnitzky

Numerade Educator

Problem 21

You are designing a machine for a space exploration vehicle. It contains an enclosed column of oil that is 1.50 m tall, and you need the pressure difference between the top and the bottom of this column to be 0.125 atm. (a) What must be the density of the oil? (b) If the vehicle is taken to Mars, where the acceleration due to gravity is $0.379 g,$ what will be the pressure difference (in earth atmospheres) between the top and bottom of the oil column?

Nathan Silvano

Numerade Educator

Problem 22

Ear damage from diving. If the force on the tympanic membrane (eardrum) increases by about 1.5 $\mathrm{N}$ above the force from atmospheric pressure, the membrane can be damaged. When you go scuba diving in the ocean, below what depth could damage to your eardrum start to occur? The eardrum is typically 8.2 $\mathrm{mm}$ in diameter. (Consult Table $13.1 . )$

Elan Stopnitzky

Elan Stopnitzky

Numerade Educator

Problem 23

A barrel contains a 0.120 $\mathrm{m}$ layer of oil of density 600 $\mathrm{kg} / \mathrm{m}^{3}$ floating on water that is 0.250 $\mathrm{m}$ deep. (a) What is the gauge pressure at the oil-water interface? (b) What is the gauge pressure at the bottom of the barrel?

K B

Numerade Educator

Problem 24

Blood pressure. Systemic blood pressure is expressed as the ratio of the systolic pressure (when the heart first ejects blood into the arteries) to the diastolic pressure (when the heart is relaxed):
systemic blood pressure $=\frac{\text { systolic pressure }}{\text { diastolic pressure }}$
Both pressures are measured at the level of the heart and are expressed in millimeters of mercury (or torr), although the units are not written. Normal systemic blood pressure is $\frac{120}{80}$ . (a) What are the maximum and minimum forces (in newtons) that the blood exerts against each square centimeter of the heart for a person with normal blood pressure? (b) As pointed out in the text, blood pressure is normally measured on the upper arm at the same height as the heart. Due to therapy for an injury, a patient's upper arm is extended 30.0 $\mathrm{cm}$ above his heart. In that position, what should be his systemic blood pressure reading, expressed in the standard way, if he has normal blood pressure? The density of blood is 1060 $\mathrm{kg} / \mathrm{m}^{3}$ .

Suzanne W.

Numerade Educator

Problem 25

Blood pressure on the moon. When we eventually establish lunar colonies, people living there will need to have their blood pressure taken. Assume that we continue to express the
systemic blood pressure as we now do on earth (see previousproblem) and that the density of blood does not change. Suppose also that normal blood pressure on the moon is still $\frac{120}{80}$ (which may not actually be true). If a lunar colonizer has her
blood pressure taken at her upper arm when it is raised 25 $\mathrm{cm}$ above her heart, what will be her systemic blood pressure reading, expressed in the standard way, if she has normal blood pressure? The acceleration due to gravity on the moon is 1.67 $\mathrm{m} / \mathrm{s}^{2}$ .

Nathan Silvano

Numerade Educator

Problem 26

The piston of a hydraulic automobile lift is 0.30 $\mathrm{m}$ in diameter. What gauge pressure, in pascals, is required to lift a car with a mass of 1200 $\mathrm{kg}$ ? Now express this pressure in atmospheres.

Elan Stopnitzky

Elan Stopnitzky

Numerade Educator

Problem 27

Hydraulic lift. You are designing a hydraulic lift for an automobile garage. It will consist of two oil-filled cylindrical pipes of different diameters. A worker pushes down on a
piston at one end, raising the car on a platform at the other end. (See Figure $13.41 .$ ) To handle a full range of jobs, you must be able to lift cars up to $3000 \mathrm{kg},$ plus the 500 $\mathrm{kg}$ platform on which they are parked. To avoid injury to your workers, the maximum amount of force a worker should need to exert is 100 $\mathrm{N}$ (a) What should be the diameter of the pipe under the platform? (b) If the worker pushes down
with a stroke 50 $\mathrm{cm}$ long, by how much will he raise the car
at the other end?

Narayan Hari

Numerade Educator

Problem 28

There is a maximum depth at which a diver can breathe through a snorkel tube (Fig. 13.42$)$ , because as the depth increases, so does the pressure difference, which the difference, if any.tends to collapse the diver's lungs. since the snorkel connects the air in the lungs to the atmosphere at the surface, the pressure inside the lungs is atmospheric pressure. What is the external-internal pressure difference when the diver's lungs are at a depth of 6.1 $\mathrm{m}$ (about 20 $\mathrm{ft}$ ? Assume that the diver is in fresh-water. (A scuba diver breathing from compressed air tanks can operate at greater depths than can a snorkeler, since the pressure of the air inside the scuba diver's lungs increases to match the external pressure of the water.)

Elan Stopnitzky

Elan Stopnitzky

Numerade Educator

Problem 29

A solid aluminum ingot weighs 89 $\mathrm{N}$ in air. (a) What is its volume? (See Table
$13.1 .$ ) (b) The ingot is suspended from a rope and totally immersed in water. What
is the tension in the rope (the apparent weight of the ingot in water)?

K B

Numerade Educator

Problem 30

Fish navigation. (a) As you can tell by watching them in an aquarium, fish are able to remain at any depth in water with no effort. What does this ability tell you about their density? (b) Fish are able to inflate themselves using a sac (called the swim bladder) located under their spinal column. These sacs can be filled with an oxygen-nitrogen mixture that comes from the blood. If a 2.75 $\mathrm{kg}$ fish in fresh water inflates itself and increases its volume by $10 \%,$ find the net force that the water exerts on it. (c) What is the net external force on it? Does the fish go up or down when it inflates itself?

Elan Stopnitzky

Elan Stopnitzky

Numerade Educator

Problem 31

When an open-faced boat has a mass of 5750 $\mathrm{kg}$ , including its cargo and passengers, it floats with the water just up to the top of its gunwales (sides) on a freshwater lake. (a) What is the volume of this boat? (b) The captain decides that it is too dangerous to float with his boat on the verge of sinking, so he decides to throw some cargo overboard so that 20$\%$ of the boat's volume will be above water. How much mass should he throw out?

Nathan Silvano

Numerade Educator

Problem 32

An ore sample weighs 17.50 $\mathrm{N}$ in air. When the sample is suspended by a light cord and totally immersed in water, the tension in the cord is 11.20 $\mathrm{N}$ . Find the total volume and the density of the sample.

Elan Stopnitzky

Elan Stopnitzky

Numerade Educator

Problem 33

A slab of ice floats on a freshwater lake. What minimum
volume must the slab have for a $45.0 \mathrm{~kg}$ woman to be able to stand on it without getting her feet wet?

Nathan Silvano

Numerade Educator

Problem 34

Using data from Appendix E, calculate the average density of the planet Saturn. How does your answer compare to the density of water, and what does this imply about the buoyancy
of Saturn, if you could find an ocean big enough to drop it into?

Elan Stopnitzky

Elan Stopnitzky

Numerade Educator

Problem 35

A hollow plastic sphere is held below the surface of a fresh- water lake by a cord anchored to the bottom of the lake. The sphere has a volume of 0.650 $\mathrm{m}^{3}$ and the tension in the cord is 900 $\mathrm{N} .$ (a) Calculate the buoyant force exerted by the water on the sphere. (b) What is the mass of the sphere? (c) The cord breaks and the sphere rises to the surface. When the sphere comes to rest, what fraction of its volume will be submerged?

Nathan Silvano

Numerade Educator

Problem 36

(a) Calculate the buoyant force of air (density 1.20 $\mathrm{kg} / \mathrm{m}^{3} )$ on a spherical party balloon that has a radius of 15.0 $\mathrm{cm}$ . (b) If the rubber of the balloon itself has a mass of 2.00 $\mathrm{g}$ and the balloon is filled with helium (density 0.166 $\mathrm{kg} / \mathrm{m}^{3}$ ), calculate the net upward force (the "lift") that acts on it in air.

Elan Stopnitzky

Elan Stopnitzky

Numerade Educator

Problem 37

The tip of the iceberg. Icebergs consist of freshwater ice and float in the ocean with only about 10$\%$ of their volume above water (the "tip of the iceberg," so to speak). This percentage can vary, depending on the condition of the ice. Assume that the ice has the density given in Table $13.1,$ although, in reality, this can vary considerably, depending on the condition of the ice and the amount of impurities in it. (a) What does this 10$\%$
observation tell us is the density of seawater? (b) What percentage of the icebergs' volume would be above water if they were floating in a large freshwater lake such as Lake Superior?

Nathan Silvano

Numerade Educator

Problem 38

At $20^{\circ} \mathrm{C},$ the surface tension of water is 72.8 dynes/cm. Find the excess pressure inside of (a) an ordinary-size water drop of radius 1.50 $\mathrm{mm}$ and (b) a fog droplet of radius 0.0100 $\mathrm{mm} .$

Elan Stopnitzky

Elan Stopnitzky

Numerade Educator

Problem 39

Find the gauge pressure in pascals inside a soap bubble 7.00 $\mathrm{cm}$ in diameter. The surface tension of this soap is 25.0 dynes/cm.

K B

Numerade Educator

Problem 40

What radius must a water drop have for the difference between the inside and outside pressures to be 0.0200 atm? The surface tension of water is 72.8 dynes/cm.

Elan Stopnitzky

Elan Stopnitzky

Numerade Educator

Problem 41

At $20^{\circ} \mathrm{C}$ , the surface tension of water is 72.8 dynes/cm and
that of carbon tetrachloride $\left(\mathrm{CCl}_{4}\right)$ is 26.8 dynes/cm. If the
gauge pressure is the same in two drops of these liquids, what is the ratio of the volume of the water drop to that of the $\mathrm{CCl}_{4}$ drop?

K B

Numerade Educator

Problem 42

At a point where an irrigation canal having a rectangular cross section is 18.5 $\mathrm{m}$ wide and 3.75 $\mathrm{m}$ deep, the water flows at 2.50 $\mathrm{cm} / \mathrm{s} .$ At a point downstream, but on the same level, the canal is 16.5 $\mathrm{m}$ wide, but the water flows at 11.0 $\mathrm{cm} / \mathrm{s} .$ How
deep is the canal at this point?

Elan Stopnitzky

Elan Stopnitzky

Numerade Educator

Problem 43

Water is flowing in a pipe with a varying cross-sectional area, and at all points the water completely fills the pipe. At area, $1,$ the cross-sectional area of the pipe is 0.070 $\mathrm{m}^{2}$ and the magnitude of the fluid velocity is 3.50 $\mathrm{m} / \mathrm{s} .$ What is the fluid speed at points in the pipe where the cross-sectional
area is $(a) 0.105 \mathrm{m}^{2},$ (b) 0.047 $\mathrm{m}^{2}$ ?

Nathan Silvano

Numerade Educator

Problem 44

Water is flowing in a cylindrical pipe of varying circular cross-sectional area, and at all points the water completely fills the pipe. (a) At one point in the pipe, the radius is 0.150 $\mathrm{m} .$ What is the speed of the water at this point if the volume flow rate in the
pipe is 1.20 $\mathrm{m}^{3} / \mathrm{s} ?$ (b) At a second point in the pipe, the water
speed is 3.80 $\mathrm{m} / \mathrm{s}$ . What is the radius of the pipe at this point?

Elan Stopnitzky

Elan Stopnitzky

Numerade Educator

Problem 45

A shower head has 20 circular openings, each with radius 1.0 $\mathrm{mm} .$ The shower head is connected to a pipe with radius 0.80 $\mathrm{cm} .$ If the speed of water in the pipe is $3.0 \mathrm{m} / \mathrm{s},$ what is its speed as it exits the shower-head openings?

Nathan Silvano

Numerade Educator

Problem 46

You're holding a hose at waist height and spraying water horizontally with it. The hose nozzle has a diameter of 1.80 $\mathrm{cm},$ and the water splashes on the ground a distance of 0.950 m horizontally from the nozzle. Suppose you now constrict the nozzle to a diameter of 0.750 $\mathrm{cm}$ ; how far horizontally from the nozzle will the water travel before hitting the ground? (Ignore air resistance.)

Elan Stopnitzky

Elan Stopnitzky

Numerade Educator

Problem 47

A small circular hole 6.00 $\mathrm{mm}$ in diameter is cut in the side of a large water tank, 14.0 $\mathrm{m}$ below the water level in the tank. The top of the tank is open to the air. Find the speed at which the water shoots out of the tank.

Nathan Silvano

Numerade Educator

Problem 48

A sealed tank containing seawater to a height of 11.0 $\mathrm{m}$ also contains air above the water at a gauge pressure of 3.00 atm. Water flows out from the bottom through a small hole. Calculate the speed with which the water comes out of the tank.

Elan Stopnitzky

Elan Stopnitzky

Numerade Educator

Problem 49

What gauge pressure is required in the city water mains for a stream from a fire hose connected to the mains to reach a vertical height of 15.0 $\mathrm{m}$ ? (Assume that the mains have a much larger diameter than the fire hose.)

Nathan Silvano

Numerade Educator

Problem 50

At one point in a pipeline, the water's speed is 3.00 $\mathrm{m} / \mathrm{s}$ and
the gauge pressure is $4.00 \times 10^{4}$ Pa. Find the gauge pressure at a second point in the line 11.0 $\mathrm{m}$ lower than the first if the pipe diameter at the second point is twice that the first.

Elan Stopnitzky

Elan Stopnitzky

Numerade Educator

Problem 51

Lift on an airplane. Air streams horizontally past a small airplane's wings such that the speed is 70.0 $\mathrm{m} / \mathrm{s}$ over the top surface and 60.0 $\mathrm{m} / \mathrm{s}$ past the bottom surface. If the plane has a mass of 1340 $\mathrm{kg}$ and a wing area of $16.2 \mathrm{m}^{2},$ what is the net vertical force (including the effects of gravity) on the airplane? The density of the air is 1.20 $\mathrm{kg} / \mathrm{m}^{3}$ .

Nathan Silvano

Numerade Educator

Problem 52

A golf course sprinkler system discharges water from a horizontal pipe at the rate of 7200 $\mathrm{cm}^{3} / \mathrm{s}$ . At one point in the pipe, where the radius is $4.00 \mathrm{cm},$ the water's absolute pressure is $2.40 \times 10^{5}$ Pa. At a second point in the pipe, the water passes through a constriction where the radius is 2.00 $\mathrm{cm} .$ What is the water's absolute pressure as it flows through this
constriction?

Elan Stopnitzky

Elan Stopnitzky

Numerade Educator

Problem 53

Water discharges from a horizontal cylindrical pipe at the rate of 465 $\mathrm{cm}^{3} / \mathrm{s}$ . At a point in the pipe where the radius is $2.05 \mathrm{cm},$ the absolute pressure is $1.60 \times 10^{5} \mathrm{Pa} .$ What is the pipe's radius at a constriction if the pressure there is reduced to $1.20 \times 10^{5} \mathrm{Pa}$ ?

Nathan Silvano

Numerade Educator

Problem 54

Artery blockage. A medical technician is trying to determine what percentage of a patient's artery is blocked by plaque. To do this, she measures the blood pressure just before the
region of blockage and finds that it is $1.20 \times 10^{4}$ Pa, while in the region of blockage it is $1.15 \times 10^{4}$ Pa. Furthermore, she knows that blood flowing through the normal artery just before the point of blockage is traveling at 30.0 $\mathrm{cm} / \mathrm{s}$ , and the specific gravity of this patient's blood is $1.06 .$ What percentage of the cross-sectional area of the patient's artery is blocked by the plaque?

Elan Stopnitzky

Elan Stopnitzky

Numerade Educator

Problem 55

At a certain point in a horizontal pipeline, the water's speed is 2.50 $\mathrm{m} / \mathrm{s}$ and the gauge pressure is $1.80 \times 10^{4}$ Pa. Find the gauge pressure at a second point in the line if the cross-sectional area at the second point is twice that at the first.

Nathan Silvano

Numerade Educator

Problem 56

With what terminal speed would a steel ball bearing 2.00 $\mathrm{mm}$ in diameter fall in a liquid of viscosity 0.150 $\mathrm{N} \cdot \mathrm{s} / \mathrm{m}^{2}$ if we could neglect buoyancy?

Elan Stopnitzky

Elan Stopnitzky

Numerade Educator

Problem 57

What speed must a gold sphere of radius 3.00 $\mathrm{mm}$ have in
castor oil for the viscous drag force to be one-fourth of the weight of the sphere? The density of gold is $19,300 \mathrm{kg} / \mathrm{m}^{3}$ and the viscosity of the oil is 0.986 $\mathrm{N} \cdot \mathrm{s} / \mathrm{m}^{2}$

Nathan Silvano

Numerade Educator

Problem 58

A copper sphere with a mass of 0.20 $\mathrm{g}$ and a density of 8900 $\mathrm{kg} / \mathrm{m}^{3}$ is observed to fall with a terminal speed of 6.0 $\mathrm{cm} / \mathrm{s}$ in an unknown liquid. Find the viscosity of the unknown liquid if its buoyancy can be neglected.

Elan Stopnitzky

Elan Stopnitzky

Numerade Educator

Problem 59

Clogged artery. Viscous blood is flowing through an artery partially clogged by cholesterol. A surgeon wants to remove enough of the cholesterol to double the flow rate of blood through this artery. If the original diameter of the artery is $D,$ what should be the new diameter (in terms of $D )$ to accomplish this for the same pressure gradient?

Nathan Silvano

Numerade Educator

Problem 60

Advertisements for a certain small car claim that it floats in water. (a) If the car's mass is 900 $\mathrm{kg}$ and its interior volume is $3.0 \mathrm{m}^{3},$ what fraction of the car is immersed when it floats? You can ignore the volume of steel and other materials. (b) Water gradually leaks in and displaces the air in the car. What fraction of the interior volume is filled with water when the car sinks?

Elan Stopnitzky

Elan Stopnitzky

Numerade Educator

Problem 61

A U-shaped tube open to the air at both ends contains some mercury. A quantity of water is carefully poured into the left arm of the U-shaped tube until the vertical height of the water column is 15.0 $\mathrm{cm}$ (Figure 13.43$)$ . (a) What is the gauge pressure at the water- mercury interface? (b) Calculate the vertical distance $h$ from the top of the mercury in the right-hand arm of the tube to the top of the water in the left-hand arm.

Nathan Silvano

Numerade Educator

Problem 62

An open barge has the dimensions shown in Figure 13.44 . If the barge is made out of 4.0 -cm-thick steel plate on each of its four sides and its bottom, what mass of coal can the barge carry in fresh water without sinking? Is there enough room in the barge to hold this amount of coal? (The density of coal is about 1500 $\mathrm{kg} / \mathrm{m}^{3} . )$

Elan Stopnitzky

Elan Stopnitzky

Numerade Educator

Problem 63

A piece of wood is 0.600 $\mathrm{m}$ long, 0.250 $\mathrm{m}$ wide, and
0.080 $\mathrm{m}$ thick. Its density is 600 $\mathrm{kg} / \mathrm{m}^{3} .$ What volume of lead must be fastened underneath it to sink the wood in calm water so that its top is just even with the water level? What is the mass of this volume of lead?

Nathan Silvano

Numerade Educator

Problem 64

A hot-air balloon has a volume of 2200 $\mathrm{m}^{3} .$ The balloon fabric (the envelope) weighs 900 $\mathrm{N} .$ The basket with gear and full propane tanks weighs 1700 $\mathrm{N}$ . If the balloon can barely lift an additional 3200 $\mathrm{N}$ of passengers, breakfast, and champagne when the outside air density is $1.23 \mathrm{kg} / \mathrm{m}^{3},$ what is the average density of the heated gases in the envelope?

Elan Stopnitzky

Elan Stopnitzky

Numerade Educator

Problem 65

In seawater, a life preserver with a volume of 0.0400 $\mathrm{m}^{3}$
will support a 75.0 $\mathrm{kg}$ person (average density 980 $\mathrm{kg} / \mathrm{m}^{3} )$ with 20$\%$ of the person's volume above water when the life
preserver is fully submerged. What is the density of the material composing the life preserver?

Nathan Silvano

Numerade Educator

Problem 66

Block $A$ in Figure 13.45 hangs by a cord from spring balance $D$ and is submerged in a liquid $C$ contained in beaker $B$ . The mass of the beaker is $1.00 \mathrm{kg} ;$ the mass of the liquid is 1.80 $\mathrm{kg} .$ Balance $D$ reads 3.50 $\mathrm{kg}$ and balance $E$ reads 7.50 $\mathrm{kg} .$ The volume of block $A$ is $3.80 \times 10^{-3} \mathrm{m}^{3}$ . (a) What is the density of the liquid? (b) What will each balance read if block $A$ is pulled up out of the liquid?

Elan Stopnitzky

Elan Stopnitzky

Numerade Educator

Problem 67

A hunk of aluminum is completely covered with a gold shell to form an ingot of weight
45.0 $\mathrm{N} .$ When you suspend the ingot from a spring balance and submerge the ingot in water, the balance reads 39.0 $\mathrm{N}$ . What is the weight of the gold in the shell?

Nathan Silvano

Numerade Educator

Problem 68

A liquid is used to make a mercury-type barometer, as described in Section $13.2 .$ The barometer is intended for spacefaring astronauts. At the surface of the earth, the column
of liquid rises to a height of 2185 $\mathrm{mm}$ , but on the surface of Planet $\mathrm{X},$ where the acceleration due to gravity is one-fourth of its value on earth, the column rises to only 725 $\mathrm{mm} .$ Find (a) the density of the liquid and (b) the atmospheric pressure at the surface of Planet $\mathrm{X}$ .

Elan Stopnitzky

Elan Stopnitzky

Numerade Educator

Problem 69

An open cylindrical tank of acid rests at the edge of a table 1.4 $\mathrm{m}$ above the floor of the chemistry lab. If this tank springs a small hole in the side at its base, how far from the foot of the table will the acid hit the floor if the acid in the tank is 75 $\mathrm{cm}$ deep?

Nathan Silvano

Numerade Educator

Problem 70

Water stands at a depth $H$ in a large, open tank whose side walls are vertical (Fig. 13.46$) .$ A hole is made in one of the walls at a depth $h$ below the water surface. (a) At
the water surface. (a) At what distance $R$ from the foot of the wall does the emerging stream strike the floor? (b) How far above the bottom of the tank could a second hole be cut so that the stream emerging from it could have the same range as for the first hole?

Elan Stopnitzky

Elan Stopnitzky

Numerade Educator

Problem 71

Exploring Europa's oceans. Europa, a satellite of Jupiter, appears to have an ocean beneath its icy surface. Proposals have been made to send a robotic submarine to Europa to see if
there might be life there. There is no atmosphere on Europa, and we shall assume that the surface ice is thin enough that we can neglect its weight and that the oceans are fresh water having the same density as on the earth. The mass and diameter of Europa have been measured to be $4.78 \times 10^{22}$ kg and 3130 $\mathrm{km}$ , respectively. (a) If the submarine intends to submerge to a depth of $100 \mathrm{m},$ what pressure must it be designed to withstand? (b) If you wanted to test this submarine before sending it to Europa, how deep would it have to go in our oceans to experience the
same pressure as the pressure at a depth of 100 $\mathrm{m}$ on Europa?

Nathan Silvano

Numerade Educator

Problem 72

The horizontal pipe shown in Figure 13.47 has a cross-sectional area of 40.0 $\mathrm{cm}^{2}$ at the wider portions and 10.0 $\mathrm{cm}^{2}$ at the constriction. Water is flowing in the pipe, and the discharge from the pipe is $6.00 \times$
$10^{-3} \mathrm{m}^{3} / \mathrm{s}(6.00 \mathrm{L} / \mathrm{s}) .$ Find
(a) the flow speeds at the wide and the narrow portions; (b) the pressure difportions; (c) the difference difporcury columns in the U-shaped tube.

Elan Stopnitzky

Elan Stopnitzky

Numerade Educator

Problem 73

Venturi meter. The Venturi meter is a device used to measure the speed of a fluid traveling through a pipe. Two cylinders are inserted in small holes in the pipes, as shown in Figure $13.48 . \quad$ since the cross-sectional area is different at the two places, the speed and pressure will be different there also. The difference $(h)$ in the heights of the two columns can easily be measured, as can the cross-sectional areas $A_{1}$ and $A_{2} .$ Notice that points 1 and 2 in the figure are both at the same vertical height. (a) Show that $\Delta p=\rho g h,$ where $\rho$ is the density of the fluid and $\Delta p$ is the pressure difference between points 1 and 2 (b) Apply Bernoulli's equation and the continuity condition to show that the speed at point 1 is given by the equation $$ \begin{array}{l}{v_{1}=\sqrt{\frac{2 g h}{\left(A_{1} / A_{2}\right)^{2}-1}},(\mathrm{c}) \text { How would you find the speed at }} \\ {\text { point } 2 ?}\end{array} $$

Nathan Silvano

Numerade Educator

Problem 74

Compressible fluids. Throughout this chapter, we have dealt only with incompressible fluids. But under very high pressure, fluids do, in fact, compress. (a) Show that the continuity condition for compressible fluids is $\rho_{1} A_{1} v_{1}=\rho_{2} A_{2} v_{2}$
where $\rho$ is the density of the fluid. (b) Show that your result reduces to the familiar result for incompressible fluids.

Elan Stopnitzky

Elan Stopnitzky

Numerade Educator

Problem 75

Roughly speaking, arteries carry blood from the heart and veins return blood to the heart. From your experience with small cuts or skinned knees, what can you say about the pres-
sure in the venous system (veins)?
$$\begin{array}{l}{\text { A. It is much less than atmospheric pressure. }} \\ {\text { B. It is slightly more than atmospheric pressure. }} \\ {\text { C. It is approximately the same as atmospheric pressure. }} \\ {\text { D. It is much greater than atmospheric pressure. }} \\ {\text { E. It is slightly greater than atmospheric pressure. }}\end{array}$$

Nathan Silvano

Numerade Educator

Problem 76

Blood pressure is normally measured on the arm of a patient at a point that is nearly at the same height as the heart. If we were to measure the blood pressure on the lower leg of a standing patient, we would expect the measurement to be
$$\begin{array}{l}{\text { A. lower than }} \\ {\text { B. higher than }} \\ {\text { C. the same as the measurement on the arm. }}\end{array}$$

Elan Stopnitzky

Elan Stopnitzky

Numerade Educator

Problem 77

On the earth, the pressure generated by the heart is sufficient to pump blood to a height of 1.3 $\mathrm{m} .$ The density of blood is 1.04 $\mathrm{g} / \mathrm{cm}^{3} . )$ If the top of your head were 0.5 $\mathrm{m}$ above your heart, what would be the strongest gravitational acceleration that you could endure on another planet before your heart would be unable to pump blood to your brain?
$$\begin{array}{l}{\text { A. } 2 g} \\ {\text { B. } 3 g} \\ {\text { C. } 5 g} \\ {\text { D. } 10 g}\end{array}$$

K B

Numerade Educator

Problem 78

The cross-sectional area of the aorta is $3 \mathrm{cm}^{2},$ and the average
velocity of blood leaving the heart into the aorta is 30 $\mathrm{cm} / \mathrm{s}$ . If
the combined effective cross sectional area of the body's capillaries is $600 \mathrm{cm}^{2},$ what is the average flow rate in a capillary?
$$\begin{array}{l}{\text { A. } 1 \mathrm{cm} / \mathrm{s}} \\ {\mathrm{B} .2 \mathrm{cm} / \mathrm{s}} \\ {\mathrm{C} \cdot 0.01 \mathrm{cm} / \mathrm{s}} \\ {\mathrm{D}, 0.15 \mathrm{cm} / \mathrm{s}} \\ {\mathrm{E} .0 .2 \mathrm{cm} / \mathrm{s}}\end{array}$$

Elan Stopnitzky

Elan Stopnitzky

Numerade Educator