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Understanding Physics

Karen Cummings, Priscilla W. Laws, Edward F. Redish

Chapter 15

Fluids - all with Video Answers

Educators


Chapter Questions

01:45

Problem 1

Syringe Find the pressure increase in the fluid in a syringe when a nurse applies a force of $42 \mathrm{~N}$ to the syringe's circular piston, which has a radius of $1.1 \mathrm{~cm}$.

James Erikson
James Erikson
Numerade Educator
04:02

Problem 2

Three Liquids Three liquids that will not mix are poured into a cylindrical container. The volumes and densitics of the liquids are $0.50 \mathrm{~L}, 2.6 \mathrm{~g} / \mathrm{cm}^{3} ; 0.25 \mathrm{~L}, 1.0 \mathrm{~g} / \mathrm{cm}^{3} ;$ and $0.40 \mathrm{~L}, 0.80 \mathrm{~g} / \mathrm{cm}^{3} .$ What is
the force on the bottom of the container due to these liquids? One liter $=1 \mathrm{~L}=1000 \mathrm{~cm}^{3}$. (Ignore the contribution due to the atmosphere.)

Matthew Baker
Matthew Baker
Numerade Educator
02:12

Problem 3

Office Window An office window has dimensions $3.4 \mathrm{~m}$ by $2.1 \mathrm{~m}$. As a result of the passage of a storm, the outside air pressure drops to $0.96 \mathrm{~atm}$, but inside the pressure is held at $1.0 \mathrm{~atm}$. What net force pushes out on the window?

James Erikson
James Erikson
Numerade Educator
03:31

Problem 4

Front Tires You inflate the front tires on your car to 28 psi. Later, you measure your blood pressure, obtaining a reading of $120 / 80$, the readings being in $\mathrm{mm} \mathrm{Hg}$. In countries using the metric system (which is to say, most of the world), these pressures are customarily reported in kilopascals (kPa). In kilopascals, what are (a) your tire pressure and (b) your blood pressure?

Matthew Baker
Matthew Baker
Numerade Educator
02:24

Problem 5

Fish $A$ fish maintains its depth in fresh water by adjusting the air content of porous bone or air sacs to make its average density the same as that of the water. Suppose that with its air sacs collapsed, a fish has a density of $1.08 \mathrm{~g} / \mathrm{cm}^{3}$. To what fraction of its expanded body volume must the fish inflate the air sacs to reduce its density to that of water?

Prabhu Ramji
Prabhu Ramji
Numerade Educator
03:26

Problem 6

Airtight Container An airtight container having a lid with negligible mass and an area of $77 \mathrm{~cm}^{2}$ is partially evacuated. If a $480 \mathrm{~N}$ force is required to pull the lid off the container and the atmospheric pressure is $1.0 \times 10^{5} \mathrm{~Pa}$, what is the air pressure in the container before it is opened?

Matthew Baker
Matthew Baker
Numerade Educator
04:15

Problem 7

Otto Von Guericke In 1654 Otto von Guericke, inventor of the air pump, gave a demonstration before the noblemen of the Holy Roman Empire in which two teams of eight horses could not pull apart two evacuated brass hemispheres. (a) Assuming that the hemispheres FiGURE $15-33=$ Problem 7
have thin walls, so that $R$ in Fig. $15-33$ may be considered both the inside and outside radius, show that the force $\vec{F}$ required to pull apart the hemispheres has magnitude $|\vec{F}|=\pi R^{2} \Delta P$, where $\Delta P$ is the difference between the pressures outside and inside the sphere. (b) Taking $R$ as $30 \mathrm{~cm}$, the inside pressure as $0.10 \mathrm{~atm}$, and the outside pressure as $1.00 \mathrm{~atm}$, find the force magnitude the teams of horses would have had to exert to pull apart the hemispheres. (c) Explain why one team of horses could have proved the point just as well if the hemispheres were attached to a sturdy wall.

Matthew Baker
Matthew Baker
Numerade Educator
00:41

Problem 8

Hydrostatic Difference Calculate the hydrostatic difference in blood pressure between the brain and the foot in a person of height $1.83 \mathrm{~m}$. The density of blood is $1.06 \times 10^{3} \mathrm{~kg} / \mathrm{m}^{3}$.

Averell Hause
Averell Hause
Carnegie Mellon University
01:39

Problem 9

Sewage Outlet The sewage outlet of a house constructed on a slope is $8.2 \mathrm{~m}$ below street level. If the sewer is $2.1 \mathrm{~m}$ below street level, find the minimum pressure difference that must be created by the sewage pump to transfer waste of average density $900 \mathrm{~kg} / \mathrm{m}^{3}$ from outlet to sewer.

Matthew Baker
Matthew Baker
Numerade Educator
04:05

Problem 10

Phase Diagram Figure $15-34$ displays the phase diagram of carbon, showing the ranges of temperature and pressure in which carbon will crystallize cither as diamond or graphite. What is the minimum depth at which diamonds can form if the temperature at that depth is $1000^{\circ} \mathrm{C}$ and the rocks there have density $3.1 \mathrm{~g} / \mathrm{cm}^{3} ?$ Assume that, as in a fluid, the pressure at any level is due to the gravitational force on the material lying above that level, and neglect variation of $g$ with depth.

Matthew Baker
Matthew Baker
Numerade Educator
03:01

Problem 11

Swimming Pool A swimming Problem 10. pool has the dimensions $24 \mathrm{~m} \times 9.0$ $\mathrm{m} \times 2.5 \mathrm{~m}$. When it is filled with water, what is the force (resulting from the water alone) on (a) the bottom, (b) each short side, and (c) each long side? (d) If you are concerned with the possibility that the concrete walls and floor will collapse, is it appropriate to take the atmospheric pressure into account? Why?

Ma Ednelyn Lim
Ma Ednelyn Lim
Numerade Educator
05:05

Problem 12

Seawater (a) Assuming the density of seawater is $1.03 \mathrm{~g} / \mathrm{cm}^{3}$, find the total weight of water on top of a nuclear submarine at a depth of $200 \mathrm{~m}$ if its (horizontal cross-sectional) hull area is $3000 \mathrm{~m}^{2}$. (b) In atmospheres, what water pressure would a diver experience at this depth? Do you think that occupants of a damaged submarine at this depth could escape without special equipment?

Matthew Baker
Matthew Baker
Numerade Educator
02:34

Problem 13

Crew Members Crew members attempt to escape from a damaged submarine $100 \mathrm{~m}$ below the surface. What force must be applied to a pop-out hatch, which is $1.2 \mathrm{~m}$ by $0.60 \mathrm{~m}$, to push it

Matthew Baker
Matthew Baker
Numerade Educator
10:14

Problem 14

Barrel A cylindrical barrel has a narrow tube fixed to the top, as shown (with dimensions) in Fig. $15-35$. The vessel is filled with water to the top of the tube. Calculate the ratio of the hydrostatic force on the bottom of the barrel to the gravitational force on the water contained inside the barrel. Why is that ratio not equal to one? (You need not consider the atmospheric pressure.)

Matthew Baker
Matthew Baker
Numerade Educator
03:59

Problem 15

Cylindrical Vessels Two identical cylindrical vessels with their bases at the same level each contain a liquid of density $\rho .$ The area of each base is $\bar{A}$. but in one vessel the liquid height is $h_{A}$, and in the other it is $h_{B}$. Find the work done by the gravitational force in equalizing the levels when the two vessels are connected.

Ma Ednelyn Lim
Ma Ednelyn Lim
Numerade Educator
04:08

Problem 16

Geological Features in analyzing certain gcological features, it is often appropriate to assume that the pressure at some horizontal level of compensation, deep inside Earth, is the same over a large region and is equal to the pressure due to the gravitational force on the overlying material. Thus, the pressure on the level of compensation is given by the fluid pressure formula. This model requires, for one thing, that mountains have roots of continental rock extending into the denser mantle (Fig. $15-36$ ). Consider a mountain $6.0 \mathrm{~km}$ high. The continental rocks have a density of $2.9 \mathrm{~g} / \mathrm{cm}^{3}$, and beneath the continent the mantle has a density of $3.3 \mathrm{~g} / \mathrm{cm}^{3}$. Calculate the depth $D$ of the root. (Hint: Set the pressure at points $a$ and $b$ equal; the depth $y$ of the level of compensation will cancel out.)

Ma Ednelyn Lim
Ma Ednelyn Lim
Numerade Educator
00:43

Problem 17

Ocean Figure $15-37$ shows FiGURE the juncture of ocean and continent. Find the depth $h$ of the ocean using the level-of-compensation technique presented in Problem $16 .$

Amy Jiang
Amy Jiang
Numerade Educator
04:53

Problem 18

L-shaped Tank The L-shaped tank shown in Fig. $15-38$ is filled with water and is open at the top. If $d=5.0 \mathrm{~m}$, what are (a) the force on face $A$ and (b) the force on face $B$ due to the water?

Matthew Baker
Matthew Baker
Numerade Educator
04:32

Problem 19

Water Stands Water stands at a depth $D$ behind the vertical upstream face of a dam, as shown in Fig. $15-39 .$ Let $W$ be the width of the dam. Find (a) the net horizontal force on the dam from the gauge pressure of the water and (b) the net torque due to that force (and thus gauge pressure) about a line through $O$ parallel to the width of the dam. (c) Find the moment arm of the net horizontal force about the line through $\underline{O}$.

Ma Ednelyn Lim
Ma Ednelyn Lim
Numerade Educator
02:21

Problem 20

Lemonade To suck lemonade of density $1000 \mathrm{~kg} / \mathrm{m}^{3}$ up a straw to a maximum height of $4.0 \mathrm{~cm}$, what minimum gauge pressure (in atmospheres) must you produce in your mouth?

Matthew Baker
Matthew Baker
Numerade Educator
04:09

Problem 21

Atmosphere What would be the height of the atmosphere if the air density (a) were uniform and (b) decreased linearly to zero with height? Assume that at sea level the air pressure is $1.0 \mathrm{~atm}$ and the air density is $1.3 \mathrm{~kg} / \mathrm{m}^{3}$.

Eric Mockensturm
Eric Mockensturm
Numerade Educator
04:30

Problem 22

Piston A piston of small crosssectional area $a$ is used in a hydraulic press to exert a small force $\vec{f}$ on the enclosed liquid. A connecting pipe leads to a larger piston of cross-sectional area $A$ (Fig. $15-40$ ).
(a) What force magnitude $|\vec{F}|$ will the larger piston sustain without FiGURE $15-40=$ moving? (b) If the small piston has Problems 22 and 23 . a diameter of $3.80 \mathrm{~cm}$ and the large piston one of $53.0 \mathrm{~cm}$, what force magnitude on the small piston will balance a $20.0 \mathrm{kN}$ force on the large piston?

Matthew Baker
Matthew Baker
Numerade Educator
03:09

Problem 23

Hydraulic Press In the hydraulic press of Problem 22, through what distance must the large piston be moved to raise the small piston a distance of $0.85 \mathrm{~m}$ ?

Matthew Baker
Matthew Baker
Numerade Educator
06:30

Problem 24

A Boat Floats A boat floating in fresh water displaces water weighing $35.6 \mathrm{kN}$. (a) What is the weight of the water that this boat would displace if it were floating in salt water with a density of $1.10 \times 10^{3} \mathrm{~kg} / \mathrm{m}^{3} ?$ (b) Would the volume of the displaced water change? If so, by how much?

Matthew Baker
Matthew Baker
Numerade Educator
02:17

Problem 25

Iron Anchor An iron anchor of density $7870 \mathrm{~kg} / \mathrm{m}^{3}$ appears $200 \mathrm{~N}$
lighter in water than in air. (a) What is the volume of the anchor? (b) How much does it weigh in air?

Eric Mockensturm
Eric Mockensturm
Numerade Educator
03:50

Problem 26

Cubical Object In Fig. $15-41$ a cubical object of dimensions $L=0.600 \mathrm{~m}$ on a side and with a mass of $450 \mathrm{~kg}$ is suspended by a rope in an open tank of liquid of density $1030 \mathrm{~kg} / \mathrm{m}^{3}$. (a) Find the magnitude of the total downward force on the top of the object from the liquid and the atmosphere, assuming that atmospheric pressure is $1.00$ atm. (b) Find the magnitude of the total upward force on the bottom of the object. (c) Find the tension in the rope. (d) Calculate the magnitude of the buoyant force on the object using Archimedes' principle. What relation exists among all these quantities?

Ma Ednelyn Lim
Ma Ednelyn Lim
Numerade Educator
06:00

Problem 27

Block of Wood A block of wood floats in fresh water with twothirds of its volume submerged. In oil the block floats with $0.90$ of its volume submerged. Find the density of (a) the wood and (b) the oil.

Matthew Baker
Matthew Baker
Numerade Educator
03:21

Problem 28

Blimp A blimp is cruising slowly at low altitude, filled as usual with helium gas. Its maximum useful payload, including crew and cargo, is $1280 \mathrm{~kg}$. The volume of the helium-filled interior space is $5000 \mathrm{~m}^{3}$. The density of helium gas is $0.16 \mathrm{~kg} / \mathrm{m}^{3}$, and the density of hydrogen is $0.081 \mathrm{~kg} / \mathrm{m}^{3}$. How much more payload could the blimp carry if you replaced the helium with hydrogen? (Why not do it?)

Matthew Baker
Matthew Baker
Numerade Educator
04:21

Problem 29

Hollow Sphere A hollow sphere of inner radius $8.0 \mathrm{~cm}$ and outer radius $9.0 \mathrm{~cm}$ floats half-submerged in a liquid of density $800 \mathrm{~kg} / \mathrm{m}^{3} .$ (a) What is the mass of the sphere? (b) Calculate the density of the material of which the sphere is made.

Matthew Baker
Matthew Baker
Numerade Educator
04:49

Problem 30

Dead Sea About onc-third of the body of a person floating in the Dead Sea will be above the water line. Assuming that the human body density is $0.98 \mathrm{~g} / \mathrm{cm}^{3}$, find the density of the water in the Dead Sea. (Why is it so much greater than $1.0 \mathrm{~g} / \mathrm{cm}^{3} ?$ )

Matthew Baker
Matthew Baker
Numerade Educator
01:51

Problem 31

Iron Shell A hollow spherical iron shell floats almost completely submerged in water. The outer diameter is $60.0 \mathrm{~cm}$, and the density of iron is $7.87 \mathrm{~g} / \mathrm{cm}^{3}$. Find the inner diameter.

Eric Mockensturm
Eric Mockensturm
Numerade Educator
05:03

Problem 32

Wood with Lead A block of wood has a mass of $3.67 \mathrm{~kg}$ and a density of $600 \mathrm{~kg} / \mathrm{m}^{3} .$ It is to be loaded with lead so that it will float in water with $0.90$ of its volume submerged. What mass of lead is needed (a) if the lead is attached to the top of the wood and (b) if the lead is attached to the bottom of the wood? The density of lead is $1.13 \times 10^{4} \mathrm{~kg} / \mathrm{m}^{3}$

Ma Ednelyn Lim
Ma Ednelyn Lim
Numerade Educator
02:49

Problem 33

Iron Casting An iron casting containing a number of cavities weighs $6000 \mathrm{~N}$ in air and $4000 \mathrm{~N}$ in water. What is the total volume of all the cavities in the casting? The density of iron (that is, a sample with no cavities) is $7.87 \mathrm{~g} / \mathrm{cm}^{3}$.

Ma Ednelyn Lim
Ma Ednelyn Lim
Numerade Educator
03:32

Problem 34

Density of Brass Assume the density of brass weights to be $8.0 \mathrm{~g} / \mathrm{cm}^{3}$ and that of air to be $0.0012 \mathrm{~g} / \mathrm{cm}^{3} .$ What percent error arises from neglecting the buoyancy of air in weighing an object of mass $m$ and density $\rho$ on a beam balance?

Prabhu Ramji
Prabhu Ramji
Numerade Educator
03:29

Problem 35

Slab of Ice (a) What is the minimum area of the top surface of a slab of ice $0.30 \mathrm{~m}$ thick floating on fresh water that will hold up an automobile of mass $1100 \mathrm{~kg} ?$ (b) Does it matter where the car is placed on the block of ice?

Ma Ednelyn Lim
Ma Ednelyn Lim
Numerade Educator
02:33

Problem 36

Three Children Three children, each of weight $356 \mathrm{~N}$, make a log raft by lashing together logs of diameter $0.30 \mathrm{~m}$ and length $1.80 \mathrm{~m}$. How many logs will be needed to keep them afloat in fresh water? Take the density of the logs to be $800 \mathrm{~kg} / \mathrm{m}^{3}$.

Eric Mockensturm
Eric Mockensturm
Numerade Educator
05:24

Problem 37

Metal Rod A metal rod of length $80 \mathrm{~cm}$ and mass $1.6 \mathrm{~kg}$ has a uniform cross-sectional area of $6.0$ $\mathrm{cm}^{2}$. Due to a nonuniform density, the center of mass of the rod is 20 $\mathrm{cm}$ from one end of the rod. The rod is suspended in a horizontal position in water by ropes attached to both ends (Fig. $15-42$ ). (a) What is the tension in the rope closer to the center of mass? (b) What is the tension in the rope farther from the center of mass? (Hint: The buoyancy force on the rod effectively acts at the rod's geometric center.)

VS
Vivek Singh
Numerade Educator
03:36

Problem 38

Floating Car A car has a total mass of $1800 \mathrm{~kg}$. The volume of air space in the passenger compartment is $5.00 \mathrm{~m}^{3} .$ The volume of the motor and front wheels is $0.750 \mathrm{~m}^{3}$, and the volume of the rear wheels, gas tank, and trunk is $0.800 \mathrm{~m}^{3}$; water cannot enter these areas. The car is parked on a hill; the handbrake cable snaps and the car rolls down the hill into a lake (Fig. $15-43$ ). (a) At first, no water enters the passenger compartment. How much of the car, in cubic meters, is below the water surface with the car floating as shown?
(b) As water slowly enters, the car sinks. How many cubic meters of water are in the car as it disappears below the water surface? (The car, with a heavy load in the trunk, remains horizontal.)

Ma Ednelyn Lim
Ma Ednelyn Lim
Numerade Educator
02:54

Problem 39

Garden Hose A garden hose with an internal diameter of $1.9 \mathrm{~cm}$ is connected to a (stationary) lawn sprinkler that consists merely of an enclosure with 24 holes, each $0.13 \mathrm{~cm}$ in diameter. If the water in the hose has a speed of $0.91 \mathrm{~m} / \mathrm{s}$, at what speed does it leave the sprinkler holes?

Mayank Tripathi
Mayank Tripathi
Numerade Educator
01:05

Problem 40

Two Streams Two streams merge to form a river. One stream has a width of $8.2 \mathrm{~m}$, depth of $3.4 \mathrm{~m}$, and current speed of $2.3 \mathrm{~m} / \mathrm{s}$. The other stream is $6.8 \mathrm{~m}$ wide and $3.2 \mathrm{~m}$ deep, and flows at $2.6 \mathrm{~m} / \mathrm{s}$. The width of the river is $10.5 \mathrm{~m}$, and the current speed is $2.9 \mathrm{~m} / \mathrm{s}$. What is its depth?

Averell Hause
Averell Hause
Carnegie Mellon University
03:08

Problem 41

Flooded Basement Water is pumped steadily out of a flooded basement at a speed of $5.0 \mathrm{~m} / \mathrm{s}$ through a uniform hose of radius $1.0$ $\mathrm{cm}$. The hose passes out through a window $3.0 \mathrm{~m}$ above the watcrline. What is the power of the pump?

Ma Ednelyn Lim
Ma Ednelyn Lim
Numerade Educator
03:26

Problem 42

Water Pipe The water flowing through a $1.9 \mathrm{~cm}$ (inside diameter) pipe flows out through three $1.3 \mathrm{~cm}$ pipes. (a) If the flow rates in the three smaller pipes are 26,19 , and $11 \mathrm{~L} / \mathrm{min}$, what is the flow rate in the $1.9 \mathrm{~cm}$ pipe? (b) What is the ratio of the speed of water in the $1.9 \mathrm{~cm}$ pipe to that in the pipe carrying $26 \mathrm{~L} / \mathrm{min}$ ?

Matthew Baker
Matthew Baker
Numerade Educator
03:22

Problem 43

Pipe Increases in Area Water is moving with a speed of $5.0 \mathrm{~m} / \mathrm{s}$ through a pipe with a cross-sectional area of $4.0 \mathrm{~cm}^{2}$. The water gradually descends $10 \mathrm{~m}$ as the pipe increases in area to $8.0 \mathrm{~cm}^{2} .$
(a) What is the speed at the lower level? (b) If the pressure at the upper level is $1.5 \times 10^{5} \mathrm{~Pa}$, what is the pressure at the lower level?

Eric Mockensturm
Eric Mockensturm
Numerade Educator
02:09

Problem 44

Torpedoes Models of torpedoes are sometimes tested in a horizontal pipe of flowing water, much as a wind tunnel is used to test model airplanes. Consider a circular pipe of internal diameter $25.0 \mathrm{~cm}$ and a torpedo model, aligned along the axis of the pipe, with a diameter of $5.00 \mathrm{~cm}$. The model is to be tested with water flowing past it at $2.50 \mathrm{~m} / \mathrm{s}$. (a) With what speed must the water flow in the part of the pipe that is unconstricted by the model? (b) What will the pressure difference be between the constricted and unconstricted parts of the pipe?

Ma Ednelyn Lim
Ma Ednelyn Lim
Numerade Educator
03:41

Problem 45

Basement Pipe A water pipe having a $2.5 \mathrm{~cm}$ inside diameter carries water into the basement of a house at a speed of $0.90 \mathrm{~m} / \mathrm{s}$ and a pressure of $170 \mathrm{kPa}$. If the pipe tapers to $1.2 \mathrm{~cm}$ and rises to the second floor $7.6 \mathrm{~m}$ above the input point, what are (a) the speed and (b) the water pressure at the second floor?

Eric Mockensturm
Eric Mockensturm
Numerade Educator
02:29

Problem 46

Water Intake A water intake at a pump storage reseryoir (Fig. $15-44$ ) has a cross-sectional area of $0.74 \mathrm{~m}^{2}$. The water flows in at a speed of $0.40$ $\mathrm{m} / \mathrm{s}$. At the generator building $180 \mathrm{~m}$ below the intake point, the cross-sectional area is FIGURE $15-44=$ Problem 46 . smaller than at the intake and the water flows out at $9.5 \mathrm{~m} / \mathrm{s}$. What is the difference in pressure, in megapascals, between inlet and outlet?

Ma Ednelyn Lim
Ma Ednelyn Lim
Numerade Educator
05:01

Problem 47

Large Area $A$ tank of large area is filled with water to a depth $D=0.30 \mathrm{~m} .$ A hole of cross-sectional area $A=6.5 \mathrm{~cm}^{2}$ in the bottom of the tank allows water to drain out. (a) What is the rate at which water flows out, in cubic meters per second? (b) At what distance below the bottom of the tank is the cross-sectional arca of the stream equal to one-half the area of the hole?

Ma Ednelyn Lim
Ma Ednelyn Lim
Numerade Educator
02:55

Problem 48

Air Flows Air flows over the top of an airplane wing of area $A$ with speed $\left|\vec{v}_{\text {tep }}\right|$ and past the undcrside of the wing (also of arca $A$ ) with speed $\left|\vec{v}_{\text {under }}\right|$. Show that in this simplificd situation Bernoulli's equation predicts that the magnitude $|\vec{L}|$ of the upward lift force on the wing will be
$$
|\vec{L}|=\frac{1}{2} \rho A\left(v_{\text {top }}^{2}-v_{\text {under }}^{2}\right)
$$
where $\rho$ is the density of the air.

Mayank Tripathi
Mayank Tripathi
Numerade Educator
01:53

Problem 49

Airplane Wing If the speed of flow past the lower surface of an airplane wing is $110 \mathrm{~m} / \mathrm{s}$, what speed of flow over the upper surface will give a pressure difference of 900 Pa between upper and lower surfaces? Take the density of air to be $1.30 \times 10^{-3} \mathrm{~g} / \mathrm{cm}^{3}$, and sec Problem 48 .

Mayank Tripathi
Mayank Tripathi
Numerade Educator
03:31

Problem 50

Two Tanks Suppose that two tanks, $A$ and $B$, each with a large opening at the top, contain different liquids. A small hole is made in the side of cach tank at the same depth $d$ below the liquid surface, but the hole in tank $A$ has half the cross-sectional area of the hole in tank $B$. (a) What is the ratio $\rho_{A} / \rho_{B}$ of the densities of the liquids if the mass flow rate is the same for the two holes? (b) What is the ratio of the volume flow rates from the two tanks? (c) To what height above the hole in tank $B$ should liquid be added or drained to equalize the volume flow rates?

Ma Ednelyn Lim
Ma Ednelyn Lim
Numerade Educator
04:20

Problem 51

Water in the Horizontal Pipe In Fig, $15-45$, water flows through a horizontal pipe, and then out into the atmosphere at a speed of $15 \mathrm{~m} / \mathrm{s}$. The diameters of the left and right sections of the pipe are $5.0 \mathrm{~cm}$ and $3.0 \mathrm{~cm}$, respectively. (a) What volume of water flows into the atmosphere during a $10 \mathrm{~min}$ period? In the left section of the pipe, what are (b) the speed $v_{B}$, and (c) the gauge pressure?

Ma Ednelyn Lim
Ma Ednelyn Lim
Numerade Educator
02:29

Problem 52

Beverage Keg An opening of area $0.25 \mathrm{~cm}^{2}$ in an otherwise closed beverage keg is $50 \mathrm{~cm}$ below the level of the liquid (of density $1.0 \mathrm{~g} / \mathrm{cm}^{3}$ ) in the keg. What is the speed of the liquid flowing through the opening if the gauge pressure in the air space above the liquid is (a) zero and (b) $0.40 \mathrm{~atm}$ ?

Suman Saurav Thakur
Suman Saurav Thakur
Numerade Educator
02:30

Problem 53

Dam The fresh water behind a reservoir dam is $15 \mathrm{~m}$ deep. A horizontal pipe $4.0 \mathrm{~cm}$ in diameter passes through the dam $6.0 \mathrm{~m}$ below the water surface, as shown in Fig. $15-46 .$ A plug secures the pipe opening. (a) Find the magnitude of the frictional force between plug and pipe wall. (b) The plug is removed. What volume of water flows out of the pipe in $3.0 \mathrm{~h}$ ?

Ma Ednelyn Lim
Ma Ednelyn Lim
Numerade Educator
05:40

Problem 54

Filled Tank A tank is filled with water to a height $H .$ A hole is punched in one of the walls at a depth $h$ below the water surface (Fig. $15-47$ ). (a) Show that the distance $x$ from the base of the tank to the point at which the resulting stream strikes the floor is given by $x=2 \sqrt{h(H-h)} .$ (b) Could a hole be punched at another depth to proFiGURE $15-47=$ duce a second stream that would Problem 54 . have the same range? If so, at what depth? (c) At what depth should the hole be placed to make the emerging stream strike the ground at the maximum distance from the base of the tank?

Ma Ednelyn Lim
Ma Ednelyn Lim
Numerade Educator
05:31

Problem 55

Venturi Meter A venturi meter is used to measure the flow speed of a fluid in a pipe. The meter is connected between two sections of the pipe (Fig. $15-48$ ); the cross-sectional area $A$ of the entrance and exit of the meter matches the pipe's cross-sectional arca At the entrance and cxit, the fluid flows through the pipe with speed $v_{A}=\left|\vec{v}_{A}\right| .$ But it flows through a narrow "throat" of cross-sectional area $B$ with speed $v_{B}=\left|\vec{v}_{B}\right| .$ A manometer connects the wider portion of the meter to the narrower portion. The change in the fluid's speed is accompanied by a change $\Delta P$ in the fluid's pressure, which causes a height difference $h$ of the liquid in the two arms of the manometer. (Here $\Delta P$ means pressure in the throat minus pressure in the pipe.) (a) By applying Bernoulli's equation and the equation of continuity to points 1 and 2 in Fig. $15-48$, show that
$$
\vec{v}_{A}=\sqrt{\frac{2 B^{2} \Delta P}{\rho\left(B^{2}-A^{2}\right)}}
$$
where $\rho$ is the density of the fluid. (b) Suppose that the fluid is fresh water, that the cross-sectional areas are $64 \mathrm{~cm}^{2}$ in the pipe and $32 \mathrm{~cm}^{2}$ in the throat, and that the pressure is $55 \mathrm{kPa}$ in the pipe and $41 \mathrm{kPa}$ in the throat. What is the rate of water flow in cubic meters per second?

Ma Ednelyn Lim
Ma Ednelyn Lim
Numerade Educator
03:24

Problem 56

Venturi Tube Consider the venturi tube of Problem 55 and Fig. $15-48$ without the manometer. Let $A$ equal $5 a .$ Suppose that the pressure $P_{1}$ at $A$ is $2.0 \mathrm{~atm} .$ Compute the values of $(\mathrm{a})\left|\vec{V}_{A}\right|$ at $A$ and
(b) $\left|\vec{v}_{a}\right|$ at $a$ that would make the pressure $P_{2}$ at $a$ equal to zero.
(c) Compute the corresponding volume flow rate if the diameter at $A$ is $5.0 \mathrm{~cm}$. The phenomenon that occurs at $a$ when $P_{2}$ falls to nearly zero is known as cavitation. The water vaporizes into small bubbles.

Ma Ednelyn Lim
Ma Ednelyn Lim
Numerade Educator
02:39

Problem 57

Pitot Tube A pitot tube (Fig. $15-49$ ) is used to determine the airspeed of an airplane. It consists of an outer tube with a number of small holes $B$ (four arc shown) that allow air into the tube; that tube is connected to one arm of a U-tube. The other arm of the Utube is connected to hole $A$ at the front end of the device, which points in the direction the plane is headed. At $A$ the air becomes stagnant so that $v_{A}=0 .$ At $B$, however, the speed of the air presumably equals the airspeed $v$ of the aircraft. (a) Use Bernoulii's equation to show that
$$
v=\sqrt{\frac{2 \rho g h}{\rho_{\text {air }}}}
$$
where $\rho$ is the density of the liquid in the U-tube and $h$ is the difference in the fluid levels in that tube. (b) Suppose that the tube contains alcohol and indicates a level difference $h$ of $26.0 \mathrm{~cm}$. What is the plane's speed relative to the air? The density of the air is $1.03 \mathrm{~kg} / \mathrm{m}^{3}$ and that of alcohol is $810 \mathrm{~kg} / \mathrm{m}^{3}$

Ma Ednelyn Lim
Ma Ednelyn Lim
Numerade Educator
01:27

Problem 58

High-Altitude Aircraft A pitot tube (see Problem 57) on a high-altitude aircraft measures a differential pressure of $180 \mathrm{~Pa}$. What is the airspeed if the density of the air is $0.031 \mathrm{~kg} / \mathrm{m}^{3}$ ?

Ma Ednelyn Lim
Ma Ednelyn Lim
Numerade Educator
01:40

Problem 59

Pool Filling You have been asked to review plans for a swimming pool in a new hotel. The water is to be supplied to the hotel by a horizontal main pipe of radius $R_{1}=6.00 \mathrm{~cm}$, with water under pressure of $2.00$ atm. A vertical pipe of radius $R_{2}=1.00 \mathrm{~cm}$ is to carry the water to a height of $9.40 \mathrm{~m}$, where the water is to pour out frecly into a square pool of width $10.0 \mathrm{~m}$ and (proposed) water depth of $2.00 \mathrm{~m}$. (a) How much time will be required to fill the pool? (b) If more than a few days is considered unacceptable and less than a few hours is considered dangerous, is the filling time acceptable and safe?

Penny Riley
Penny Riley
Numerade Educator
02:28

Problem 60

Hydraulic $\quad$ Engineers Figure $15-50$ shows two sections of an old pipe system that runs through a hill. On each side of the hill, the pipe radius is $2.00 \mathrm{~cm}$. However, FiGURE $15-50=$ Problem 60 . the radius of the pipe inside the hill is no longer known. To determine it, hydraulic engineers first cstablish that water flows through the left-hand and right-hand sections at $2.50 \mathrm{~m} / \mathrm{s}$. Then they release a dye in the water at point $A$ and find that it takes $88.8 \mathrm{~s}$ to reach point $B$. What is the radius (or average radius) of the pipe within the hill?

Averell Hause
Averell Hause
Carnegie Mellon University
02:04

Problem 61

Floating and Sinking Suppose you have the following collection of objects: a pencil, a coin, an empty plastic box for CDs with its edges taped shut, the same box opened up, a needle, an unopened can of soda pop, and an empty can of soda pop. Which of these objects do you expect will float on water and which will sink? Will it make a difference if you carefully place the object with its largest surface on the surface of the water? In which cases? Discuss the criteria you come up with, explaining carefully why you decided on cach one and why it plays a role. After you have written your answer, perform the experiments and compare your results with your predictions.

Surjit Tewari
Surjit Tewari
Numerade Educator
01:58

Problem 62

Balloon in a Car Explain why a helium balloon in a closed automobile moves to the front of the car when the car accelerates, whereas the passengers feel pushed backwards. Discuss this in terms of the physics you have learned.

Ma Ednelyn Lim
Ma Ednelyn Lim
Numerade Educator
01:57

Problem 63

At the Pool If an inflated beach ball is placed beneath the surfacc of a pool and released, it shoots upward, out of the water. Explain why.

Ma Ednelyn Lim
Ma Ednelyn Lim
Numerade Educator
03:45

Problem 64

The Meteor and the Dolphin The curator of a science museum is transporting a chunk of meteor iron (i.e., a piece of iron that fell from the sky-see Fig. $15-51 a$ ) from one part of the museum to another. Since the chunk of iron weighs $250 \mathrm{lb}$ and is too big for her to lift by herself, she is using a handtruck (see Fig. $15-51 b$ ). While passing through the marine mammals section of the museum, she accidentally hits a bump and the meteorite tips off the handtruck and falls into the dolphin pool. Fortunately, the iron doesn't hit a dolphin, but it quickly sinks to the bottom. "Rats!" she cries. Unfortunately, the meteorite has many sharp edges and she is worried that the dolphins, curious creatures that they are, will come to inspect it and be cut when they rub against it. She wants to get it up out of the pool as quickly as possible. Fortunately, the meteorite has lots of holes in it and there are ropes with hooks on one end lying around. If she could get a hook into one of the holes, she might be able to pull it up to the top, tie the rope FIGURE $15-51(a)=$ Problem $64 .$ around a post, and lever it out with the handtruck. Unfortunatcly, she remembers that the metcorite is too heavy for her to lift. (a) Will the fact that the meteorite is in the pool under water make it harder or easier for her to lift with the rope? Explain. (b) The meteorite is sitting on the concrete bottom of the pool. Is the force the meteorite exerts on the bottom bigger or smaller than the force it would exert if the pool had no water in it? Explain. (c) Can she lift the meteorite? Calculate how much force she would have to cxert on a rope hooked to FiGURE $15-51(b)=$ the meteorite to pull it up from the bottom Problem 64 . of the pool. She can lift about 100 pounds, the pool is 12 feet deep, and the density of iron is about $8000 \mathrm{~kg} / \mathrm{m}^{3}$.

Lottie Adams
Lottie Adams
Numerade Educator
03:19

Problem 65

Pushing Iron For each of the following partial sentences, indicate whether they are correctly completed by the symbol corresponding to the phrase greater than $(>)$, less than $(<)$, or the same as $(=) .$ (a) A chunk of iron is sitting on a table. It is then moved from the table into a bucket of water sitting on the table. The iron now rests on the bottom of the bucket. The force the bucket exerts on the block when the block is sitting on the bottom of the bucket is the force that the table exerted on the block when the block was sitting on the table. (b) A chunk of iron is sitting on a table. It is then moved from the table into a bucket of water sitting on the table. The iron now rests on the bottom of the bucket. The total force on the block when it is sitting on the bottom of the bucket is it was on the table. (c) A chunk of iron is sitting on a table. It is then covered by a bell jar, which has a nozzle connected to a vacuum pump. The air is extracted from the bell jar. The force the table exerts on the block when the block is sitting in a vacuum is the force that the table exerted on the block when the block was sitting in the air. (d) A chunk of iron is sitting on a scale. The iron and the scale are then both immersed in a large vat of water. After being immersed in the water, the scale reading will be the scale reading when they were simply sitting in the air. (Assume the scale would read zero if nothing were sitting on it, even when it is underwater.)

Keshav Singh
Keshav Singh
Numerade Educator
02:27

Problem 66

The Three-Vase Puzzle* Water is poured to the same level in each of the three vessels shown in Fig. $15-52 .$ Each vessel has the same base area. Since the water is to the same depth in each vessel, each will have the same pressure at the bottom. Since the area and pressure are the same, each liquid should exert the same force on the base of the vessel. Yet, if the vessels are weighed, three different values are obtained. (The one in the center clearly holds less liquid than the one at the left, so it must weigh less.) How can you justify this apparent contradiction?

Ma Ednelyn Lim
Ma Ednelyn Lim
Numerade Educator
View

Problem 67

Hanging $\quad$ Blockst Three cubical blocks of equal volume are suspended from strings. Blocks $A$ and $B$ have the same mass and block $C$ has less mass. Each block is lowered into a fish tank and they hang at rest as shown in Fig. $15-53$.
(a) Is the force exerted by the water on the top surface of block $A$ greater than, less than, or cqual to the force cxerted by the water on the top surface of block $B$ ? FIGURE $15-53=$ Explain. (b) Is the force exerted by the Problem 67 . water on the top surface of block $A$ greater than, less than, or equal to the force exerted by the water on the top surface of block $C$ ? Explain. (c) Is the force exerted on the water by block $C$ greater than, less than or equal to the force excrted on the water by block $A$ ? Explain. (d) Rank the buoyant forces acting on the three blocks from largest to smallest. If any buoyant forces are equal, indicate that explicitly. Explain.

Victor Salazar
Victor Salazar
Numerade Educator
02:41

Problem 68

Floating Blocks\div? Figure $15-54$ shows five blocks increasing in mass from block $A$ to block $E$ as indicated. The blocks have cqual volumes but different masses. The blocks are placed in an aquarium tank filled with water and blocks $B$ and $E$ come to rest as shown in Fig. $15-54$. Sketch on the figure where you would expect blocks $A$, $C$, and $D$ to come to rest. (The differences in mass between successive blocks is significant - not just a tiny amount.)

Matthew Baker
Matthew Baker
Numerade Educator