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Physics for Scientists and Engineers with Modern Physics

Raymond A. Serway, John W. Jewett, Jr.

Chapter 14

Fluid Mechanics - all with Video Answers

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Chapter Questions

01:29

Problem 1

Calculate the mass of a solid iron sphere that has a diameter of $3.00 \mathrm{cm} .$

Surjit Tewari
Surjit Tewari
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00:36

Problem 2

Find the order of magnitude of the density of the nucleus of an atom. What does this result suggest concerning the structure of matter? Model a nucleus as consisting of protons and neutrons closely packed together. Each has mass $1.67 \times 10^{-27} \mathrm{kg}$ and radius on the order of $10^{-15} \mathrm{m}$ .

Surjit Tewari
Surjit Tewari
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01:26

Problem 3

A 50.0 -kg woman balances on one heel of a pair of highheeled shoes. If the heel is circular and has a radius of $0.500 \mathrm{cm},$ what pressure does she exert on the floor?

Surjit Tewari
Surjit Tewari
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01:48

Problem 4

What is the total mass of the Earth's atmosphere? (The radius of the Earth is $6.37 \times 10^{6} \mathrm{m},$ and atmospheric pressure at the surface is $1.013 \times 10^{5} \mathrm{N} / \mathrm{m}^{2} . )$

Surjit Tewari
Surjit Tewari
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02:21

Problem 5

The spring of the pressure gauge shown in Figure 14.2 has a force constant of $1000 \mathrm{N} / \mathrm{m},$ and the piston has a diameter of $2.00 \mathrm{cm} .$ As the gauge is lowered into water,
what change in depth causes the piston to move in by 0.500 $\mathrm{cm}$ ?

Surjit Tewari
Surjit Tewari
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02:09

Problem 6

(a) Calculate the absolute pressure at an ocean depth of 1000 $\mathrm{m}$ . Assume the density of seawater is 1024 $\mathrm{kg} / \mathrm{m}^{3}$ and the air above exerts a pressure of 101.3 $\mathrm{kPa}$ . (b) At this depth, what force must the frame around a circular submarine porthole having a diameter of 30.0 $\mathrm{cm}$ exert to counterbalance the force exerted by the water?

Surjit Tewari
Surjit Tewari
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01:30

Problem 7

What must be the contact area between a suction cup (completely exhausted) and a ceiling if the cup is to support the weight of an $80.0-\mathrm{kg}$ student?

Surjit Tewari
Surjit Tewari
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00:57

Problem 8

The small piston of a hydraulic lift has a cross-sectional area of 3.00 $\mathrm{cm}^{2}$ and its large piston has a cross-sectional area of 200 $\mathrm{cm}^{2}$ (Fig. $14.4 \mathrm{a} ) .$ What force must be applied to the small piston for the lift to raise a load of 15.0 $\mathrm{kN}$ ? (In service stations, this force is usually exerted by compressed air.)

Surjit Tewari
Surjit Tewari
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02:31

Problem 9

For the basement of a new house, a hole is dug in the ground, with vertical sides going down $2.40 \mathrm{m} .$ A concrete foundation wall is built across the 9.60 -m width of the excavation. This foundation wall is 0.183 $\mathrm{m}$ from the front of the basement hole. During a rainstorm,
drainage from the street fills up the space in front of the concrete wall, but not the basement behind the wall. The water does not soak into the clay soil. Find the force the water causes on the foundation wall. For comparison, the gravitational force exerted on the water is $(2.40 \mathrm{m})(9.60 \mathrm{m})(0.183 \mathrm{m})\left(1000 \mathrm{kg} / \mathrm{m}^{3}\right)\left(9.80 \mathrm{m} / \mathrm{s}^{2}\right)=$ $41.3 \mathrm{kN} .$

Surjit Tewari
Surjit Tewari
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03:17

Problem 10

(a) A powerful vacuum cleaner has a hose 2.86 $\mathrm{cm}$ in diameter. With no nozzle on the hose, what is the weight of the heaviest brick that the cleaner can lift (Fig. Pl4.10a)? (b) What If? An octopus uses one sucker of diameter 2.86 $\mathrm{cm}$ on each of the two shells of a clam in 0an attempt to pull the shells apart (Fig. Pl4. 10 b). Find the greatest force the octopus can exert in seawater 32.3 $\mathrm{m}$ deep. Caution: Experimental verification can be interesting, but do not drop a brick on your foot. Do not overheat the motor of a vacuum cleaner. Do not get an octopus mad at you.

Surjit Tewari
Surjit Tewari
Numerade Educator
02:45

Problem 11

A swimming pool has dimensions $30.0 \mathrm{m} \times 10.0 \mathrm{m}$ and a flat bottom. When the pool is filled to a depth of 2.00 $\mathrm{m}$ with fresh water, what is the force caused by the water on the bottom? On each end? On each side?

Surjit Tewari
Surjit Tewari
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01:50

Problem 12

The tank in Figure $\mathrm{P} 14.12$ is filled with water 2.00 $\mathrm{m}$ deep. At the bottom of one sidewall is a rectangular hatch 1.00 $\mathrm{m}$ high and 2.00 $\mathrm{m}$ wide that is hinged at the top of the hatch. (a) Determine the force the water causes on the hatch. (b) Find the torque caused by the water about the hinges.

Dominador Tan
Dominador Tan
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03:56

Problem 13

Review problem. The Abbott of Aberbrothock paid for a bell moored to the Inchcape Rock to warn sailors away. Assume the bell was 3.00 $\mathrm{m}$ in diameter and cast from brass with a bulk modulus of $14.0 \times 10^{10} \mathrm{N} / \mathrm{m}^{2}$ . The pirate Ralph the Rover cut loose the bell and threw it into the ocean. By how much did the diameter of the bell decrease as it sank to a depth of 10.0 $\mathrm{km}$ ? Years later, the klutz drowned when his ship collided with the rock. Note: The brass is compressed uniformly, so you may model the bell as a sphere of diameter $3.00 \mathrm{m} .$

Surjit Tewari
Surjit Tewari
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01:49

Problem 14

Figure P14.14 shows Superman attempting to drink water through a very long straw. With his great strength he achieves maximum possible suction. The walls of the tubular straw do not collapse. (a) Find the maximum height through which he can lift the water. (b) What If? Still thirsty, the Man of Steel repeats his attempt on the Moon, which has no atmosphere. Find the difference between the water levels inside and outside the straw.

Surjit Tewari
Surjit Tewari
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01:07

Problem 15

Blaise Pascal duplicated Torricelli's barometer using a red Bordeaux wine, of density 984 $\mathrm{kg} / \mathrm{m}^{3}$ , as the working liquid (Fig. Pl4.15). What was the height $h$ of the wine column for normal atmospheric pressure? Would you expect the vacuum above the column to be as good as
for mercury?

Surjit Tewari
Surjit Tewari
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01:35

Problem 16

Mercury is poured into a U-tube as shown in Figure Pl4. 16a. The left arm of the tube has cross-sectional area $A_{1}$ of $10.0 \mathrm{cm}^{2},$ and the right arm has a crosssectional area $A_{2}$ of 5.00 $\mathrm{cm}^{2}$ . One hundred grams of water are then poured into the right arm as shown in Figure Pl4. 16b. (a) Determine the length of the water column in the right arm of the U-tube. (b) Given that the density of mercury is $13.6 \mathrm{g} / \mathrm{cm}^{3},$ what distance $h$ does the mercury rise in the left arm?

Dominador Tan
Dominador Tan
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01:15

Problem 17

Normal atmospheric pressure is $1.013 \times 10^{5}$ Pa. The approach of a storm causes the height of a mercury barometer to drop by 20.0 $\mathrm{mm}$ from the normal height. What is the atmospheric pressure? (The density of mercury is $13.59 \mathrm{g} / \mathrm{cm}^{3} . )$

Surjit Tewari
Surjit Tewari
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06:46

Problem 18

A tank with a flat bottom of area $A$ and vertical sides is filled to a depth $h$ with wath water. The pressure is 1 atm at the top surface. (a) What is the absolute pressure at the bot- tom of the tank? (b) Suppose an object of mass $M$ and density less than the density of water is placed in the tank and floats. No water overflows. What is the resulting increase in pressure at the bottom of the tank? (c) Evalu-
ate your results for a backyard swimming pool with depth 1.50 $\mathrm{m}$ and a circular base with diameter 6.00 $\mathrm{m}$ . Two persons with combined mass 150 $\mathrm{kg}$ enter the pool and float quietly there. Find the original absolute pressure and the pressure increase at the bottom of the pool.

Khoobchandra Agrawal
Khoobchandra Agrawal
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01:39

Problem 19

The human brain and spinal cord are immersed in the cerebrospinal fluid. The fluid is normally continuous
between the cranial and spinal cavities and exerts a pressure of 100 to 200 $\mathrm{mm}$ of $\mathrm{H}_{2} \mathrm{O}$ above the prevailing atmospheric pressure. In medical work, pressures are often measured in units of millimeters of $\mathrm{H}_{2} \mathrm{O}$ because body fluids, including the cerebrospinal fluid, typically have the same density as water. The pressure of the cerebrospinal fluid can be measured by means of a spinal tap 0as illustrated in Figure P14.19. A hollow tube is inserted into the spinal column, and the height to which the fluid rises is observed. If the fluid rises to a height of 160 $\mathrm{mm}$ , we write its gauge pressure as 160 $\mathrm{mm} \mathrm{H}_{2} \mathrm{O}$ . (a) Express this pressure in pascals, in atmospheres, and in millimeters of mercury. (b) Sometimes it is necessary to deter0mine whether an accident victim has suffered a crushed vertebra that is blocking flow of the cerebrospinal fluid in the spinal column. In other cases, a physician may suspect that a tumor or other growth is blocking the spinal column and inhibiting flow of cerebrospinal fluid. Such conditions can be investigated by means of Queckenstedt's test. In this procedure, the veins in the patient's neck are compressed to make the blood pressure rise in the brain. The increase in pressure in the blood vessels is transmitted to the cerebrospinal fluid. What should be the normal effect on the height of the fluid in the spinal tap? (c) Suppose compressing the veins had no effect on the fluid level. What might account for this result?

Dominador Tan
Dominador Tan
Numerade Educator
02:43

Problem 20

(a) A light balloon is filled with 400 $\mathrm{m}^{3}$ of helium. At $0^{\circ} \mathrm{C},$ the balloon can lift a payload of what mass? (b) What If? In Table $14.1,$ observe that the density of hydrogen is
nearly one-half the density of helium. What load can the balloon lift if filled with hydrogen?

Surjit Tewari
Surjit Tewari
Numerade Educator
09:10

Problem 21

A table-tennis ball has a diameter of 3.80 $\mathrm{cm}$ and average density of $0.0840 \mathrm{g} / \mathrm{cm}^{3} .$ What force is required to hold it completely submerged under water?

Yaqub Khan
Yaqub Khan
Numerade Educator
03:52

Problem 22

The gravitational force exerted on a solid object is 5.00 $\mathrm{N}$ . When the object is suspended from a spring scale and submerged in water, the scale reads 3.50 $\mathrm{N}$ (Fig. Pl4.22). Find the density of the object.

Keshav Singh
Keshav Singh
Numerade Educator
05:24

Problem 23

A 10.0 -kg block of metal measuring $12.0 \mathrm{cm} \times 10.0 \mathrm{cm} \times$ 10.0 $\mathrm{cm}$ is suspended from a scale and immersed in water as shown in Figure $\mathrm{P} 14.22 \mathrm{b}$ . The $12.0-\mathrm{cm}$ dimension is vertical, and the top of the block is 5.00 $\mathrm{cm}$ below the surface of the water. (a) What are the forces acting on the top and on the bottom of the block? (Take $P_{0}=101.30 \mathrm{kPa}$ . (b) What is the reading of the spring scale? (c) Show that the buoyant force equals the difference between the forces at the top and bottom of the block.

Surjit Tewari
Surjit Tewari
Numerade Educator
01:42

Problem 24

The weight of a rectangular block of low-density material is 15.0 $\mathrm{N}$ . With a thin string, the center of the horizontal bottom face of the block is tied to the bottom of a 0beaker partly filled with water. When 25.0$\%$ of the block's volume is submerged, the tension in the string is 10.0 $\mathrm{N}$ .
(a) Sketch a free-body diagram for the block, showing all forces acting on it. (b) Find the buovant force on the four sidewalls of the block that the oil touches. What are the directions of these forces? (d) What happens to the string tension as the oil is added? Explain how the oil has this effect on the string tension. (e) The string break when its tension reaches 60.0 $\mathrm{N}$ . At this moment, 25.0$\%$ of the block's volume is still below the waterline. What additional fraction of the block's volume is below the top surface of the oil? (f) After the string breaks, the block comes to a new equilibrium position in the beaker. It is now in contact only with the oil. What fraction of the block's volume is submerged?

Dominador Tan
Dominador Tan
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01:22

Problem 25

Preparing to anchor a buoy at the edge of a swimming area, a worker uses a rope to lower a cubical concrete block, 0.250 $\mathrm{m}$ on each edge, into ocean water. The block moves down at a constant speed of 1.90 $\mathrm{m} / \mathrm{s}$ . You can accurately model the concrete and the water as incompressible. (a) At what rate is the force the water exerts on one face of the block increasing? (b) At what rate is the buoyant force on the block increasing?

Dominador Tan
Dominador Tan
Numerade Educator
03:03

Problem 26

To an order of magnitude, how many helium-filled toy balloons would be required to lift you? Because helium is an irreplaceable resource, develop a theoretical answer rather than an experimental answer. In your solution, state what physical quantities you take as data and the values you measure or estimate for them.

Surjit Tewari
Surjit Tewari
Numerade Educator
02:57

Problem 27

A cube of wood having an edge dimension of 20.0 $\mathrm{cm}$ and a density of 650 $\mathrm{kg} / \mathrm{m}^{3}$ floats on water. (a) What is the distance from the horizontal top surface of the cube
to the water level? (b) What mass of lead should be placed on the cube so that the top of the cube will be just level with the water?

Salamat Ali
Salamat Ali
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04:50

Problem 28

A spherical aluminum ball of mass 1.26 $\mathrm{kg}$ contains an empty spherical cavity that is concentric with the ball. The ball barely floats in water. Calculate (a) the outer radius of the ball and (b) the radius of the cavity.

Mayukh Banik
Mayukh Banik
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01:21

Problem 29

Determination of the density of a fluid has many important applications. A car battery contains sulfuric acid, for which density is a measure of concentration. For the battery to function properly, the density must be within a range specified by the manufacturer. Similarly, the effectiveness of antifreeze in your car's engine coolant depends on the density of the mixture (usually ethylene glycol and water). When you donate blood to a blood bank, its screening includes determination of the density of the blood because higher density correlates with higher hemoglobin content. A hydrometer is an instrument used to determine liquid density. A simple one is sketched in Fig-ure $P 14.29 .$ The bulb of a syringe is squeezed and released to let the atmosphere lift a sample of the liquid of interest into a tube containing a calibrated rod of known density. The rod, of length $L$ and average density
$\rho_{0}$ , floats partially immersed in the liquid of density $\rho$ . A length $h$ of the rod protrudes above the surface of the liquid. Show that the density of the liquid is
$$
\rho=\frac{\rho_{0} L}{L-h}
$$

Surjit Tewari
Surjit Tewari
Numerade Educator
01:31

Problem 30

Refer to Problem 29 and Figure $\mathrm{P} 14.29$ . A hydrometer is to be constructed with a cylindrical floating rod. Nine fiduciary marks are to be placed along the rod to indicate densities having values of $0.98 \mathrm{g} / \mathrm{cm}^{3}, 1.00 \mathrm{g} / \mathrm{cm}^{3}, 1.02 \mathrm{g} / \mathrm{cm}^{3},$ $1.04 \mathrm{g} / \mathrm{cm}^{3}, \ldots, 1.14 \mathrm{g} / \mathrm{cm}^{3} .$ The row of marks is to start, 0.200 $\mathrm{cm}$ from the top end of the rod and end 1.80 $\mathrm{cm}$ from the top end. (a) What is the required length of the rod? (b) What must be its average density? (c) Should the marks be equally spaced? Explain your answer.

Dominador Tan
Dominador Tan
Numerade Educator
02:01

Problem 31

How many cubic meters of helium are required to lift a balloon with a 400 -kg payload to a height of 8000 $\mathrm{m}$ ? (Take $\rho_{\mathrm{Hc}}=0.180 \mathrm{kg} / \mathrm{m}^{3} . )$ Assume the balloon maintains a constant volume and the density of air decreases with the altitude $z$ according to the expression $\rho_{\text { air }}=\rho_{0} e^{-z / 8} 000$ where $z$ is in meters and $\rho_{0}=1.25 \mathrm{kg} / \mathrm{m}^{3}$ is the density of nair at sea level.

Surjit Tewari
Surjit Tewari
Numerade Educator
02:31

Problem 32

A bathysphere used for deep-sea exploration has a radius of 1.50 $\mathrm{m}$ and a mass of $1.20 \times 10^{4} \mathrm{kg}$ . To dive, this submarine takes on mass in the form of seawater. Determine
the amount of mass the submarine must take on if it is to descend at a constant speed of 1.20 $\mathrm{m} / \mathrm{s}$ , when the resistive force on it is 1100 $\mathrm{N}$ in the upward direction. The density of seawater is $1.03 \times 10^{3} \mathrm{kg} / \mathrm{m}^{3}$ .

Surjit Tewari
Surjit Tewari
Numerade Educator
03:27

Problem 33

A plastic sphere floats in water with 50.0$\%$ of its volume submerged. This same sphere floats in glycerin with 40.0$\%$ of its volume submerged. Determine the densities of the glycerin and the sphere.

Surjit Tewari
Surjit Tewari
Numerade Educator
01:42

Problem 34

The United States possesses the eight largest warships in 0the world - aircraft carriers of the Nimitz class-and is building two more. Suppose one of the ships bobs up to float 11.0 $\mathrm{cm}$ higher in the water when 50 fighter planes take off from it in 25 minutes, at a location where the free-fall acceleration is 9.78 $\mathrm{m} / \mathrm{s}^{2}$ . Bristling with bombs and missiles, the planes have an average mass of 29000 $\mathrm{kg}$ . Find the horizontal area enclosed by the waterline of the
$\$ 4$ billion ship. By comparison, its flight deck has area 18000 $\mathrm{m}^{2}$ . Below decks are passageways hundreds of meters long, so narrow that two large men cannot pass each other.

Surjit Tewari
Surjit Tewari
Numerade Educator
02:31

Problem 35

A large storage tank, open at the top and filled with water, develops a small hole in its side at a point 16.0 $\mathrm{m}$ below the water level. The rate of flow from the leak is $2.50 \times 10^{-3} \mathrm{m}^{3} / \mathrm{min}$ . Determine (a) the speed at which the water leaves the hole and (b) the diameter of the hole.

Surjit Tewari
Surjit Tewari
Numerade Educator
10:37

Problem 36

A village maintains a large tank with an open top, containing water for emergencies. The water can drain from the tank through a hose of diameter $6.60 \mathrm{cm} .$ The hose nends with a nozzle of diameter $2.20 \mathrm{cm} .$ A rubber stopper is inserted into the nozzle. The water level in the tank is
kept 7.50 $\mathrm{m}$ above the nozzle. (a) Calculate the friction force exerted on the stopper by the nozzle. (b) The stopper is removed. What mass of water flows from the nozzle in 2.00 $\mathrm{h}$ ? (c) Calculate the gauge pressure of the flowing water in the hose just behind the nozzle.

Vipender Yadav
Vipender Yadav
Numerade Educator
01:49

Problem 37

Water flows through a fire hose of diameter 6.35 $\mathrm{cm}$ at a rate of 0.0120 $\mathrm{m}^{3} / \mathrm{s}$ . The fire hose ends in a nozzle of inner diameter $2.20 \mathrm{cm} .$ What is the speed with which the water exits the nozzle?

Surjit Tewari
Surjit Tewari
Numerade Educator
03:48

Problem 38

Water moves through a constricted pipe in steady, ideal flow. At one point as shown in Figure 14.16 where the pressure is $2.50 \times 10^{4} \mathrm{Pa}$ , the diameter is $8.00 \mathrm{cm} .$ At another point 0.500 $\mathrm{m}$ higher, the pressure is equal to $1.50 \times 10^{4} \mathrm{Pa}$ and the diameter is $4.00 \mathrm{cm} .$ Find the speed of flow (a) in the lower section and (b) in the upper section. (c) Find the volume flow rate through the pipe.

Surjit Tewari
Surjit Tewari
Numerade Educator
06:23

Problem 39

Figure $\mathrm{P} 14.39$ shows a stream of water in steady flow from a kitchen faucet. At the faucet, the diameter of the stream is $0.960 \mathrm{cm} .$ The stream fills a $125-\mathrm{cm}^{3}$ container in 16.3 $\mathrm{s}$ . Find the diameter of the stream 13.0 $\mathrm{cm}$ below the opening of the faucet.

Sheh Lit Chang
Sheh Lit Chang
University of Washington
01:43

Problem 40

Water falls over a dam of height $h$ with a mass flow rate of $R,$ in units of kilograms per second. (a) Show that the power available from the water is
$$
\mathscr{P}=R g h
$$
where $g$ is the free-fall acceleration. (b) Each hydroelectric unit at the Grand Coulee Dam takes in water at a rate of $8.50 \times 10^{5} \mathrm{kg} / \mathrm{s}$ from a height of 87.0 $\mathrm{m}$ . The power developed by the falling water is converted to electric power with an efficiency of 85.0$\%$ . How much electric power does each hydroelectric unit produce?

Mayukh Banik
Mayukh Banik
Numerade Educator
02:28

Problem 41

A legendary Dutch boy saved Holland by plugging a 1.20 -cm diameter hole in a dike with his finger. If the
hole was 2.00 $\mathrm{m}$ below the surface of the North Sea (density $1030 \mathrm{kg} / \mathrm{m}^{3} ),$ (a) what was the force on his finger? (b) If he pulled his finger out of the hole, during what time interval would the released water fill 1 acre of land to a depth of 1 $\mathrm{ft}$ ? Assume the hole remained constant in nsize. (A typical U.S. family of four uses 1 acre-foot of water, $1234 \mathrm{m}^{3},$ in 1 year.)

Nicholas Mogoi
Nicholas Mogoi
Numerade Educator
07:42

Problem 42

In ideal flow, a liquid of density 850 $\mathrm{kg} / \mathrm{m}^{3}$ moves from a horizontal tube of radius 1.00 $\mathrm{cm}$ into a second horizontal tube of radius $0.500 \mathrm{cm} .$ A pressure difference $\Delta P$ exists between the tubes. (a) Find the volume flow rate as a function of $\Delta P$ . Evaluate the volume flow rate (b) for $\Delta P=6.00 \mathrm{kPa}$ and $(\mathrm{c})$ for $\Delta P=12.0 \mathrm{kPa}$ . (d) State how the volume flow rate depends on $\Delta P .$

Surjit Tewari
Surjit Tewari
Numerade Educator
04:00

Problem 43

Water is pumped up from the Colorado River to supply Grand Canyon Village, located on the rim of the canyon. The river is at an elevation of 564 $\mathrm{m}$ , and the village is at an elevation of 2096 $\mathrm{m}$ . Imagine that the water is pumped through a single long pipe 15.0 $\mathrm{cm}$ in diameter, driven by a single pump at the bottom end. (a) What is the minimum pressure at which the water must be pumped if it is to arrive at the village? (b) If 4500 $\mathrm{m}^{8}$ of water is pumped per day, what is the speed of the water in the pipe? (c) What additional pressure is necessary to deliver this flow? Nole. Assume the free-fall acceleration and the density of air are constant over this range of elevations. The pressures you calculate are too high for an ordinary pipe. The water is actually lifted in stages by several pumps through shorter pipes.

Surjit Tewari
Surjit Tewari
Numerade Educator
02:45

Problem 44

Old Faithful Geyser in Yellowstone National Park erupts at approximately 1-h intervals, and the height of the water column reaches 40.0 m (Fig. P14.44). (a) Model the rising stream as a series of separate drops. Analyze the free-fall motion of one of the drops to determine the speed at which the water leaves the ground. (b) What If? Model the rising stream as an ideal fluid in streamline flow. Use Bernoulli's equation to determine the speed of the water as it leaves ground level. (c) How does the answer from part (a) compare with the answer from part (b)? (d) What is the pressure (above atmospheric) in the heated underground chamber if its depth is 175 $\mathrm{m}^{\prime}$ . Assume the chamber is large compared with the geyser's vent.

Surjit Tewari
Surjit Tewari
Numerade Educator
04:26

Problem 45

A Venturi tube may be used as a fluid flowmeter (see Fig, $14.19 ) .$ Taking the difference in pressure as $P_{1}-P_{2}=$ 21.0 $\mathrm{kPa}$ , find the fluid flow rate in cubic meters per second given that the radius of the outlet tube is 1.00 $\mathrm{cm}$ , the radius of the inlet tube is $2.00 \mathrm{cm},$ and the fluid is gasoline $\left(\rho=700 \mathrm{kg} / \mathrm{m}^{3}\right) .$

Surjit Tewari
Surjit Tewari
Numerade Educator
01:46

Problem 46

An airplane has a mass of $1.60 \times 10^{4} \mathrm{kg}$ , and each wing has an area of 40.0 $\mathrm{m}^{2}$ . During level flight, the pressure on the lower wing surface is $7.00 \times 10^{4} \mathrm{Pa}$ . Determine the pressure on the upper wing surface.

Surjit Tewari
Surjit Tewari
Numerade Educator
02:16

Problem 47

A siphon of uniform diameter is used to drain water from a tank as illustrated in Figure $\mathrm{P} 14.47$ . Assume steady flow without friction. ( a) If $h=1.00 \mathrm{m}$ , find the speed of out- flow at the end of the siphon. (b) What If? What is the limitation on the height of the top of the siphon above
the water surface? (For the flow of the liquid to be continuous, the pressure must not drop below the vapor pressure of the liquid.)

Surjit Tewari
Surjit Tewari
Numerade Educator
05:37

Problem 48

An airplane is cruising at altitude 10 $\mathrm{km}$ . The pressure outside the craft is 0.287 atm; within the passenger compartment, the pressure is 1.00 $\mathrm{atm}$ and the temperature is $20^{\circ} \mathrm{C} .$ A small leak occurs in one of the window seals in the passenger compartment. Model the air as an ideal fluid to find the speed of the stream of air flowing through the leak.

Kon Aoki
Kon Aoki
Numerade Educator
01:32

Problem 49

A hypodermic syringe contains a medicine having the density of water (Fig. P14.49). The barrel of the syringe has a cross-sectional area $A=2.50 \times 10^{-5} \mathrm{m}^{2},$ and the needle has a cross-sectional area $a=1.00 \times 10^{-8} \mathrm{m}^{2} .$ Int he absence of a force on the plunger, the pressure everywhere is 1 atm. A force $\overrightarrow{\mathbf{F}}$ of magnitude 2.00 $\mathrm{N}$ acts on the plunger, making medicine squirt horizontally from the needle. Determine the speed of the medicine as it leaves the needle's tip.

Penny Riley
Penny Riley
Numerade Educator
01:48

Problem 50

The Bernoulli effect can have important consequences for the design of buildings. For example, wind can blow around a skyscraper at remarkably high speed, creating low pressure. The higher atmospheric pressure in the still air inside the buildings can cause windows to pop out. As originally constructed, the John Hancock Building in Boston popped windowpanes that fell many stories to the
sidewalk below. (a) Suppose a horizontal wind blows with a speed of 11.2 $\mathrm{m} / \mathrm{s}$ outside a large pane of plate glass with dimensions $4.00 \mathrm{m} \times 1.50 \mathrm{m}$ . Assume the density of the air to be $1.30 \mathrm{kg} / \mathrm{m}^{3} .$ The air inside the density of atmospheric pressure. What is the total force exerted by air on the windowpane? (b) What If? If a second sky- scraper is built nearby, the airspeed can be especially high where wind passes through the narrow separation between the buildings. Solve part (a) again with a wind
speed of 22.4 $\mathrm{m} / \mathrm{s}$ , twice as high.

Surjit Tewari
Surjit Tewari
Numerade Educator
03:19

Problem 51

A helium-filled balloon is tied to a $2.00-\mathrm{m}$ -long, $0.0500-\mathrm{kg}$ uniform string. The balloon is spherical with a radius of $0.400 \mathrm{m} .$ When released, it lifts a length $h$ of string and then remains in equilibrium as shown in Figure $\mathrm{P} 14.51 .$ Determine the value of $h .$ The envelope of the balloon has a mass of 0.250 $\mathrm{kg}$ .

Surjit Tewari
Surjit Tewari
Numerade Educator
03:13

Problem 52

Figure $P 14.52$ shows a water tank with a valve at the bottom. If this valve is opened, what is the maximum height attained by the water stream coming out of the right side of the tank? Assume $h=10.0 \mathrm{m}, L=2.00 \mathrm{m},$ and $\theta=$ $30.0^{\circ}$ and assume the cross-sectional area at $A$ is very large compared with that at $B$ .

Khoobchandra Agrawal
Khoobchandra Agrawal
Numerade Educator
02:35

Problem 53

The true weight of an object can be measured in a vacuum, where buoyant forces are absent. An object of volume $V$ is weighed in air on an equal-arm balance with the use of counterweights of density $\rho$ . Representing the density of air as $\rho_{\text { air }}$ and the balance reading as $F_{g}^{\prime}$ , show that the true weight $F_{g}$ is
$$
F_{\varepsilon}=F_{\varepsilon}^{\prime}+\left(V-\frac{F_{g}^{\prime}}{\rho g}\right) \rho_{\mathrm{air}} g
$$

Surjit Tewari
Surjit Tewari
Numerade Educator
01:30

Problem 54

Water is forced out of a fire extinguisher by air pressure as shown in Figure $\mathrm{P} 14.54$ . How much gauge air pressure in the tank (above atmospheric) is required for the water jet to have a speed of 30.0 $\mathrm{m} / \mathrm{s}$ when the water level is 0.500 $\mathrm{m}$ below the nozzle?

Surjit Tewari
Surjit Tewari
Numerade Educator
03:46

Problem 55

A light spring of constant $k=90.0 \mathrm{N} / \mathrm{m}$ is attached vertically to a table (Fig. Pl4.55 a). A 2.00 -g balloon is filled with helium (density $=0.180 \mathrm{kg} / \mathrm{m}^{3} )$ to a volume of 5.00 $\mathrm{m}^{3}$ and is then connected to the spring, causing the spring to stretch as shown in Figure $\mathrm{P} 14.55 \mathrm{b}$ . Determine the extension distance $L$ when the balloon is in equilibrium.

Surjit Tewari
Surjit Tewari
Numerade Educator
05:59

Problem 56

We can't call it Fluber. Assume a certain liquid, with density 1230 $\mathrm{kg} / \mathrm{m}^{3}$ , exerts no friction force on spherical objects. A ball of mass 2.10 $\mathrm{kg}$ and radius 9.00 $\mathrm{cm}$ is dropped from rest into a deep tank of this liquid from a height of 3.30 $\mathrm{m}$ above the surface. (a) Find the speed at which the ball enters the liquid. (b) What two forces are exerted on the ball as it moves through the liquid? (e) How does the time interval $\Delta t_{\text { down }}$ , during which the ball moves from the surface down to its lowest point, compare with the time interval $\Delta l_{\text { up }}$ for the return trip between the same two points? (f) What If? Now modify the model to suppose the liquid exerts a small friction force on the ball, opposite in direction to its motion. In this case, how do the time intervals $\Delta l_{\text { down }}$ and $\Delta t_{\text { up }}$ compare? Explain your answer with a conceptual argument rather than a numerical calculation.

Dominador Tan
Dominador Tan
Numerade Educator
01:11

Problem 57

As a 950-kg helicopter hovers, its horizontal rotor pushes a column of air downward at 40.0 m/s. What can you say about the quantity of this air? Explain your answer. You may model the air motion as ideal flow.

Dominador Tan
Dominador Tan
Numerade Educator
01:26

Problem 58

Evangelista Torricelli was the first person to realize that we live at the bottom of an ocean of air. He correctly surmised that the pressure of our atmosphere is attributable to the weight of the air. The density of air at $0^{\circ} \mathrm{C}$ at the Earth's surface is $1.29 \mathrm{kg} / \mathrm{m}^{3} .$ The density decreases with increasing altitude (as the atmosphere thins). On the other hand, if we assume the density is constant at 1.29 $\mathrm{kg} / \mathrm{m}^{3}$ up to some altitude $h$ and is zero above that altitude, then $h$ would represent the depth of the ocean of air. Use this model to determine the value of $h$ that gives a pressure of 1.00 atm at the surface of the Earth. Would the peak of Mount Everest rise above the surface of such an atmosphere?

Surjit Tewari
Surjit Tewari
Numerade Educator
03:42

Problem 59

A Review problem. With reference to Figure $14.5,$ show that the total torque exerted by the water behind the dam about a horizontal axis through $O$ is $\frac{1}{6} \rho g w H^{3} .$ Show that the effective line of action of the total force exerted by the water is at a distance $\frac{1}{3} H$ above $O$ .

Surjit Tewari
Surjit Tewari
Numerade Educator
01:42

Problem 60

In about $1657,$ Otto von Guericke, inventor of the air pump, cvacuated a sphere made of two brass hemi-
spheres. Two teams of eight horses each could pull the hemispheres apart only on some trials and then "with greatest difficulty," with the resulting sound likened to a cannon firing (Fig. Pl4.60). (a) Show that the force $F$ required to pull the thin-walled evacuated hemispheres apart is $\pi R^{2}\left(P_{0}-P\right),$ where $R$ is the radius of the hemispheres and $P$ is the pressure inside the hemispheres, which is much less than $P_{0}$ . (b) Determine the force for $P=0.100 P_{0}$ and $R=0.300 \mathrm{m} .$

Surjit Tewari
Surjit Tewari
Numerade Educator
03:46

Problem 61

A 1.00 -kg beaker containing 2.00 $\mathrm{kg}$ of oil (density = 916.0 $\mathrm{kg} / \mathrm{m}^{3} )$ rests on a scale. A $2.00-\mathrm{kg}$ block of iron suspended from a spring scale is completely submerged in the oil as shown in Figure $\mathrm{P} 14.61 .$ Determine the equilibrium readings of both scales.

Prashant Bana
Prashant Bana
Numerade Educator
04:42

Problem 62

A beaker of mass $m_{b}$ containing oil of mass $m_{o}$ and density $\rho_{o}$ rests on a scale. A block of iron of mass $m_{\mathrm{Fe}}$ suspended from a spring scale is completely submerged in the oil as shown in Figure $\mathrm{P} 14.61$ . Determine the equilibrium readings of both scales.

Vipender Yadav
Vipender Yadav
Numerade Educator
06:20

Problem 63

In 1983 , the United States began coining the cent piece out of copper-clad zinc rather than pure copper. The mass of the old copper penny is 3.083 g and that of the new cent is 2.517 g. Calculate the percent of zinc (by vol- ume) in the new cent. The density of copper is 8.960 $\mathrm{g} / \mathrm{cm}^{3}$ and that of zinc is $7.133 \mathrm{g} / \mathrm{cm}^{3} .$ The new and old coins have the same volume.

Surjit Tewari
Surjit Tewari
Numerade Educator
02:56

Problem 64

Show that the variation of atmospheric pressure with altitude is given by $P=P_{0} e^{-\alpha y},$ where $\alpha=\rho_{0} g / P_{0}, P_{0}$ is atmospheric pressure at some reference level $y=0$ , and $\rho_{0}$ is the atmospheric density at this level. Assume the decrease in atmospheric pressure over an infinitesimal change in altitude (so that the density is approximately uniform) is given by $d P=-\rho g d y$ and that the density of air is proportional to the pressure.

Mayukh Banik
Mayukh Banik
Numerade Educator
04:37

Problem 65

Review problem. A uniform disk of mass 10.0 $\mathrm{kg}$ and radius 0.250 $\mathrm{m}$ spins at 300 $\mathrm{rev} / \mathrm{min}$ on a low-friction axle. It must be brought to a stop in 1.00 $\mathrm{min}$ by a brake pad that makes contact with the disk at an average distance of 0.220 $\mathrm{m}$ from the axis. The coefficient of friction between the pad and the disk is $0.500 .$ A piston in a cylinder of diameter 5.00 $\mathrm{cm}$ presses the brake pad against the disk. Find the pressure required for the brake fluid in the cylinder.

Surjit Tewari
Surjit Tewari
Numerade Educator
View

Problem 66

A cube of ice whose edges measure 20.0 $\mathrm{mm}$ is floating in a glass of ice-cold water, and one of the ice cube's faces is parallel to the water's surface. (a) How far below the water surface is the bottom face of the ice cube? (b) Ice-cold ethyl alcohol is gently poured onto the water surface to form a layer 5.00 $\mathrm{mm}$ thick above the water. The alcohol does not mix with the water. When the ice cube again attains hydrostatic equilibrium, what is the distance from the top of the water to the bottom face of the block? (c) Additional cold ethyl alcohol is poured onto the water's surface until the top surface of the alcohol coincides with the top surface of the ice cube (in hydrostatic equilibrium). How thick is the required layer of ethyl alcohol?

Oliver Mcneely
Oliver Mcneely
Numerade Educator
01:26

Problem 67

An incompressible, nonviscous fluid is initially at rest in the vertical portion of the pipe shown in Figure P14.67a, where $L=2.00 \mathrm{m}$ . When the valve is opened, the fluid flows into the horizontal section of the pipe. What is the speed of the fluid when it is all in the horizontal section as shown in Figure $\mathrm{P} 14.67 \mathrm{b}$ ? Assume the cross-sectional area of the entire pipe is constant.

Surjit Tewari
Surjit Tewari
Numerade Educator
05:21

Problem 68

The water supply of a building is fed through a main pipe 6.00 $\mathrm{cm}$ in diameter. A $2.00-\mathrm{cm}$ -diameter faucet tap, located 2.00 $\mathrm{m}$ above the main pipe, is observed to fill a
$25.0-\mathrm{L}$ container in 30.0 $\mathrm{s}$ . (a) What is the speed at which the water leaves the faucet? (b) What is the gauge pres- sure in the 6 -cm main pipe? (Assume the faucet is the only "leak" in the building.)

Surjit Tewari
Surjit Tewari
Numerade Educator
04:35

Problem 69

A U-tube open at both ends is partially filled with water (Fig. P14.69a). Oil having a density 750 $\mathrm{kg} / \mathrm{m}^{3}$ is then poured into the right arm and forms a column $L=$ 5.00 $\mathrm{cm}$ high (Fig. Pl4.69b). (a) Determine the difference $h$ in the heights of the two liquid surfaces. (b) The right arm is then shielded from any air motion while air is blown across the top of the left arm until the surfaces of the two liquids are at the same height (Fig. Pl4.69 c). Determine the speed of the air being blown across the left arm. Take the density of air as 1.29 $\mathrm{kg} / \mathrm{m}^{3}$ .

Surjit Tewari
Surjit Tewari
Numerade Educator
03:15

Problem 70

A woman is draining her fish tank by siphoning the water into an outdoor drain as shown in Figure Pl4.70 (page 416$)$ . The rectangular tank has footprint area $A$ and depth $h .$ The drain is located a distance $d$ below the surface of the water in the tank, where $d>>h$ . The cross- sectional area of the siphon tube is $A^{\prime} .$ Model the water as flowing without friction. (a) Show that the time interval required to empty the tank is
$$
\Delta t=\frac{A h}{A^{\prime} \sqrt{2 g d}}
$$
(b) Evaluate the time interval required to empty the tank if it is a cube 0.500 $\mathrm{m}$ on each edge, taking $A^{\prime}=2.00 \mathrm{cm}^{2}$ and $d=10.0 \mathrm{m}$

Surjit Tewari
Surjit Tewari
Numerade Educator
04:18

Problem 71

The hull of an experimental boat is to be lifted above the water by a hydrofoil mounted below its keel as shown in Figure $\mathrm{P} 14.71 .$ The hydrofoil is shaped like an airplane wing. Its area projected onto a horizontal surface is $A .$ When the boat is towed at sufficiently high speed, water of density $\rho$ moves in streamline flow so that its average speed at the top of the hydrofoil is $n$ times larger than its speed $v_{b}$ below the hydrofoil. (a) Ignoring the buoyant force, show that the upward lift force exerted by the water on the hydrofoil has a magnitude
$$
F \approx \frac{1}{2}\left(n^{2}-1\right) \rho v_{b}^{2} A
$$
(b) The boat has mass $M$ . Show that the liftoff speed is
$$
v \approx \sqrt{\frac{2 M g}{\left(n^{2}-1\right) A \rho}}
$$
(c) Assume an $800-\mathrm{kg}$ boat is to lift off at 9.50 $\mathrm{m} / \mathrm{s}$ . Evaluate the area $A$ required for the hydrofoil if its design yields $n=1.05 .$

Surjit Tewari
Surjit Tewari
Numerade Educator