Deck 9: Fluids

Question 1

Atmospheric pressure is $1.013 \times 10^{5} \mathrm{~N} / \mathrm{m}^{2}$ . The pressure of the atmosphere in pounds/in 2 is

A) $12.30 \mathrm{lb} / \mathrm{in}^{2}$ .
B) $10.90 \mathrm{lb} / \mathrm{in}^{2}$ .
C) $14.70 \mathrm{lb} / \mathrm{in} 2$ .
D) $16.30 \mathrm{lb} / \mathrm{in}^{2}$ .
E) $9.800 \mathrm{lb} / \mathrm{in}^{2}$ .

Answer 1

$14.70 \mathrm{lb} / \mathrm{in} 2$ .

Question 2

Atmospheric pressure is $1.013 \times 10^{5} \mathrm{~N} / \mathrm{m}^{2}$ . The pressure of the atmosphere in $\mathrm{kPa}$ is

A) $98.10 \mathrm{kPa}$ .
B) $66.70 \mathrm{kPa}$ .
C) $75.40 \mathrm{kPa}$ .
D) $101.3 \mathrm{kPa}$ .
E) $55.20 \mathrm{kPa}$ .

Answer 2

$101.3 \mathrm{kPa}$ .

Question 3

Mercury has a density of $13,600 \mathrm{~kg} / \mathrm{m}^{3}$ . The height of a column of mercury that would produce a pressure of $1.013 \times 10^{5} \mathrm{~N} / \mathrm{m}^{2}$ is

A) 19.8 in.
B) $32.1 \mathrm{in}$ .
C) 25.4 in.
D) $9.80 \mathrm{in}$ .
E) $29.9 \mathrm{in}$ .

Answer 3

$29.9 \mathrm{in}$ .

Question 4

Water has a density of $1,000 \mathrm{~kg} / \mathrm{m}^{3}$ . The height of a column of water that would produce a pressure of 1.013 $\times 105 \mathrm{~N} / \mathrm{m}^{2}$ is

A) $20.01 \mathrm{in}$
B) $15.72 \mathrm{~m}$
C) $7.330 \mathrm{~m}$
D) $10.34 \mathrm{~m}$
E) $9.820 \mathrm{~m}$

Question 5

The cork in a bottle is $2.00 \mathrm{~cm}$ in diameter. If the pressure inside the bottle is $3.00 \mathrm{~atm}$ , then the net force on the cork due to the pressure difference is

A) $55.3 \mathrm{~N}$ .
B) $48.9 \mathrm{~N}$ .
C) $63.6 \mathrm{~N}$ .
D) $45.5 \mathrm{~N}$ .
E) $37.5 \mathrm{~N}$ .

Question 6

What is the density of a mixture of $90 \%$ air (density air $1.20 \mathrm{~kg} / \mathrm{m}^{3}$ ) and $10 \%$ helium (density of 0.180 $\left.\mathrm{kg} / \mathrm{m}^{3}\right)$ ?

A) $0.980 \mathrm{~kg} / \mathrm{m}^{3}$
B) $0.680 \mathrm{~kg} / \mathrm{m}^{3}$
C) $1.098 \mathrm{~kg} / \mathrm{m}^{3}$
D) $1.103 \mathrm{~kg} / \mathrm{m}^{3}$
E) $0.750 \mathrm{~kg} / \mathrm{m}^{3}$

Question 7

What is the density of a mixture of $85 \%$ air (density air $1.20 \mathrm{~kg} / \mathrm{m}^{3}$ ) and $15 \%$ water vapor (density of water vapor $\left.0.600 \mathrm{~kg} / \mathrm{m}^{3}\right)$ ?

A) $1.70 \mathrm{~kg} / \mathrm{m}^{3}$
B) $1.05 \mathrm{~kg} / \mathrm{m}^{3}$
C) $1.11 \mathrm{~kg} / \mathrm{m}^{3}$
D) $1.87 \mathrm{~kg} / \mathrm{m}^{3}$
E) $1.19 \mathrm{~kg} / \mathrm{m}^{3}$

Question 8

A $100 \mathrm{~kg}$ mass has a density of $2,000 \mathrm{~kg} / \mathrm{m}^{3}$ . If the volume is decreased by $2 \%$ due to compression, then the density is

A) $2,522 \mathrm{~kg} / \mathrm{m}^{3}$ .
B) $2,440 \mathrm{~kg} / \mathrm{m}^{3}$ .
C) $2,041 \mathrm{~kg} / \mathrm{m}^{3}$ .
D) $3,011 \mathrm{~kg} / \mathrm{m}^{3}$ .
E) $2,940 \mathrm{~kg} / \mathrm{m}^{3}$ .

Question 9

A force of $120.0 \mathrm{~N}$ is applied to $2.000 \mathrm{~cm}$ diameter piston, which is in contact with a closed container of water (density of water $=1,000 \mathrm{~kg} / \mathrm{m}^{3}$ ). A second piston, with a diameter of $25.00 \mathrm{~cm}$ and at the same height as the first piston, is also in contact with the water. What force does the water pressure exert on the second piston?

A) $9,150 \mathrm{~N}$ .
B) $8,450 \mathrm{~N}$ .
C) $18,750 \mathrm{~N}$ .
D) $10,450 \mathrm{~N}$
E) $9,500 \mathrm{~N}$ .

Question 10

A container has a large cylindrical lower part with a long thin cylindrical neck. The lower part of the container holds $12.5 \mathrm{~m}^{3}$ of water and the surface area of the bottom of the container is $5.00 \mathrm{~m}^{2}$ . The height of the lower part of the container is $2.50 \mathrm{~m}$ and the neck contains a column of water $8.50 \mathrm{~m}$ high. The total volume of the column of water in the neck is $0.200 \mathrm{~m}^{3}$ . What is the magnitude of the force exerted by the water on the bottom of the container?

A) $1.35 \times 10^{6} \mathrm{~N}$
B) $1.15 \times 106 \mathrm{~N}$
C) $1.05 \times 10^{6} \mathrm{~N}$
D) $1.65 \times 10^{6} \mathrm{~N}$

Question 11

The water level in a water tower is $50.00 \mathrm{~m}$ above the ground. What is the gauge pressure of the water at a faucet that is $2.000 \mathrm{~m}$ above the ground?

A) $451,300 \mathrm{~N} / \mathrm{m}^{2}$
B) $410,400 \mathrm{~N} / \mathrm{m}^{2}$
C) $470,400 \mathrm{~N} / \mathrm{m}^{2}$
D) $422,400 \mathrm{~N} / \mathrm{m}^{2}$
E) $500,200 \mathrm{~N} / \mathrm{m}^{2}$

Question 12

A submarine is located 1.000 km below the surface of the water. What is the absolute pressure of the seawater on the outside of the submarine? (density of seawater is $1,025 \mathrm{~kg} / \mathrm{m}^{3}$ )

A) $190.8 \mathrm{~atm}$
B) $100.1 \mathrm{~atm}$
C) $121.2 \mathrm{~atm}$
D) $198.2 \mathrm{~atm}$
E) $193.5 \mathrm{~atm}$

Question 13

A submarine is located $2.000 \mathrm{~km}$ below the surface of the water. What is the absolute pressure of the seawater on the outside of the submarine? (density of seawater is $1,025 \mathrm{~kg} / \mathrm{m}^{3}$ )

A) $199.3 \mathrm{~atm}$
B) $210.0 \mathrm{~atm}$
C) $187.3 \mathrm{~atm}$
D) $175.0 \mathrm{~atm}$
E) $205.5 \mathrm{~atm}$

Question 14

A mercury manometer measures a pressure of $200.0 \mathrm{mmHg}$ . What is this pressure in $\mathrm{Pa}$ ?

A) $30,230 \mathrm{~Pa}$
B) $26,660 \mathrm{~Pa}$
C) $19,770 \mathrm{~Pa}$
D) $39,600 \mathrm{~Pa}$
E) $36,760 \mathrm{~Pa}$

Question 15

A mercury manometer measures a pressure of $200 \mathrm{mmHg}$ . What is this pressure in atm?

A) $0.204 \mathrm{~atm}$
B) $0.301 \mathrm{~atm}$
C) $0.375 \mathrm{~atm}$
D) $0.325 \mathrm{~atm}$
E) $0.263 \mathrm{~atm}$

Question 16

A $10.0 \mathrm{~kg}$ ball weighs $98.0 \mathrm{~N}$ in air and weighs $65.0 \mathrm{~N}$ when submerged in water. The volume of the ball is

A) $0.00980 \mathrm{~m}^{3}$ .
B) $0.00245 \mathrm{~m}^{3}$ .
C) $0.00766 \mathrm{~m}^{3}$ .
D) $0.00337 \mathrm{~m}^{3}$ .
E) $0.00457 \mathrm{~m}^{3}$ .

Question 17

A ball with a diameter of $10.0 \mathrm{~cm}$ is submerged in water. The buoyant force of the water on the ball is

A) $5.75 \mathrm{~N}$ .
B) $6.00 \mathrm{~N}$ .
C) $5.13 \mathrm{~N}$ .
D) $4.25 \mathrm{~N}$ .
E) $4.75 \mathrm{~N}$ .

Question 18

What is the buoyant force on a $1.200 \mathrm{~kg}$ solid steel ball submerged in water? (density of steel is $7,900 \mathrm{~kg} / \mathrm{m}^{3}$ )

A) $1.245 \mathrm{~N}$
B) $1.136 \mathrm{~N}$
C) $1.489 \mathrm{~N}$
D) $1.566 \mathrm{~N}$
E) $1.750 \mathrm{~N}$

Question 19

A $1.10 \mathrm{~kg}$ hollow steel ball is submerged in water. Its weight in water is $8.75 \mathrm{~N}$ . The volume of the cavity inside the ball is (density of steel is $7,900 \mathrm{~kg} / \mathrm{m}^{3}$ )

A) $1.59 \times 10^{-5} \mathrm{~m}^{3}$ .
B) $6.79 \times 10^{-5} \mathrm{~m}^{3}$ .
C) $2.07 \times 10^{-4} \mathrm{~m}^{3}$ .
D) $1.39 \times 10^{-4} \mathrm{~m}^{3}$ .
E) $1.13 \times 10^{-4} \mathrm{~m}^{3}$

Question 20

A $1.50 \mathrm{~kg}$ hollow steel ball is submerged in water. Its weight in water is $10.75 \mathrm{~N}$ . The volume of the cavity inside the ball is (density of steel is $7,900 \mathrm{~kg} / \mathrm{m}^{3}$ )

A) $0.000213 \mathrm{~m}^{3}$
B) $0.000348 \mathrm{~m}^{3}$ .
C) $0.000476 \mathrm{~m}^{3}$ .
D) $0.000401 \mathrm{~m}^{3}$ .
E) $0.000139 \mathrm{~m}^{3}$ .

Question 21

A $2 \mathrm{~kg}$ ball is floating in water. The volume of water displaced by the ball is

A) $0.002 \mathrm{~m}^{3}$ .
B) $0.001 \mathrm{~m}^{3}$ .
C) $0.005 \mathrm{~m}^{3}$ .
D) $0.003 \mathrm{~m}^{3}$ .
E) $0.004 \mathrm{~m}^{3}$ .

Question 22

A $1.5 \mathrm{~kg}$ ball is floating in water. The volume of water displaced by the ball is

A) $0.0027 \mathrm{~m}^{3}$ .
B) $0.0036 \mathrm{~m}^{3}$ .
C) $0.0015 \mathrm{~m}^{3}$ .
D) $0.0051 \mathrm{~m}^{3}$ .
E) $0.0040 \mathrm{~m}^{3}$ .

Question 23

An incompressible fluid is flowing through a pipe with a constriction. The pipe is on an incline with an angle of 30.0 degrees from the horizontal. The narrow section is $10.0 \mathrm{~m}$ from the wide section and the narrow section is higher than the wide section. The velocity of the fluid in the wide section of the pipe is $4.00 \mathrm{~m} / \mathrm{s}$ and the velocity of the fluid in the narrow section of pipe is $9.00 \mathrm{~m} / \mathrm{s}$ . The pressure of the fluid in the wide section is $250 \mathrm{kPa}$ . What is the pressure in the narrow section of the pipe? (density of the fluid is $1,000 \mathrm{~kg} / \mathrm{m}^{3}$ )

A) $193 \mathrm{kPa}$
B) $169 \mathrm{kPa}$
C) $180 \mathrm{kPa}$
D) $175 \mathrm{kPa}$
E) $205 \mathrm{kPa}$

Question 24

An incompressible fluid is flowing through a pipe with a constriction. The pipe is on an incline with an angle of 20.0 degrees. The narrow section is $15.0 \mathrm{~m}$ from the wide section and the narrow section is higher than the wide section. The velocity of the fluid in the wide section of the pipe is $6.00 \mathrm{~m} / \mathrm{s}$ and the velocity of the fluid in the narrow section of pipe is $9.00 \mathrm{~m} / \mathrm{s}$ . The pressure of the fluid in the wide section is $250 \mathrm{kPa}$ . What is the pressure in the narrow section of the pipe? (density of the fluid is $1,000 \mathrm{~kg} / \mathrm{m}^{3}$ )

A) $177 \mathrm{kPa}$
B) $180 \mathrm{kPa}$
C) $205 \mathrm{kPa}$
D) $157 \mathrm{kPa}$
E) $217 \mathrm{kPa}$

Question 25

An incompressible fluid is flowing through a pipe with a constriction. The pipe is on an incline with an angle of 20.0 degrees. The narrow section is $15.0 \mathrm{~m}$ from the wide section and the narrow section is lower than the wide section. The velocity of the fluid in the wide section of the pipe is $6.00 \mathrm{~m} / \mathrm{s}$ and the velocity of the fluid in the narrow section of pipe is $9.00 \mathrm{~m} / \mathrm{s}$ . The pressure of the fluid in the wide section is $250 \mathrm{kPa}$ . What is the pressure in the narrow section of the pipe? (density of the fluid is $1,000 \mathrm{~kg} / \mathrm{m}^{3}$ )

A) $167 \mathrm{kPa}$
B) $278 \mathrm{kPa}$
C) $228 \mathrm{kPa}$
D) $145 \mathrm{kPa}$
E) $195 \mathrm{kPa}$

Question 26

An incompressible fluid is flowing through a pipe with a constriction. The pipe is on an incline with an angle of 30.0 degrees. The narrow section is $15.0 \mathrm{~m}$ from the wide section and the narrow section is lower than the wide section. The velocity of the fluid in the wide section of the pipe is $4.00 \mathrm{~m} / \mathrm{s}$ and the velocity of the fluid in the narrow section of pipe is $9.00 \mathrm{~m} / \mathrm{s}$ . The pressure of the fluid in the wide section is $250 \mathrm{kPa}$ . What is the pressure in the narrow section of the pipe? (density of the fluid is $1,000 \mathrm{~kg} / \mathrm{m}^{3}$ )

A) $301 \mathrm{kPa}$
B) $291 \mathrm{kPa}$
C) $320 \mathrm{kPa}$
D) $275 \mathrm{kPa}$
E) $260 \mathrm{kPa}$

Question 27

An incompressible fluid is flowing through a pipe with a constriction. The pipe is on an incline with an angle of 30.0 degrees. The narrow section is $10.0 \mathrm{~m}$ from the wide section and the narrow section is lower than the wide section. The velocity of the fluid in the wide section of the pipe is $2.00 \mathrm{~m} / \mathrm{s}$ and the velocity of the fluid in the narrow section of pipe is $10.0 \mathrm{~m} / \mathrm{s}$ . The pressure of the fluid in the wide section is $250 \mathrm{kPa}$ . What is the pressure in the narrow section of the pipe? (density of the fluid is $1,000 \mathrm{~kg} / \mathrm{m}^{3}$ )

A) $251 \mathrm{kPa}$
B) $245 \mathrm{kPa}$
C) $212 \mathrm{kPa}$
D) $199 \mathrm{kPa}$
E) $175 \mathrm{kPa}$

Question 28

An incompressible fluid is flowing through a pipe with a constriction. The pipe is on an incline with an angle of 30.0 degrees. The narrow section is $10.0 \mathrm{~m}$ from the wide section and the narrow section is higher than the wide section. The velocity of the fluid in the wide section of the pipe is $4.00 \mathrm{~m} / \mathrm{s}$ . The diameter of the wide section is $12.00 \mathrm{~cm}$ and the diameter of the narrow section is $9.00 \mathrm{~cm}$ . The pressure of the fluid in the wide section is $250 \mathrm{kPa}$ . What is the pressure in the narrow section of the pipe? (density of the fluid is 1,000 $\left.\mathrm{kg} / \mathrm{m}^{3}\right)$

A) $195 \mathrm{kPa}$
B) $175 \mathrm{kPa}$
C) $205 \mathrm{kPa}$
D) $210 \mathrm{kPa}$
E) $184 \mathrm{kPa}$

Question 29

An incompressible fluid is flowing through a pipe with a constriction. The pipe is on an incline with an angle of 30.0 degrees. The narrow section is $10.0 \mathrm{~m}$ from the wide section and the narrow section is lower than the wide section. The velocity of the fluid in the wide section of the pipe is $4.00 \mathrm{~m} / \mathrm{s}$ . The diameter of the wide section is $12.00 \mathrm{~cm}$ and the diameter of the narrow section is $9.00 \mathrm{~cm}$ . The pressure of the fluid in the wide section is $250 \mathrm{kPa}$ . What is the pressure in the narrow section of the pipe? (density of the fluid is 1,000 $\left.\mathrm{kg} / \mathrm{m}^{3}\right)$

A) $275 \mathrm{kPa}$
B) $295 \mathrm{kPa}$
C) $240 \mathrm{kPa}$
D) $252 \mathrm{kPa}$
E) $282 \mathrm{kPa}$

Question 30

An incompressible fluid is flowing through a vertical pipe with a constriction. The wide section is $2.00 \mathrm{~cm}$ in diameter and is at the top of the pipe. The pressure of the fluid in the wide section at the top is $200 \mathrm{kPa}$ . The velocity of the fluid in the wide section is $4.00 \mathrm{~m} / \mathrm{s}$ . The narrow section is $1.00 \mathrm{~cm}$ in diameter and is located 2.00 m below the wide section. What is the pressure of the fluid in the narrow section? (density of the fluid is $1,000 \mathrm{~kg} / \mathrm{m}^{3}$ )

A) $116 \mathrm{kPa}$
B) $80.0 \mathrm{kPa}$
C) $105 \mathrm{kPa}$
D) $99.6 \mathrm{kPa}$
E) $72.0 \mathrm{kPa}$

Question 31

An incompressible fluid is flowing through a vertical pipe with a constriction. The wide section is $2.00 \mathrm{~cm}$ in diameter and is at the top of the pipe. The pressure of the fluid in the wide section at the top is $200 \mathrm{kPa}$ . The velocity of the fluid in the wide section is $4.00 \mathrm{~m} / \mathrm{s}$ . The narrow section is located $2.00 \mathrm{~m}$ below the wide section. What is the diameter of the narrow section, if the pressure of the fluid in the narrow section is equal to the pressure in the wide section? (density of the fluid is $1,000 \mathrm{~kg} / \mathrm{m}^{3}$ )

A) $0.75 \mathrm{~cm}$
B) $1.10 \mathrm{~cm}$
C) $1.47 \mathrm{~cm}$
D) $1.20 \mathrm{~cm}$
E) $0.90 \mathrm{~cm}$

Question 32

An incompressible fluid is flowing through a vertical pipe with a constriction. The wide section is $2.00 \mathrm{~cm}$ in diameter and is at the top of the pipe. The pressure of the fluid in the wide section at the top is $200 \mathrm{kPa}$ . The velocity of the fluid in the wide section is $4.00 \mathrm{~m} / \mathrm{s}$ . The narrow section is located $4.00 \mathrm{~m}$ below the wide section. What is the diameter of the narrow section for the pressure of the fluid in the narrow section to equal the pressure in the wide section? (density of the fluid is $1,000 \mathrm{~kg} / \mathrm{m}^{3}$ )

A) $1.36 \mathrm{~cm}$
B) $1.00 \mathrm{~cm}$
C) $1.50 \mathrm{~cm}$
D) $1.28 \mathrm{~cm}$
E) $1.12 \mathrm{~cm}$

Question 33

An incompressible fluid is flowing through a vertical pipe with a constriction. The wide section is $2.00 \mathrm{~cm}$ in diameter and is at the top of the pipe. The pressure of the fluid in the wide section at the top is $200 \mathrm{kPa}$ . The velocity of the fluid in the wide section is $4.00 \mathrm{~m} / \mathrm{s}$ . The narrow section is located 4.00 m below the wide section. What is the diameter of the narrow section , if the pressure of the fluid in the narrow section is equal to the pressure in the wide section? (density of the fluid is $680 \mathrm{~kg} / \mathrm{m}^{3}$ )

A) $1.50 \mathrm{~cm}$
B) $1.28 \mathrm{~cm}$
C) $1.36 \mathrm{~cm}$
D) $1.43 \mathrm{~cm}$
E) $1.15 \mathrm{~cm}$

Question 34

An incompressible fluid is flowing through a vertical pipe with a constriction. The wide section is $2.00 \mathrm{~cm}$ in diameter and is at the top of the pipe. The pressure of the fluid in the wide section at the top is $200 \mathrm{kPa}$ . The velocity of the fluid in the wide section is $4.00 \mathrm{~m} / \mathrm{s}$ . The narrow section is located $8.00 \mathrm{~m}$ below the wide section. What is the diameter of the narrow section, if the pressure of the fluid in the narrow section is equal to the pressure in the wide section? (density of the fluid is $680 \mathrm{~kg} / \mathrm{m}^{3}$ )

A) $1.42 \mathrm{~cm}$
B) $1.20 \mathrm{~cm}$
C) $1.10 \mathrm{~cm}$
D) $1.55 \mathrm{~cm}$
E) $1.31 \mathrm{~cm}$

Question 35

The surface tension of water is $0.0730 \mathrm{~N} / \mathrm{m}$ . What is the height of the water in a capillary tube of diameter $1.00 \mathrm{~mm}$ ?

A) $2.75 \mathrm{~cm}$
B) $2.98 \mathrm{~cm}$
C) $2.40 \mathrm{~cm}$
D) $2.55 \mathrm{~cm}$
E) $3.02 \mathrm{~cm}$

Question 36

The surface tension of water is $0.0730 \mathrm{~N} / \mathrm{m}$ . What is the height of the water in a capillary tube of diameter $2.00 \mathrm{~mm}$ ?

A) $1.37 \mathrm{~cm}$
B) $1.58 \mathrm{~cm}$
C) $1.49 \mathrm{~cm}$
D) $1.27 \mathrm{~cm}$
E) $1.63 \mathrm{~cm}$

Question 37

The surface tension of soapy water is $0.0250 \mathrm{~N} / \mathrm{m}$ . What is the height of the water in a capillary tube of diameter $2.00 \mathrm{~mm}$ ?

A) $5.10 \mathrm{~mm}$
B) $4.21 \mathrm{~mm}$
C) $3.98 \mathrm{~mm}$
D) $4.77 \mathrm{~mm}$
E) $3.66 \mathrm{~mm}$

Question 38

A small hole is cut in the bottom of a water storage tank. The depth of the water is $12.00 \mathrm{~m}$ . If the diameter of the small hole in the bottom of the tank is $4.00 \mathrm{~mm}$ , then what is the flow rate of the water leaving the tank?

A) $1.36 \times 10^{-4} \mathrm{~m} 3 / \mathrm{s}$
B) $1.93 \times 10^{-4} \mathrm{~m} 3 / \mathrm{s}$
C) $2.65 \times 10^{-4} \mathrm{~m} 3 / \mathrm{s}$
D) $2.53 \times 10^{-4} \mathrm{~m} 3 / \mathrm{s}$
E) $1.05 \times 10^{-4} \mathrm{~m} 3 / \mathrm{s}$

Question 39

A small hole is cut in the bottom of a water storage tank. The depth of the water is $8.00 \mathrm{~m}$ . If the diameter of the small hole in the bottom of the tank is $1.00 \mathrm{~cm}$ , then what is the flow rate of the water leaving the tank?

A) $7.45 \times 10^{-4} \mathrm{~m} 3 / \mathrm{s}$
B) $8.75 \times 10^{-4} \mathrm{~m} 3 / \mathrm{s}$
C) $9.83 \times 10^{-4} \mathrm{~m}^{3} / \mathrm{s}$
D) $7.21 \times 10^{-4} \mathrm{~m} 3 / \mathrm{s}$
E) $8.21 \times 10^{-4} \mathrm{~m}^{3} / \mathrm{s}$

Question 40

Glycerin at $30^{\circ} \mathrm{C}$ has a density of $1,260 \mathrm{~kg} / \mathrm{m}^{3}$ and a viscosity of $0.630 \mathrm{~Pa} \mathrm{~s}$ . In a laboratory experiment, some glycerin is forced through a horizontal tube that is $10.0 \mathrm{~cm}$ long and $1.00 \mathrm{~cm}$ in diameter. The high-pressure end of the tube is held at a gauge pressure of $618 \mathrm{~Pa}$ , while the other end is open to the atmosphere. What is the flow rate of the glycerin through the tube?

A) $1.70 \times 10^{-6} \mathrm{~m} 3 / \mathrm{s}$
B) $1.95 \times 10^{-6} \mathrm{~m} 3 / \mathrm{s}$
C) $2.05 \times 10^{-6} \mathrm{~m} 3 / \mathrm{s}$
D) $1.87 \times 10^{-6} \mathrm{~m} 3 / \mathrm{s}$
E) $2.41 \times 10^{-6} \mathrm{~m}^{3} / \mathrm{s}$

Question 41

Water undergoes viscous flow through two pipes with the same pressure difference between the ends. Pipe 1 has three times the diameter and twice the length of pipe 2 . If the flow rate through pipe 1 is $0.400 \mathrm{~cm} 3 / \mathrm{s}$ , then what is the flow rate through pipe 2 ?

A) $8.33 \times 10^{-3} \mathrm{~cm}^{3} / \mathrm{s}$
B) $10.80 \times 10^{-3} \mathrm{~cm}^{3} / \mathrm{s}$
C) $6.22 \times 10^{-3} \mathrm{~cm} 3 / \mathrm{s}$
D) $9.88 \times 10^{-3} \mathrm{~cm}^{3} / \mathrm{s}$
E) $7.78 \times 10^{-3} \mathrm{~cm}^{3} / \mathrm{s}$

Question 42

Water with a density of $1,000 \mathrm{~kg} / \mathrm{m}^{3}$ flows through a $2.00 \mathrm{~cm}$ diameter pipe with a velocity of $2.40 \mathrm{~m} / \mathrm{s}$ . What is the volume flow rate?

A) $5.43 \times 10^{-4} \mathrm{~m} 3 / \mathrm{s}$
B) $9.00 \times 10^{-4} \mathrm{~m}^{3} / \mathrm{s}$
C) $8.14 \times 10^{-4} \mathrm{~m} 3 / \mathrm{s}$
D) $7.54 \times 10^{-4} \mathrm{~m} 3 / \mathrm{s}$
E) $6.24 \times 10^{-4} \mathrm{~m} 3 / \mathrm{s}$

Question 43

Water with a density of $1,000 \mathrm{~kg} / \mathrm{m}^{3}$ flows through a $4.00 \mathrm{~cm}$ diameter pipe with a velocity of $1.20 \mathrm{~m} / \mathrm{s}$ . What is the mass flow rate?

A) $1.40 \mathrm{~kg} / \mathrm{s}$
B) $1.32 \mathrm{~kg} / \mathrm{s}$
C) $1.01 \mathrm{~kg} / \mathrm{s}$
D) $1.21 \mathrm{~kg} / \mathrm{s}$
E) $1.51 \mathrm{~kg} / \mathrm{s}$

Question 44

Air with a density of $1.20 \mathrm{~kg} / \mathrm{m}^{3}$ flows through a $10.0 \mathrm{~cm}$ diameter pipe with a velocity of $1.20 \mathrm{~m} / \mathrm{s}$ . What is the mass flow rate?

A) $0.0148 \mathrm{~kg} / \mathrm{s}$
B) $0.0098 \mathrm{~kg} / \mathrm{s}$
C) $0.0113 \mathrm{~kg} / \mathrm{s}$
D) $0.0120 \mathrm{~kg} / \mathrm{s}$
E) $0.0131 \mathrm{~kg} / \mathrm{s}$

Question 45

Air with a density of $1.20 \mathrm{~kg} / \mathrm{m}^{3}$ flows through a $75.0 \mathrm{~cm}$ diameter pipe with a velocity of $2.00 \mathrm{~m} / \mathrm{s}$ . What is the mass flow rate?

A) $1.06 \mathrm{~kg} / \mathrm{s}$
B) $1.20 \mathrm{~kg} / \mathrm{s}$
C) $1.48 \mathrm{~kg} / \mathrm{s}$
D) $1.26 \mathrm{~kg} / \mathrm{s}$
E) $0.95 \mathrm{~kg} / \mathrm{s}$

Question 46

What force must be applied to a $2.5 \mathrm{~cm}$ -diameter piston in a hydraulic lift system in order to lift a truck of mass $1,210 \mathrm{~kg}$ upon a platform supported by a $15 \mathrm{~cm}$ -diameter piston?

A) $33.6 \mathrm{~N}$
B) $4,850 \mathrm{~N}$
C) $202 \mathrm{~N}$
D) $494 \mathrm{~N}$
E) $1,980 \mathrm{~N}$
F) $330 \mathrm{~N}$

Question 47

The pressure at a depth of $1.25 \mathrm{~m}$ in a tank of liquid is measured to be $125.5 \mathrm{kPa}$ . The tank is open to the outside air, which is at a pressure of $102.0 \mathrm{kPa}$ . What is the density of the fluid?

A) $10,200 \mathrm{~kg} / \mathrm{m}^{3}$
B) $18,800 \mathrm{~kg} / \mathrm{m}^{3}$
C) $2,400 \mathrm{~kg} / \mathrm{m}^{3}$
D) $1,920 \mathrm{~kg} / \mathrm{m}^{3}$

Question 48

The pressure at what depth in seawater (density $1,025 \mathrm{~kg} / \mathrm{m}^{3}$ ) is equivalent to that at a depth of $10.0 \mathrm{~m}$ in fresh water (density $1,000 \mathrm{~kg} / \mathrm{m}^{3}$ )?

A) $9.76 \mathrm{~m}$
B) $10.3 \mathrm{~m}$
C) $9.81 \mathrm{~m}$
D) $10.2 \mathrm{~m}$

Question 49

What is the force on the top surface of a $10.5 \mathrm{~cm}$ -diameter soup can that is submerged in seawater (density $1,017 \mathrm{~kg} / \mathrm{m}^{3}$ ) at a depth of $350 \mathrm{~m}$ ? The air pressure at the surface is $101.5 \mathrm{kPa}$ .

A) $30.2 \mathrm{kN}$
B) $121 \mathrm{kN}$
C) $31.1 \mathrm{kN}$
D) $124 \mathrm{kN}$

Question 50

Two balls float on the surface of a pool filled with fresh water of density $1,000 \mathrm{~kg} / \mathrm{m}^{3}$ . If ball A has $45 \%$ of its volume above the surface of the water, and ball $\mathrm{B}$ has $55 \%$ of its volume above the surface, what is the ratio of the density of ball A to that of ball B?

A) 0.818
B) 1.07
C) 0.935
D) 0.905
E) 1.22
F) None of the above

Question 51

Two balls of different material, but the same radius, float on the surface of a pool filled with fresh water of density $1,000 \mathrm{~kg} / \mathrm{m}^{3}$ . If ball A has $75 \%$ of its volume above the surface of the water, and ball B has $25 \%$ of its volume above the water, what is the ratio of the mass of ball $\mathrm{A}$ to that of $\mathrm{B}$ ?

A) 0.935
B) 0.33
C) 3.0
D) 1.73
E) 0.1
F) None of the above

Question 52

Two cylinders, one made of lead (density $11,340 \mathrm{~kg} / \mathrm{m}^{3}$ ) and one of copper (density $8,940 \mathrm{~kg} / \mathrm{m}^{3}$ ), have the same radius and height. They are thrown into a pool of water (density $1,000 \mathrm{~kg} / \mathrm{m}^{3}$ ) and sink to the bottom. As they are sinking, describe the buoyant forces on the cylinders.

A) The buoyant force on the copper cylinder is greater than that on the lead.
B) There is no buoyant force on either, as they are sinking.
C) The buoyant force is the same on each cylinder.
D) The buoyant force on the lead cylinder is greater than that on the copper.

Question 53

A spheres are made of wood - the first is of a variety of wood whose density is equal to that of water, while the second is of a variety whose density is greater than that of water. These spheres have the same volume, and the first remains wherever it is placed in the water (so it is effectively suspended in mid-water). The second rests on the bottom, being more dense than water. Compare the buoyant forces on the two spheres.

A) The force on the second is zero, and therefore less than that on the first, which is non-zero.
B) The force on the second is non-zero and is less than that on the first.
C) They are identical
D) Nothing specifically can be concluded without knowing exactly the densities of the spheres.

Question 54

A U-sphere is made up of two layers: The first is lead (density $11,340 \mathrm{~kg} / \mathrm{m}^{3}$ ) and is of radius $\mathrm{R}$ . The second is tin, $\left(7,310 \mathrm{~kg} / \mathrm{m}^{3}\right)$ and is concentric with the first, from radius $R$ to radius $2 \mathrm{R}$ . The sphere is placed in a pool of mercury (density 13,600 kg/m3). How much of the volume of the sphere is below the surface?

A) $57.0 \%$
B) $64.2 \%$
C) $57.5 \%$
D) $68.5 \%$

Question 55

U-shaped manometer, filled with a liquid of unknown density, is connected on one side to a vessel containing gas at gauge pressure $10.0 \mathrm{kPa}$ , and the other side is open to the atmosphere (pressure 101.3 $\mathrm{kPa}$ ). The level of the liquid in the side connected to the gas vessel is lower than on the open side. The difference in height between the two sides is $10 \mathrm{~cm}$ . What is the density of the liquid in the manometer?

A) $1.03 \times 10^{2} \mathrm{~kg} / \mathrm{m}^{3}$
B) $1.13 \times 10^{3} \mathrm{~kg} / \mathrm{m}^{3}$
C) $2.27 \times 10^{5} \mathrm{~kg} / \mathrm{m}^{3}$
D) $1.13 \times 10^{5} \mathrm{~kg} / \mathrm{m}^{3}$
E) $1.02 \times 10^{4} \mathrm{~kg} / \mathrm{m}^{3}$

Question 56

Two objects of different shapes, sizes, and materials, are floating in water (density $1000 \mathrm{~kg} / \mathrm{m}^{3}$ ). Object A floats with $60 \%$ of its volume submerged, while object B floats with $50 \%$ of its volume submerged. What can be concluded about the densities $\rho_{\mathrm{A}}$ and $\rho_{\mathrm{B}}$ of the two objects?

A) $\rho_{\mathrm{A}}=\rho_{\mathrm{B}}$
B) $\rho_{\mathrm{A}}>\rho_{\mathrm{B}}$
C) $\rho_{\mathrm{A}}<\rho_{\mathrm{B}}$
D) Not enough information