Deck 12: Fluid Mechanics

Question 1

Salt water is more dense than fresh water.A ship floats in both fresh water and salt water.Compared to the fresh water,the volume of salt water displaced by the ship is

A) greater than the volume of fresh water.
B) less than the volume of fresh water.
C) the same as the volume of fresh water.

Answer 1

less than the volume of fresh water.

Question 2

As the speed of a moving fluid increases,the pressure in the fluid

A) increases.
B) remains constant.
C) decreases.
D) may increase or decrease, depending on the density of the fluid.

Answer 2

decreases.

Question 3

A certain coin has a diameter of 21.21 mm,a thickness of 1.95 mm,and weighs 0.04905 N.What is its density?

A) 29.1 × 10³ kg/m³
B) 7.26 × 10³ kg/m³
C) 9.25 × 10³ kg/m³
D) 2.31 × 10³ kg/m³
E) 71.2 × 10³ kg/m³

Answer 3

7.26 × 10³ kg/m³

Question 4

At a certain depth in the ocean,the absolute pressure is p.If you go to twice that depth (treating the water as incompressible)

A) the absolute pressure will be 2p.
B) the absolute pressure will be less than 2p.
C) the absolute pressure will be greater than 2p.
D) the gauge pressure will not change.
E) the gauge pressure will increase but will not double.

Question 5

A cubical box,5.00 cm on each side,is immersed in a fluid.The gauge pressure at the top surface of the box is 594 Pa and the gauge pressure on the bottom surface is 1133 Pa.What is the density of the fluid?

A) 1000 kg/m³
B) 1100 kg/m³
C) 1220 kg/m³
D) 2340 kg/m³
E) 12,000 kg/m³

Question 6

You are driving a late model convertible car at the 65 mph speed limit with its soft flexible roof closed up and the windows closed.You observe that the roof

A) bows inward.
B) is no different from when the car was at rest.
C) bows outward.
D) bows inward only when you are driving uphill.
E) bows inward only when you are driving downhill.

Question 7

On planet X,the absolute pressure at a depth of 2.00 m below the surface of a liquid nitrogen lake is .At a depth 5.00 m below the surface,the absolute pressure is .The density of liquid nitrogen is 808 kg/m³.
(a)What is the atmospheric pressure on planet X?
(b)What is the acceleration due to gravity on planet X?

Question 8

A rock is under water in a shallow lake.As the rock sinks deeper and deeper into water,the buoyant force on it

A) increases.
B) decreases.
C) remains constant.

Question 9

What is the radius of a sphere that has a density of 5000 kg/m³ and a mass of 6.00 kg?

A) 4.98 cm
B) 1.27 cm
C) 6.59 cm
D) 1.56 cm
E) 7.22 cm

Question 10

Water flows through a pipe having a varying width.More water flows per second through the wide section than through the narrow section because there is more room for it to flow.

Question 11

A piece of wood is floating in a bathtub.A second piece of wood sits on top of the first piece,and does not touch the water.If the top piece is taken off and placed in the water,what happens to the water level in the tub?

A) It goes up.
B) It goes down.
C) It does not change.
D) This cannot be determined without knowing the volume of the top piece of wood.

Question 12

When you blow some air above the upper face of a paper strip,the paper rises.This occurs because

A) the air above the upper face of the paper moves faster, which makes the pressure higher than at the lower face.
B) the air above the upper face of the paper moves faster, which makes the pressure lower than at the lower face.
C) the air above the upper face of the paper moves faster but the pressure remains constant.
D) the air above the upper face of the paper moves slower, which makes the pressure higher than at the lower face.
E) the air above the upper face of the paper moves slower, which makes the pressure lower than at the lower face.

Question 13

As shown in the figure,a container has a vertical tube,whose inner radius is 32.00 mm,connected to it at its side.An unknown liquid reaches level A in the container and level B in the tube-level A being 5.0 cm higher than level B.The liquid supports a 20.0-cm high column of oil,between levels B and C,whose density is 460 kg/m³.What is the density of the unknown liquid?

A) 1800 kg/m³
B) 2000 kg/m³
C) 1400 kg/m³
D) 1600 kg/m³
E) 1700 kg/m³

Question 14

If you double the pressure on the surface of a can of water,the buoyant force on a stone placed in that water will

A) increase, but not double.
B) double.
C) decrease, but not by one-half.
D) not change.

Question 15

One of the dangers of tornados and hurricanes is the rapid drop in air pressure that is associated with such storms.Assume that the air pressure inside of a sealed house is 1.02 atm when a hurricane hits.The hurricane rapidly decreases the external air pressure to 0.910 atm.A square window in an outside wall of the house measures 2.02 m on each side.What net force (directed outwards)is exerted on this window? (1 atm = 1.01 × 10⁵ Pa.)

A) 4.53 × 10⁴ N
B) 5.14 × 10⁴ N
C) 4.78 × 10⁵ N
D) 5.37 × 10⁵ N

Question 16

Fluid fills the container shown in the figure.At which of the indicated points is the pressure greatest?

A) A
B) B
C) C
D) D
E) The pressure is the same at each of the labeled points.

Question 17

A sphere is constructed of two concentric parts.The inner part is a solid sphere of radius 10.0 cm made of a material with density .The outer part is a spherical shell with inner radius 10.0 cm and outer radius 20.0 cm.The material in the outer shell has a density .
(a)What is the mass of the sphere?
(b)What is the average density of this sphere?

Question 18

A cup of water containing an ice cube at 0°C is filled to the brim.The tip of the ice cube sticks out of the surface.As the ice melts,you observe that

A) the cup overflows.
B) the cup might overflow but it depends on the actual mass of the ice cube.
C) the water level remains the same.
D) the water level actually goes down.
E) There is not enough information to answer this question.

Question 19

A 50-cm³ block of wood is floating partially submerged in water,and a 50-cm³ block of iron is totally submerged in water.Which block has the greater buoyant force on it?

A) the wood
B) the iron
C) Both have the same buoyant force.
D) The answer cannot be determined without knowing the densities of the blocks.

Question 20

The weight of a car of mass 1.20 × 10³ kg is supported equally by the four tires,which are inflated to the same gauge pressure.What gauge pressure in the tires is required so the area of contact of each tire with the road is 1.00 × 10² cm²? (1 atm = 1.01 × 10⁵ Pa.)

A) 11.6 × 10⁵ Pa
B) 11.6 × 10⁴ Pa
C) 2.94 × 10⁵ Pa
D) 2.94 × 10⁴ Pa
E) 2.94 × 10³ Pa

Question 21

A 12,000-N car is raised using a hydraulic lift,which consists of a U-tube with arms of unequal areas,filled with incompressible oil with a density of 800 kg/m³ and capped at both ends with tight-fitting pistons.The wider arm of the U-tube has a radius of 18.0 cm and the narrower arm has a radius of 5.00 cm.The car rests on the piston on the wider arm of the U-tube.The pistons are initially at the same level.What is the force that must be applied to the smaller piston in order to lift the car after it has been raised 1.20 m? (For purposes of this problem,you can neglect the weight of the pistons.)

A) 0.954 kN
B) 1.88 kN
C) 1.96 kN
D) 3.67 kN
E) 1.20 kN

Question 22

A circular cylinder of height 1.20 m having faces of diameter 0.620 m is immersed in water of density with its axis vertical so that its faces are parallel to the surface of the water.The upper face is 2.50 m below the surface of the water.The net force on this cylinder is observed to be 1120 N downward.Atmospheric pressure is .What is the weight of the cylinder?

A) 2430 N
B) 3550 N
C) 4670 N
D) 10,900 N
E) 12,100 N

Question 23

Water is flowing in a horizontal pipe of diameter d.If you want to change the diameter of this pipe so that the speed of the water would be half as great as it was,what should be the new diameter?

A) d/4
B) d/2
C) d /
D) d
E) 2d

Question 24

The two water reservoirs shown in the figure are open to the atmosphere,and the water has density 1000 kg/m³.The manometer contains incompressible mercury with a density of 13,600 kg/m³.What is the difference in elevation h if the manometer reading m is 25.0 cm?

A) 1.58 m
B) 4.20 m
C) 3.75 m
D) 3.40 m
E) 3.15 m

Question 25

A 6.1-kg solid sphere,made of metal whose density is 2600 kg/ ,is suspended by a cord.When the sphere is immersed in a liquid of unknown density,the tension in the cord is 26 N.Find the density of the liquid.

A) 1500 kg/
B) 1400 kg/
C) 1300 kg/
D) 1200 kg/
E) 1100 kg/

Question 26

The two water reservoirs shown in the figure are open to the atmosphere,and the water has density .The manometer contains incompressible oil with a density of .What is the difference in elevation h if the manometer reading m is 25.0 cm?

A) 0.045 m
B) 0.025 m
C) 0.065 m
D) 0.115 m
E) 0.205 m

Question 27

In the figure,an open tank contains a layer of oil floating on top of a layer of water (of density that is 3.0 m thick,as shown.What must be the thickness of the oil layer if the gauge pressure at the bottom of the tank is to be The density of the oil is .

Question 28

A rock is suspended from a scale reads 20.0 N.A beaker of water (having a density of 1000 kg/m³)is raised up so the rock is totally submerged in the water.The scale now reads .What is the density of the rock?

A) 1.60 × 10³ kg/m³
B) 2.50 × 10³ kg/m³
C) 2.33 × 10³ kg/m³
D) 3.00 × 10³ kg/m³
E) 2.67 × 10³ kg/m³

Question 29

A 7.8-kg solid sphere,made of metal whose density is 2500 kg/ ,is suspended by a cord.When the sphere is immersed in water (of density 1000 kg/m³),what is the tension in the cord?

A) 46 N
B) 61 N
C) 76 N
D) 92 N
E) 110 N

Question 30

A board that is 20.0 cm wide,5.00 cm thick,and 3.00 m long has a density .The board is floating partially submerged in water of density 1000 kg/m³.What fraction of the volume of the board is above the surface of the water?

A) 0.350
B) 0.650
C) zero
D) 0.200
E) The answer depends on which edge of the board is vertical.

Question 31

A 12,000-N car is raised using a hydraulic lift,which consists of a U-tube with arms of unequal areas,filled with incompressible oil and capped at both ends with tight-fitting pistons.The wider arm of the U-tube has a radius of and the narrower arm has a radius of .The car rests on the piston on the wider arm of the U-tube.The pistons are initially at the same level.What is the initial force that must be applied to the smaller piston in order to start lifting the car? (For purposes of this problem,you can neglect the weight of the pistons.)

A) 727 N
B) 926 N
C) 2900 N
D) 3330 N
E) 1.20 kN

Question 32

A person who weighs 550 N empties her lungs as much as possible and is then completely immersed in water (of density 1000 kg/m³)while suspended from a harness.Her apparent weight is now 21.2 N.What is her density?

A) 1050 kg/m³
B) 1040 kg/m³
C) 1030 kg/m³
D) 960 kg/m³
E) 56.1 kg/m³

Question 33

Water,of density 1000 kg/m³,is flowing in a drainage channel of rectangular cross-section.The width of the channel is 15 m,the depth of the water is 8.0 m and the speed of the flow is .At what rate is water flowing in this channel?

A) 2.0 × 10⁵ kg/s
B) 2.0 × 10³ kg/s
C) 3.0 × 10⁵ kg/s
D) 3.0 × 10³ kg/s
E) 3.0 × 10² kg/s

Question 34

A circular cylinder of height 1.20 m having faces of diameter 0.620 m is immersed in water of density with its axis vertical so that its faces are parallel to the surface of the water.The upper face is 2.50 m below the surface of the water.The net force on this cylinder is observed to be 1120 N downward.Atmospheric pressure is .What net force does the water exert on the lower face of the cylinder?

A) 7.40 × 10³ N
B) 1.09 × 10⁴ N
C) 3.79 × 10⁴ N
D) 4.14 × 10⁴ N
E) 1.37 × 10⁵ N

Question 35

The small piston of a hydraulic lift has a diameter of 8.0 cm,and its large piston has a diameter of 40 cm.The lift raises a load of 15,000 N.
(a)Determine the force that must be applied to the small piston.
(b)Determine the pressure applied to the fluid in the lift.

Question 36

A barge is 15.0 m wide and 75.0 m long and has vertical sides.The bottom of the hull is 1.20 m below the water surface.What is the weight of the barge and its cargo,if it is floating in fresh water of density 1000 kg/m³?

A) 22.6 MN
B) 13.2 MN
C) 1.35 MN
D) 1.13 MN
E) 11.3 MN

Question 37

A wooden raft has a mass of 50 kg.When empty it floats in water (density with 69% of its volume submerged.What mass of sand can be put on the raft without it sinking?

Question 38

Water flowing through a pipe suddenly comes to a section of pipe where the pipe diameter decreases to 86% of its previous value.If the speed of the water in the larger section of the pipe was what is its speed in this smaller section?

A) 49 m/s
B) 42 m/s
C) 31 m/s
D) 27 m/s

Question 39

A hollow steel ball of diameter 3.0 m barely floats in water.What is the thickness of the wall of the ball? The density of iron is 7.87 g/cm³ and that of water is 1000 kg/m³.

A) 6.6 cm
B) 37 cm
C) 131 cm
D) 79 cm

Question 40

An incompressible fluid flows steadily through a pipe that has a change in diameter.The fluid speed at a location where the pipe diameter is 8.0 cm is 1.28 m/s.What is the fluid speed at a location where the diameter has narrowed to 4.0 cm?

A) 0.32 m/s
B) 0.64 m/s
C) 1.28 m/s
D) 2.56 m/s
E) 5.12 m/s

Question 41

Consider a very small hole in the bottom of a tank in diameter filled with water to a height of Find the speed at which the water exits the tank through the hole.

A) 3.13 m/s
B) 9.80 m/s
C) 31.8 m/s
D) 34.9 m/s

Question 42

In a section of horizontal pipe with a diameter of 3.00 cm the pressure is 5.21 kPa and water is flowing with a speed of 1.50 m/s.The pipe narrows to 2.50 cm.What is the pressure in the narrower region if water behaves like an ideal fluid of density 1000 kg/m³?

A) 4.00 kPa
B) 7.50 kPa
C) 5.82 kPa
D) 6.42 kPa
E) 4.61 kPa

Question 43

Water flows in the horizontal pipe shown in the figure.At point A the area is 25.0 cm² and the speed of the water is At B the area is 16.0 cm².The fluid in the manometer is mercury,which has a density of .We can treat water as an ideal fluid having a density of .What is the manometer reading h?

A) 0.546 cm
B) 1.31 cm
C) 2.81 cm
D) 2.16 cm
E) 3.36 cm

Question 44

A large cylindrical water tank is mounted on a platform with its central axis vertical.The water level is 3.75 m above the base of the tank,and base is 6.50 m above the ground.A small hole 2.22 mm in diameter has formed in the base of the tank.Both the hole and the top of the tank are open to the air.We can ignore air resistance and treat water as an ideal fluid with a density of 1000 kg/m³.
(a)How many cubic meters of water per second is this tank losing?
(b)How fast is the water from the hole moving just as it reaches the ground?

Question 45

A paint sprayer pumps air through a constriction in a 2.50-cm diameter pipe,as shown in the figure.The flow causes the pressure in the constricted area to drop and paint rises up the feed tube and enters the air stream.The speed of the air stream in the 2.50-cm diameter sections is 5.00 m/s.The density of the air is 1.29 kg/m³,and the density of the paint is 1200 kg/m³.We can treat the air and paint as incompressible ideal fluids.What is the maximum diameter of the constriction that will allow the sprayer to operate?

A) 8.07 mm
B) 4.05 mm
C) 12.2 mm
D) 9.65 mm
E) 14.3 mm

Question 46

Air is flowing through a rocket nozzle.Inside the rocket the air has a density of and a speed of 1.20 m/s.The interior diameter of the rocket is 15.0 cm.At the nozzle exit,the diameter is 2.50 cm and the density is 1.29 kg/m³.What is the speed of the air when it leaves the nozzle?

A) 123 m/s
B) 176 m/s
C) 88.0 m/s
D) 45.7 m/s
E) 29.3 m/s

Question 47

A level pipe contains a nonviscous,incompressible fluid with a density that is flowing steadily.At one position within the pipe,the pressure is 300 kPa and the speed of the flow is 20.0 m/s.At another position,the pressure is 200 kPa.What is the speed of the flow at this second position?

A) 567 m/s
B) 16.2 m/s
C) 32.9 m/s
D) 23.8 m/s
E) 186 m/s

Question 48

A horizontal tube consists of a pipe that narrows to a 2.0-cm-diameter throat.In the pipe,the water pressure is twice atmospheric pressure and the water flows with a speed of What is the pressure in the throat,assuming that the water behaves like an ideal fluid? The density of water is 1000 kg/m³,and atmospheric pressure is .

A) 1.9 atm
B) 0.12 atm
C) 2.1 atm
D) 2.0 atm

Question 49

Water flows in the horizontal pipe shown in the figure.At A the diameter is 5.00 cm and at B the diameter is 4.00 cm The fluid in the manometer is mercury,which has a density of .The manometer reading h is 4.40 cm.We can treat water as an ideal fluid having a density of .What volume of water is flowing through the pipe per second?

A) 0.0206 /s
B) 0.0426 /s
C) 0.00560 /s
D) 0.372 /s
E) 0.186 /s

Question 50

Incompressible water flows out of a large reservoir through a pipe that opens to the atmosphere 5.70 m below the level of the water in the reservoir.What is the speed of the water as it comes out of the pipe?

A) 1.72 m/s
B) 7.47 m/s
C) 55.8 m/s
D) 10.6 m/s
E) 27.9 m/s