Deck 15: Fluids

Question 1

Does atmospheric pressure affect the buoyant force on a rigid submarine?
Explain why or why not.

Answer 1

No.Adding a constant value to the pressure does not affect the net force.If the submarine were not rigid,a constant pressure would decrease the volume of the submarine,and thus decrease the buoyancy.

Question 2

An object floats on a fluid if its density is less than that of the fluid.

Answer 2

True

Question 3

The upward pressure on the bottom surface of a submerged object is less than the downward pressure on its top surface.

Answer 3

False

Question 4

To determine gauge pressure, add the atmospheric pressure to the absolute pressure.

Question 5

Density is

A) proportional to both mass and volume.
B) proportional to mass and inversely proportional to volume.
C) inversely proportional to mass and proportional to volume.
D) inversely proportional to both mass and volume.
E) proportional only to volume.

Question 6

State Bernoulli's principle.

Question 7

State Archimedes' Principle.

Question 8

State Pascal's Principle

Question 9

The buoyant force acts through the center of mass of the displaced fluid.

Question 10

Pressure in a fluid decreases with depth.

Question 11

What is the difference between the pressures inside and outside a tire called?

A) absolute pressure
B) atmospheric pressure
C) fluid pressure
D) gauge pressure
E) N/m²

Question 12

A person weighting 700 N stands in the middle of an otherwise empty 4 m x 5 m x 3 m room. How does the weight of the person compare with the weight of the air (the density of air is 1.29 kg/m³) in the room?

A) The weight of the air is much more than the weight of the person.
B) The weight of the air is about the same as the weight of the person.
C) The weight of the air is much less than the weight of the person.
D) It makes no sense to speak of weight for a gas like air.

Question 13

Consider ice cubes floating in a glass of water. What will happen to the level of the water as the ice melts?

Question 14

Atmospheric pressure is approximately

A) 1.01 × 10² Pa
B) 1.01 × 10³ Pa
C) 1.01 × 10⁴ Pa
D) 1.01 × 10⁵ Pa
E) 1.01 × 10⁶ Pa

Question 15

If an external pressure is applied to a confined fluid, the pressure at every point within the fluid increases by that amount.

Question 16

The buoyant force acting on an object is equal to the weight of the object.

Question 17

When atmospheric pressure changes, what happens to the absolute pressure at the bottom of a pool?

A) It does not change.
B) It increases by a lesser amount.
C) It increases by the same amount.
D) It increases by a greater amount.
E) It depends on the depth of the pool.

Question 18

At any depth in a fluid at rest, the pressure is the same in all directions at the given depth.

Question 19

Pressure is

A) proportional to both force and area.
B) proportional to force and inversely proportional to area.
C) inversely proportional to force and proportional to area.
D) inversely proportional to both force and area.
E) proportional only to area.

Question 20

What is meant by gauge pressure?

Question 21

Consider three drinking glasses. All three have the same area base, and all three are filled to the same depth with water. Glass A is cylindrical. Glass B is wider at the top than at the bottom, and so holds more water than A. Glass C is narrower at the top than at the bottom, and so holds less water than A. Which glass has the greatest liquid pressure at the bottom?

A) Glass A
B) Glass B
C) Glass C
D) All three have equal non-zero pressure at the bottom.
E) All three have zero pressure at the bottom.

Question 22

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 water displaced in the salt water is

A) more.
B) less.
C) the same.
D) Cannot be determined from the information given.

Question 23

A flask of water rests on a scale. If you dip your finger into the water, without touching the flask, the reading on the scale will

A) decrease.
B) stay the same.
C) increase.
D) behave unpredictably.

Question 24

FIGURE 15-1
Each of the three containers shown in Figure 15-1 weighs the same amount and is filled with water to the same level. All three have the same surface area in contact with the table. Which of the following statements are true?
I. The pressure at the bottom surface of the container is the same for all three containers.
II. The force exerted by the water on the bottom surface of the container is the same
For all three containers.
III. The force exerted by the container on the table is the same for all three containers.

A) Statements I, II, and III are true.
B) Only Statements I and II are true.
C) Only Statements II and III are true.
D) Only Statements I and III are true.
E) None of the statements are true.

Question 25

One day, while swimming below the surface of the ocean, you let out a number of bubbles of air from your mouth. As the bubbles rise toward the surface, their diameters will

A) decrease.
B) stay the same.
C) increase.
D) increase for half of the bubbles and decrease for the other half.

Question 26

The lift on an airplane wing is an application of

A) Bernoulli's principle.
B) Pascal's principle.
C) Archimedes' principle.
D) Poiseuille's equation.
E) Torricelli's equation.

Question 27

Water flows through a pipe. The diameter of the pipe at point B is larger than at point A. Where is the speed of the water greater?

A) point A
B) point B
C) same at both A and B
D) Cannot be determined from the information given.

Question 28

Two horizontal pipes are the same length, but pipe B has twice the diameter of pipe A. Water undergoes viscous flow in both pipes, subject to the same pressure difference across the lengths of the pipes. If the flow rate in pipe A is Q, what is the flow rate in pipe B?

A) 1/2Q
B) 2Q
C) 4Q
D) 8Q
E) 16Q

Question 29

Salt water has greater density than fresh water. A boat floats in both fresh water and in salt water. Where is the buoyant force greater on the boat?

A) salt water
B) fresh water
C) Buoyant force is the same in both.
D) Cannot be determined from the information given.

Question 30

A boat loaded with ice is floating in a swimming pool. If the ice is thrown into the pool, the water level in the pool, once the ice stops bobbing and floats steadily,

A) rises.
B) falls.
C) stays the same.
D) There is not enough information to answer this question.

Question 31

FIGURE 15-2
Water flows in a pipe as shown in Figure 15-2. The pipe is horizontal at points A and B, then rises in elevation while decreasing in diameter and is again horizontal at points C and D. The vertical tubes at B and D are open at the top, but they enter the pipe and bend at right angles along the centerline of the pipe with their mouths facing the flow (these are Pitot tubes). Water enters the Pitot tube and rises until the hydrostatic pressure in the tube balances the pressure at the mouth of the tube. Because no more water enters the tube, the speed of the water just outside the mouth of the tube is zero m/s. The pressure in the pipe is unaffected by the Pitot tube. Which of the following statements is correct?

A) h_B > h_D
B) h_B < h_D
C) h_B = h_D
D) The answer depends on the direction of the flow.
E) The answer depends on the speed of the flow.

Question 32

FIGURE 15-2
Water flows in a pipe as shown in Figure 15-2. The pipe is horizontal at points A and B, then rises in elevation while decreasing in diameter and is again horizontal at points C and D. Vertical tubes, open at the top, are connected to the pipe at A and C, flush with the edge of the pipe. Which of the following statements is correct?

A) h_A > h_C
B) h_A < h_C
C) h_A = h_C
D) The answer depends on the direction of the flow.
E) The answer depends on the speed of the flow.

Question 33

"An external pressure applied to an enclosed fluid is transmitted unchanged to every point within the fluid" is known as

A) Archimedes' principle.
B) Bernoulli's principle.
C) Torricelli's law.
D) Pascal's principle.
E) Fermet's principle.

Question 34

You have two identical pure silver ingots. You place one of them in a glass of water and observe it to sink to the bottom. You place the other in a container full of mercury and observe that it floats. Comparing the buoyant forces in the two cases you conclude that

A) the buoyant force in the water is equal to that in mercury.
B) the buoyant force in the water is larger than that in mercury.
C) the buoyant force in water is smaller than the that in mercury.
D) the buoyant force in the water is zero and that in mercury is non-zero.
E) No conclusion can be made about the respective values of the buoyant forces.

Question 35

The pressure differential across a wing cross section due to the difference in air flow is explained by

A) Pascal's Principle.
B) Bernoulli's equation.
C) Poiseuille's law.
D) Archimedes Principle.
E) Torricelli's law.

Question 36

How a ship floats is described in terms of

A) Bernoulli's principle.
B) Pascal's principle.
C) Archimedes' principle.
D) Poiseuille's equation.
E) Torricelli's equation.

Question 37

The equation of continuity is a statement of the

A) conservation of linear momentum.
B) conservation of mass.
C) conservation of energy.
D) conservation of kinetic energy.
E) conservation of angular momentum.

Question 38

The hydraulic lift is an application of

A) Bernoulli's principle.
B) Pascal's principle.
C) Archimedes' principle.
D) Poiseuille's equation.
E) Torricelli's equation.

Question 39

A boat loaded with rocks is floating in a swimming pool. If the rocks are thrown into the pool, the water level in the pool, after the rocks have settled to the bottom,

A) rises.
B) falls.
C) stays the same.
D) There is not enough information to answer this question.

Question 40

Bernoulli's principle is a statement of the

A) conservation of linear momentum.
B) conservation of mass.
C) conservation of energy.
D) conservation of kinetic energy.
E) conservation of angular momentum.

Question 41

The pressure drop in a tube carrying a viscous fluid is described by

A) Bernoulli's principle.
B) Pascal's principle.
C) Archimedes' principle.
D) Poiseuille's equation.
E) Newton's Second law.

Question 42

The fact that a pin placed carefully on the surface of the water can remain there without sinking is best explained by

A) gravitation.
B) gauge pressure.
C) surface tension.
D) Archimedes' principle.
E) viscosity.

Question 43

The fact that a dew drop is spherical is best described in terms of

A) gravitation.
B) gauge pressure.
C) surface tension.
D) Archimedes' principle.
E) viscosity.

Question 44

When soup gets cold, it often tastes greasy. This "greasy" taste seems to be associated with oil spreading out all over the surface of the soup, instead of staying in little globules. This is readily explained in terms of

A) the Bernoulli effect.
B) Archimedes Principle.
C) Pascal's Principle.
D) the decrease in the surface tension of water with increasing temperature.
E) the increase in the surface tension of water with increasing temperature.

Question 45

A sphere is constructed of two concentric pieces. The inner part is a solid sphere of radius 10.0 cm made of a material with density 4000 kg/m³. The outer part is a spherical shell with inner radius 10.0 cm and outer radius 20.0 cm. The outer shell has a density 9000 kg/m³.
(a) What is the mass of this sphere?
(b) What is the average density of this sphere?

Question 46

The deepest point of the Pacific Ocean is 11,033 m, in the Mariana Trench. What is the water pressure at that point? The density of seawater is 1025 kg/m³.

A) 5.55 × 10⁷ Pa
B) 8.88 × 10⁷ Pa
C) 1.11 × 10⁸ Pa
D) 2.22 × 10⁸ Pa
E) 3.33 × 10⁸ Pa

Question 47

Substance A has a density of 3.0 g/cm³ and substance B has a density of 4.0 g/cm³. In order to obtain equal masses of these two substances, the ratio of the volume of A to the volume of B will be equal to

A) 1:3.
B) 4:3.
C) 3:4.
D) 1:4.
E) 4:1.

Question 48

A sphere of radius 10.0 cm floats in equilibrium partially submerged in water with its lowest point 5.00 cm below the water's surface.
(a) What is the buoyant force acting on the sphere?
(b) What is the weight of the sphere?

Question 49

A 1938 nickel has a diameter of 21.21 mm, a thickness of 1.95 mm, and weighs 0.04905 N. What is its density?

A) 1.37 × 10^-4 kg/m³
B) 1.82 × 10³ kg/m³
C) 19.3 × 10³ kg/m³
D) 3.63 × 10³ kg/m³
E) 7.26 × 10³ kg/m³

Question 50

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 51

A U-tube with a cross-sectional area of 1.00 cm² is open to the atmosphere at both ends. Water is poured into the tube until the water rises part-way along the straight sides, and then 5.00 cm³ of oil is poured into one end. As a result, the top surface of the oil ends up 0.550 cm higher than the water surface on the other side of the U. What is the density of the oil?

Question 52

A 100-kg person sits on a 5-kg bicycle. The weight is borne equally by the two wheels of the bicycle. The tires are inflated to a gauge pressure of 8.0 x 10⁵ Pa and are 2.0 cm wide. What length of each tire is in contact with the ground?

A) 1.6 cm
B) 1.8 cm
C) 3.2 cm
D) 2.4 cm
E) 6.4 cm

Question 53

A basketball player pushes down with a force of 50 N on a basketball that is inflated to a gauge pressure of 8.0 x 10⁴ Pa. What is the diameter of contact between the ball and the floor?

A) 2.8 cm
B) 1.4 cm
C) 1.7 cm
D) 2.1 cm
E) 5.6 cm

Question 54

The flow of water emerging from a hole in a container is best described in terms of

A) Torricelli's law.
B) Pascal's principle.
C) Archimedes' principle.
D) Poiseuille's equation.
E) Newton's Second law.

Question 55

A 1959 penny has a diameter of 19.55 mm, a thickness of 1.55 mm, and a mass of 2.500 g. What is its density?

A) 5.37 × 10³ kg/m³
B) 21.5 × 10³ kg/m³
C) 1.34 × 10³ kg/m³
D) 2.68 × 10³ kg/m³
E) 1.86 × 10^-4 kg/m³

Question 56

The density of air is 1.29 kg/m³. What is the mass of the air inside a room 4.0 m × 3.0 m × 2.0 m?

A) 0.32 kg
B) 3.1 kg
C) 31 kg
D) 1.9 kg
E) 19 kg

Question 57

A piece of aluminum with a mass of 1.0 kg and density of 2700 kg/m³ is suspended from a string and then completely immersed in a container of water. The density of water is 1000 kg/m³.
(a) Determine the volume of the piece of aluminum.
(b) Determine the tension in the string after the metal is immersed in the container of water.

Question 58

The weight of a 1200-kg car is supported equally by the four tires, which are inflated to the same gauge pressure. What gauge pressure is required so the area of contact of each tire with the road is 100 cm²?

A) 11.6 × 10⁵ Pa
B) 11.6 × 10⁴ Pa
C) 2.9 × 10⁵ Pa
D) 2.9 × 10⁴ Pa

Question 59

When you blow some air above a paper strip, the paper rises. This is because

A) the air above the paper moves faster and the pressure is higher.
B) the air above the paper moves faster and the pressure is lower.
C) the air above the paper moves faster and the pressure remains constant.
D) the air above the paper moves slower and the pressure is higher.
E) the air above the paper moves slower and the pressure is lower.

Question 60

The Aswan High Dam is 111 m high. What is the water pressure at the foot of the dam?

A) 1.09 × 10⁶ Pa
B) 1.16 × 10⁶ Pa
C) 1.09 × 10³ Pa
D) 1.11 × 10⁵ Pa
E) 1.11 × 10² Pa

Question 61

A rock is suspended from a scale reads 10.0 N. A beaker of water is raised up so the rock is totally submerged in the water. The scale now reads 6.25 N.What is the density of the rock?

A) 2.00 times the density of water
B) 2.33 times the density of water
C) 2.67 times the density of water
D) 3.00 times the density of water
E) 2.50 times the density of water

Question 62

A hot air balloon plus its cargo has a mass of 400 kg, and it holds 700 m³ of hot air. It is floating at a constant height in air with a density of 1.29 kg/m³. What is the density of the hot air in the balloon?

A) 1.39 kg/m³
B) 0.72 kg/m³
C) 0.57 kg/m³
D) 0.86 kg/m³
E) 0.43 kg/m³

Question 63

In a certain one-lane road there are no entrances or exits. As the road passes through open country and populated areas, the speed limit changes. Assume that cars travel at the posted speed limit. In the open road, where the speed limit is 55 mph, the cars are spaced so there are 51 cars per mile. If the flow of cars is steady, how many cars per mile are there in a stretch of road where the speed limit is 40 mph?

A) 56 cars/mile
B) 60 cars/mile
C) 66 cars/mile
D) 70 cars/mile
E) 76 cars/mile

Question 64

A person who weighs 550 N empties her lungs as much as possible and is then completely immersed in water 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 65

A cylinder, semicircular in cross-section, 10.0 m long and 5.00 m in radius, is completely submerged in water. What is the buoyant force on the cylinder?

A) 1.92 × 10⁶ N
B) 3.85 × 10⁶ N
C) 5.78 × 10⁶ N
D) 6.28 × 10⁶ N
E) 7.70 × 10⁶ N

Question 66

The bathyscaphe Trieste consists of a cylindrical hull, 15.2 m long and 3.66 m in diameter, filled with gasoline with a density of 880 kg/m³ to make it buoyant. If it is totally submerged in salt water with a density of 1025 kg/m³ and neither rising nor sinking, what is the weight of the craft?

A) 127 kN
B) 227 kN
C) 327 kN
D) 427 kN
E) 527 kN

Question 67

A 12,000-N car is raised using a hydraulic lift, which consists of a U-tube with arms of unequal areas, filled with oil 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 initial force that must be applied to the smaller piston in order to start lifting the car? For purposes of this problem, neglect the weight of the pistons.

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

Question 68

A 12,000-N car is raised using a hydraulic lift, which consists of a U-tube with arms of unequal areas, filled with 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, 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 69

FIGURE 15-8
A cylinder, semicircular in cross-section, 10.0 m long and 5.00 m in radius, is completely submerged, with its flat 5.00 m × 10.0 m side horizontal and 8,00 m below the water surface, as shown in Figure 15-8. What is the force on the curved surface of the half-cylinder? Neglect atmospheric pressure.

A) 2.00 × 10⁶ N
B) 2.50 × 10⁶ N
C) 3.00 × 10⁶ N
D) 3.50 × 10⁶ N
E) 4.00 × 10⁶ N

Question 70

FIGURE 15-5
A reservoir manometer consists of a U-tube in which the two arms have different diameters, as shown in Figure 15-5. The diameter on the narrow side is 10.0 mm and the diameter on the reservoir side is 25.0 mm. The liquid in the manometer is oil with a density of 830 kg/m³ and the fluids in contact with the oil are gases of negligible density. The dotted line indicates the level of the oil when the pressures p₁ and p₂ are equal. What is the value of h when p₁ - p₂ = 1000 Pa?

A) 10.6 cm
B) 12.3 cm
C) 8.40 cm
D) 9.81 cm
E) 13.2 cm

Question 71

FIGURE 15-3
The U-tube shown in Figure 15-3 contains mercury with a density of 13,600 kg/m³. It is open on one end and the other end is connected to a boiler, which contains water at high pressure. The water from the boiler pushes directly on the mercury column. What is the gauge pressure at point A in the boiler?

A) 4.54 kPa
B) 4.41 kPa
C) 128 Pa
D) 441 Pa
E) 449 Pa

Question 72

A barge with vertical sides is 10.0 m wide and 60.0 m long and is floating in fresh water. How much deeper into the water does the barge sink when 300,000 kg of coal are loaded on the barge?

A) 25.0 cm
B) 50.0 cm
C) 75.0 cm
D) 1.00 m
E) 1.50 m

Question 73

FIGURE 15-7
The two water reservoirs shown in Figure 15-7 are open to the atmosphere. The manometer contains oil with a density of 820 kg/m³. 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 74

A cubical box 25.00 cm on each side is immersed in a fluid. The pressure at the top surface of the box is 109.4 kPa and the pressure on the bottom surface is 112 kPa. What is the density of the fluid?

A) 1000 kg/m³
B) 1030 kg/m³
C) 1060 kg/m³
D) 1090 kg/m³
E) 1120 kg/m³

Question 75

FIGURE 15-4
The circular pipes shown in Figure 15-4 both contain water, but at different pressures. They are connected by means of an inverted U-tube, which contains oil with a density of 800 kg/m³. The heights are: h_A = 7.0 cm, h_B = 20.0 cm, and h_C = 13.0 cm. What is the pressure difference (P_B - P_A)?

A) 235 Pa
B) 240 Pa
C) 255 Pa
D) 270 Pa
E) 285 Pa

Question 76

A U-tube is open to the atmosphere at both ends. Water is poured into the tube until the water rises part-way along the straight sides, and then some oil with a density of 920 kg/m³ is poured into one end. This causes the water surface on that side of the tube to go down by 5.50 mm and the surface on the other side to go up by the same amount. How much higher is the top surface of the oil on that side of the tube compared with the surface of the water on the other side of the tube?

A) 0.96 mm
B) 1.2 mm
C) 0.44 mm
D) 1.2 cm
E) 1.1 cm

Question 77

The circular pipes shown in Figure 15-4 both contain water, but there is a pressure difference between them, (P_B - P_A) = 1000 Pa. They are connected by means of an upside-down U-tube, which contains oil with a density of 800 kg/m³. The heights are: h_A = 5.0 cm and h_B = 40.0 cm. What is h_C?

A) 28.0 cm
B) 29.0 cm
C) 30.0 cm
D) 31.0 cm
E) 32.0 cm

Question 78

A spar buoy consists of a circular cylinder, which floats with its axis oriented vertically. One such buoy has a radius of 1.00 m, a height of 2.00 m, and weighs 40.0 kN. What portion of it is submerged when it is floating in fresh water?

A) 1.35 m
B) 1.30 m
C) 1.25 m
D) 1.20 m
E) 1.50 m

Question 79

A barge is 10.0 m wide and 60.0 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?

A) 3.53 MN
B) 6.39 MN
C) 6.82 MN
D) 7.06 MN
E) 9.54 MN

Question 80

FIGURE 15-6
The two water reservoirs shown in Figure 15-6 are open to the atmosphere. The manometer contains mercury with a density of 13,600 kg/m³. What is the difference in elevation h if the manometer reading m is25.0 cm?

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