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Fluid Mechanics 1. The three normal states of matter are a. steam, plasma, gas. b. solid, liquid, gas. c. atomic, solid, liquid. d. atomic, molecular, fluid. e. solid, fluid, plasma. ANS: b 2. If thermal energy is added to a cube of aluminum in the solid state, the cube’s surface area a. increases. b. decreases. c. remains unchanged. d. rearranges its crystalline structure. e. liquifies. ANS: a 3. By definition, density is a. inversely proportional to volume. b. proportional to mass. c. proportional to area. d. described by (a), (b), and (c). e. described by (a) and (b) only. ANS: e 4. Pressure is defined as a. the ratio of area to force. b. force times volume. c. the sum of volume and force. d. force per unit volume. e. force per unit area. ANS: e 281 282 Fluid Mechanics 5. If the density of a given volume of fluid does not change when the pressure on the surface of the fluid changes, we say that the fluid is a. incompressible. b. steady. c. moderated. d. irrotational. e. turbulent. ANS: a 6. When one fast-moving vehicle passes another at close proximity, the vehicles tend to a. increase their forward velocity. b. decrease their forward velocity. c. move away from each other. d. move towards each other. e. remain in an equilibrium state. ANS: d 7. As a submarine dives, the pressure on its hull a. increases. b. decreases. c. remains constant. d. depends on the thickness of the walls of the submarine. e. depends on the decrease in volume of the submarine. ANS: a 8. One should argue that a large ship floats because a. the density of the ship is less than that of the water it displaces. b. the density of the ship is the same as that of the water it displaces. c. the surface area of the ship contacting the water is the same as the surface area of the water contacting the ship. d. the gravitational force on the ship is less than the buoyant force on the ship. e. the mass of the ship is greater than the mass of the water it displaces. ANS: a 9. The specific gravity (sp.gr.) of a substance is defined as the ratio of that substance’s density to the density of water. If the sp.gr. of ice is 0.92, what is the mass of one cubic meter of ice in grams? a. 1,090,000 b. 920,000 c. 545,000 d. 460,000 e. 80,000 ANS: b Chapter 15 283 10. Which of two identical hollow spheres containing equal volumes, one filled with helium and sealed, the other evacuated and sealed, has the greatest weight? a. The sphere with helium b. The sphere with vacuum c. Either; it depends where on earth they are weighed. d. Either; it depends on whether they are weighed in air or submerged in a liquid. e. Either; it depends on whether or not enough helium has been added to the first sphere to make it float in air. ANS: a 11. A 400 N woman steps on a carpet with high heels on. If one quarter of her weight is distributed on one of the heels and the heel has an area of 1.0 cm 2 , what pressure in N m 2 is she exerting on the carpet? a. 106 b. 105 c. 104 d. 103 e. 102 ANS: a 12. Of the following properties, the one that is not characteristic of an ideal fluid is a. a lack of turbulence. b. a steady state velocity everywhere in the fluid. c. a steady state density at each point in the fluid. d. a steady state pressure at each point in the fluid. e. high viscosity. ANS: e 13. A 400 N woman is totally immersed in a water tank and displaces 0.0368 m 3 of water. What is her density in kg m 3 ? a. 0.999 10 3 b. 1.00 10 3 c. 1.11 103 d. 1.23 10 3 e. 1.25 10 3 ANS: c 14. A 4.0 cm diameter pipe has a flow rate of 0.8 10 3 m 3 s . What is the average fluid velocity in the pipe in m/s? a. 0.32 b. 0.64 c. 2.0 d. 0.04 e. 6.3 284 Fluid Mechanics ANS: b 15. A chisel has an edge area of 0.6 cm 2 . It is struck with a hammer with a force of 42 N. What pressure is exerted by the chisel in N m 2 ? a. 25.2 b. 30,000 c. 300,000 d. 700,000 e. 650,000 ANS: d 16. What is the volume of a 50 kg woman whose density is equal to that of water? a. 0.070 b. 0.085 c. 0.007 d. 0.050 e. 0.035 ANS: d 17. An alloy of copper and gold displaces 1.935 cm 3 of water. It has a mass of 33.44 gm. If gold has a density of 19.3 g cm 3 and copper has a density of 8.9 g cm 3 , what is the percent of gold by mass in the object? a. 46 b. 88 c. 90 d. 91.2 e. 15 ANS: c 18. A star has a mass of 2.0 10 30 kg and a radius of 6.4 106 m . What is its average density in kg m 3 ? a. 1.8 10 9 b. 1.8 10 7 c. 9 10 6 d. 3.2 1010 e. 1.28 10 6 ANS: a 19. A star has a mass of 20 10 30 kg and a radius of 150 109 m . What is its average density in kg m 3 ? a. 1.4 10 2 b. 0.007 c. 1.4 d. 700 e. 1.4 10 3 Chapter 15 ANS: e 285 286 Fluid Mechanics 20. The water behind a dam is 200 m deep. One atmosphere is 1.01 10 5 N m 2 . What is the absolute pressure in atmospheres at the bottom of the dam? g 9.80 m s 2 ; water 1.00 10 3 kg m 3 . a. 19.6 b. 24.7 c. 29.4 d. 20.6 e. 75.1 ANS: d 21. What would the pressure on a diver be in atmospheres if she could dive to a depth of one km in sea water? One atmosphere is 1.01 10 5 N m 2 . The density of sea water is 1.03 10 3 kg m 3 . a. 101 b. 130 c. 111 d. 9 e. 90 ANS: a 22. Sea water has a density of 1025 kg m 3 . Ice has a density of 917 kg m 3 . What fraction of an iceberg is above water? a. 0.05 b. 0.07 c. 0.09 d. 0.11 e. 0.19 ANS: d 23. The density of air is 1/800 that of water and the density of helium is 1/7 that of air. How many kilograms can a balloon filled with 200 m 3 of helium lift? water 1.00 10 3 kg m 3 a. 27 b. 214 c. 114 d. 314 e. 414 ANS: b 24. An oil tanker fully loaded has a mass of 6 10 8 kg . Assume the ship has a shape like a shoebox: 300 m long, 80 m wide, and 40 m high. How far in meters is the bottom of the ship below sea level when the density of sea water is 1020 kg m 3 ? a. 7 b. 12 c. 15 d. 25 Chapter 15 e. 35 ANS: d 287 288 Fluid Mechanics 25. What is the mass in kg of a ship floating in sea water if it displaces 1000 m 3 ? The density of sea water is 1020 kg m 3 . a. 1.02 10 6 b. 4.3 10 c. 5.1 10 d. 7.6 10 e. 9.8 10 6 ANS: a 26. An ice floe one meter thick is floating in sea water of density 1020 kg m 3 . What minimum area in m 2 is needed for the ice floe to support a 2000 kg auto at sea level? The density of ice is 920 kg m 3 . a. 20 b. 25 c. 30 d. 35 e. 40 ANS: a 27. A person is in a boat in a swimming pool. She throws a 20 kg iron anchor from the boat into the water. What happens to the water level in the pool? a. It becomes lower. b. It becomes higher. c. It stays the same. d. The answer cannot be determined from the information given. ANS: a 28. A person is in a boat in a swimming pool. She throws out a 20 kg log from the boat. The log floats. What happens to the water level in the pool? a. It becomes lower. b. It becomes higher. c. It stays the same. d. The answer cannot be determined from the information given. ANS: c 29. A person is in a boat in a swimming pool. He empties 20 kg of water from the boat into the pool. What happens to the water level in the pool? a. It becomes lower. b. It becomes higher. c. It stays the same. d. The answer cannot be determined from the information given. ANS: c Chapter 15 289 30. A 20 kg block of ice is floating in a swimming pool of fresh water. The temperature of the water in the pool is 90°. The ice melts while the temperature of the water surrounding the ice stays virtually constant. Which of the graphs below best shows the water height in the pool vs. time during the melting process? (All beginning heights are the same. All times are the same.) h h h t t a. b. h t c. h t d. t e. ANS: d 31. The pascal (Pa) is the same as a. kg m s 2 . b. N m 2 . c. N s 2 . d. N m 2 . e. kg m 3 . ANS: d 32. The density of an ideal fluid is 850 kg m 3 . This fluid flows at the rate of 0.25 kg/s through a pipe of radius 0.01 m. What is the velocity of the fluid in m/s? a. 3.0 b. 0.94 c. 0.85 d. 1.3 e. 0.75 ANS: b 33. An ideal fluid flows through a level pipe of radius 0.5 cm at a velocity of 6.0 m/s. The density of the fluid is 900 kg m 3 and the pressure is 1.30 10 5 N m 2 . When this fluid flows into a connecting pipe of radius 1.5 cm, what is the pressure in N m 2 ? a. 1.30 10 5 b. 1.74 10 5 c. 1.58 10 5 d. 1.44 10 5 290 Fluid Mechanics e. 1.10 10 5 ANS: d Chapter 15 291 34. The average human aorta has a radius of 1.0 cm. The flow rate is approximately 90 cm 3 s . What is the velocity of blood flow in cm/s? a. 18 b. 12 c. 29 d. 37 e. 32 ANS: c 35. Water is flowing through a pipe of radius 4 cm with a speed of 15 m/s. The pipe increases 3 m in height with no change in pressure or pipe diameter. What is the speed in m/s of the water at this new height? a. 11 b. 13 c. 15 d. 17 e. 19 ANS: b 36. Water is flowing through a pipe of radius 4 cm with a speed of 15 m/s. The pipe increases 3 m in height with no change in pressure or speed. What is the radius of the pipe in cm at this new height? a. 5.2 b. 4.6 c. 4.3 d. 3.7 e. 3.4 ANS: c 37. An open milk carton is pierced by an ice pick 10 cm below the surface of the liquid. At what speed in m/s does the liquid exit the carton? a. 1.4 b. 1.6 c. 1.9 d. 2.4 e. 3.8 ANS: a 38. A vat filled with a liquid is drained by a pipe located 3 m below the surface. At what speed in m/s does the liquid leave the pipe? a. 2.5 b. 3.0 c. 4.9 d. 7.7 e. 36 292 Fluid Mechanics ANS: d Chapter 15 293 39. A ping pong ball of density 0.084 g cm 3 and diameter 3.8 cm, is held under water. What is the force in N necessary to do this? a. 0.0645 b. 0.258 c. 0.516 d. 1.032 e. 1.10 ANS: b 40. A gas pipeline delivers 1.55 m 3 of gas per second. If the pipe has a diameter of 25 cm, what is the flow speed in m/s? a. 3.95 b. 7.90 c. 23.7 d. 31.6 e. 39.5 ANS: d 41. A water bed is 2.5 m long, 2 m wide, and has a depth of 50 cm. What is the weight of the bed in N if the bed is filled with water of density 1000 kg m 3 ? a. 122 10 4 b. 2.45 10 4 c. 3.68 10 4 d. 2.50 10 3 e. 5.00 10 3 ANS: b 42. A hydraulic press of square cross section has a 162 N girl standing on one platform that measures 0.500 m on each side. The other platform of the press measures 4.00 m on a side. How heavy an object in N will she balance? a. 648 b. 1296 c. 2592 d. 5184 e. 10368 ANS: e 43. An object is constructed of two different materials, A and B, which have densities A and B with B A . Its volume is V V A VB . It will float in a medium of density C if B C . a. A 2 b. AV A BVB C V . c. AV A BVB C V . d. B A C . 294 Fluid Mechanics e. material A is air contained in material B. ANS: c Chapter 15 295 44. The volume of an object made of a uniform substance is a. inversely proportional to the weight of the object. b. equal to the weight of the object. c. inversely proportional to the mass of the object. d. the maximum number of marbles of unit diameter that would fit in the space occupied by the object. e. the number of standard unit cubes that would exactly fill the space occupied by the object. ANS: e 45. Someone steps on your foot accidentally. You would most likely feel the greatest pressure if that person was a. a 100 kg football player wearing sneakers. b. a 120 kg football player wearing snowshoes. c. a 50 kg woman wearing spike heels. d. a 50 kg woman wearing no shoes. e. an 80 kg cowboy wearing boots. ANS: c 46. An open tube manometer is used to measure the pressure in the gas enclosed in vessel V. The gas supports a column of liquid of density to a height h in the tube. The atmospheric pressure outside the tube is P0 . The total pressure in vessel V is V h a. the gauge pressure gh . b. the gauge pressure P0 . c. the gauge pressure P0 gh . d. the absolute pressure P0 . e. the absolute pressure P0 gh . ANS: e 47. A large number of helium balloons are tied to a 0.454 kg (formerly known as a pound) box of chocolates. When the box is released, the balloons rise to the ceiling. While the balloons are at the ceiling, the total force on the balloons is a. zero. b. equal to the weight of the box of chocolates. c. equal to the normal force of the ceiling on the balloons. d. equal to the vector sum of the weight of the chocolates, the normal force of the ceiling, and the weight of the balloons. e. equal to the vector sum of the weight of the chocolates, the normal force of the ceiling, the weight of the balloons, and the buoyant force of the air on the box of chocolates. 296 Fluid Mechanics ANS: a Chapter 15 297 48. An aquarium tank with water in it ( 1.0 10 3 kg m 3 ) is fixed to the flat bed of a truck. When the truck accelerates the water takes the shape shown below. What is the acceleration in m s 2 of the truck? (The positive horizontal axis points to the right.) 2m 1m 4m a. –4.95 b. –2.45 c. 0 d. +2.45 e. +4.95 ANS: d 49. An aquarium tank with water in it ( 1.0 10 3 kg m 3 ) is fixed to the flat bed of a truck. When the truck accelerates the water takes the shape shown below. What is the acceleration in m s 2 of the truck? (The positive horizontal axis points to the right.) 2m 1m 4m a. –4.95 b. –2.45 c. 0 d. +2.45 e. +4.95 ANS: b 50. The water in each of three vessels of different shapes has the same height. Rank the pressures on the bottoms of the vessels from highest to lowest. A a. PA PB PC b. PC PA PB c. PB PA PC d. PC PA PB B C 298 Fluid Mechanics e. PA PB PC ANS: e Chapter 15 299 51. When a deep-sea diver, weighted to be able to make the descent, is pulled up, the force needed to pull him up the last 10 m to the surface compared to the force needed to pull him up the first 10 m when near the bottom is a. greater near the surface. b. greater near the bottom. c. the same near the surface as it is near the bottom. d. greater in sea water, less in fresh water. e. less in fresh water, greater in sea water. ANS: c 52. The table below shows the densities of several substances. substance aluminum gold lead platinum density (kg/m3) 2.70 10 3 19.3 10 3 11.3 10 3 21.4 10 3 If we have cubes of these materials 1.00 m on a side, the pressure on the base will be greatest when the cube is a. aluminum. b. gold. c. lead. d. platinum. e. water. ANS: d 53. An 8-ounce glass of water is 10 cm high. The water pressure at the bottom of the water in the glass is greater than the surrounding air pressure, in N m 2 , by a. 800. b. 980. c. 1000. d. 9800. e. 10,000. ANS: b 54. The total force, in N, that water of density 1.00 10 3 kg m 3 exerts on a 1000 m long dam holding back water to a height of 200 m is a. 9.8 1010 . b. 1.96 1011 . c. 3.92 1011 . d. 9.8 1011 . e. 1.96 1012 . ANS: b 300 Fluid Mechanics 55. A person floats with just five percent of her body above sea water of density 1.03 10 3 kg m 3 . The person’s density in g cm 3 is a. 0.950. b. 0.979. c. 1.00. d. 1.03. e. 1.05. ANS: b 56. A 1.00 kg gold cube hangs at the end of a 4.00 m long string. gold 19.3 103 kg m 3 ; mercury 13.6 103 kg m 3 . When the gold cube is immersed in mercury, the tension in the string, in N, is a. 0.98. b. 2.9. c. 3.4. d. 6.9 e. 9.8. ANS: b 57. Water is flowing at the rate of 6.28 m 3 s through a hose of radius 1.00 cm lying on the ground. When the hose develops a bulge of radius 1.20 cm, the speed of the water, in m/s, through the bulge is a. 1.4. b. 1.6. c. 2.0. d. 2.4. e. 2.9. ANS: a 58. A container of orange juice filled to height h sits on a table. Juice will strike the table farthest from the container if a hole is made in the container at height h a. . 4 h b. . 3 h c. . 2 2h d. . 3 3h e. . 4 ANS: c Chapter 15 301 59. A 750 g pail holding 4.00 kg of water sits on a scale. A 200 g aluminum block is lowered into the water by a string attached to another scale. aluminum 2.70 10 3 kg m 3 ; water 1.00 10 3 kg m 3 . scale scale The scale on which the bucket sits now reads a. 46.6 N. b. 47.3 N. c. 48.5 N. d. 49.2 N. e. 51.3 N. ANS: b 60. A 750 g pail holding 4.00 kg of water sits on a scale. A 200 g aluminum block is lowered into the water by a string attached to another scale. aluminum 2.70 10 3 kg m 3 ; water 1.00 10 3 kg m 3 . scale scale The scale from which the aluminum block hangs now reads a. 0.73 N. b. 1.23 N. c. 1.96 N. d. 2.46 N. e. 3.92 N. ANS: b