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Fluid Mechanics Questions: Solutions and Explanations

Get answers to your fluid mechanics questions with detailed solutions and explanations. Improve your understanding of fluid flow and pressure concepts.

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Fluid Mechanics Questions: Solutions and Explanations

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  1. How much air must be pushed downward at 40 m/s in order to keep an 800 kg helicopter aloft? • 98 kg/s • 196 kg/s • 294 kg/s • 392 kg/s

  2. A jet of water flowing at 5 m/s is directed against a flat plate. If the mass flow in the fluid stream is 3 kg/s, what force is necessary to hold the plate in place? • 15 N • 30 N • 60 N • 147 N

  3. A venturi tube may be used as the inlet to an automobile carburetor. If the inlet pipe of 2 cm diameter narrows to 1 cm diameter, what is the pressure drop in the constricted section for airflow of 3 m/s in the 2 cm section? (Assume air density is 1.25 kg/ 3 ). • 70 Pa • 85 Pa • 100 Pa • 115 Pa

  4. Water is sent from a fire hose at 30 m/s at an angle of 30° above the horizontal. What is the maximum height reached by the water? • 7.5 m • 11.5 m • 15 m • 19 m

  5. A Boeing 737 airliner has a mass of 20,000 kg and the total area of the wings is 100 m2 . What must be the pressure difference between the top and bottom surface of the wings to keep the airplane aloft? • 1,960 N/m2 • 3,920 N/m2 • 7,840 N/m2 • 15,680 N/m2

  6. How much power is theoretically available from a mass flow of 1000 kg/s of water which falls a vertical distance of 100 m? • 980 kW • 98 kW • 4900 W • 980 W

  7. Water comes down the spillway of a dam from an initial vertical height of 100 meters. What is the velocity of the water at the end of the spillway? (Neglect frictional losses). • 28 m/s • 36 m/s • 44 m/s • 52 m/s

  8. Water pressurized to 105 Pa is flowing at 5 m/s in a pipe which contracts to 1/3 of its former area. What is the pressure and velocity of the water after the contraction? • 2 x 105 Pa, 15 m/s • 3 x 105 Pa, 10 m/s • 3 x 105 Pa, 15 m/s • 4 x 105 Pa, 1.5 m/s

  9. A fountain sends water to a height of 100 meters. What must be the pressurization (above atmospheric) of the underground water system? (1 ATM = 105 N/m2 .) • 1 ATM • 4.2 ATM • 7.2 ATM • 9.8 ATM

  10. The Garfield Thomas water tunnel at Pennsylvania State University has a circular cross-section which constricts from a diameter of 3.6 m to the test section, which is 1.2 m in diameter. If the velocity of flow is 3 m/s in the large-diameter pipe, determine the velocity of flow in the test section. • 9 m/s • 18 m/s • 27 m/s • 54 m/s

  11. A hole is punched in a full milk carton 10 cm below the top. What is the initial velocity of outflow? • 1.4 m/s • 1.96 m/s • 2.8 m/s • 3.9 m/s

  12. Water (density = 1 x 103 kg/m3 ) is flowing through a pipe whose radius is 0.04 m with a speed of 15 m/s. This same pipe goes up to the second floor of the building, 3 m higher, and the pressure remains unchanged. What is the speed of the water flow on the second floor? • 13 m/s • 14 m/s • 15 m/s • 16 m/s

  13. Water (density = 1 x 103 kg/m3 ) is flowing through a pipe whose radius is 0.04 m with a speed of 15 m/s. This same pipe goes up to the second floor of the building, 3 m higher, and the pressure remains unchanged. What is the radius of the pipe on the second floor? • 0.046 m • 0.043 m • 0.037 m • 0.034 m

  14. Air pressure is 1 x 105 N/m2 , air density is 1.3 kg/m3 , and the density of soft drinks is 1 x 103 kg/m3 . If one blows carefully across the top of a straw sticking up 0.10 m from the liquid in a soft drink can, it is possible to make the soft drink rise half way up the straw and stay there. How fast must the air be blown across the top of the straw? • 76.0 m/s • 27.6 m/s • 19.5 m/s • 0.99 m/s

  15. The flow rate of blood through the average human aorta, of radius 1.0 cm, is about 90 cm3 /s. What is the velocity of the blood flow through the aorta? • 14 cm/s • 32 cm/s • 37 cm/s • 29 cm/s

  16. Bernoulli's equation as it pertains to an ideal fluid flowing through a horizontal pipe, states that the sum of the pressure and energy per unit volume along the pipe does which of the following as measurements are taken along the pipe in the direction of fluid flow? • increases as the pipe diameter increases • decreases as the pipe diameter increases • remains constant as the pipe diameter increases • none of these

  17. An ideal fluid, of density 0.85 x 103 kg/m3 , flows at the rate of 0.25 kg/s through a pipe of radius 0.01 m. What is the fluid velocity? • 0.85 m/s • 1.3 m/s • 3.0 m/s • 0.94 m/s

  18. An ideal fluid, of density 0.9 x 103 kg/m3 , flows through a level pipe with radius of 0.5 cm at a velocity of 6.0 m/s; the pressure in the fluid is 1.3 x 105 N/m2 . This pipe connects to a second pipe, also level and with radius of 1.5 cm, into which the fluid flow continues. What is the velocity of flow in the larger radius pipe? • 54 m/s • 18 m/s • 0.67 m/s • 0.33 m/s

  19. If the flow rate of a liquid going through a 2.0 cm radius pipe is measured at 0.008 m3 /s, the average fluid velocity in the pipe is which of the following? • 0.64 m/s • 2.00 m/s • 0.04 m/s • 6.37 m/s

  20. A blimp is filled with 400 m3 of helium. How big a payload can the balloon lift? (The density of air is 1.29 kg/m3 , the density of helium is 0.18 kg/m3). • 111 kg • 129 kg • 215 kg • 444 kg

  21. What is the total mass of the Earth's atmosphere? (The radius of the Earth is 6.4 x 106 m, and atmospheric pressure at the surface is 105 N/m2 ). • 5.0 x 10316 kg • 1.0 x 1018kg • 5.0 x 1018kg • 1.0 x 1020kg

  22. An ideal fluid flows through a pipe made of two sections with diameters of 1.0 and 3.0 inches, respectively. The velocity of the fluid flow through the 3.0 inch section will be what factor times that through the 1.0 inch section? • 6.0 • 9.0 • 1/3 • 1/9

  23. What is the hydrostatic force on the back of Grand Coulee Dam if the water in the reservoir is 150 m deep and the width of the dam is 1200 m? (Hint: the total force is the average pressure times the area). • 5.2 x 109 N • 8.8 x 1010 N • 13.2 x 1010 N • 18.0 x 1010 N

  24. When water freezes, it expands about 9 percent. What would be the pressure increase inside your automobile engine block if the water in there froze? (The bulk modulus of ice is 2 x 109 N/m2 , and 1 ATM = 105 N/m2 ). • 18 ATM • 270 ATM • 1080 ATM • 1800 ATM

  25. How large a force is necessary to stretch a 2 mm - diameter steel wire (Y = 2 x 1011 N/m2 ) by 1%? • 3,140 N • 6,280 N • 9,420 N • 12,560 N

  26. In some places, the Greenland ice sheet is 1 kilometer thick. Estimate the pressure underneath the ice. (The density of ice is 918 kg/m3 ). • 9.0 x 105 Pa (9 ATM) • 2.5 x 106 Pa (25 ATM) • 4.5 x 106 Pa (45 ATM) • 9.0 x 106 Pa (90 ATM)

  27. A stonecutter's chisel has an edge area of 0.5 cm2 . If the chisel is struck with a force of 45 N, what is the pressure exerted on the stone? • 9,000 N/m2 • 90,000 N/m2 • 450,000 N/m2 • 900,000 N/m2

  28. Atmospheric pressure is 1.0 x 105 N/m2 and the density of air is 1.29 kg/m3 . If the density of air were constant as you get higher and higher, calculate the height of the atmosphere needed to produce this pressure. • 7,850 m • 77,000 m • 1,260 m • 10,300 m

  29. A large stone is resting on the bottom of the swimming pool. The normal force of the bottom of the pool on the stone • is equal to the weight of the stone. • is equal to the weight of the water displaced. • is equal to the sum of the weight of the stone and the weight of the displaced water. • is equal to the difference between the weight of the stone and the weight of the displaced water.

  30. The pressure inside a commercial airliner is maintained at 1 ATM (105 N/m2 ). What is the outward force exerted on a 1 m x 2 m cabin door if the outside pressure (at 10 km height) is 0.3 ATM? • 140 N • 1,400 N • 14,000 N • 140,000 N

  31. Dams at two different locations are needed to form a lake. When the lake is filled, the water level will be at top of both dams. The second dam is twice as high and twice as wide as the first dam. The force of the water on the second dam is how much greater than the force on the first? (Ignore atmospheric pressure since it is pushing on both sides of the dams.) • 2 • 4 • 8 • 16

  32. There are two steel rods, and the second has three times the area and twice the length of the first. Young's modulus for the second will be what factor times Young's modulus for the first? • 3.0 • 0.5 • 1.5 • 1.0

  33. The modulus that should be used in calculating stress and strain on a tire when, through friction, it stops a car is • Young's modulus • Compression modulus • Shear modulus • Bulk modulus

  34. As ice floats in water, about 10% of the ice floats above the surface of the water. There is some ice floating in a glass of water. What will happen to the water level as the ice melts? • The water level will rise 10% of the volume of the ice that melts. • The water level will rise, but not by as much as the 10% of the volume of the ice that melts. • The water level will remain unchanged. • The water level will become lower.

  35. If one bar has a Young's modulus that is bigger than the other, this indicates that the first bar • is longer than the second. • has a greater cross-sectional area than the second. • has a greater elastic limit than the second. • is made of material that is different from the second.

  36. If the column of mercury in a barometer stands at 72.6 cm, what is the atmospheric pressure? (The density of mercury is 13.6 x 103 kg/m3 and g = 9.8 m/s2 ) • 0.967 x 105 N/m2 • 1.03 x 105 N/m2 • 0.925 x 105 N/m2 • 1.073 x 105 N/m2

  37. A solid rock, suspended in air by a spring scale, has a measured mass of 9.0 kg. When the rock is submerged in water, the scale reads 3.3 kg. What is the density of the rock? (water density = 1000 kg/m3 ) • 4.55 x 103 kg/m3 • 3.50 x 103 kg/m3 • 1.20 x 103 kg/m3 • 2.73 x 103 kg/m3

  38. Legend says that Archimedes, in determining whether or not the king's crown was made of pure gold, measured its volume by the water displacement method. If the density of gold is 19.3 gm/cm3 and the crown's mass is 600 gm, what volume would be necessary to prove that it is pure gold? • 31.1 cm3 • 114 x 103 cm3 • 22.8 x 103 cm3 • 1.81 x 10-2 cm3

  39. The bottom of a flat-bottom aluminum boat has an area of 4.0 m2 and the boat's mass is 60 kg. When set afloat in water, how far below the water surface is the boat bottom? (water density = 1.0 x 103 kg/m3 ) • 0.060 m • 0.015 m • 0.030 m • 0.075 m

  40. The bottom of a flat-bottom aluminum boat has an area of 4.0 m 2 and the boat's mass is 60 kg. If two fishermen and their fishing gear, with total mass of 300 kg, are now placed in the boat, how much lower than before does the boat now ride in the water? (water density = 1.0 x 103 kg/m3 ) • 0.15 m • 0.12 m • 0.075 m • 0.06 m

  41. A uniform pressure of 7.0 x 105 N/m2 is applied to all six sides of a copper cube. What is the percentage change in volume of the cube? (for copper, B = 14 x 1010 N/m2 ) • 2.4 x 10-2 % • 0.4 x 10-2 % • 8.4 x 10-2 % • 0.5 x 10-3 %

  42. A cube of wood of density 0.78 gm/cm3 is 10 cm. on a side. When placed in water, what height of the block will float above the surface? (water density = 1.00 gm/cm3 ) • 7.8 cm • 5.0 cm • 2.2 cm • 6.4 cm

  43. By what factor is the total pressure greater at a depth of 850 m of sea water than at the surface where pressure is one atmosphere? (water density = 1000 kg/m3 , 1 atmosphere pressure = 1.01 x 105 N/m2 and g = 9.8 m/s2 ) • 100 • 83 • 74 • 19

  44. What volume of water is displaced by a submerged 4.0 kg cylinder made of solid iron? (iron density = 7.86 x 10 3 kg/m3 and water density = 1.0 x 103 kg/m3 ) • 5.1 x 10-4 m3 • 3.9 x 103 m3 • 9.9 x 103 m3 • 6.0 x 102 m3

  45. A ping pong ball has an average density of 0.084 grams/cm3 and a diameter of 3.8 cm. What force would be required to keep the ball completely submerged under water? • 1.000 N • 0.788 N • 0.516 N • 0.258 N

  46. A 15,000 N car on a hydraulic lift rests on a cylinder with a piston of radius 0.20 m. If a connecting cylinder with a piston of 0.04 m radius is driven by compressed air, what force must be applied to this smaller piston in order to lift the car? • 600 N • 1,500 N • 3,000 N • 15,000 N

  47. The quantity, strain, expressed in terms of the fundamental quantities (mass, length, time) is equivalent to which of the following? • MLT-1 • ML-1T-2 • M2L-1T-3 • a dimensionless quantity

  48. In a large tank containing a liquid, the hydrostatic pressure at a given depth is a function of which of the following? • depth • liquid density • both depth and liquid density • surface area

  49. The quantity pressure expressed in terms of the fundamental quantities (mass, length, time) is equivalent to which of the following? • MLT-1 • ML-1T-2 • M2L-1T-3 • a dimensionless quantity

  50. The quantity, stress, expressed in terms of the fundamental quantities (mass, length, time) is equivalent to which of the following? • MLT-1 • ML-1T-2 • M2L-1T-3 • a dimensionless quantity

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