1. (AP SAMPLE QUESTION) An ideal fluid is flowing with a speed of 12 cm/s through a pipe of diameter 5 cm. The pipe splits into three smaller pipes, each with a diameter of 2 cm. What is the speed of the fluid in the smaller pipes? a. 4 cm/s b. 12 cm/s c. 25 cm/s d. 75 cm/s 2. A horizontal pipe narrows from a radius R 1 to a radius of 0.5 R 1. If the speed of the water in the pipe is V 1 in the larger radius pipe, what is the speed in the smaller pipe? a. 0.5 V 1 b. 2 V 1 c. 4 V 1 d. 5 V 1 3. Three vessels of different shapes are each filled with the same depth of water as shown. The area of the base is the same for all three vessels. Which of the following statements is valid? Choose all that apply. a. The pressure at the surface of vessel A is largest because the area is largest. b. The pressure in the fluid at the bottom of vessel A is largest since it has the largest surface area. c. The force exerted by each vessel on a table would be the same. d. The pressure in the fluid at the bottom of each vessel is the same. 4. If you hold a cylinder vertically, what is the direction of the net force exerted by the atmosphere on it? Note, consider even small differences in pressure. a. Downward b. Upward c. Zero the up and down pressure are equal and cancel 5. Three blocks of equal volume are completely submerged into water. The blocks made of different materials: aluminum, iron and lead. Which of the following is the correct statement about the buoyant force on each block? (Note: aluminum = 2700 kg/m 3, ρ iron = 7800 kg/m 3, ρ lead = 11300 kg/m 3 ) a. F aluminum > F iron > F lead b. F aluminum < F iron < F lead c. F aluminum < F iron > F lead d. F aluminum = F iron = F lead Page 1
6. A 3.24 kg solid cylinder of aluminum ( aluminum = 2700 kg/m 3 ) with a string attached to the top is completely submerged in water ( water = 1000 kg/m 3 ). If a spring scale is used to keep the block of aluminum in equilibrium, what is the reading on the scale? a. 0.5 N b. 5.0 N c. 20 N d. 45 N e. 50 N 7. A hose is pointed straight up, and the water flowing from is reaches a height of h above the tip of the hose. Neglecting air resistance, which of the following adjustments would allow the water to reach a height of 4h, assuming that the flow rate from the hose is constant? Hint: Use kinematics to determine how the velocity of the jet must change in order to quadruple the height, then apply fluid equations. a. Decrease the area of the opening by a factor of 16. b. Decrease the area by a factor of 8. c. Decrease the area by a factor of 4. d. Decrease the area by a factor of 2. 8. A hose of inner radius 0.01 m is used to fill a 0.5 m 2 m 0.8 m rectangular tub. If the water flows through the hose with a speed of 2 m/s, how long does it take to fill the tub? 9. A perpendicular force is applied to a certain area and produces a pressure P on a fluid. If the same force is applied to an area half as large, the new pressure on the surface would be: a. 2P b. 4P c. P d. P/2 e. P/4 10. A helium-filled balloon floats in a car with the windows closed. In which direction will the balloon move with respect to the ground when the car accelerates from a stop sign? a. Opposite the direction of the car s motion b. In the same direction as the car s motion c. It will remain stationary 11. Estimate the absolute pressure 100 m deep in a fresh-water lake. The density of water is 1000 kgm -3. a. 1.0x10 3 Pa b. 1.0x10 5 Pa c. 1.0x10 6 Pa d. 1.0x10 8 Pa 12. An empty balloon has a mass of 1.20 kg. The balloon is then filled with helium gas at a density of 0.18 kg/m 3. At this density the spherical balloon has a radius of 1.30 m. If the filled balloon is fastened to a light vertical thread, what is the tension in the thread? (ρ air = 1.29 kg/m 3 ). Page 2
13. A wind tunnel is shaped as shown. If it is completely filled with a moving, incompressible fluid, what is true of the pressure gauge readings? a. P 1 > P 2 > P 3 b. P 1 < P 2 < P 3 c. P 2 < P 1 < P 3 d. P 1 < P 2 > P 3 e. P 3 = P 2 = P 1 14. A hydraulic jack has an input piston with an area of A 1 and an output piston with an area of A 2. If you apply a force of F 1 to the input piston, which of the following correctly gives the force on the output piston? a. F 1 ( A 1 A 2 ) b. F 1 ( A 2 A 1 ) c. F 1 ( A 1 A 2 ) 2 d. F 1 ( A 2 A 1 ) 2 15. An ice cube is placed into a glass which is then filled to the brim. Which of the following explains what will happen to the level of the water when the ice melts and gives a correct explanation why? a. The water level will rise because the ice cube is less dense than the water. b. The water level will remain the same because the displacement necessary to provide the buoyant force on the ice cube matches the volume of water in the ice cube. c. The water level will remain the same because the ice cube and water have the same density. d. The water level will fall because the density of the ice cube is less than that of water. 16. A U-tube manometer is filled partially with water, and then oil is added to one side. Which of the following diagrams best illustrates the resulting configuration of water and oil? Page 3
17. After a practical joke gone wrong, you find yourself in need of a way to lift a whale carcass off of your property. The whale has a mass of 3.4x10 4 kg. In a flash of insight, you remember how hydraulics work, and you set out to build a hydraulic jack. On the whale side, the piston area is to be 1.0 m 2. a. If you can push on the jack with a force of 120 lbs, what piston area must your side have to successfully lift the whale? Neglect whale-tissue deformation, and remember that pressure is transmitted throughout a fluid and is only a function of depth, density, and gravitational acceleration. b. If the fluid in the hydraulic jack is incompressible, and you pushed your side of the jack down by 0.75 m, how much would you raise the whale? c. As gases build up in the whale, a cavity with a volume of 40 m 3 expands in the whale. If the pressure inside reaches an exciting 2x10 5 Pa at 310 K, how many moles of decayed-whale-gas are inside? Are you prepared for this, Erik? inside joke. 18. Jupiter s icy moon Europa is thought to have an ocean as much as 100 km deep under its ice cap. Many scientists see this moon as having great potential to harbor life, and would like to visit the ocean floor to check for hydrothermal vents. You are tasked with designing a submersible which can descend to the dark depths of the ocean (with a crew member). Note that the gravitational acceleration on Europa is 1.315 m/s 2, and the density of the water is likely similar to our own sea water, 1020 kg/m 3. The probe you design can be approximated as a sphere 2.0 m in diameter with a weight of 1460 kg including the crew. a. Issue number #1 is that your submersible needs additional ballast in order to be neutrally buoyant (so it can sink). Determine the mass you must add inside the sphere in order to be neutrally buoyant. b. What is the fluid pressure at the bottom of the ocean your submersible must contend with? c. What is the total force on the outside wall of your craft? d. The implosion of spherical shells is well modeled by the following equation*: P CR = 0.37 Et2 R 2, where E is Young s Modulus for a given material, R is the radius of the shell, and t is the thickness of the shell. If the submersible is built with carbon fiber (E = 90 GPa), how thick does it need to be? Page 4
19. Consider the cross-section of a volcano shown below. The magma chamber is located 1.8 km below the surface, and the magma has a density of 2.5 10 3 kg m3. The absolute pressure in the magma chamber is 70 MPa. a. If the magma chamber is large, we may assume that the fluid velocity in it is negligible (i.e., zero). Determine the velocity of the magma once it reaches the surface where the pressure is atmospheric pressure. Hint: Consider the Bernoulli Equation here. b. Next, using kinematics (or the Bernoulli equation again), determine the maximum height of the magma jet (labeled h in the figure). c. Finally, if the magma is blasted out of a circular vent 75 m in diameter, what is the rate of lava erupted (in kg/s)? Dimensional analysis might be handy. 20. Here s something amazing about the human body. When your heart beats, blood moves through your 1.2 cm diameter aorta at approximately 40 cm/s. Assume the blood has a density of 1000 kg/m 3. Your blood vessels keep branching until they reach the size of capillaries 10 m in radius. These are so narrow that blood cells must pass through them single-file at 0.03 cm/s. a. So, consider conservation of mass, assume all of the blood leaving your aorta passes through capillaries, and determine how many of these capillaries are fed by the blood from your aorta. The absolute pressure in your blood vessels varies, but it is generally about 15 mmhg (2000 Pa) in your jugular vein during a heartbeat. Furthermore, it passes through the jugular vein at 0.35 m/s. Now, this might sound morbid, but it is important for crime scene investigators: if your jugular vein is cut 1.6 m above the ground. b. What would be the velocity of the blood leaving the jugular? Hint: Use good ole Bernoulli. c. Using kinematics, determine how far from the body this jet could spray assuming it leaves your vein horizontally. Page 5
21. Do you remember the heat engine you designed in the last homework assignment? Well, you have shifted the colony to a polar region in order to start producing hydrogen fuel for a return mission, and now the gas in the engine starts at an initial volume, pressure, and temperature of 0.1 m 3, 0.8 kpa, and 60 K, respectively. a. How many moles of Martian air are present in the engine? Next, the fixed amount of gas is heated more than before to 700 K, causing it to expand to 0.2 m 3. b. What is the new pressure of the gas? During the next part of the cycle, the pressure returns to its initial state while the gas is compressed to a volume of 0.15 m 3. c. What is the temperature of the gas at this point? Finally, the gas returns to its initial volume, temperature, and pressure. d. Sketch the P-V diagram and calculate the work done by the engine in one complete cycle. *http://traktoria.org/files/pressure_hull/spherical/buckling_of_spherical_shells.pdf Page 6