Exam 13: Fluids

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A barge with vertical sides is 10 m wide and 60 m long and is floating in fresh water of density 1000 kg/m3. How much deeper into the water does the barge sink when 3.0 x 105 kg of coal are loaded on the barge?

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A steel ball sinks in water but floats in a pool of mercury, which is much denser than water. Where is the buoyant force on the ball greater?

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A person weighing 900 N is standing on snowshoes. Each snowshoe has area 2500 cm2 and has negligible weight. What pressure does this person's weight exert on the snow?

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The Tonga Trench in the Pacific Ocean is 36,000 feet deep. Assuming that sea water has an average density of 1.04 g/cm3, calculate the absolute (total) pressure at the bottom of the trench in atmospheres. (1.00 in = 2.54 cm, 1.00 atm = 1.01 × 105 Pa)

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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?

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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 = ΔVΔt\frac { \Delta V } { \Delta t } , what is the flow rate in pipe B?

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A block of metal weighs 40 N in air and 30 N in water. What is the buoyant force on the block due to the water? The density of water is 1000 kg/m3.

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An object floats with half its volume beneath the surface of the water. The weight of the displaced water is 2000 N. What is the weight of the object? The density of water is 1000 kg/m3.

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A hollow steel ball of diameter 3.0 m just barely floats in water. What is the wall thickness of the ball? (ρFe = 7.87 g/cm3, ρwater = 1.00 g/cm3)

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A 13,000-N vehicle is to be lifted by a 25-cm diameter hydraulic piston. What force needs to be applied to a 5.0 cm diameter piston to accomplish this? Assume the pistons each have negligible weight.

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An object weighs 7.84 N when it is in air and 6.86 N when it is immersed in water of density 1000 kg/m3. What is the density of the object?

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A cubical block of stone is lowered at a steady rate into the ocean by a crane, always keeping the top and bottom faces horizontal. Which one of the following graphs best describes the buoyant force B on this block as a function of time t if the block just enters the water at time t = 0 s?

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A pressurized cylindrical tank, 5.0 m in diameter, contains water that emerges from the pipe at point C with a speed of 84 m/s84 \mathrm {~m} / \mathrm { s } as shown in the figure. Point A is 10 m above point B and point C is 3.0 m above point B. The area of the pipe at point B is 0.080 m20.080 \mathrm {~m} ^ { 2 } and the pipe narrows to an area of 0.070 m20.070 \mathrm {~m} ^ { 2 } at point C. Assume that the water is an ideal fluid in laminar flow. The density of water is 1000 kg/m3. The rate at which the water level is falling in the tank is closest to  A pressurized cylindrical tank, 5.0 m in diameter, contains water that emerges from the pipe at point C with a speed of  84 \mathrm {~m} / \mathrm { s }  as shown in the figure. Point A is 10 m above point B and point C is 3.0 m above point B. The area of the pipe at point B is  0.080 \mathrm {~m} ^ { 2 }  and the pipe narrows to an area of  0.070 \mathrm {~m} ^ { 2 }  at point C. Assume that the water is an ideal fluid in laminar flow. The density of water is 1000 kg/m<sup>3</sup>. The rate at which the water level is falling in the tank is closest to

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

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A 500-N weight sits on the small piston of a hydraulic machine. The small piston has an area of 2.0 cm2. If the large piston has an area of 40 cm2, how much weight can the large piston support? Assume the pistons each have negligible weight.

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When a box rests on a round sheet of wood on the ground, it exerts an average pressure p on the wood. If the wood is replaced by a sheet that has half the diameter of the original piece, what is the new average pressure?

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Ideal incompressible fluid flows through a 4.0-cm-diameter pipe at 1.0 m/s. There is a 2.0 cm diameter constriction in the line. What is the speed of the fluid in this constriction?

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Two horizontal pipes have the same diameter, but pipe B is twice as long as 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 B is Q = ΔVΔt\frac { \Delta V } { \Delta t } what is the flow rate in pipe A?

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Water flows through a horizontal pipe of cross-sectional area 10.0 cm2 at a pressure of 0.250 atm with a flow rate is 1.00 L/s. At a valve, the effective cross-sectional area of the pipe is reduced to 5.00 cm2. What is the pressure at the valve? The density of water is 1000 kg/m3, and treat it as an ideal incompressible fluid.

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A solid object floats in water with three-fourths of its volume beneath the surface. What is the object's density? The density of water is 1000 kg/m3.

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