Chapter 14

# Chapter 14 - 14 Fluid Mechanics CHAPTER OUTLINE 14.1 14.2...

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14 CHAPTER OUTLINE 14.1 Pressure 14.2 Variation of Pressure with Depth 14.3 Pressure Measurements 14.4 Buoyant Forces and Archimede’s Principle 14.5 Fluid Dynamics 14.6 Bernoulli’s Equation 14.7 Other Applications of Fluid Dynamics Fluid Mechanics ANSWERS TO QUESTIONS Q14.1 The weight depends upon the total volume of glass. The pressure depends only on the depth. Q14.2 Both must be built the same. The force on the back of each dam is the average pressure of the water times the area of the dam. If both reservoirs are equally deep, the force is the same. FIG. Q14.2 Q14.3 If the tube were to fill up to the height of several stories of the building, the pressure at the bottom of the depth of the tube of fluid would be very large according to Equation 14.4. This pressure is much larger than that originally exerted by inward elastic forces of the rubber on the water. As a result, water is pushed into the bottle from the tube. As more water is added to the tube, more water continues to enter the bottle, stretching it thin. For a typical bottle, the pressure at the bottom of the tube can become greater than the pressure at which the rubber material will rupture, so the bottle will simply fill with water and expand until it bursts. Blaise Pascal splintered strong barrels by this method. Q14.4 About 1 000 N: that’s about 250 pounds. Q14.5 The submarine would stop if the density of the surrounding water became the same as the average density of the submarine. Unfortunately, because the water is almost incompressible, this will be much deeper than the crush depth of the submarine. Q14.6 Yes. The propulsive force of the fish on the water causes the scale reading to fluctuate. Its average value will still be equal to the total weight of bucket, water, and fish. Q14.7 The boat floats higher in the ocean than in the inland lake. According to Archimedes’s principle, the magnitude of buoyant force on the ship is equal to the weight of the water displaced by the ship. Because the density of salty ocean water is greater than fresh lake water, less ocean water needs to be displaced to enable the ship to float. 411

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412 Fluid Mechanics Q14.8 In the ocean, the ship floats due to the buoyant force from salt water . Salt water is denser than fresh water. As the ship is pulled up the river, the buoyant force from the fresh water in the river is not sufficient to support the weight of the ship, and it sinks. Q14.9 Exactly the same. Buoyancy equals density of water times volume displaced. Q14.10 At lower elevation the water pressure is greater because pressure increases with increasing depth below the water surface in the reservoir (or water tower). The penthouse apartment is not so far below the water surface. The pressure behind a closed faucet is weaker there and the flow weaker from an open faucet. Your fire department likely has a record of the precise elevation of every fire hydrant.
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