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Unformatted text preview: 14 Fluid Mechanics CHAPTER OUTLINE 14.1 Pressure 14.2 Variation of Pressure with Depth 14.3 Pressure Measurements 14.4 Buoyant Forces and Archimedess Principle 14.5 Fluid Dynamics 14.6 Bernoullis Equation 14.7 Other Applications of Fluid Dynamics ANSWERS TO QUESTIONS *Q14.1 Answer (c). 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. Q14.2 The weight depends upon the total volume of water in the glass. The pressure at the bottom depends only on the depth. With a cylindrical glass, the water pushes only horizontally on the side walls and does not contribute to an extra downward force above that felt by the base. On the other hand, if the glass is wide at the top with a conical shape, the water pushes outward and downward on each bit of side wall. The downward components add up to an extra downward force, more than that exerted on the small base area. Q14.3 The air in your lungs, the blood in your arteries and veins, and the protoplasm in each cell exert nearly the same pressure, so that the wall of your chest can be in equilibrium. Q14.4 Yes. The propulsive force of the f ish on the water causes the scale reading to f luctuate. Its aver- age value will still be equal to the total weight of bucket, water, and f ish. Q14.5 Clap your shoe or wallet over the hole, or a seat cushion, or your hand. Anything that can sustain a force on the order of 100 N is strong enough to cover the hole and greatly slow down the escape of the cabin air. You need not worry about the air rushing out instantly, or about your body being sucked through the hole, or about your blood boiling or your body exploding. If the cabin pres- sure drops a lot, your ears will pop and the saliva in your mouth may boilat body temperature but you will still have a couple of minutes to plug the hole and put on your emergency oxygen mask. Passengers who have been drinking carbonated beverages may f ind that the carbon dioxide suddenly comes out of solution in their stomachs, distending their vests, making them belch, and all but frothing from their ears; so you might warn them of this effect. Q14.6 The boat f loats higher in the ocean than in the inland lake. According to Archimedess 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 f loat. 365 FIG. Q14.1 13794_14_ch14_p365-394.indd 365 13794_14_ch14_p365-394.indd 365 12/2/06 12:29:32 PM 12/2/06 12:29:32 PM 366 Chapter 14 *Q14.7 Answer (b). The apple does not change volume appreciably in a dunking bucket, and the water also keeps constant density. Then the buoyant force is constant at all depths....
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