14.1 14.2 14.3 14.4 14.5 14.6 14.7 Pressure Variation of Pressure with Depth Pressure Measurements Buoyant Forces and Archimedes’s Principle Fluid Dynamics Bernoulli’s Equation 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 watertimes the area of the dam. If both reservoirs are equally deep, the force is the same.
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 otherhand, 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. 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 inequilibrium. Yes. The propulsive force of the f ish on the water causes the scale reading to f luctuate. Its average value will still be equal to the total weight of bucket, water, and f ish. 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 cabinair. 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 pressure drops a lot, your ears will pop and the saliva in your mouth may boil—at body temperature— but you will still have a couple of minutes to plug the hole and put on your emergency oxygen mask. Passengers who havebeen 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. The boat f loats 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 weightof 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.
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*Q14.7 Answer (b). The apple does not change volume appreciably in a dunking bucket, and thewater also keeps constant density. Then the buoyant force is constant at all depths. Q14.8 The horizontal force exerted by the outside f luid, on an area element of the object’s side wall, has equal magnitude and opposite direction to the horizontal force the f luid exerts on another element diametrically opposite the f irst. No. The somewhat lighter barge will f loat higher in the water.
Q14.9Q14.10 The metal is more dense than water. If the metal is sufficiently thin, it can float like a ship, with the lip of the dish above the water line. Most of the volume below the water line is f illed with air. The mass of the dish divided by the volume of the part below the water line is just equal to the density of water. Placing a bar of soap into this space to replace the air raises theaverage density of the compound object and the density can become greater than that of water. The dish sinks with its cargo. *Q14.11 Answer (c). The water keeps nearly constant density as it increases in pressure with depth. The beach ball is compressed to smaller volume as you take it deeper, so the buoyant force decreases. Q14.12 Like the ball, the balloon will remain in front of you. It will not...