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 Archimede’s Principle Fluid Dynamics Bernoulli’s Equation Other Applications of Fluid Dynamics
ANSWERS TO QUESTIONS
Q14.1 Q14.2 The weight depends upon the total volume of glass. The pressure depends only on the depth. Both must be builtthe 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 muchlarger 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 bottlewill simply fill with water and expand until it bursts. Blaise Pascal splintered strong barrels by this method. About 1 000 N: that’s about 250 pounds. 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. 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. 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 saltyocean water is greater than fresh lake water, less ocean water needs to be displaced to enable the ship to float. 411
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 sufficientto support the weight of the ship, and it sinks. Exactly the same. Buoyancy equals density of water times volume displaced. 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 andthe flow weaker from an open faucet. Your fire department likely has a record of the precise elevation of every fire hydrant. As the wind blows over the chimney, it creates a lower pressure at the top of the chimney. The smoke flows from the relatively higher pressure in front of the fireplace to the low pressure outside. Science doesn’t suck; the smoke is pushed from below. The rapidly movingair above the ball exerts less pressure than the atmospheric pressure below the ball. This can give substantial lift to balance the weight of the ball. The ski–jumper gives her body the shape of an airfoil. She deflects downward the air stream as it rushes past and it deflects her upward by Newton’s third law. The air exerts on her a lift force, giving her a higher and longer trajectory. To say itin different words, the pressure on her back is less than the pressure on her front. FIG. Q14.13
The horizontal force exerted by the outside fluid, on an area element of the object’s side wall, has equal magnitude and opposite direction to the horizontal force the fluid exerts on another element diametrically opposite the first. The glass...