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SM_PDF_chapter15

# SM_PDF_chapter15 - Fluid Mechanics CHAPTER OUTLINE 15.1...

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407 Fluid Mechanics CHAPTER OUTLINE 15.1 Pressure 15.2 Variation of Pressure with Depth 15.3 Pressure Measurements 15.4 Buoyant Forces and Archimedes’s Principle 15.5 Fluid Dynamics 15.6 Streamlines and the Continuity Equation for Fluids 15.7 Bernoulli’s Equation 15.8 Other Applications of Fluid Dynamics 15.9 Context Connection A Near Miss Even Before Leaving Southampton ANSWERS TO QUESTIONS Q15.1 The weight depends upon the total volume of glass. The pressure depends only on the depth. Q15.2 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. Q15.2 Q15.3 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 15.4. 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. Q15.4 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. Q15.5 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. Q15.6 Exactly the same. Buoyancy equals density of water times volume displaced.

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408 Fluid Mechanics Q15.7 The buoyant force is a conservative force. It does positive work on an object displaced upward, negative work on an object displaced downward, and zero work on an object displaced through a closed path. Potential energy is associated with it and it is gravitational potential energy of the object-fluid-Earth system. This system possesses extra energy when you hold a tennis ball at the bottom of a pool of water. As the tennis ball bobs up after it is released, the ball can do work in pushing obstacles out of the way. This work is just the work that can be done by the water sinking down to occupy the space vacated by the ball. Q15.8 The rapidly moving air 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. Q15.9 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
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