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Unformatted text preview: ME 330 Fluid Mechanics Spring 2007 Department of Engineering Western Kentucky University CHAPTER 5D HW  Homework Solutions Problem #s 539, 540 and 541, Due March 5, 2007 539 Solution A water pipe bursts as a result of freezing, and water shoots up into the air a certain height. The gage pressure of water in the pipe is to be determined. Assumptions 1 The flow is steady, incompressible, and irrotational with negligible frictional effects (so that the Bernoulli equation is applicable). 2 The water pressure in the pipe at the burst section is equal to the water main pressure. 3 Friction between the water and air is negligible. 4 The irreversibilities that may occur at the burst section of the pipe due to abrupt expansion are negligible. Properties We take the density of water to be 1000 kg/m 3 . Analysis This problem involves the conversion of flow, kinetic, and potential energies to each other without involving any pumps, turbines, and wasteful components with large frictional losses, and thus it is suitable for the use of the Bernoulli equation. The water height will be maximum under the stated assumptions. The velocity inside the hose is relatively low ( V 1 0) and we take the burst section of the pipe as the reference level ( z 1 = 0). At the top of the water trajectory V 2 = 0, and atmospheric pressure pertains. Then the Bernoulli equation simplifies to...
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