ME330_S07_HWSet3B - ME 330 Fluid Mechanics Department of Engineering Western Kentucky University Spring 2007 CHAPTER 3B HW Homework Solutions

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ME 330 Fluid Mechanics Spring 2007 Department of Engineering Western Kentucky University CHAPTER 3B HW - Homework Solutions Problem #’s 3-28, 3- 36, 3-38E, 3-45, 3-46 and 3-63E, Due February 9, 2007 3-28 Solution The air pressure in a tank is measured by an oil manometer. For a given oil-level difference between the two columns, the absolute pressure in the tank is to be determined. Properties The density of oil is given to be ρ = 850 kg/m 3 . Analysis The absolute pressure in the tank is determined from 32 2 1 kPa (98 kPa) (850 kg/m )(9.81 m/s )(0.45m) 1000 N/m 101 75 kPa atm PP g h . =+ ⎛⎞ ⎜⎟ ⎝⎠ =≅ 102 kPa Discussion If a heavier liquid, such as water, were used for the manometer fluid, the column height would be smaller, and thus the reading would be less precise (lower resolution). 3-36 Solution Fresh and seawater flowing in parallel horizontal pipelines are connected to each other by a double U-tube manometer. The pressure difference between the two pipelines is to be determined. Assumptions 1 All the liquids are incompressible. 2 The effect of air column on pressure is negligible. Properties The densities of seawater and mercury are given to be sea = 1035 kg/m 3 and Hg = 13,600 kg/m 3 . We take the density of water to be w =1000 kg/m 3 . Analysis Starting with the pressure in the fresh water pipe (point 1) and moving along the tube by adding (as we go down) or subtracting (as we go up) the gh terms until we reach the sea water pipe (point 2), and setting the result equal to P 2 gives AIR P atm = 98 kPa 0.45 m Fresh water h se h air Sea water Mercury Air h Hg h w
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ME 330 Fluid Mechanics Spring 2007 Department of Engineering Western Kentucky University 2 sea sea air air Hg Hg w 1 P gh gh gh gh P w = + + ρ Rearranging and neglecting the effect of air column on pressure, ) ( sea sea w Hg Hg sea sea Hg Hg w 2 1 h h h g gh gh gh P P w w = + = Substituting, kPa 3.39 = = = 2 2 3
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This homework help was uploaded on 04/19/2008 for the course ME 330 taught by Professor An during the Spring '08 term at Western Kentucky University.

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ME330_S07_HWSet3B - ME 330 Fluid Mechanics Department of Engineering Western Kentucky University Spring 2007 CHAPTER 3B HW Homework Solutions

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