3-Practice Problems - Chapter 3 Fluid Statics Problem 3.1...

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Unformatted text preview: Chapter 3 Fluid Statics Problem 3.1 For a lake, g31 nd the depth g107 at which the gage pressure is 1 atmosphere. The speci g31 c weight of water is 62.3 lbf/ft 3 . Solution At the free surface of the lake, pressure will be g115 surface = 1 g61 atm absolute or 0.0 atm gage. At a depth g107 , the pressure will be 1 atm gage. In a static g32 uid of constant density, the piezometric head ( g115g64g16 + g125 ) is constant. Thus g115 surface g16 + g125 surface = 1 atm g16 + ( g125 surface g3 g107 ) (1) 9 10 CHAPTER 3. FLUID STATICS Since g115 surface = 0 atm gage, Eq. (1) becomes g107 = 1 atm g16 = (14 g61 7 lbf/in 2 )(144 in 2 g64 ft 2 ) 62 g61 3 lbf/ft 3 = 34.0 ft Problem 3.2 A tank that is open to the atmosphere contains a 1.0-m layer of oil ( g29 = 800 kg/m 3 ) g32 oating on a 0.5-m layer of water ( g29 = 1000 kg/m 3 ). Determine the pressure at elevations g68 , g69 , g70g62 and g71 . Note that g69 is midway between g68 and g70 . Solution At a horizontal interface of two g32 uids, pressure will be constant across the inter- face. Thus the pressure in the oil at g68 equals the pressure in the air (atmospheric pressure). g115 g68 = g115 g100g119g112 = 0 kPa gage Since the oil layer is a static g32 uid of constant density, the piezometric pressure is constant g115 g68 + g16 g114g108g111 g125 g68 = g115 g69 + g16 g114g108g111 g125 g69 = g115 g70 + g16 g114g108g111 g125 g70 = constant (1) where g125 denotes elevation. Let g125 g68 = 0 g62 g125 g69 = g3 g61 5 m, g125 g70 = g3 1 g61 m. Then, Eq. (1) becomes g115 g68 = g115 g69 + g16 g114g108g111 ( g3 g61 5 m ) = g115 g70 + g16 g114g108g111 ( g3 1 g61 m ) So g115 g69 = g115 g68 + g16 g114g108g111 (0 g61 5 m ) = g115 g100g119g112 + (800) (9 g61 81) (0 g61 5) g64 1000 = 3.92 kPa-gage 11 Similarly g115 g70 = g115 g68 + g16 g114g108g111 (1 g61 m ) = g115 g100g119g112 + (800) (9 g61 81) (1 g61 0) g64 1000 = 7.85 kPa-gage At elevation C, pressure in the oil equals pressure in the water. Since the piezo- metric pressure in the water is constant, we can write g115 g70 + g16 g122g100g119g104g117 g125 g70 = g115 g71 + g16 g122g100g119g104g117...
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This note was uploaded on 01/07/2012 for the course ENGINEERIN 101 taught by Professor Johnw.walder during the Spring '11 term at American Public University.

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3-Practice Problems - Chapter 3 Fluid Statics Problem 3.1...

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