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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 1.0m layer of oil ( g29 = 800 kg/m 3 ) g32 oating on a 0.5m 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 kPagage 11 Similarly g115 g70 = g115 g68 + g16 g114g108g111 (1 g61 m ) = g115 g100g119g112 + (800) (9 g61 81) (1 g61 0) g64 1000 = 7.85 kPagage 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.
 Spring '11
 JohnW.Walder
 Statics

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