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Unformatted text preview: 57:020 Mechanics of Fluids and Transport Fall 2010 EXAM3 Solutions Problem 1: Hydrostatic Forces on Plane Surface (Chapter 2) Information and assumptions • Circular gate with diameter D = 2 m; R = D /2 = 1 m • Gate orientation = 60 ° • Vertical centroid location h c = 3 m from the water surface • γ = 9.8 kN/m 3 for water • I xc = π R 4 /4 for a circle of radius R Find • Water force acting on the gate F R and the center of pressure y R . Solution (a) Water force: = = ℎ (+3 points) Thus, = 9.8 kN m 3 ¡ (3 m) ¢ 4 (2 m) 2 £ = 92.4 kN (+2 points) (b) Center of pressure: = + where, = ¤ 4 4 = (1 m) 4 4 = 4 m 4 = ℎ cos30 ∘ = 3 m cos30 ∘ = 3.464 m (+4 points) Hence, = 4 m 4 (3.464 m) ¢ 4 (2 m) 2 £ + 3.464 m = 3.536 m (+1 point) 57:020 Mechanics of Fluids and Transport Fall 2010 EXAM3 Solutions Problem 2: Linear Momentum (Chapter 5) Information and assumptions • Mass flow rate ̇ = 25 kg/s • Elbow diameter D = 0.1 m • Pressure at the exit p 2 = p a = 0 (gage) • Elevation change between the in and outlet ∆ z = 0.35 m • = 1000 kg/m 3 for water • The weight of the elbow and the water in it is negligible • Steady, frictionless, and irrotational Find • Velocities at the inlet and outlet, and the inlet pressure, and the anchoring force Solution (a) Continuity equation: 1 = 2 = ̇ = 25 kg s ⁄ (1000 kg m 3 ⁄ ) 4 (0.1 m) 2 ¡ = 3.18 m s ⁄ (+2 points) (b) Bernoulli equation: 1 + 1 2 2 + 1 =...
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This note was uploaded on 12/08/2011 for the course MECHANICS 57:020 taught by Professor Fredrickstern during the Fall '10 term at University of Iowa.
 Fall '10
 FredrickStern
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