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Exam1_2010_solution - 57:020 Mechanics of Fluids and...

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57:020 Mechanics of Fluids and Transport Fall 2009 EXAM1 Solutions Problem 1: Shear stress (Chapter 1) Information and assumptions 𝑢𝑢 𝑈𝑈 = 2 𝑦𝑦 𝑦𝑦 2 2 𝜇𝜇 = 1.12 × 10 -3 N s/m 2 U = 2 m/s h = 0.1 m Find shearing stress that the water exerts on the fixed surface Solution 𝜏𝜏 = 𝜇𝜇 𝑑𝑑𝑢𝑢 𝑑𝑑𝑦𝑦 (+4 points) where 𝑑𝑑𝑢𝑢 𝑑𝑑𝑦𝑦 = 2 𝑈𝑈 1 𝑦𝑦 (+3 points) At the fixed surface ( 𝑦𝑦 = 0) 𝑑𝑑𝑢𝑢 𝑑𝑑𝑦𝑦 𝑦𝑦 =0 = 2 𝑈𝑈 (+1 point) So that 𝜏𝜏 = 𝜇𝜇 � 2 𝑈𝑈 = 1.12 × 10 3 N s m 2 (2) 2 m s (0.1 m) = 𝟒𝟒 . 𝟒𝟒𝟒𝟒 × 𝟏𝟏𝟏𝟏 −𝟐𝟐 𝐍𝐍 𝐦𝐦 𝟐𝟐 (+2 points)
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57:020 Mechanics of Fluids and Transport Fall 2009 EXAM1 Solutions Problem 2: Hydrostatic force (Chapter 2) Information and assumptions 𝛾𝛾 = 9790 N/m 3 A quarter-circle 50 m wide dam Water depth = 20 m Find
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