Homework 1 Solutions

# Homework 1 Solutions - Problem 2.2 Given Velocity fields...

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Problem 2.2 [Difficulty: 1] Given: Velocity fields Find: Whether flows are 1, 2 or 3D, steady or unsteady. Solution: (1) V V y ( ) = 1D V V t ( ) = Unsteady (2) V V x ( ) = 1D V V t ( ) Steady (3) V V x y , ( ) = 2D V V t ( ) = Unsteady (4) V V x y , ( ) = 2D V V t ( ) = Unsteady (5) V V x ( ) = 1D V V t ( ) = Unsteady (6) V V x y , z , ( ) = 3D V V t ( ) Steady (7) V V x y , ( ) = 2D V V t ( ) = Unsteady (8) V V x y , z , ( ) = 3D V V t ( ) Steady

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Problem 2.40 [Difficulty: 2] Given: Velocity distribution between flat plates Find: Shear stress on upper plate; Sketch stress distribution Solution: Basic equation τ yx μ du dy = du dy d dy u max 1 2 y h 2 = u max 4 h 2 2 y = 8 u max y h 2 = τ yx 8 μ u max y h 2 = At the upper surface y h 2 = and h 0.1 mm = u max 0.1 m s = μ 1.14 10 3 × N s m 2 = (Table A.8) Hence τ yx 8 1.14 × 10 3 × N s m 2 0.1 × m s 0.1
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