Problem 4.101 - Problem 4.101 Given: Data on flow in 2D...

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Problem 4.101 [Difficulty: 3] CS x c y 2 h d Given: Data on flow in 2D channel Find: Maximum velocity; Pressure drop Solution: Basic equations: Continuity, and momentum flux in x direction Assumptions: 1) Steady flow 2) Neglect friction Given data w2 5 m m = h5 0 m m = Q 0.025 m 3 s = ρ 750 kg m 3 = From continuity QU 1 2 h w = U 1 Q 2w h = U 1 10.0 m s = Also ρ U 1 A 1 A ρ u 2 d + 0 = U 1 2 h w w h h y u max 1 y 2 h 2 d = wu max hh () [] h 3 h 3 = max 4 3 h = Hence u max 3 2 U 1 = u max 15 m s = For x momentum p 1 A p 2 A V 1 ρ 1 V 1 A A 2 ρ 2 u 2 u 2 d + = Note that there is no R x (no friction) p 1 p 2
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