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Problem 4.105

# Problem 4.105 - Problem 4.105[Difficulty 4 CS b c y x a d...

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Problem 4.105 [Difficulty: 4] CS x y a b d c F f Given: Data on flow of boundary layer Find: Plot of velocity profile; force to hold plate Solution: Basic equations: Continuity, and momentum flux in x direction Assumptions: 1) Steady flow 2) Incompressible 3) No net pressure force Given data ρ 750 kg m 3 = w 1 m = U 0 10 m s = L 1 m = δ 5 mm = 0 0.2 0.4 0.6 0.8 1 0.2 0.4 0.6 0.8 1 y δ u y ( ) U 0 From continuity ρ U 0 w δ m bc + 0 δ y ρ u w d + 0 = where m bc is the mass flow rate across bc (Note: sotware cannot render a dot!) Hence m bc 0 δ y ρ U 0 u ( ) w d = For x momentum F f U 0 ρ U 0 w δ ( ) U 0 m bc + 0 δ y u ρ u w d + = 0 δ y U 0 2 u 2 + U 0 U 0 u ( ) + w d = Then the drag force is F f 0 δ y ρ u U 0 u ( ) w d = 0 δ y ρ U 0 2 u U 0 1 u U 0 d =

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