Problem 4.59[Difficulty: 3]CS x cy 2h dGiven:Data on flow at inlet and outlet of channelFind:Ratio of outlet to inlet momentum fluxSolution:∫⋅=AxdAVurρmfBasic equation: Momentum flux in x direction at a sectionAssumptions: 1) Steady flow 2) Incompressible flowEvaluating at 1 and 2mfx1Uρ⋅U−2⋅h⋅()⋅w⋅=mfx12ρ⋅w⋅U2⋅h⋅=Hencemfx2h−hyρu2⋅w⋅⌠⎮⌡d=ρw⋅umax2⋅h−hy1yh⎛⎝⎞⎠2−⎡⎢⎣⎤⎥⎦2⌠⎮⎮⎮⌡d⋅=ρw⋅umax2⋅h−hy12yh⎛⎝⎞⎠2⋅−yh⎛⎝⎞⎠4+⎡⎢⎣⎤⎥⎦⌠⎮⎮⎮⌡d⋅=mfx2ρw⋅umax2⋅2h⋅43h⋅−25h⋅+⎛⎝⎞⎠⋅=ρw⋅umax2⋅1615⋅h⋅=Then the ratio of momentum fluxes ismfx2mfx11615
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This note was uploaded on 10/19/2011 for the course EGN 3353C taught by Professor Lear during the Fall '07 term at University of Florida.