Problem 4.60[Difficulty: 3]Given:Data on flow at inlet and outlet of pipeFind: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−π⋅R2⋅()⋅=mfx1ρπ⋅U2⋅R2⋅=Hencemfx20Rrρu2⋅2⋅π⋅r⋅⌠⎮⌡d=2ρ⋅π⋅umax2⋅0Rrr1rR⎛⎝⎞⎠2−⎡⎢⎣⎤⎥⎦2⋅⌠⎮⎮⎮⌡d⋅=2ρ⋅π⋅umax2⋅0Ryr2r3R2⋅−r5R4+⎛⎜⎝⎞⎠⌠⎮⎮⎮⌡d⋅=mfx22ρ⋅π⋅umax2⋅R22R22−R26+⎛⎜⎝⎞⎠⋅=⋅umax2⋅R23⋅=Then the ratio of momentum fluxes ismfx2mfx113ρ⋅π⋅umax
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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.