Problem 4.170[Difficulty: 3]y x CSat speed V VeY X Given:Data on rocketFind:Speed after 5 s; Maximum velocity; Plot of speed versus timeSolution:Basic equation: Momentum flux in y directionAssumptions: 1) No resistance 2) pe= patm3) Uniform flow 4) Use relative velocities 5) Constant mass flow rateFrom continuitydMdtmrate=constant=soMM0mratet⋅−=(Note: Software cannot render a dot!)Hence from momentumM−g⋅arfyM⋅−ueρeVe⋅Ae⋅()⋅=Ve−mrate⋅=orarfydVdt=Vemrate⋅Mg−=Vemrate⋅M0mratet⋅−g−=Separating variablesdVVemrate⋅M0mratet⋅−g−⎛⎜⎝⎞⎠dt⋅=Integrating from V = at t = 0 to V = V at t = tVVe−ln M
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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.