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Problem 4.170

# Problem 4.170 - Problem 4.170[Difficulty 3 CS at speed V y...

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Problem 4.170 [Difficulty: 3] y x CS at speed V V e Y X Given: Data on rocket Find: Speed after 5 s; Maximum velocity; Plot of speed versus time Solution: Basic equation: Momentum flux in y direction Assumptions: 1) No resistance 2) p e = p atm 3) Uniform flow 4) Use relative velocities 5) Constant mass flow rate From continuity dM dt m rate = constant = so M M 0 m rate t = (Note: Software cannot render a dot!) Hence from momentum M g a rfy M u e ρ e V e A e ( ) = V e m rate = or a rfy dV dt = V e m rate M g = V e m rate M 0 m rate t g = Separating variables dV V e m rate M 0 m rate t g dt = Integrating from V = at t = 0 to V = V at t = t V V e ln M 0 m rate t
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