Problem 4.176

# Problem 4.176 - Problem 4.176[Difficulty 4 CS at speed V y...

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Problem 4.176 [Difficulty: 4] y x CS at speed V V e Y X Given: Data on rocket Find: Maximum speed and height; Plot of speed and distance 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 MM 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 = Hence 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 VV e ln M 0 m rate t ln M 0 gt = V e ln 1 m rate t M 0 = e ln 1 m rate t M 0 = for tt b (burn time) (1) To evaluate at t b = 1.7 s, we need V e and m rate m rate m f t b = m rate 12.5 gm 1.7 s = m rate 7.35

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Problem 4.176 - Problem 4.176[Difficulty 4 CS at speed V y...

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