Problem 4.156 - Problem 4.156 [Difficulty: 3] Given: Data...

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Problem 4.156 [Difficulty: 3] Given: Data on system Find: Jet speed to stop cart after 1 s; plot speed & position; maximum x; time to return to origin Solution: Apply x momentum Assumptions: 1) All changes wrt CV 2) Incompressible flow 3) Atmospheric pressure in jet 4) Uniform flow 5) Constant jet area The given data is ρ 999 kg m 3 = M 100 kg = A 0.01 m 2 = U 0 5 m s = Then a rf M u 1 ρ VU + () A [] u 2 m 2 + u 3 m 3 + = where a rf dU dt = u 1 + = and u 2 u 3 = 0 = Hence dU dt M ρ + 2 A = or dU dt ρ + 2 A M = which leads to dV U + + 2 ρ A M dt = Integrating and using the IC U = U 0 at t = 0 UV 0 + 1 ρ A 0 + M t + + = To find the jet speed V to stop the cart after 1 s, solve the above equation for V , with U = 0 and t = 1 s. (The equation becomes a quadratic in V ). Instead we use Excel 's Goal Seek in the associated workbook From Excel V5 m s = For the position x we need to integrate dx dt U = V 0 + 1 ρ A 0 + M t + + = The result is xV t M ρ A ln 1 ρ A 0 + M t + + = This equation (or the one for U with U = 0) can be easily used to find the maximum value of x by differentiating, as well as the time for x to be zero again. Instead we use Excel 's Goal Seek and Solver in the associated workbook From Excel
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Problem 4.156 - Problem 4.156 [Difficulty: 3] Given: Data...

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