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Question: an incompressible nonviscous fluid rests in the vertical portion length...

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An incompressible, non-viscous fluid rests in the vertical portion (length L) of the elbow-shaped pipe shown in the figure. The Initial Position of the Fluid A Later Position of the Fluid When a valve is open allowing the fluid will flow into the horizontal sec- tion of the pipe, the length r of the horizontal section of fluid satisfies the differential equation x(2L - x) for 0 < | < L, where t is time, g = 9.8 m/s2 is the acceleration due to Earths constant gravity, and ro-0 at t-to-0. You may use the fact hat a.) (10 Points) Solving the resulting ODE obtaining a relationship between t and z b.) (5 Points) Determine (in terms of L and g) an expression for the time t1/2 when half the fluid past through the valve. c.) (5 Points) Determine (in terms of L and g) an expression for the time ti when all the fuid past through the valve.

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