A factory is using the piping system of Figure P4.37 to discharge environmentally safe waste-water into a small river. The velocity of the river is estimated as \(5.5 \mathrm{~m} / \mathrm{s}\). Determine the allowable values of \(l\) such that the amplitude of torsional oscillations of the vertical pipe due to vortex shedding is less than \(1^{\circ}\). Assume the vertical pipe is rigid and rotates about an axis perpendicular to the page through the elbow. The horizontal pipe is restrained from rotation at the river bank. Assume a damping ratio of 0.05 .

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Fresh water 20C T Pim 1 m 3 m Steel pipes: G=80 10" N/m p- 7800 kg/m Dinner 14 cm 1=1 cm (pipe thickness) FIGURE P4.37 v = 5.5 m/s