A fluid, with density \(ho\), flows through a cantilevered steel pipe of length \(l\) and cross-sectional area \(A\) (Fig. 3.68). Determine the velocity ( \(v\) ) of the fluid at which instability occurs. Assume that the total mass and the bending stiffness of the pipe are \(m\) and \(E I\), respectively.

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FIGURE 3.68 Fluid flow through a cantilever pipe.