Question #123646

Consider a rigid square plate of 1m side, its left edge being attached to a torsional spring of stiffness 10Nm/rad. There is an air flow coming from the right. The equilibrium position of the plate without flow is the horizontal position, as represented on the figure. At which velocity (m/s) does the static instability occur?

Expert's answer

Here, we have given density of air as 1.225 "\\frac{kg}{m^3}" , Torsional stifness= 10 Nm/rad

Here figure attached to this question is below

So here ,

Net torque= Force*perpendicular distance

Torsional stiffness"\\times angle=\\rho A v^2 \\times side"

"10\\times 10 \\times \\frac{\\pi}{180}=1.225 \\times 1\\times v^2 \\times0.5"

v=1.687 m/s is the velocity of air

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