Question

9.Consider a rigid square plate of 1m side, its left edge being attached to a torsionnal spring of stiffness 10Nm/rad. There isan air flow coming from the right. The equilibrium position of the plate without flow is the horizontal position, asrepresented on the figure. At which velocity (m/s) does the static instability occur?1m1mUC= 10Nm / rad​

Answer 1

Answer:

Here, we have given density of air as 1.225 \frac{kg}{m^3}

m

3

kg

, 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×angle=ρAv

2

×side

10\times 10 \times \frac{\pi}{180}=1.225 \times 1\times v^2 \times0.510×10×

180

π

=1.225×1×v

2

×0.5

v=1.687 m/s is the velocity of air