$(20$ points$)$ You are designing an experiment to test a scale model of a private jet in a

wind tunnel. At cruise conditions, this jet flies at a speed of $200\frac{m}{s}.$ The density at the

cruise altitude is $0\mathrm{.}4k\frac{g}{m^3}$ and the temperature is $220$ K $.$ The temperature of the air in

your wind tunnel set up is fixed at $260$ K $,$ but you are working with a variable density

wind tunnel, so you can adjust the air density in the wind tunnel. You can set your

density to any value between $1k\frac{g}{m^3}$ and $10k\frac{g}{m^3}.$ If $c_m$ is the chord length of the wing

on the model and $c_p$ is the chord length of the wing on the real jet, determine the

minimum model scale $($minimum $\frac{c_m}{c_p})$ you can use in this wind tunnel to achieve flow

similarity.

Assume that air viscosity and speed of sound both are proportional to $T^{\frac{1}{2}}.$