A flag will flutter in the wind at a frequency that depends upon the wind speed, the air density, the size of the flag (length and width), gravity, and the "area density" of the cloth (i.e., the mass per unit area). You have a very large flag ( $40 \mathrm{ft}$ long and $30 \mathrm{ft}$ wide) that weighs $240 \mathrm{lb}$, and you want to find the frequency at which it will flutter in a wind of $20 \mathrm{mph}$.

(a) Perform a dimensional analysis to determine an appropriate set of dimensionless groups that could be used to describe this problem.(b) To find the flutter frequency you run a test in a wind tunnel (at normal atmospheric temperature and pressure) using a flag made from a cloth that weighs $0.05 \mathrm{lb} / \mathrm{ft}^{2}$. Determine (1) the size of the flag and the wind speed that you should use in the wind tunnel and (2) the ratio of the flutter frequency of the big flag to that which you observe for the model flag in the wind tunnel.