Air enters a $5 \mathrm{~cm} \times 5 \mathrm{~cm}$ smooth, insulated square duct with a velocity of $900 \mathrm{~m} / \mathrm{s}$, and a static temperature of $300 \mathrm{~K}$. If the duct length is $2 \mathrm{~m}$, determine the flow conditions at the exit. Use Colebrook's formula to calculate the friction factor.