A cylindrical furnace has height (H) and diameter (D) both 1 m. It is maintained at temperature 360 K. The air gets heated inside the furnace at constant pressure P_a and its temperature becomes T=360 K. The hot air with density  $\rho$ rises up a vertical chimney of diameter d=0.1 m and height h=9 m above the furnace and exits the chimney (see the figure). As a result, atmospheric air of density ${\mathrm{\rho }}_{\mathrm{a}}=1.2{\mathrm{kgm}}^{-3}$ ,pressure P_a and temperature T_a=300 K enters the furnace. Assume air as an ideal gas, neglect the variations in  and T inside the chimney and the furnace. Also ignore the viscous effects.
[Given: The acceleration due to gravity g=10 m s^-2 and  $\mathrm{\pi }=3.14$]