JEE Advanced 2023 Physics question on Properties of Matter

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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 $\rho_a = 1.2\text{ kg m}^{-3}$, pressure $P_a$ and temperature $T_a = 300\text{ K}$ enters the furnace. Assume air as an ideal gas, neglect the variations in $\rho$ and $T$ inside the chimney and the furnace. Also ignore the viscous effects.

[Given: The acceleration due to gravity $g = 10\text{ m s}^{-2}$ and $\pi = 3.14$]

Considering the air flow to be streamline, the steady mass flow rate of air exiting the chimney is _______ $\text{gm s}^{-1}$.