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A cylindrical furnace has height \( H \) and diameter \( D \) both \( 1 \, \text{m} \). It is maintained at temperature \( 360 \, \text{K} \). The air gets heated inside the furnace at constant pressure \( P_a \) and its temperature becomes \( T = 360 \, \text{K} \). The hot air with density \( \rho \) rises up a vertical chimney of diameter \( d = 0.1 \, \text{m} \) and height \( h = 9 \, \text{m} \) above the furnace and exits the chimney (see 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 \( g = 10 \, \text{ms}^{-2} \) and \( \pi = 3.14 \)]
Considering the air flow to be streamline, the steady mass flow rate of air exiting the chimney is ______ \( \text{gm s}^{-1} \).
