Question

PARAGRAPH "II" 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 𝑃𝑎 and its temperature becomes 𝑇 = 360 𝐾. The hot air with density 𝜌 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 𝜌𝑎 = 1.2 kg m−3, pressure 𝑃𝑎 and temperature 𝑇𝑎 = 300 K enters the furnace. Assume air as an ideal gas, neglect the variations in 𝜌 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 𝜋 = 3.14] Considering the air flow to be streamline, the steady mass flow rate of air exiting the chimney is _______ gm s−1.

Answer 1

Let $v'$be the speed of air in the chimney.
⇒ By continuity equation,
πD2 . $v$ = , πd2 . $v'$
⇒ $v'$ = 100$v$ = 1000 m/s Also, pressure difference △p
= ρ$v'$2 . area
= 7850 N/m2