A tank fitted with a convergent nozzle contains air at a temperature of 20°C. The diameter at the outlet of the nozzle is 25 mm. Assuming adiabatic flow, find the mass rate of flow of air through the nozzle to the atmosphere when the pressure in the tank is :

(i) 140 kN/m2 (abs.),

(ii) 300 kN/m2

Solution:

Temperature of air in the tank, $ T_{1}=20+273=293 \mathrm{~K} \\ $

Diameter at the outlet of the nozzle, $ D_{2}=25 \mathrm{~mm}=0.025 \mathrm{~m} \\ $

Area, $\quad A_{2}=\pi / 4 \times 0.025^{2}=0.0004908 \mathrm{~m}^{2} \\ $

$ R=287 \mathrm{~J} / \mathrm{kg} \mathrm{K}, \gamma=1.4 \\ $

(i) Mass rate of flow of …