Question 5.22: Air enters a convergent nozzle from a reservoir at 2200 kPa ...
Air enters a convergent nozzle from a reservoir at 2200 kPa and 100°C. If the exit area is 3.25 cm², what is the maximum mass flow rate that this nozzle can handle ? Assume the process to be isentropic and that the air behaves as an ideal gas. (AMIE Winter, 1998)
For maximum mass flow rate, and γ = 1.4, the pressure at the exit will be critical,
p^{*} = (\frac{2}{γ + 1})^{[γ / (γ – 1)]}p_{0} = (\frac{2}{1.4 + 1})^{(1.4 / 1.4.1)} × p_{0} = 0.528 × 2200
and T^{*} = T_{0} (\frac{p^{*} }{p_{0}}) ^{[ (γ – 1) / γ]}
= (100 + 273) (\frac{1161.6}{2200})^{(0.4 / 1.4)} = 310.78 K
Sonic velocity, C^{*} = \sqrt{γ R T^{*} } = \sqrt{1.4 × 287 × 310.78} = 353.37 m/s
ρ^{*} = \frac{p^{*}}{R T^{*} } = \frac{1161.6}{0.287 × 310.78} = 13.02 kg/m³
\dot{m} = ρ^{*} A_{e} C^{*} = 13.02 × \frac{3.25 }{10^{4}} × 353.37 = 1.495 kg/s
