Question

Air enters a nozzle steadily at 280 kPa and 77°C with a velocity of 50 m/s and exits at 85 kPa and 320 m/s. The heat losses from the nozzle to the surroundings medium at 20°C are estimated to be 3.2 kJ/kg. Determine (a) the exit temperature and (b) the entropy generation for this process. Assume that the air has variable specific heats.

Answer 1

The input values are the following

`\left.T_(1)=350 K\right\ then`

`h_(1)=350.49 (k j)/(k g), s_(1)=1.85708 (K j)/(K g \cdot K)`

By using the energy equilibrium

`\dot{E}_(i n)-\dot{E}_(o u t)=\Delta \dot{E}_(s y s t e m)=0` ,
`\dot{E}_(i n)=\dot{E}_(o u t)`

we have
`T_(2)=297.2 K`

eq (1)
`\dot{m}\left(h_(1)+(V_(1)^(2))/(2)\right)=\dot{m}\left(h_(2)+(V_(2)^(2))/(2)\right)+\dot{Q}_(o u t)` ∴

`0=q+h_(2)-h_(1)+(V_(2)^(2)-V_(1)^(2))/(2)`

Now, for specific energy h2:

`h_(2)=h_(1)-q_(o u t)-(V_(2)^(2)-V_(1)^(2))/(2)`

By replacing the eq (1) we have

`h_(2)=350.49 (k j)/(k g)-3.2-(\left(320 (m)/(s)\right)^(2)-\left(50 (m)/(m)\right)^(2))/(2)\left((1 (k j)/(k g))/(1000 (m^(2))/(s^(2)))\right)`

`h_(2)=297.34 (k j)/(k g)`

By using a standard ideal-gas properties of air we have

`T_(2)=297.2 K`