Question 9.PS.32: A compressor receives air at 290 K, 100 kPa and a shaft work......
A compressor receives air at 290 K, 100 kPa and a shaft work of 5.5 kW from a gasoline engine. It should deliver a mass flow rate of 0.01 kg/s air to a pipeline. Find the maximum possible exit pressure of the compressor.
Step-by-Step
C.V. Compressor, Steady single inlet and exit flows. Adiabatic: \dot{ Q }=0.
Continuity Eq.6.11: \dot{ m }_{ i }=\dot{ m }_{ e }=\dot{ m },
Energy Eq.6.12: \dot{ mh }_{ i }=\dot{ mh }_{ e }+\dot{ W }_{ C } \text {, }
Entropy Eq.9.8: \dot{ ms }_{ i }+\dot{ S }_{ gen }=\dot{ m }s_{ e } \quad\left(\text { Reversible } \dot{ S }_{ gen }=0\right)
\dot{ W }_{ c }=\dot{ m }w_{ c } \Rightarrow- w _{ c }=-\dot{ W } / \dot{ m }=5.5 / 0.01=550 \,kJ / kg
Use Table A.7, h _{ i }=290.43 \,kJ / kg , P _{ r\,i }=0.9899
\begin{aligned}& h _{ e }= h _{ i }+\left(- w _{ c }\right)=290.43+550=840.43 \,kJ / kg \\& A .7 \Rightarrow T _{ e }=816.5 K , P _{ r\,e }=41.717 \\& P _{ e }= P _{ i }\left( P _{ r\,e } / P _{ r\,i }\right)=100 \times(41.717 / 0.9899)= 4 2 1 4 \,k P a\end{aligned}
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