An uninsulated compressor delivers ethylene, C2H4, to a pipe, D = 10 cm, at 10.24 MPa, 94°C and velocity 30 m/s. The ethylene enters the compressor at 6.4 MPa, 20.5°C and the work input required is 300 kJ/kg. Find the mass flow rate, the total heat transfer and entropy generation, assuming the

Question

An uninsulated compressor delivers ethylene, [latex]C _{2} H _{4}[/latex], to a pipe, D = 10 cm, at 10.24 MPa, 94°C and velocity 30 m/s. The ethylene enters the compressor at 6.4 MPa, 20.5°C and the work input required is 300 kJ/kg. Find the mass flow rate, the total heat transfer and entropy generation, assuming the surroundings are at 25°C.

Accepted Answer

[latex]T _{ ri }=\frac{293.7}{282.4}=1.040, P _{ ri }=\frac{6.4}{5.04}=1.270[/latex]

From D.2 and D.3,

[latex]\begin{aligned}&\left( h _{ i }^{*}- h _{ i } ight)=0.29637 imes 282.4 imes 2.65=221.8 kJ / kg \&\left( s _{ i }^{*}- s _{ i } ight)=0.29637 imes 2.08=0.6164 kJ / kg K\end{aligned}[/latex]

[latex]T _{ re }=\frac{367.2}{282.4}=1.30, P _{ re }=\frac{10.24}{5.04}=2.032 \Rightarrow[/latex] From D.1: [latex]Z _{ e }[/latex] = 0.69

[latex]v _{ e }=\frac{ Z _{ e } RT _{ e }}{ P _{ e }}=\frac{0.69 imes 0.29637 imes 367.2}{10240}=0.0073 m ^{3} / kg[/latex]

[latex]A_{e}=\frac{\pi}{4} D_{e}^{2}=0.00785 m ^{2} \Rightarrow \quad \dot{m}=\frac{A_{e} V_{e}}{v_{e}}=\frac{0.00785 imes 30}{0.0073}=32.26 kg / s[/latex]

From D.2 and D.3,

[latex]\begin{aligned}&\left( h _{ e }^{*} -h _{ e } ight)=0.29637 imes 282.4 imes 1.6=133.9 kJ / kg \&\left( s _{ e }^{*}- s _{ e } ight)=0.29637 imes 0.90=0.2667 kJ / kg K \&\left( h _{ e }^{*}- h _{ i }^{*} ight)=1.5482(367.2-293.7)=113.8\end{aligned}[/latex]

[latex]\begin{aligned}&\left( s _{ e }^{*}- s _{ i }^{*} ight)=1.5482 \ln \frac{367.2}{293.7}-0.29637 \ln \frac{10.24}{6.4}=0.2065 \&\left( h _{ e }- h _{ i } ight)=-133.9+113.8+221.8=201.7 kJ / kg \&\left( s _{ e }- s _{ i } ight)=-0.2667+0.2065+0.6164=0.5562 kJ / kg K\end{aligned}[/latex]

Energy Eq.:

[latex]\begin{aligned}& q =\left( h _{ e }- h _{ i } ight)+ KE _{ e }+ w =201.7+\frac{30^{2}}{2 imes 1000}-300=-97.9 kJ / kg \&\dot{ Q }_{ cv }=\dot{ m } q =32.26(-97.9)=- 3 1 5 8 k W \&\dot{ S }_{ gen }=-\frac{\dot{ Q }_{ cv }}{ T _{ o }}+\dot{ m }\left( s _{ e }- s _{ i } ight)=+\frac{3158}{298.2}+32.26(0.5562)= 2 8 . 5 3 k W / K\end{aligned}[/latex]

Question 12.118: An uninsulated compressor delivers ethylene, C2H4, to a pipe...

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