Air enters an insulated compressor at ambient conditions, 14.7 lbf/in.^2, 70 F, at the rate of 0.1 lbm/s and exits at 400 F. The isentropic efficiency of the compressor is 70%. What is the exit pressure? How much power is required to drive the compressor?

Question

Air enters an insulated compressor at ambient conditions, 14.7 [latex]lbf / in .^{2}[/latex], 70 F, at the rate of 0.1 lbm/s and exits at 400 F. The isentropic efficiency of the compressor is 70%. What is the exit pressure? How much power is required to drive the compressor?

Accepted Answer

C.V. Compressor: [latex]P _{1}, T _{1}, T _{ e }( ext { real }), \eta_{ s COMP }[/latex] known, assume constant [latex]C _{ P 0}[/latex]

Energy Eq.4.13 for real: [latex]- w = C _{ P 0}\left( T _{ e }- T _{ i } ight)=0.24(400-70)=79.2 Btu / lbm[/latex]

Ideal [latex]- w _{ s }=- w imes \eta_{ s }=79.2 imes 0.7=55.4 Btu / lbm[/latex]

Energy Eq.4.13 for ideal:

[latex]55.4= C _{ P 0}\left( T _{ es }- T _{ i } ight)=0.24\left( T _{ es }-530 ight), \quad T _{ es }=761 R[/latex]

Constant entropy for ideal as in Eq.6.23:

[latex]P_{e}=P_{i}\left(T_{e s} / T_{i} ight)^{\frac{k}{k-1}}=14.7(761 / 530)^{3.5}=52.1 lbf / in ^{2}[/latex]

[latex]-\dot{ W }_{ REAL }=\dot{ m }(- w )=0.1 imes 79.2 imes 3600 / 2544= 1 1 . 2 hp[/latex]

......................................

Eq.4.13 : [latex]q+h_{i}+\frac{ V _{i}^{2}}{2}+g Z_{i}=h_{e}+\frac{ V _{e}^{2}}{2}+g Z_{e}+w[/latex]

Eq.6.23 : [latex]\frac{T_{2}}{T_{1}}=\left(\frac{P_{2}}{P_{1}} ight)^{(k-1) / k}[/latex]

Question 7.231E: Air enters an insulated compressor at ambient conditions, 14...

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