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Question 17.CSGP.76: Air is expanded in a nozzle from 700 kPa, 200°C, to 150 kPa ......

Air is expanded in a nozzle from 700 kPa, 200°C, to 150 kPa in a nozzle having an efficiency of 90%. The mass flow rate is 4 kg/s. Determine the exit area of the nozzle, the exit velocity, and the increase of entropy per kilogram of air. Compare these results with those of a reversible adiabatic nozzle.

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\begin{aligned}& T _{2 s }= T _1\left( P _2 / P _1\right)^{( k -1) / k }=473.2(150 / 700)^{0.286}=304.6 \,K \\& \mathbf{V} _{2 s }^2=2 \times 1000 \times 1.004(473.2-304.6)=338400 \,J / kg \\& \mathbf{V} _2^2=0.9 \times 338400 \Rightarrow \mathbf{V} _2= 5 5 2 ~ m / s\end{aligned}

\begin{aligned}& h _2+ \mathbf{V}_2^2 / 2= h _1 \Rightarrow T _2= T _1- \mathbf{V} _2^2 / 2 C _{ p } \\& T _2=473.2-552^2 /(2 \times 1000 \times 1.004)=321.4 \,K \\& v _2=0.287 \times 321.4 / 150=0.6149 \,m ^3 / kg \\& A _2=4 \times 0.6149 / 552=0.00446 \,m ^2=4460 \,mm ^2\end{aligned}

s _2- s _1=1.0035 \ln \left\lgroup\frac{321.4}{473.2} \right\rgroup -0.287 \ln \left\lgroup\frac{150}{700} \right\rgroup= 0 . 0 5 3 9 ~ k J / k g ~ K

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