What is the maximum work that can be obtained from steam at 2 MPa and 700°C that is flowing continuously at 5 m/sec in a pipe that is 5 m above ground level?

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Accepted Answer

Using the steam tables

[latex] ext { At } 2 MPa ext { and } 700^{\circ} C : \hat{H}=3071.8 kJ / kg , \hat{S}=7.8926 kJ / kg \cdot K[/latex] , so that [latex]\hat{ B }=3071.8-298.15 imes 7.8926=718.62 kJ / kg[/latex] and at 0.10135 MPa and 25°C

[latex]\hat{H}=104.89 kJ / kg , \hat{S}=0.3674 kJ / kg \cdot K[/latex] , so that [latex]\hat{ B }=104.89-298.15 imes 0.3674=[/latex] -4.65 kJ/kg

So that

[latex]\begin{aligned}\frac{\dot{W}_{s, \max }}{\dot{M}_{1}} &=\hat{ B }\left(T_{ amb }, P_{ amb } ight)-\hat{ B }\left(T_{1}, P_{1} ight)-\frac{1}{2} \upsilon _{1}^{2}-g h_{1}=\&=((-4.65)-718.62) \frac{ kJ }{ kg }-\frac{25 \frac{ m ^{2}}{ s ^{2}} imes \frac{ J / kg }{ m ^{2} / s ^{2}}}{2 \cdot 1000 \frac{ J }{ kJ }}-5 m imes 9.8 \frac{ m }{ s ^{2}} imes \frac{\frac{ J / kg }{ m ^{2} / s ^{2}}}{1000 \frac{ J }{ kJ }} \&=-723.27-0.01-0.049 \frac{ kJ }{ kg }=-723.77 \frac{ kJ }{ kg }\end{aligned}[/latex]

where the minus sign indicates work done by the maximum shaft work that could be done by system on the surroundings. We see that the maximum useful shaft work that can be obtained from this flowing stream is 723.77 kJ/kg, and that the kinetic and potential energy terms, that is the terms due to the stream velocity and the initial stream height, contribute very little (0.059 kJ/kg) to the maximum work that can be obtained. This is generally the case if there is a significant difference between the entering fluid and the ambient temperature.

Question 4.6-1: What is the maximum work that can be obtained from steam at ...

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