Measuring Steam Quality
A supply line carries a two-phase liquid–vapor mixture of steam at 300 lbf / in .^{2} A small fraction of the flow in the line is diverted through a throttling calorimeter and exhausted to the atmosphere at 14.7 lbf / in .^{2} The temperature of the exhaust steam is measured as 250°F. Determine the quality of the steam in the supply line.
Known Steam is diverted from a supply line through a throttling calorimeter and exhausted to the atmosphere.
Find Determine the quality of the steam in the supply line.
Schematic and Given Data:
Engineering Model
1. The control volume shown on the accompanying figure is at steady state.
2. The diverted steam undergoes a throttling process.
Analysis For a throttling process, the energy and mass balances reduce to give h_{2}=h_{1}, which agrees with Eq. 4.22. Thus, with state 2 fixed, the specific enthalpy in the supply line is known, and state 1 is fixed by the known values of p_{1} \text { and } h_{1}.
h_{2}=h_{1} \quad\left(p_{2}<p_{1}\right) (4.22)
1 As shown on the accompanying p–v diagram, state 1 is in the two-phase liquid–vapor region and state 2 is in the superheated vapor region. Thus,
h_{2}=h_{1}=h_{ f 1}+x_{1}\left(h_{ g 1}-h_{ f 1}\right)
Solving for x_{1},
x_{1}=\frac{h_{2}-h_{ f 1}}{h_{ g 1}-h_{ f 1}}
From Table A-3E at 300 \text { lbf/in. }^{2}, h_{ fl }=394.1 Btu / lb \text { and } h_{ g 1}=1203.9 Btu / lb \text { . At } 14.7 lbf / in .{ }^{2} \text { and } 250^{\circ} F , h_{2}=1168.8 Btu/lb from Table A-4E. Inserting values into the above expression, the quality of the steam in the line is x_{1}=0.957(95.7 \%).
1 For throttling calorimeters exhausting to the atmosphere, the
quality of the steam in the line must be greater than about 94% to ensure that the steam leaving the calorimeter is superheated.
Skills Developed
Ability to…
• apply Eq. 4.22 for a throttling process.
• retrieve property data for water.
Quick Quiz
If the supply line carried saturated vapor at 300 \text { lbf/in.}^{2}, determine the temperature at the calorimeter exit, in °F, for the same exit pressure, 14.7 \text { lbf/in.}^{2} Ans. 324°F.
