3. (30) Steam at 5 bar and 300 C flows through a valve at a mass flaw rate of 15

Question

3. (30) Steam at 5 bar and 300 C flows through a valve at a mass flaw rate of 150 kg/hr and exits at a pressure of 1 bar. Because the valve is not insulated, heat is lost at a rate of 90,000 kJ/hr. (10 bar 1 MPa) (i Determine the exit stream temperature (c). (i) Specify the phase of the outlet slream (e.g. superheated vapor, saturated vapor, or a vaporliquid mixture). If the stream in a 2-phasc mixture, estimate the quality (ii If the valve is now well-insulated, is the tinal temperature higher or lower than 300'C

Explanation / Answer

For steam, at 5 bar and 300 C, from steam table we get,

specific enthalpy H = 3064.6 kJ/kg

By energy balance,

energy in = energy out + heat lost

.: energy out = 150 kg/hr x 3064.6 kJ/kg - 90000 kJ/hr = 369690 kJ/hr

specific enthalpy at outlet = 369690 kJ/hr / ( 150 kg/hr) = 2464.6 kJ

Now, for saturated steam at 1 bar,

T = 99.9 C

Hv = 2674.95 kJ/kg

Hl = 417.436 kJ/kg

As H outlet = 2464.6 kJ/kg lies between Hv and Hl, then the phase of the steam is wet steam of quality x.

x = vapor mass fraction

H = xHv + (1-x)Hl

2464.6 = x*2674.95 + (1-x)*417.436

.: x = 0.906

Exit steam temperature = Tsat = 99.9 C

Exit phase: wet steam of quality 0.906

If value is well insulated, then outlet enthalpy = inlet enthalpy = 3064.6 kJ/kg

Now, at exit H = 3064.6 kJ/kg and P = 1bar

Hexit > Hv at 1 bar saturation condition, therefore, steam is superheated.

For superheated steam at 1 bar and H = 3064.6 kJ/kg, search in the superheated steam table.

We get,

T = 295 C

hence temperature at the exit is < 300 C

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