Three streams are added to a boiler. Stream 1 is saturated liquid water at 50 de

Question

Three streams are added to a boiler. Stream 1 is saturated liquid water at 50 degree C and a mass flow rate of 1.5 kg/s. Stream 2 is saturated water vapor at 10 bar and a mass flow rate of 1.5 kg/s. Stream 3 is water vapor at 300 degree C, 1 bar and a mass flow rate of 2 kg/s. There is heat input to the boiler of 500 kW. The outlet stream (stream 4) is at 1 bar. You may neglect changes in kinetic and potential energy. What is the specific volume of stream 1? What is the temperature of stream 2? Is the water vapor in stream 3 saturated or superheated? What is the specific enthalpy of stream 4, relative to liquid water at the triple point? What is the temperature and physical state (subcooled liquid, saturated liquid, saturated vapor, liquid/vapor mixture or superheated vapor) of stream 4? If it is a liquid/vapor mixture, determine the fraction of stream 4 that is liquid.

Explanation / Answer

mass balance

m1 + m2 + m3 = m4

1.5 +1.5 + 2 = m4 = 5 kg/s

case(a)

from temperature steam table at 50 degreeecelcius

specic volume Vf = 0.001012 m3 /kg

h1 = 209.3 kj/kg

temperature at 10 bar is 179.9 degree celcius

at 10 bar h2 = 2776.2 kj/kg

at 1 bar saturated temperature is 99.63 degree celcius

but given temperature is 300 degree celcius which is greater than saturated temperature

so the steam is in superheated state

h3 = 3074.5 kj/kg (from superheated table)

case(b)

Energy balance

m1 h1 + m2 h2 + m3 h3 + Q  = m4 h4

(1.5*209.3)+(1.5*2776.2)+(2*3074.5)+500 = 5 * h4

h4 = 2225.45 kj/kg

case(c) at 1 bar pressure

2225.45 = 417.5 + x * 2257.9

x = 0.80 (80 % dryness fraction)

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