In a particular reheat-cycle power plant, steam enters the high-pressure turbine

Question

In a particular reheat-cycle power plant, steam enters the high-pressure turbine at 5 MPa. 450 degree C and expands to 0.5MPa. after which it is reheated to 450 degree C. The steam is then expanded through the low-pressure turbine to 7.5 kPa. Liquid water leaves the condenser at 30 degree C. is pumped to 5MPa. and then returned to the steam generator. Hath turbine is adiabatic with an isentropic efficiency of 87% and the pump efficiency is 82%. If the total power output of the turbines is 10MW, determine the mass flow rate of steam, the pump power input and the thermal efficiency of the power plant.

Explanation / Answer

state 3:

P3=5Mpa T3=450C

h3=3317.2kj/kg S3=6.8210kj/kg.k

state 4:

P4=.5Mpa S3=S4s=6.8210kj/kg.k

h4s=2748.1kj/kg

h4=h3-eff(h3-h4s)=2850.538 kj/kg

state 5:

T5=4500c S5=7.9424j/kg.k

P5=0.5Mpa h5=3378.45 kj/kg

state 6:

P6=7.5 Kpa x6=.87(saturated mix.)

S6s=S5=7.9424kj/kg.k

h6s=2405.3 kj/kg

h6=h5-eff(h5-h6s)=2531.80j/kg

state 1:

P1=7.5Kpa T1=30C

h1=hf=168.75kj/kg v1=vf=0.001008m3/kg

Wp,in=v1(P2-P1)/eff.=6.137 kj/kg

h2=h1+Wp,in=174.88kj/kg

q,in=h3-h2+h5-h4=3670.232kj/kg

q,out=h6-h1=2363.05kj/kg

W,net=m.(q,in-q,out) => m.=10.000/(q,in-q,out)=7.65kg/s

pump power=6.137*7.65=46.95KW

efficiency=w,net/q,in=.3561 or 35.61%

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