SOLVED: Water is the working fluid in an ideal rankine cycle. saturated vapor enters the turbine at 16 mpa…

Water is the working fluid in an ideal Rankine cycle. The saturated vapor enters the turbine at 16 MPa, and the condenser pressure is 8 kPa. The mass flow rate of steam entering the turbine is 120 kg/s. Determine:

(a) the net power developed, in kW.

(b) the rate of heat transfer to the steam passing through the boiler, in kW.

(c) the thermal efficiency.

(d) the mass flow rate of condenser cooling water, in kg/s, if the cooling water undergoes a temperature increase of 18 C with neglectible pressure change in passing through the condenser.

This example was solved using Engineering Equation Solver, or just EES, but steam charts can be used also.

 

"State 1"
P1=16000 [kPa]
s1=s4
h1=Enthalpy(Steam;s=s1;P=P1)

"State 2"
P2=16000 [kPa]
x2=1
h2=Enthalpy(Steam;x=x2;P=P2)
s2=Entropy(Steam;x=x2;P=P2)

"State 3"
P3=8 [kPa]
s3=s2
h3=Enthalpy(Steam;s=s3;P=P3)

"State 4"
P4=8 [kPa]
x4=0
h4=Enthalpy(Steam;x=x4;P=P4)
s4=Entropy(Steam;x=x4;P=P4)

"a) the net power developed, in kW."
m=120 [kg/s]
W_turb=m*(h2-h3)
W_pump=m*(h1-h4)
W_net=W_turb-W_pump

"b) the rate of heat transfer to the steam passing through the boiler, in kW."
Q_in=m*(h2-h1)

"c) the thermal efficiency."
eta_therm=W_net/Q_in

"d) the mass flow rate of condenser cooling water, in kg/s, if the cooling water undergoes a temperature increase of 18 C with negligible pressure change in passing through the condenser."

"The heat lost by the steam is equal to the heat gained by de water"

cp_water=4,19 [kJ/kg.k]
deltaT=18 [C]

m*(h3-h4)=m_water*cp_water*deltaT