Question

3. Water is the working fluid in an ideal Rankine cycle. The condenser pressure is 10 kPa (0.10 bar), and saturated vapor enters the turbine at 18 MPa (180 bar). The net power output of the cycle is 100 MW. For this cycle determine the: a) mass flow rate of the steam, in kg/h. b) heat transfer rates for the working fluid passing through the boiler and condenser, each in kW. c) thermal efficiency of the cycle.

Answer 1

Answer:

a) 116.51 kg/s = 419436 kg/hour

b) for boiler ( Q 1 ) = 265547 kW  

for condenser ( Q2 ) = 165639.93 kW

c) 37.65%

Explanation:

Given data:

condenser pressure ( P1 ) = 10 kPa ≈ 0.10 bar

saturated vapor pressure ( P2 ) = 18 MPa ≈ 180 bar

Net power output of cycle = 100 MW

attached below is  detailed solution to the question

a) calculate mass flow rate of steam in Kg/h

applying the formula for calculating power

P = м ( h3 - h4 - h2 + h1 ) ------ ( 1 )

power ( p ) = 100 * 10^3 Kw

h3 = 2510.0

h4 = 1613.49

h2 = 230.82

h1 = 191.01

input the given values into equation 1

mass flow rate of steam ( m ) = 116.51 kg/h

b) Heat transfer rates for working fluid passing through boiler and condenser

for boiler ( Q 1 ) = 265547 kW  

for condenser ( Q2 ) = 165639.93 kW

C) Determine thermal efficiency of the cycle

N = $\frac{P}{Q2}$ = 100 / 265.547 = 0.3765 = 37.65%