College of Engineering
Spring Semester- 2016
Thermodynamics II - ME 272
Section: MA, MB and MC
Due Day: Thursday-March 31st -2016
PROBLEM 1.1 STATEMENT
(25%)
Consider a steam power plant that operates on a simple ideal Rankine cycle and has a net power
output of 45 MW. Steam enters the turbine at 7 MPa and 500oC and is cooled in the condenser at
a pressure of 10 kPa by running cooling water from a lake through the tubes of the consider at a
rate of 2000 kg/s. Show the cycle on T-s diagram with respect to saturation lines, and determine
a- The thermal efficiency,
b- The mass flow rate of the steam,
c- The temperature rise of the cooling water?
[Ans. a- 38.9 % , b) 36 kg/s , and c) 8.4ᵒC]
State [1], P1 = 10 kPa, x1 = 0 [ Sat. Liquid] h1 = 191.7
kJ
m3
, v1 = 0.00101
kg
kg
From water saturated Tab:
State[2], P2 = 7000 kPa, h2 = v1 (P2 − P1 ) + h1 = 0.00101(7000 − 10) + 191.7
kJ
= 198.8
kg
State[3], P3 = 7000 kPa, T3 = 500,
Superheated Table: h3 = 3411
kJ
kJ
, s3 = 6.798
kg
kgK
College of Engineering
Spring Semester- 2016
Thermodynamics II - ME 272
Section: MA, MB and MC
Due Day: Thursday-March 31st -2016
State[4], P4 = 10 kPa, s4 = 𝑠3 ,
Superheated Table: h4 = 2153
kJ
kg
The thermal efficiency can be evaluated as:
ηth = 1 −
q out
h4 − h1
2153 − 191.7
=1−
= 1−
= 0.389
q in
h3 − h2
3411 − 198.8
The steam mass flowrate:
ṁ =
Wnet
45000
kg
=
= 35.97
(h3 − h2 ) − (h4 − h1 ) (3411 − 198.8) − (2153 − 191.7)
s
Ein = Eout → Qcondeser = Qwater → ṁ(h4 − h1 ) = ṁw Cpw ∆T → ∆T
35.97 × (2153 − 191.7)
=
= 8.441° C
4.18 × 2000
College of Engineering
Spring Semester- 2016
Thermodynamics II - ME 272
Section: MA, MB and MC
Due Day: Thursday-March 31st -2016
PROBLEM 1.2 STATEMENT
(25%)
Repeat Prob.1.1 assuming an isentropic efficiency of 87 percent for both the turbine and the
pump?
[Ans. a) 33.8 %, b) 41.4 kg/s, c) 10.5oC]
State [1], P1 = 10 kPa, x1 = 0 [ Sat. Liquid] h1 = 191.7
kJ
m3
, v1 = 0.00101
kg
kg
From water saturated Table:
State[2], P2 = 7000 kPa, h2s = v1 (P2 − P1 ) + h1 = 0.00101(7000 − 10) + 191.7 = 198.8
h2a =
h2s − h1
198.8 − 191.7
kJ
+ h1 =
+ 191.7 = 199.86
ηP
0.87
kg
State[3], P3 = 7000 kPa, T3 = 500,
State[4], P4 = 10 kPa, s4 = 𝑠3 ,
Superheated Table: h3 = 3411
Superheated Table: h4s = 2153
kJ
kJ
, s3 = 6.798
kg
kgK
kJ
kg
ℎ4𝑎 = ℎ3 − 𝜂𝑇 (ℎ3 − ℎ4𝑠 ) = 3411 − 0.87 × (3411 − 2153) = 2316.54
kJ
kg
The thermal efficiency can be evaluated as:
ηth = 1 −
q out
h4 − h1
2316.5 − 191.7
=1−
= 1−
= 0.338 = 33.8 %
q in
h3 − h2
3411 − 199.86
The steam mass flowrate:
ṁ =
kJ
kg
Wnet
45000
kg
=
= 41.423
(h3 − h2 ) − (h4 − h1 ) (3411 − 199.86) − (2316.5 − 191.7)
s
Ein = Eout → Qcondeser = Qwater → ṁ(h4 − h1 ) = ṁw Cpw ∆T → ∆T
41.423 × (2316.5 − 191.7)
=
= 10.53° C
4.18 × 2000
College of Engineering
Spring Semester- 2016
Thermodynamics II - ME 272
Section: MA, MB and MC
Due Day: Thursday-March 31st -2016
PROBLEM 1.3 STATEMENT
(25%)
A steam power plant operates on the reheat Rankine cycle. Steam enters the high-pressure turbine
at 12.5 MPa and 550ᵒC at a rate of 7.7 kg/s and leaves at 2 MPa. Steam is then reheated at constant
pressure to 450oC before it expands in the low pressure turbine. The isentropic efficiencies of the
turbine and the pump are 85 percent and 90 percent, respectively. . Steam leaves the condenser as
a saturated liquid. If the moisture content at the exist of the turbine is not exceed 5 percent,
determine
a- The thermal efficiency,
b- The net power output?
[Ans. a) 34.66 %, and b) 9.296 MW]
Fig.1.3. Reheat Rankine Cycle
College of Engineering
Spring Semester- 2016
Thermodynamics II - ME 272
Section: MA, MB and MC
Due Day: Thursday-March 31st -2016
PROBLEM 1.4 STATEMENT
(25%)
A steam power plant operates on the reheat regenerative Rankine cycle with a closed feed water
heater. Steam enters the turbine at 12.5 MPa and 550oC at a rate of 24 kg/s and is condensed in the
condenser at a pressure of 20 kPa. Steam is reheated at 5 MPa to 550oC. Some steam is extracted
from the low pressure turbine at 1.0 MPa, is completely condensed in the closed feed water heater,
and pumped to 12.5 MPa before it mixes with the feed water at the same pressure. Assuming an
isentropic efficiency of 88 percent for both the turbine and the pump.
a- The temperature of the steam at the inlet of the closed feed water heater,
b- The mass flowrate of the steam extracted from the turbine for the closed feed water
heater,
c- The net power output,
d- The thermal efficiency?
[Ans. a) 328C,b) 4.29 kg/s, c) 28.6 MW, d) 39.3 %]
Fig.1.4. Reheat and Regenerative Power Plant Cycle
College of Engineering
Spring Semester- 2016
Thermodynamics II - ME 272
Section: MA, MB and MC
Due Day: Thursday-March 31st -2016