Chapter 8 Examples
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University Of Georgia *
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3140
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Mechanical Engineering
Date
Dec 6, 2023
Type
Pages
13
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1
8.25
Superheated steam at 20 MPa, 560
o
C enters the turbine of a vapor power plant.
The
pressure at the exit of the turbine is 0.5 bar, and liquid leaves the condenser at 0.4 bar at 75
o
C.
The pressure is increased to 20.1 MPa across the pump.
The turbine and pump have isentropic
efficiencies of 81 and 85%, respectively.
Cooling water enters the condenser at 20
o
C with a
mass flow rate of 70.7 kg/s and exits the condenser at 38
o
C.
For the cycle, determine
(a) the mass flow rate of steam, in kg/s.
(b) the thermal efficiency.
KNOWN:
Water is the working fluid in a vapor power plant.
Data are given at various states in
the cycle.
FIND:
(a) the mass flow rate of steam, in kg/s and (b) the thermal efficiency.
SCHEMATIC AND GIVEN DATA:
ENGINEERING MODEL:
1.
Each component of the cycle is analyzed as a control volume at steady state.
The control
volumes are shown on the accompanying sketch by dashed lines.
2.
Stray heat transfer in the turbine, condenser, and pump is ignored.
3.
Kinetic and potential energy effects are negligible.
ANALYSIS:
First fix each principal state.
State 1
:
p
1
= 20 MPa (200 bar),
T
1
= 560
o
C →
h
1
= 3423.0 kJ/kg,
s
1
= 6.3705
kJ/kg∙K
State 2s
:
p
2s
=
p
2
= 0.5 bar,
s
2s
=
s
1
= 6.3705
kJ/kg∙K →
x
2s
= 0.8119,
h
2s
= 2212.2 kJ/kg
State 2
:
p
2
= 0.5 bar,
h
2
= 2442.3 kJ/kg (see below)
t
W
±
Turbine
Cooling
water
2
Condenser
Pump
p
W
±
3
4
1
Boiler
in
Q
±
p
3
= 0.4 bar
T
3
= 75
o
C
p
1
= 20 MPa
T
1
= 560
o
C
p
2
= 0.5 bar
p
4
= 20.1 MPa
out
Q
±
h
t
= 81%
h
p
= 85%
6
5
T
5
= 20
o
C
T
6
= 38
o
C
kg/s
7
.
70
cw
m
±
T
4
3
2
1
20 MPa
s
2s
T
1
= 560
o
C
0.5 bar
0.4 bar
20.1 MPa
2
kg
kJ
)
2
.
2212
0
.
3423
)(
81
.
0
(
kg
kJ
0
.
3423
)
(
2
1
t
1
2
2
1
2
1
t
±
±
±
±
o
±
±
s
s
h
h
h
h
h
h
h
h
h
h
= 2442.3 kJ/kg
State 3
:
p
3
= 0.4 bar,
T
3
= 75
o
C
→
From Table A-2
p
3
>
p
sat
@ 75
o
C.
Thus, state 3 is a sub-
cooled liquid state.
Since the pressure is low,
h
3
≈
h
f3
at 75
o
C = 313.93 kJ/kg,
v
3
≈
v
f3
at 75
o
C = 0.0010259 m
3
/kg
State 4
:
p
4
= 20.1 MPa (201 bar),
h
4
= 338.14 kJ/kg (see below)
p
3
4
3
3
4
3
4
3
4
3
p
)
(
)
(
h
h
p
p
h
h
h
h
p
p
±
²
o
±
±
v
v
m
N
1000
kJ
1
kPa
1
m
N
1000
bar
1
kPa
100
85
.
0
bar
)
4
.
0
201
)(
kg
m
0010259
.
0
(
kg
kJ
93
.
313
2
3
4
±
²
h
= 338.14 kJ/kg
State 5
:
T
5
= 20
o
C, liquid →
h
5
≈
h
f5
at 20
o
C = 83.96 kJ/kg
State 6
:
T
6
= 38
o
C, liquid →
h
6
≈
h
f6
at 38
o
C = 159.21 kJ/kg
(a)
The mass flow rate of the steam can be determined by writing an energy balance for the
condenser. With no stray heat transfer with the surroundings and no work, the energy balance
for the condenser reduces to
)
(
)
(
0
6
5
cw
3
2
h
h
m
h
h
m
±
²
±
±
±
where
m
±
is the mass flow rate of the steam and
cw
m
±
is the mass flow rate of the cooling water.
Rearranging to solve for the mass flow rate of steam gives
)
(
)
(
3
2
5
6
cw
h
h
h
h
m
m
±
±
±
±
Substituting values and solving give
kJ/kg
)
93
.
313
.3
2442
(
kJ/kg
)
96
.
83
.21
159
(
kg/s)
0.7
7
(
±
±
m
±
=
2.50 kg/s
(b)
The thermal efficiency is
3
)
(
)
(
)
(
4
1
3
4
2
1
h
h
h
h
h
h
±
±
±
±
h
Substituting enthalpy values and solving yield
kJ/kg
)
.14
338
3423.0
(
kJ/kg
)
93
.
313
.14
338
(
kJ/kg
)
3
.
2442
3423.0
(
±
±
±
±
h
=
0.3101 (31.01%)
1
8.33
Steam heated at constant pressure in a steam generator enters the first stage of a
supercritical reheat cycle at 28 MPa, 520
o
C.
Steam exiting the first-stage turbine at 6 MPa is
reheated at constant pressure to 500
o
C.
Each turbine stage has an isentropic efficiency of 78%
while the pump has an isentropic efficiency of 82%.
Saturated liquid exits the condenser that
operates at constant pressure,
p
.
(a) For
p
= 6 kPa, determine the quality of the steam exiting the second stage of the turbine and
the thermal efficiency.
(b) Plot the quantities of part (a) versus
p
ranging from 4 kPa to 70 kPa.
KNOWN:
A supercritical reheat cycle operates with steam as the working fluid.
FIND:
(a) For
p
= 6 kPa, determine the quality of the steam exiting the second stage of the
turbine and the thermal efficiency, and (b) plot the quantities of part (a) versus
p
ranging from 4
kPa to 70 kPa.
SCHEMATIC AND GIVEN DATA:
ENGINEERING MODEL:
1.
Each component of the cycle is analyzed as a control volume at steady state.
The control
volumes are shown on the accompanying sketch by dashed lines.
2.
For all components stray heat transfer is ignored.
3.
Flow through the steam generator, reheater, and condenser is at constant pressure.
4.
Kinetic and potential energy effects are negligible.
ANALYSIS:
First fix each principal state
s
.
State 1:
p
1
= 28 MPa,
T
1
= 520
o
C →
h
1
= 3192.3 kJ/kg,
s
1
= 5.9566 kJ/kg∙K
t
W
±
4
Condenser
out
Q
±
Pump
p
W
±
5
6
1
Steam
Generator
in
Q
±
p
5
=
p
4
x
5
= 0 (saturated liquid)
p
1
= 28 MPa
T
1
= 520
o
C
p
4
=
p
p
6
=
p
1
= 28 MPa
Turbine
2
Turbine
1
2
3
p
2
= 6 MPa
p
3
=
p
2
= 6 MPa
T
3
= 500
o
C
Reheat
Section
h
t1
=
h
t2
= 78%
h
p
= 82%
2
State 2s
:
p
2s
=
p
2
= 6 MPa,
s
2s
=
s
1
= 5.9566 kJ/
kg∙K
→
h
2s
= 2822.2 kJ/kg
State 2
:
p
2
= 6 MPa,
h
2
= 2903.6 kJ/kg (see below)
kg
kJ
)
2
.
2822
3
.
3192
)(
78
.
0
(
kg
kJ
3
.
3192
)
(
2
1
t1
1
2
2
1
2
1
t1
±
±
±
±
o
±
±
s
s
h
h
h
h
h
h
h
h
h
h
= 2903.6 kJ/kg
State 3:
p
3
= 6 MPa,
T
3
= 500
o
C →
h
3
= 3422.2 kJ/kg,
s
3
= 6.8803 kJ/kg∙K
State 4s
:
p
4s
=
p
4
= 6 kPa,
s
4s
=
s
3
= 6.8803 kJ/kg∙K →
x
4s
= 0.8143,
h
4s
= 2118.8 kJ/kg
State 4
:
p
4
= 6 MPa,
h
4
= 2405.5 kJ/kg (see below)
kg
kJ
)
8
.
2118
2
.
3422
)(
78
.
0
(
kg
kJ
2
.
3422
)
(
4
3
t2
3
4
4
3
4
3
t2
±
±
±
±
o
±
±
s
s
h
h
h
h
h
h
h
h
h
h
=
2405.5 kJ/kg
State 5
:
p
5
= 6 kPa
, saturated liquid →
h
5
=
h
f5
= 151.53 kJ/kg,
v
5
=
v
f5
= 0.0010064 m
3
/kg
State 6
:
p
6
=
p
1
= 28 MPa,
h
6
= 185.89 kJ/kg (see below)
p
5
6
5
5
6
5
6
5
6
5
p
)
(
)
(
h
h
p
p
h
h
h
h
p
p
±
²
o
±
±
v
v
m
N
1000
kJ
1
kPa
1
m
N
1000
82
.
0
kPa
)
6
000
,
28
(
kg
m
0010064
.
0
kJ/kg
53
.
151
2
3
6
±
²
h
= 185.89 kJ/kg
(a)
The quality of the steam at the exit of the second stage of the turbine (state 4) is determined
using values from Table
A-
3
,
h
f4
= 151.53 kJ/kg and
h
fg4
= 2415.9 kJ/kg, as follows:
kJ/kg
9
.
2415
kJ/kg
)
53
.
151
5
.
2405
(
4
fg
4
f
4
4
±
±
h
h
h
x
=
0.9330
The cycle thermal efficiency is
m
Q
m
Q
m
W
m
W
m
W
m
Q
m
W
±
±
±
±
±
±
±
±
±
±
±
±
±
±
/
/
/
/
/
/
/
23
61
p
t2
t1
in
cycle
²
±
²
h
)
(
)
(
)
(
)
(
)
(
2
3
6
1
5
6
4
3
2
1
h
h
h
h
h
h
h
h
h
h
±
²
±
±
±
±
²
±
h
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Answer the following: fill up the blanks in the items below:
1. Equipment layout and TS diagram for the cycle
2. Actual mass of steam bled into the open heater m1'=
kg/kg for the
_kg/sec for the
heater nearest to the SGU/boiler and m2' =
heater nearest to the condenser.
3. Actual turbine work in KW Answer:
4. Energy Chargeable (actual) Answer:
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exit of the turbine is 0.06 bar, and liquid leaves the condenser at 0.045 bar, 26C. The pressure is
increased to 18.2 MPa across the pump. The turbine and pump have isentropic efficiencies of 82 and
77%, respectively. For the cycle, determine (a) the net work per unit mass of steam flow, in kJ/kg. (b) the
heat transfer to steam passing through the boiler, in kJ per kg of steam flowing. (c) the thermal
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condensed.
In t he preliminary design of a power plant, water is chosen as the working fluid and it is determined
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4.
Superheated steam at 18 MPa, 560°C, enters the turbine of a vapor power plant. The
pressure at the exit of the turbine is 0.06 bar, and saturated liquid leaves the condenser at 0.06
bar. The pressure is then increased by a pump to the boiler pressure at 18 MPa. The turbine and
pump efficiencies are 82 and 77%, respectively. For the cycle, determine
(a) The net-work per unit mass of steam flow, in kJ/kg
(b) Heat transfer to steam passing through the boiler, in kJ/kg
(c) The thermal efficiency of the cycle
(d) Heat transfer to cooling water passing through the condenser, in kJ/kg.
(e) Draw complete T-s diagram
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What is the specific enthalpy in kj/kg for state 2
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Solve question 8.4 in the given image.
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This steam is expanded isentropic ally in the low pressure turbine to the
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consumption for 10 MW output.
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Steam at 200 bar, 760°C enters the throttle of a reheater engine and expands to 10 bar. At this point itleaves the engine, enters the reheater, and returns at 9 bar, 600°C, expansion then occurs to the condenser pressure of 0.5 bar (hf = 138 kJ/kg) on the basis of flow of 1 kg steam. Find (a) W and e of the cycle, (b) W, e, and m for the ideal engine, (c) In the actual engine the steam enters the reheater at 10 bar, 300°C and later expands to a saturated state at the exhaust to the condenser, find W, e and m.
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In a Reheat Cycle steam enters the turbine @ 40 bar and 400 C. It expands isentropic ally to 6 bar and is reheated at constant pressure
to 400 C. This steam expanded isentropic ally to 1 bar and is reheated at constant pressure to 200 C. Finally this steam is expanded isentropic ally in the condenser pressure of 0.1 bar. Determine the thermal efficiency and the capacity of the boiler if 10,000 KW of power output is required.
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Steam at 4800 lbf/in.2, 1000 deg F enters the first stage of a supercritical reheat cycle including two turbine stages. The steam exiting the first-stage turbine at 600 lbf/in.2 is reheated at constant pressure to 1000 deg F. Each turbine stage and the pump have an isentropic efficiency of 85%. The condenser
pressure is 1 lbf/in.2 If the net power output of the cycle is 100 MW, determine
(a) the rate of heat transfer to the working fluid passing
through the steam generator, in MW.
(b) the rate of heat transfer from the working fluid passing
through the condenser, in MW.
(c) the cycle thermal efficiency.
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- 2. please answer asaparrow_forwardIn a steam plant 100 kg/min of dry-saturated steam at 30 bar enters the turbine. After expanding isentropic ally the exhaust steam enters the condenser. The condenser pressure is maintained at 0.1 bar by the cooling water taken from a nearby river. Calculate the following: a. Heat supplied to the boiler KJ/sec b. Heat rejected to the cooling water KJ/sec c. Efficiency of the plant and Net power output.arrow_forwardSteam enters the turbine of a simple vapor power plant with a pressure of 12 MPa and a temperature of 600°C and expands adiabatically to condenser pressure, p. Saturated liquid exits the condenser at pressure p. The isentropic efficiency of both the turbine and the pump is 84%. a. For p = 30 kPa, determine the turbine exit quality and the cycle thermal efficiency. b. Plot the quantities of part (a) versus p ranging from 6 kPa to 100 kPa.arrow_forward
- Steam enters the turbine of a vapor power plant at 600 lbf/in.?, 700°F and exits as a two-phase liquid-vapor mixture at 90°F. Condensate exits the condenser at 85°F and is pumped to 600 lbf/in.2 The turbine and pump isentropic efficiencies are 90 and 80%, respectively. The net power developed is 1 MW. Determine: (a) the percent steam quality at the turbine exit. (b) the percent thermal efficiency. (c) the steam mass flow rate, in Ib/h.arrow_forwardQ1) Steam is supplied to a turbine at 30 bar and 350°C. The turbine exhaust pressure is 0.08 bar. The main condensate is heated regeneratively in two stages by steam bled from the turbine at 5 bar and 1.0 bar respectively. Calculate masses of steam bled off at each pressure per kg of steam entering the turbine and the theoretical thermal efficiency of the cycle. 1 kg Turbine 1- m- m2 O 1-m, w -u -11 Condenser m. h, m2. h2 1 kg 1 kg Heater-1 Drain cooler m, Heater-2 (LP.) m,+ m. (Н.Р.)arrow_forwardIn a steam plant 100 kg/min of dry-saturated steam at 30 bar enters the turbine. After expanding isentropic ally the exhaust steam enters the condenser. The condenser pressure is maintained at 0.1 bar by the cooling water taken from a nearby river. Calculate the following: a. Dryness fraction of exhaust steam. b. Turbine work output. c. Work input to the feed pump. d. Heat supplied to the boiler. e. Heat rejected to the cooling water. f. Efficiency of the plant. g. Net power output.arrow_forward
- What is the specific enthalpy in kj/kg-K for state 4 to 4 d.p.arrow_forwardSteam is supplied to a two-stage turbine at 40 bar and 350 o It expands in the first turbine until it is just dry saturated, then it is reheated to 350 oC and expanded through the second stage turbine; the isentropic efficiencies of the first and second stage turbines are 84 % and 78 % respectively. The condenser pressure is 0.035 bar. Sketch the process on a T-s diagram and calculate; i. The work output and heat supplied per kg of steam for the plant assuming ideal processes ii. The thermal efficiency of the cycle iii. The specific steam consumptionarrow_forwardProblem 1 In a Rankine Thermodynamic cycle, steam leaves the boiler and enters the turbine at 600 psia, 800 °F. The condenser pressure is 1 psia. After presenting a schematic of the problem in addition to clearly labeled and explained T-s and h-s diagrams, you are asked to determine the following: (a) Pump work required per Ibm of working fluid. Quality of fluid at turbine inlet. Work output of turbine per lbm of working fluid. Energy input to the boiler per lbm of working fluid. Heat rejection by the condenser per Ibm of working fluid. Determine the cycle thermal efficiency. (d) (e) (f)arrow_forward
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- Refrigeration and Air Conditioning Technology (Mi...Mechanical EngineeringISBN:9781305578296Author:John Tomczyk, Eugene Silberstein, Bill Whitman, Bill JohnsonPublisher:Cengage Learning
Refrigeration and Air Conditioning Technology (Mi...
Mechanical Engineering
ISBN:9781305578296
Author:John Tomczyk, Eugene Silberstein, Bill Whitman, Bill Johnson
Publisher:Cengage Learning