ME 304: Problem Set #10
DUE: GRADESCOPE, 10 pm APRIL 26th
Reading: Moran & Shapiro: 8: 1 - 4
• Draw out all diagrams and show all steps. State the answer to 3 significant figures.
• Show ALL unit conversions.
1. Water is the working fluid in an ideal Rankine cycle with reheat. Superheated vapor enters
the turbine at 10 MPa, 480 C, and the condenser pressure is 6 kPa. Steam expands through the
first-stage turbine to 0.7 MPa and then is reheated to 480 C. Determine for the cycle
a.) the heat addition, in kJ per kg of steam entering the first-stage turbine.
b.) the thermal efficiency.
c.) the heat transfer from the working fluid passing through the condenser to the cooling water,
in kJ per kg of steam entering the first-stage turbine.
⑥
⑤
⑤
H
O
②
06
0
①
P,
T
h
100
=
480 (
=
,
P
bar
=
=
Sz
%
3321 4
15
xz
Ky
6 5282k5/ky K
=
=
7
P3
3)
Tz T
3
=
a) Din
=
h2
=
-
b)
13321 4
.
=
z
=
Q in
-
16359
.
=
3913 9
=
=
7 8723
-
by
0 9413
.
=
=
151 53
.
11
.
59k5/y
hu
=
2425 6
.
.
I
C
.
For the
got
1
ha)]
.
.
-
2684 8)
concensor
hu-h5
mi
I
.
I
9 k5/g
1639
I
=
.
=
7
hy= h5 + up P5)
.
.
Chihal + Cha-hul-
-
xy
=
=
x = 0
=
hy 3438 9
161 59) + (3438 9
-
3913
W
Ps
06
.
in [ (hi hs) + Cha
=
.
Sy Sy
2684 S
-
in
0
=
,
=
S3
·
.
00
Py
7
=
.
S= =
=
.
Chy-hs)
8 K5/y
I
41 9 %
.
.
1
=
2274 1
.
2425 6-151 53
.
K5/y
.
2. Water is the working fluid in an ideal regenerative Rankine cycle. Superheated vapor enters the
turbine at 10 MPa, 480 C, and the condenser pressure is 6 kPa. Steam expands through the firststage turbine to 0.7 MPa where some of the steam is extracted and diverted to an open feedwater
heater operating at 0.7 MPa. The remaining steam expands through the second-stage turbine to
the condenser pressure of 6 kPa. Saturated liquid exits the feedwater heater at 0.7 MPa. Determine
for the cycle
a.) the heat addition, in kJ per kg of steam entering the first-stage turbine.
b.) the thermal efficiency.
c.) the heat transfer from the working fluid passing through the condenser to the cooling water,
in kJ per kg of steam entering the first-stage turbine.
a
in hiha
= (3321
b)
y
CV
h
=
332
hi
=
hz
=
=
h
+
w(p7 ps)
4-707 52)
.
2613
=
.
-
.
152 23
22
697 22 + 11 1080x10"(193))
.
.
.
0
.
215
152 23
-
.
.
turbine stages
enclosing the
Wit
in
=
(h1
,
=
-
hz) + (1 y)(hz 43)
-
(3321 %
.
-
-
2684 8) 11
+
.
For the
pumps
-
0
.
2152)(2684 8 - 2009 8)
=
.
1166 3
.
.
:
= (l-y)(h5-hu) Che-hal
+
=
(1-0 2152) (152 23
.
.
-
151
.
53) + 1707 52 697 22)
-
.
.
=
glWp
10
=
.
85k5/y
3
1155
i
==
ch
2)
% 707 52" hy
=
-
9
.
=
2684 8
=
-
Goot (l-y)Chs-hy)
=
=
Cl-0 2152 (2009 8-15
.
=
.
1458 4
.
.
5
Ky
2
T/y
3. Steam at 4800 lbf/in2 , 1000 F enters the first stage of a supercritical reheat cycle including
two turbine stages. The steam exiting the first-stage turbine at 600 lbf/in2 is reheated at constant
pressure to 1000 F. Each turbine stage and the pump have an isentropic efficiency of 85%. The
condenser pressure is 1 lbf/in2 . 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.
Wret
nihihul
Chey-hal-the-hi)
Mass flow rate:
+
=
a Qin miChi-hy + hy-hal
=
2
=
b) Qout
=
.
=
m(hy - h5)
=
-
(1317 4 -1189 98) + (1517 8 -1042 24 186 61
·
.
161 7 1b/s
.
(161 7) (1317 4-86 61 + 1517 8-1189 42)
(161 7/(1042 24- 69
.
.
.
.
.
.
.
B151)
52x105
"100MWloi
=
=
.
265 9 MW
.
74))
Qoot 165 9 Mu
=
4) y
.
Mt .
=
=
Overall
energy
balance holds :
①in Wit
=
265 9 MW
.
=
=
Qurt
100 MW + 165 9 MW
.
3
.
,
-
.
-
69 74)
.