This preview shows pages 1–3. Sign up to view the full content.
HOMEWORK SET 5
6.57
A small stream with 20
o
C water runs out over a cliff creating a 100 m tall
waterfall. Estimate the downstream temperature when you neglect the horizontal
flow velocities upstream and downstream from the waterfall. How fast was the
water dropping just before it splashed into the pool at the bottom of the waterfall?
Solution:
CV. Waterfall, steady state. Assume no Q
.
nor W
.
Energy Eq.6.13:
h +
1
2
V
2
+ gZ = const.
State 1: At the top zero velocity
Z
1
= 100 m
State 2: At the bottom just before impact,
Z
2
= 0
State 3: At the bottom after impact in the pool.
h
1
+ 0 + gZ
1
= h
2
+
1
2
V
2
2
+ 0 = h
3
+ 0 + 0
Properties:
h
1
≅
h
2
same T, P
=>
1
2
V
2
2
= gZ
1
V
2
=
2gZ
1
=
2
×
9.806
×
100
= 44.3 m/s
Energy equation from state 1 to state 3
h
3
= h
1
+ gZ
1
use
Δ
h = C
p
Δ
T with value from Table A.4 (liquid water)
T
3
= T
1
+ gZ
1
/ C
p
= 20 + 9.806
×
100 /4180 =
20.23
°
C
6.63
A steam turbine receives steam from two boilers. One flow is 5 kg/s at 3 MPa,
700
°
C and the other flow is 15 kg/s at 800 kPa, 500
°
C. The exit state is 10 kPa,
with a quality of 96%. Find the total power out of the adiabatic turbine.
Solution:
C.V. whole turbine steady, 2 inlets, 1 exit, no heat transfer Q
.
= 0
Continuity Eq.6.9:
m
.
1
+ m
.
2
= m
.
3
= 5 + 15 = 20 kg/s
Energy Eq.6.10:
m
.
1
h
1
+ m
.
2
h
2
= m
.
3
h
3
+ W
.
T
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document Table B.1.3:
h
1
= 3911.7 kJ/kg,
h
2
= 3480.6 kJ/kg
Table B.1.2:
h
3
= 191.8 + 0.96
×
2392.8
= 2488.9 kJ/kg
W
T
1
2
3
W
.
T
= 5
×
3911.7 + 15
×
3480.6 – 20
×
2488.9
= 21 990 kW =
22 MW
6.72
An automotive radiator has glycerine at 95
o
C enter and return at 55
o
C as shown
in Fig.
P6.72. Air flows in at 20
This is the end of the preview. Sign up
to
access the rest of the document.
This homework help was uploaded on 04/10/2008 for the course ME 235 taught by Professor Borgnakke during the Spring '07 term at University of Michigan.
 Spring '07
 Borgnakke

Click to edit the document details