HOMEWORK SET 4b
6.9
In a boiler you vaporize some liquid water at 100 kPa flowing at 1 m/s. What is
the velocity of the saturated vapor at 100 kPa if the pipe size is the same? Can the
flow then be constant P?
The continuity equation with average values is written
m
.
i
= m
.
e
=
m
.
=
ρ
A
V
= A
V
/v = A
V
i
/v
i
= A
V
e
/v
e
From Table B.1.2 at 100 kPa we get
v
f
= 0.001043
m
3
/kg;
v
g
= 1.694
m
3
/kg
V
e
=
V
i
v
e
/v
i
= 1
1.694
0.001043
= 1624 m/s
To accelerate the flow up to that speed you need a large force (
Δ
PA ) so a
large pressure drop is needed.
P
i
cb
P
e
<
P
i
6.17
A nozzle receives 0.1 kg/s steam at 1 MPa, 400
o
C with negligible kinetic energy.
The exit is at 500 kPa, 350
o
C and the flow is adiabatic. Find the nozzle exit
velocity and the exit area.
Solution:
Energy Eq.6.13:
h
1
+
1
2
V
2
1
+ gZ
1
= h
2
+
1
2
V
2
2
+ gZ
2
Process:
Z
1
= Z
2
State 1:
V
1
= 0 ,
Table B.1.3
h
1
= 3263.88 kJ/kg
State 2:
Table B.1.3
h
2
= 3167.65 kJ/kg
Then from the energy equation
1
2
V
2
2
= h
1
– h
2
= 3263.88 – 3167.65 = 96.23 kJ/kg
V
2
=
2(h
1
 h
2
)
=
2 × 96.23 × 1000
= 438.7 m/s
The mass flow rate from Eq.6.3
m
.
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 Spring '07
 Borgnakke
 Energy, Kinetic Energy, kPa

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