Sample calculations:
In order to solve for the density of the Helium gas at 3.2 atm of pressure, the ideal gas
relationship was utilized at ambient conditions (23˚C),
3
324,240
0.527
/
(2077
/
)(296
)
P
Pa
Kg
m
RT
J
Kg
K
ρ
=
=
=
Velocity of the fluid,
Based on the results, the Reynolds number can be solved by using
The friction factor f can now be obtained by using the Colebrook equation,
Consequently, the total minor head loss can be computed from,
Furthermore, the total head loss of the system can be obtained by using the inlet and
outlet conditions; noticing that the H
required
is equal to h
pump
as shown below:
(
29
2
2
2
1
2
2
1
1
2
1
,
(Eq. 146 C&C)
2
required
L total
required
pump
P
P
V
V
H
Z
Z
h
g
g
H
h
α
α
ρ


=
+
+

+
=
2
3
2
4
(Eq. 827 Cengel)
4(0.1
/ sec)
5.51
/ sec
(0.152
)
V
V
V
A
D
V
m
V
m
A
m
=
=
Π
=
=
=
Π
g
g
g
3
6
Re
(Eq. 83 Cengel)
(0.527
/
)(5.51
/ sec)
Re
53186
8.30 10
/ (
.sec)
VD
VD
Kg
m
m
D
x
Kg
m
ρ
ν
μ

=
=
=
=
1
2.51
2.0
(Colebrook Eq. 850 Cengel)
3.7
Re
0.020643
D
f
f
f
ε
= 
+
≈
2
,
2
,
2
(Eq. 859 Cengel)
2
150
(5.51
/ sec)
0.020643
0.3(5)
31.56
0.152
2(9.81
/ sec )
L total
L
L total
L
V
h
f
K
D
g
m
m
h
m
m
m
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 Spring '09
 TranSonTay
 Trigraph, initial cost, operation cost, total cos, L V hL

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