Civil Engineering Reference
In-Depth Information
Table 11.4
Pressure and leakage losses in air mains and related power in typical operating
conditions
Pressure drop
per 100 m
Equivalent power
Air flow
in standard
conditions
(Sm
3
/min)
Air flow
at 0.8 MPa
(absolute)
(m
3
/min)
Air speed
at 0.8 MPa
(absolute)
(m/s)
Pressure
losses
(100 m)
(kW)
Nominal
bore
(mm)
Leakage
losses
(kW)
40
a
11.9 1.5 19.9 0.07 10.15 1.7 4.1 86
50 9.2 1.2 9.9 0.015 2.18 0.3 3.2 89
65 15.8 2.0 10.1 0.01 1.45 0.3 5.5 89
80 21.1 2.7 8.8 0.006 0.87 0.3 7.3 90
100 29.0 3.7 7.8 0.005 0.73 0.3 10.1 90
125 46.1 5.8 7.9 0.004 0.58 0.4 16.1 90
Flow leaks through an orifice can be calculated by using the Bernoulli equation for the flow of
compressible gas and by considering the process as adiabatic:
k
Pipe
efficiency
(%)
MPa
psi
p
ρ
þ
k
1
constant
The air speed in the pipe is negligible in comparison with that immediately outside the orifice
(typical ratio between the two speeds is roughly 30-40)
It follows:
1
2
v
2
¼
r
2
h
i
k
1
p
i
ρ
i
r
2
=k
1
r
k
1
ð
Þ=k
k
m
kg
=
s
ð
Þ¼C
d
A ρ
i
p
p
orifice area (m
2
),
air density (kg/m
3
)
C
d
¼
discharge coefficient
¼
0.96 (typical value),
A
¼
ρ
i,
p
i
¼
and pressure (Pa) in the pipeline,
k
¼
adiabatic coefficient
¼
1.4,
r
p
¼
ratio between the external
and the internal pressure (
p
o
/
p
i
atmospheric pressure/
p
i
)
Data for calculation (e.g., hole diameter 0.005 m)
p
o
¼
1.23 kg/Sm
3
,
p
i
¼
0.1013 MPa,
ρ
¼
¼
0.8 MPa
o
0
:
101
kg
=
m
3
0
:
8
ρ
i
¼
1
:
23
2
m
2
¼
4
10
3
A
5
r
p
¼
0.1013/0.8,
m
¼
0.0212 kg/s
¼
Sm
3
60
1
:
23
034 Sm
3
Q
¼
=
min
m
kg
ð
=
s
Þ
¼
1
:
=
min
(see Table
11.1
for
related power)
a
Anomalous condition due to a high air speed
standard atmospheric condition 15.6
C, 60 F, 0.1013 MPa, 14.5 psi
compression ratio equal to 7.9; m
3
air flow at 0.8 MPa
Sm
3
/7.9
percentage of flow leaks assumed equal to 10 % of the pipe air flow
equivalent power is evaluated by the isothermal compression formula. Practical values are higher
(see footnote in Table
11.1
)
¼
