Geoscience Reference
In-Depth Information
Sand gradation:
D
10
=
100
μ
m,
D
20
=
140
μ
m,
D
30
=
178
μ
m,
D
40
=
216
μ
m
D
50
=
255
μ
m,
D
60
=
292
μ
m,
D
70
=
308
μ
m,
D
80
=
312
μ
m en
D
90
=
340
μ
m;
Porosity of sand in tube:
n
=
0.4;
Sand density:
ρ
s
=
2650 kg/m
3
;
Water density:
ρ
w
=
1000 kg/m
3
;
Acceleration due to gravity:
g
=
9.81 m/s
2
;
Diameter of sand pump: 0.400 m;
Summer level: MSL - 0.2 m;
Winter level: MSL - 0.4 m;
Significant wave height:
H
s
=
0.8 m;
Sand concentration in mixture: 20%.
Solution
Pump speed and pump capacity
The first step is to determine the critical pump speed
v
cr
. For this purpose, the
D
mf
has
to be established first according to 5.2.2:
DDD
D
D
++
=
90
D
10
20
30
mf
9
100
178
255
340
140
216
292
308
312
++++++++
238
=μ
238
m
=
9
v
cr
can now be determined using Table 5.1. At a
D
mf
=
0.238 mm and a pipe
∅
of 400 mm,
v
cr
4.22 m/s is recommended. The corresponding sand production is determined from
Table 5.2
=
3.72 m/s and the pipeline speed
V
pipe
=
v
cr
+
0.5
=
3.72
+
0.5
=
381 m
3
/hour. This is a theoretical value. During the filling process
it will be necessary to vary the sand concentration of the sand-water mixture and the
related flow rate to fill the tube evenly. The presented value is indicative.
⇒
Q
=
Sedimentation rate
A sand-water mixture with a sand concentration of 20% is assumed along with a water
temperature at 12
°
C. The sedimentation rate can be determined from formulae (5.2)
and (5.3):
6
40 10
20
−
⋅
=
⋅
−
62
/s
12510
v
.
251
0
6
m
=
12
+
2650 1000
1000
Δ =
−
165
=
Δ⋅
gD
⋅
2
−
62
1.65 9.81 (238 10
⋅
⋅
⋅
)
mf
wX
=⋅
= ⋅
0.7
=
2.85 10
⋅
−
2
m/s
0
18
⋅
v
18 1.25 10
⋅
⋅
−
6
4
−
2
4
wc
⋅⋅ −
(1
c
)
2.85 10
⋅
⋅
0.2 (1
⋅
−
0.2)
v
=
0
=
=
5.8 10
⋅
−
3
m/s
sed
1
−−
nc
1
−
0.4
−
0.2
