The magnitude of sediment
transport capacity of flow is mainly determined by the hydrodynamic condition
(Qi et al., 2002). It
is found that in turbulent region, the friction characteristics of
hyperconcentrated flow are the same as those of the clear water flow，which can be
calculated with Manning’s formula. As shown in Table 1, while sediment concentration
ranges from 55 to 843 kg /m3,
Manning’s coefficients of hyperconcentrated flow (S >= 200 kg/m3) and
low sediment-laden flow (S < 200 kg/m3) at Xiaolangdi Station
(Figure 1) on the lower Yellow River are almost the same. The average Manning’s
n value for hyperconcentrated flow is
0.041, and 0.039 for low sediment-laden flow. The value of Manning’s
coefficient of hyperconcentrated flow is a little bit higher, which is mainly caused
by the velocity measurement device itself.
Table 1 Comparison of
Manning’s Coefficients between Hyperconcentrated Flow and Low Sediment-laden Flow
at Xiaolangdi Station
Hyperconcentrated Flow (S >= 200 kg/m3)
|
Low Sediment-laden Flow (S <
200 kg/m3)
|
|||||||||||
Date
|
Q
(m3/s) |
S
(kg/m3) |
H
(m) |
V
(m/s) |
n
|
Date
|
Q
(m3/s) |
S
(kg/m3) |
H
(m) |
V
(m/s) |
n
|
|
08/07/77
|
5,240
|
268
|
7.5
|
2.93
|
0.036
|
08/01/82
|
7,450
|
56.5
|
8.1
|
3.48
|
0.038
|
|
08/07/77
|
5,120
|
324
|
7.5
|
2.74
|
0.041
|
08/01/82
|
7,220
|
56.5
|
7.4
|
3.66
|
0.036
|
|
08/07/77
|
6,910
|
592
|
8.6
|
3.1
|
0.043
|
08/01/82
|
6,230
|
56.5
|
7.1
|
3.35
|
0.038
|
|
08/07/77
|
9,720
|
843
|
9.7
|
3.87
|
0.042
|
08/02/82
|
9,400
|
55
|
8.6
|
4.05
|
0.036
|
|
08/08/77
|
6,550
|
356
|
8.9
|
2.91
|
0.049
|
08/02/82
|
9,290
|
55
|
9.2
|
3.76
|
0.041
|
|
08/08/77
|
4,950
|
405
|
7.6
|
2.43
|
0.045
|
08/02/82
|
7,710
|
55
|
8.6
|
3.4
|
0.039
|
|
08/28/73
|
3,110
|
440
|
7.2
|
2.19
|
0.041
|
08/02/82
|
5,150
|
69.1
|
7.9
|
3.03
|
0.038
|
|
08/28/73
|
3,520
|
508
|
7.8
|
2.39
|
0.037
|
08/03/82
|
5,660
|
91.1
|
7.6
|
2.84
|
0.041
|
|
08/28/73
|
2,880
|
324
|
7.8
|
2.32
|
0.036
|
08/03/82
|
4,790
|
99.6
|
7
|
2.72
|
0.037
|
|
09/02/73
|
4,150
|
313
|
7.7
|
2.53
|
0.040
|
08/04/82
|
4,150
|
82
|
7.1
|
2.37
|
0.041
|
|
08/04/82
|
3,550
|
82
|
6.6
|
2.29
|
0.040
|
|||||||
08/05/82
|
2,970
|
66.4
|
7.2
|
2.01
|
0.043
|
|||||||
Average
|
0.041
|
Average
|
0.039
|
|||||||||
Note: in this table, Q, S, H,
V and n stand for discharge (m3/s), sediment concentration (kg/m3),
average water depth (m), flow velocity (m/s) and Manning’s coefficient. Dates
are expressed in MM/DD/YY notation.
2. Effect of Sediment Concentration on Its Vertical Distribution
The increase in sediment
concentration and fine particle content results in the increase of flow viscosity
and specific weight, and consequently decreases of particle fall velocity. In
some cases even mud flow is formed. Based on 96 sets of field data collected
from 9 stations along the main stream and tributaries, namely, Huayuankou, Jiahetan,
Gaocun, Sunkou, Aishan, Luokou of the lower Yellow River (Figure 1), and
Huaxian, Huayin of lower Weihe River (tributary), and Chaoyi of Beiluohe River
(tributary), the vertical sediment concentration profile was studied by
comparing value of Ks with the cross sectional average sediment
concentrations S. Here Ks is the ratio of sediment concentration at
the relative depth 0.2h to that at 0.8h (measured from free surface), e.g. Ks
= S0.2 / S0.8, when median sediment grain size d50
is 0.03 - 0.10 mm. As shown in Figure 2, when the average sediment
concentration is lower than 200 kg /m3,
even with Froude’s number (Fr) higher than 0.2, the sediment concentration is
not uniformly distributed in the vertical direction, where Ks is
around 0.4 to 0.8. When the average sediment concentration is higher than 300
kg/m3, the sediment concentration becomes more uniform in the
vertical direction, where Ks is around 0.9 to 1.0.
Figure 2 Relationship between Sediment Concentration Ratio
(Ks) and Sediment Concentration (S)
The effect of changes in rheological characteristics of
fluid on sediment transport can be analyzed as followings. The ratio of fall
velocity of a particle in clear water to that in sediment-water mixture (or
muddy-water) can be written with Stokes equation:
Where ω0 and ωs
are particle fall velocities in clear water and in sediment water,
respectively. γs and γm are the specific weights of
sediment particles and sediment water. μr is the ratio of the viscosity of sediment water over clear
water. With the increase of sediment concentration, μr also increases, which
means fall velocity of particles decreases dramatically in sediment water. When
d50 = 0.036 mm and percentage of sediment with grain size finer than
0.01 mm is 20% (equivalent to the average sediment gradient of the Yellow
River), calculated values of mr and w0/ws corresponding to the long
term average sediment and field observed sediment of lower Yellow River are
listed in Table 2.
Table 2 Impact of Sediment
Concentration on Fall Velocity
S (kg/m3)
|
0
|
100
|
200
|
300
|
400
|
500
|
600
|
700
|
800
|
Notes
|
mr
|
1.0
|
1.49
|
2.08
|
2.74
|
3.48
|
4.32
|
5.40
|
6.93
|
9.33
|
Average Sediment Data
|
mr
|
1.0
|
1.50
|
2.0
|
2.4
|
3.0
|
4.0
|
4.50
|
6.50
|
8.50
|
Observed Sediment Data
|
w0/ws
|
1.0
|
1.55
|
2.25
|
3.09
|
4.10
|
5.32
|
6.97
|
9.38
|
13.4
|
As shown in Table 2, with
the increase of sediment concentration, w0/ws increases continuously,
and the fall velocity decreases significantly. When the sediment concentration
is 300 kg/m3, the fall velocity in muddy water is only one-third of
that in clear water. When the sediment concentration increases to 700 kg /m3, the fall velocity in
muddy water is only one-tenth of that in clear water. The above result is in
good agreement with the vertical sediment concentration distribution shown in Figure
2. Both indicate that fall velocity decreases with the increasing sediment
concentration, and the vertical sediment distribution also becomes more
uniform, which makes the sediment particles easier to be transported.
