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Figure 3.4 Drag coefficient as function of Reynolds number for naturally worn sediment particles
( S P = 0.7 ) (Wu and Wang, 2006).
factor of 1.0 may not be exactly spherical, and other factors, such as particle surface
roughness, also affect the settling process.
Inserting Eq. (3.15) into Eq. (3.3) yields the general relation of settling velocity (Wu
and Wang, 2006):
1
4 +
n
4 N
3 M 2 D 3
1 / n
M
ν
Nd
1
2
ω
=
(3.18)
s
Note that the sediment size d in Eq. (3.18) should be the nominal diameter (in
meters), on which the drag coefficient C d in Fig. 3.3 was based.
Eq. (3.18) is applied with coefficients M , N , and n determined using Eq. (3.17). It is
an explicit relation of settling velocity with sediment size and shape factor; thus, it can
be easily used. The predictions using Eq. (3.18) and the curves recommended by the
U.S. Interagency Committee (1957) are compared in Fig. 3.5. Here, the temperature
is 24 C, the Corey shape factors are in the range of 0.3-0.9, and the sediment sizes
are between 0.2 and 64 mm. It can be seen that these two methods give very close
predictions. The average deviation between them is about 2.75%. However, larger
deviations are expected for fine sediments (less than 0.2 mm in diameter). The reason,
which has been mentioned above, is that the U.S. Interagency Committee's curves
approach the Stokes law, Eq. (3.5), that might result in 30% error for the settling
velocity of natural sediment particles as shown in Fig. 3.4. Eq. (3.18) has been validated
using measurement data and should have better accuracy than the U.S. Interagency
Committee's curves for fine sediment particles.
In addition, Wu and Wang (2006) compared more than ten sediment settling veloc-
ity formulas, and found that the formulas of Zhang (1961), Hallermeier (1981),
Dietrich (1982), Cheng (1997), Ahrens (2000), Jimenez and Madsen (2003), and
Wu and Wang (2006) have comparable and reasonable reliabilities for predicting the
 
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