Geoscience Reference
In-Depth Information
and shape factor in the turbulent settling region. Dietrich (1982) proposed an empirical
formula to determine the settling velocity of sediment from laminar to turbulent settling
regions, considering the effects of sediment size, density, shape factor, and roundness
factor. However, the roundness factor used in the Dietrich formula is rarely measured
in practice, and his formula is very complicated and relatively difficult to use. Jimenez
and Madsen (2003) simplified the Dietrich formula, but still graphically related two
coefficients to the shape factor.
For more generality and convenience to use, Wu and Wang (2006) calibrated the
coefficients
M
,
N
, and
n
in Eq. (3.15) as follows by using the natural sediment settling
data of Krumbein (1942), Corey (1949), Wilde (1952), Schulz
et al
. (1954), and
Romanovskii (1972):
53.5
e
−
0.65
S
P
,
N
5.65
e
−
2.5
S
P
,
=
=
=
+
M
n
0.7
0.9
S
P
(3.17)
where
S
P
is the Corey shape factor defined in Eq. (2.9). Fig. 3.3 compares the measured
drag coefficients and those calculated using Eq. (3.15) with coefficients determined
by Eq. (3.17). Because the data in Fig. 3.3 were in the range of R
e
>
3, the trend
of the
C
d
−
3 was determined using the data sets of
Zegzhda, Arkhangel'skii, and Sarkisyan compiled by Cheng (1997). Because naturally
worn sediment particles were used in these three sets of experiments, their Corey shape
factors were assumed to be 0.7. The relationship between
C
d
and
R
e
in the range of
these data is shown in Fig. 3.4.
It should be noted that when
S
P
R
e
relation in the range of
R
e
<
=
1.0, the proposed Eq. (3.15) with coefficients
determined by Eq. (3.17) deviates from the relation of spheres obtained by Rouse
(1938). The reason is that the naturally worn sediment particles with a Corey shape
Figure 3.3
Drag coefficient as function of Reynolds number and particle shape (Wu and Wang, 2006).
