Geoscience Reference
In-Depth Information
13.95 ν d 2
1.09 ρ
1 gd
13.95 ν d
s
ρ
ω
=
+
(3.12)
s
The Zhang formula can be used in a wide range of sediment sizes from laminar to
turbulent settling regions. It can be simplified to Eq. (3.5) with a coefficient of 1/25.6 in
the laminar settling region, and to Eq. (3.8) with a coefficient of 1.044 in the turbulent
settling region.
Van Rijn (1984b) suggested the use of the Stokes law, Eq. (3.5), in computing the
settling velocity for sediment particles smaller than 0.1 mm, the Zanke (1977) formula
for particles from 0.1 to 1 mm:
1
1 / 2
0.01 ρ s
1 gd 3
ν
10 ν d
ω
=
+
ρ
1
(3.13)
s
2
and the following formula for particles larger than 1 mm:
1.1 ρ
1 gd 1 / 2
s
ρ
ω
=
(3.14)
s
In fact, the formulas of Rubey, Zhang, and Zanke have the same formulation with
different coefficients. Similar formulas were also proposed by Cancharov (1954; see
Cheng, 1997), Sha (1965), Graf (1971), Hallermeier (1981), Raudkivi (1990), Julien
(1995), and Ahrens (2000). In general, the drag coefficient can be approximated by
(Cheng, 1997)
M
R e
N 1 / n n
1 / n
C d =
+
(3.15)
where M , N , and n are coefficients. Table 3.1 lists the values of these three coefficients
given by different investigators for naturally worn sediment particles. The coefficient
M was given a value of 24 by Rubey (1933), Zanke (1977), and Julien (1995), and
values between 32-34 by Zhang (1961), Raudkivi (1990), and Cheng (1997). The tests
against measurement data performed by Cheng have shown that for natural sediment
particles the values of 32-34 for M give better predictions than the value of 24. Note
that the latter corresponds to the Stokes law, Eq. (3.5), for spherical particles. Rubey
gave the coefficient N a value of 2.1, which significantly underestimates the settling
velocity for coarse sediment particles.
Cheng (1997) used M
1.5, and derived the following formula
for the settling velocity of naturally worn sediment particles:
=
32, N
=
1, and n
=
25
5 1.5
= ν d
1.2 D 2
ω
+
(3.16)
s
2
1
/
3 .
where D =
d
[ s
1
)
g
]
 
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