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Figure 3.1 Relation between C d and R e for spheres.
3.1.3 Settling velocity of sediment particles
Sediment particles in natural rivers, which usually have irregular shapes and rough
surfaces, exhibit differences in settling velocity in comparison with spherical parti-
cles. Rubey (1933) derived the following formula for the settling velocity of natural
sediment particles:
F ρ s
1 gd
ω
=
ρ
(3.9)
s
where F
0.79 for particles larger than 1 mm settling in water with temperatures
between 10 and 25 C. For smaller grain sizes, F is determined by
=
2
3 +
1 / 2
1 / 2
2
2
36
ν
36
ν
=
F
(3.10)
gd 3
( ρ s
gd 3
s
)
1
)
1
Zhang (1961; also see Zhang and Xie, 1993) assumed the drag force on a sediment
particle in the transition between laminar and turbulent settling regions as
d 2
2
s
F d =
C 1 ρν
d
ω s +
C 2 ρ
ω
(3.11)
where C 1 and C 2 are coefficients. Based on many laboratory data, Zhang obtained
the formula for the settling velocity of naturally worn sediment particles:
 
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