Sediment Properties - Sediment Transport in Irrigation Canals: A New Approach - page 53

then the drag coefficient is inversely proportional to the Reynolds number.
The fall velocity is proportional to the square of the sphere diameter and
the density, but it is inversely proportional to the viscosity of the fluid.
Stokes law is valid for Re < 0.4 and in water at normal temperature the
fall velocity is valid for particles smaller than d 0.076 mm.

For larger quartz particles Stokes law has to be adjusted and the fall
velocity reads:

=

1

1

0 . 5

1) gd 3 10 ν

d

0 . 01( s −

w s = + − 100 ≤ d ≤ 1000 m

µ

ν 2

(3.12)

1 . 1 ( s w s = − 1) gd d ≥ 1000 m (3.13)

µ

where:
w s = fall velocity in clear water (m/s) (see Table 3.3)

s = relative density of the sediment particles (dimensionless)

acceleration due to gravity (m/s 2 ) g =

d = diameter (m)

kinematic viscosity (m 2 /s)

ν =

Table 3.3. Fall velocity for sediment particles.

d (mm) 0.06 0.1 0.2 0.3 0.4 0.5 0.75 1.0

w s (mm/s) 3.2 8.9 25 44 59 72 98 140

The presence of a large number of other particles during the settling
process will decrease the fall velocity of a single particle. The fall
velocity of a single particle influenced by the presence of other particles
follows from:

c ) γ w s w s,m = (1 − with 2 . 3 ≤ γ ≤ 4 . 6 and 0 ≤ c ≤ 0 . 3 (3.14)

where:
w s,m = fall velocity influenced by other particles (m/s)

w s =

fall velocity in clear water (m/s)

c = volumetric sediment concentration (percent)

γ = coefficient, which is a function of the Reynolds number

(see Table 3.4)

The coefficient γ is slightly dependent on the particle shape, but this
can be ignored. For fine sediments with a concentration of 1%, the reduc-
tion in fall velocity will be around 5%. The fall velocity of a particle in
turbulent water is different from the velocity in quiescent water. A cluster
of particles (cohesive sediments) will have a greater fall velocity.