Sediment Properties - Sediment Transport in Irrigation Canals: A New Approach - page 52

3.5 FALL VELOCITY

The velocity of sediment particles settling in a liquid is called the fall
velocity w s . This velocity is an important physical value to describe the
sedimentation and suspension behaviour of sediment particles. The basic
fall velocity of sediment particles is derived from a single sphere with
diameter d falling with a constant velocity in quiescent (quiet) water. At
the beginning of the settling process, the fall velocity is small and the
force of gravity is greater than the resistance. Hence, the sphere moves
with acceleration, and the resistance increases with the velocity. In time
the resistance equals the force of gravity and the sphere then falls with a
constant velocity. The force of gravity acting on the sphere is in equilibrium
with the resistance to the motion, which depends on the velocity and a
drag coefficient.
From resistance force

= gravity force follows:

C d 1

π
4 d 2

π
6 d 3 g( ρ s − 2 ρ w w s

= ρ w ) (3.9)

4
3

gd
C d

w s = (3.10)

The drag coefficient C d is a function of the Reynolds number ( w s d / ν ).
For low Reynolds numbers C d =

24/Re.
For natural sand, a Reynolds number lower than 0.1 and C d = 24/Re,

Stokes law gives the fall velocity as:

1) gd 2
18 ν

( s −

w s = 1 ≤ d ≤ 100 m (3.11)

µ

where:
w s =

fall velocity in clear water (m/s)

s = specific density of the sediment particle (dimensionless)

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

d = diameter of the particle (m)

ν = kinematic viscosity (m 2 /s)

During the settling process, the motion of a particle also causes the sur-
rounding fluid to move. If the Reynolds number (Re w s d / ν ) is less than

approximately 0.4, the effect of inertia forces induced in the fluid by the
motion is much less than those due to the fluid viscosity. The settling
of a single particle affects a large region of the surrounding fluid if the
Reynolds number is low. When the inertia forces in the fluid are negligible

=