Geoscience Reference
In-Depth Information
Fundamentals of sediment transport
Introduced in this chapter are basic theories and empirical formulas of sediment
transport, which are essentially used to close the mathematical models of flow,
sediment transport, and morphological change in alluvial rivers. Some of them can be
found in Graf (1971), Vanoni (1975), Chien and Wan (1983), Chang (1988), Zhang
et al.
(1989), Raudkivi (1990), Simons and Senturk (1992), Julien (1995), and Yang
(1995). However, many recently developed non-uniform sediment transport formulas
are particularly included here.
3.1 SETTLING OF SEDIMENT PARTICLES
3.1.1 General considerations
Settling or fall velocity is the average terminal velocity that a sediment particle attains
in the settling process in quiescent, distilled water. It is related to particle size, shape,
submerged specific weight, water viscosity, sediment concentration, etc.
A sediment particle experiences gravity, buoyant force, and drag force during its
settling. Its submerged weight, which is the difference between the gravity and buoyant
force, is expressed as
ga
1
d
3
W
s
=
(ρ
−
ρ)
(3.1)
s
where
d
is the sediment size,
a
1
d
3
is the volume of the sediment particle, and
a
1
has
a value of
π/
6 for a spherical particle. Note that
ρ
is actually given as the pure water
density
f
because a single particle (or low concentration) is considered.
The drag force is the result of the tangential shear stress exerted by the fluid (skin
drag) and the pressure difference (form drag) on the particle. It is written in the general
form:
ρ
s
2
a
2
d
2
ω
F
d
=
C
d
ρ
(3.2)
s
is the settling velocity,
a
2
d
2
is the projected area
of the particle on the plane normal to the direction of settling, and
a
2
has a value of
π/
where
C
d
is the drag coefficient,
ω
4 for a spherical particle.
