Geoscience Reference
In-Depth Information
Mathematical description of flow
and sediment transport
This chapter presents a mathematical basis for computational river dynamics,
including definition of water and sediment properties, sediment diffusion the-
ory, Reynolds-averaged flow and sediment transport equations and their
turbulence closures, derivation of 1-D and 2-D model equations from 3-D model
equations, formulation of equilibrium and non-equilibrium sediment transport mod-
els, and equations of non-uniform sediment transport and bed material sorting.
2.1 PROPERTIES OF WATER AND SEDIMENT
2.1.1 Properties of water
Density and specific weight of water
Water density,
m
−
3
(kilograms
ρ
f
, is the mass of water per unit volume, often in kg
·
m
−
3
at 4
◦
C and
per cubic meter) in the international unit (SI) system. It is 1,000 kg
·
varies slightly with temperature, as shown in Table 2.1.
The specific weight of water,
γ
f
, is the weight of water per unit volume, often in
m
−
3
(Newtons per cubic meter). It is related to the water density by
N
·
γ
f
=
ρ
f
g
(2.1)
s
−
2
(meters per
where
g
is the gravitational acceleration and equals about 9.80665 m
·
square second).
Viscosity of water
Water deforms under the action of shear. The dynamic viscosity of water,
µ
, is the
constant of proportionality relating the shear stress,
τ
, to the deformation rate,
du
/
dz
,
as follows:
du
dz
τ
=
µ
(2.2)
where
u
is the flow velocity, and
z
is the coordinate normal to the flow direction.
