Environmental Engineering Reference
In-Depth Information
Table 3.4.
Coefficient
γ
as function of Reynolds number.
Reynolds number
<
0.2
0.2-1
1-200
>
200
4.35 Re
−
0
.
03
4.45 Re
−
0
.
1
γ
4.65
2.39
3.6 CHARACTERISTIC DIMENSIONLESS PARAMETERS
The equations of motion and continuity, both for water and sediment,
roughly define the transport of water and sediment. An analytical
description of all the physical processes by the equations is not yet
possible and therefore, the sediment transport theories still rely on
data from field and experimental investigations and from dimensional
analysis. Based on dimensional analysis several processes related to
sediment transport can be expressed as a function of independent
dimensionless parameters. The following parameters are widely used to
describe the sediment transport in open channels (van Rijn, 1993).
Particle parameter (
D
∗
) reflects the influence of gravity, density and
viscosity on sediment transport and is given by:
(
s
1
/
3
−
1)
g
ν
2
D
∗
=
d
50
(3.15)
where:
s
=
specific density of the sediment particle (dimensionless)
acceleration due to gravity (m/s
2
)
g
=
d
50
=
median diameter (m)
kinematic viscosity (m
2
/s)
Particle mobility parameter (
θ
) is the ratio of the drag force and the weight
of the submerged particle and reads:
ν
=
u
2
∗
τ
cr
cr
θ
cr
=
1)
gd
50
=
(3.16)
(
s
−
(
s
−
1)
ρgd
50
where:
τ
=
shear stress (N/m
2
)
critical shear stress according to Shields (N/m
2
)
τ
cr
=
shear velocity (m/s)
u
∗
=
√
(
τ/ρ
)
u
∗
cr
=
u
∗
=
critical shear velocity (m/s)
u
∗
crit
=
√
(
τ
crit
/ρ
)
ρ
density (kg/m
3
)
=
acceleration due to gravity (m/s
2
)
g
=
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