Geoscience Reference
In-Depth Information
Yang formula
Yang (1973, 1984) related the bed-material load transport to the unit stream power
as follows:
N
log
US
f
ω
U
c
S
f
ω
log
C
t
∗
=
+
s
−
M
(3.106)
s
where
C
t
∗
is the sediment concentration in parts per million (ppm) by weight,
U
c
is
determined using Eq. (3.29), and
M
and
N
are coefficients. For sand (
d
≤
2 mm)
0.286 log
ω
s
d
ν
−
0.457 log
U
∗
ω
s
M
=
5.435
−
0.409 log
ω
s
d
ν
−
0.314 log
U
∗
N
=
1.799
−
(3.107)
ω
s
and for gravel
(
2mm
<
d
<
10 mm
)
0.633 log
ω
s
d
ν
−
4.816 log
U
∗
ω
M
=
6.681
−
s
0.305 log
ω
s
d
ν
−
0.282 log
U
∗
ω
N
=
2.784
−
(3.108)
s
Ackers-White formula
The transport of coarse sediments, which are mainly in bed load, is attributed to the
stream power corresponding to the grain shear stress,
τ
b
U
, while the transport of fine
sediments, which are mainly in suspended load, is related to the turbulence intensity
and in turn the total stream power,
τ
b
U
. Based on this concept, Ackers and White
(1973) proposed a mobility factor of sediment transport:
1
−
n
U
n
∗
U
√
32 log
F
gr
=
(3.109)
[
(γ
/γ
−
1
)
gd
]
1
/
2
(
/
)
10
h
d
s
and related the bed-material load to this mobility factor as follows:
U
U
n
F
gr
A
c
−
1
m
C
t
∗
h
d
G
gr
=
=
(3.110)
γ
/γ
s
where
C
t
∗
is an empirical coefficient,
m
is an empirical exponent,
n
is the transition exponent, and
A
c
may be interpreted as
the critical value of
F
gr
for sediment incipient motion. Coefficients
is the sediment concentration by weight,
,
A
c
,
m
, and
n
3
, as listed
in Table 3.5, based on best-fit curves of laboratory data with sediment sizes greater
than 0.04 mm and Froude numbers less than 0.8.
2
1
/
were related to the dimensionless grain diameter
D
∗
=
d
[
(ρ
/ρ
−
1
)
g
/ν
]
s