Environmental Engineering Reference
In-Depth Information
The dimensionless mobility parameter
F
gr
is given by:
⎡
⎤
1
−
n
u
n
∗
gd
35
(
s
V
√
32 log
10
h
⎣
⎦
F
gr
=
d
35
(5.98)
−
1)
F
g
, is the grain Froude number and is given by:
V
F
g
=
(5.99)
[(
s
−
1)
gd
50
]
0
.
5
The critical grain Froude number
F
gcr
is:
4
.
596
τ
0
.
5293
∗
0
S
−
0
.
1405
σ
−
0
.
1696
s
F
gr
=
(5.100)
Similarly the Brownlie's predictor is given by (see Appendix A):
F
g
cr
)
1
.
978
S
0
.
6601
R
d
50
−
0
.
3301
0
.
007115
q
s
q
s
=
c
f
(
F
g
−
(5.101)
Differentiation gives:
1
.
978
F
g
F
g
−
N
=
1
+
(5.102)
F
gcr
The assessment of
N
(Klaassen, 1995; Méndez, 1998) shows that the
value
N
depends upon the flow conditions and sediment characteristics.
In most cases, except for Engelund-Hansen (Bagnold, 1966)
N
increases
with a decrease in flow velocity and in particle size (see Figure 5.23). For
a higher velocity the value of
N
remains fairly constant for a specified
particle size.
For the Brownlie predictor the exponent
N
is for a geometric standard
deviation for the grain Froude numbers
F
g
larger than 10, independent of
the bed slope and sediment size (see Figure 5.23). A standard deviation
for
F
g
more than 10 refers to a velocity that is slightly larger than that
required for the initiation of motion. Moreover the value of
N
is always
more than 3 for sediment smaller than 0.50 mm and Froude numbers
smaller than 0.6.
The exponent
N
for the Ackers-White predictor is more sensitive to
the sediment size (Figure 5.24). Near the initiation of motion the value
of
N
cannot be determined.
N
is always more than 4 for Froude numbers
less than 0.6, which is also the upper limit of the normal flow conditions
in irrigation canals.
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