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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