where:
Unit sediment transport rate, ft2/s (m2/s)
qs
=
cs2, cs3
=
fine gravel
Coefficient based on mean particle diameter (note that cs1 must be
cs1
=
adjusted for SI units)
y
=
Mean flow depth, ft (m)
V
=
Mean flow velocity, ft/s (m/s)
This relationship can be applied in steep streams with sand and fine gravel beds that
normally exhibit critical or supercritical flow. This is the only transport relationship specifically
developed for upper flow regime conditions. These power relationships were developed by
Simons et al., from a computer solution of the Meyer-Peter and Mller bed load transport
equation and the integration of the Einstein method for suspended bed material discharge
(Julien 1995).
Table 4.1 provides the coefficient and exponents for Equation 4.48 (for English units) for
different gradation coefficients and sizes of bed material. Note that if sediment transport
in SI units is desired, CS1 needs to be multiplied by a factor of 0.3048(2 - Cs2 - Cs3). The
1 D 50 D 84
Gr =
+
(4.49)
2 D16 D 50
where:
=
Size of the bed material for which n percent of a sediment sample is finer.
Dn
In this case, n = 84, 50, and 16, respectively.
Table 4.1. Coefficient and Exponents of Equation 4.48 (Simons et al.).*
D50 (mm)
0.1
0.25
0.5
1.0
2.0
3.0
4.0
5.0
-5
-5
-6
-6
-6
-6
-6
-6
cs1
Gr = 1
3.30x10 1.42 x10 7.60 x10
5.62 x10 5.64 x10 6.32 x10 7.10 x10 7.78 x10
cs2
0.715
0.495
0.28
0.06
-0.14
-0.24
-0.3
-0.34
cs3
3.3
3.61
3.82
3.93
3.95
3.92
3.89
3.87
-5
-6
-6
-6
-6
-6
Gr = 2 cs1
1.59 x10 9.80 x10
6.94 x10 6.32 x10 6.62 x10 6.94 x10
cs2
0.51
0.33
0.12
-0.09
-0.196
-0.27
cs3
3.55
3.73
3.86
3.91
3.91
3.9
-5
-6
-6
Gr = 3 cs1
1.21 x10
9.14 x10 7.44 x10
cs2
0.36
0.18
-0.02
cs3
3.66
3.76
3.86
-5
Gr = 4 cs1
1.05 x10
cs2
0.21
Cs3
3.71
(2-Cs2 -Cs3 )
* c s1 (SI units) = 0.3048
(c s1 )
4.28
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