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**

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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