Table B.5 provides the coefficient and exponents for Equation B.3 (for English units) for

as the gradation coefficient of the bed material and is

1 D

D

Gr = 50 + 84

(B.4)

2 D16 D 50

where:

Size of the bed material for which n percent is finer

Dn

=

Equation B.3 was obtained for steep, sand- and fine gravel-bed channels experiencing

critical and super-critical flows [Simons, et al. (1981), Julien (1995)]. The range of

parameters utilized to develop this equation is shown in Table B.6.

The results for the total bed sediment discharge are presented in Table B.5. The high values

of Cs3 (3.3 < Cs3 < 3.9) show the high level of dependence that sediment transport rates have

with respect to velocity. Comparatively, the influence of depth is less important (-0.34 < Cs2

< 0.7). For smaller sizes the exponent Cs2 is positive since the smaller material is more

easily suspended and resulting sediment concentration profiles are more uniform. Thus, the

larger the depth, the more sediment will be suspended at a given velocity. For the larger

sediment sizes the sediment is more difficult to suspend and keep in suspension.

Table B.5. Coefficient and Exponents of Equation B.3 (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

Gr = 1

cs1

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

Table B.6. Range of Parameters Equation B.3 Developed by Simons et al.

Parameter

Value Range

SI Units

Froude Number

14

--

Velocity

1.98 7.92

m/s

Bed Slope

0.005 0.040

m/m

2

Unit Discharge, q

3.05 60.96

m /s

Particle Size, D50

> 0.062

mm

B.16

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