Kodoatie adapted the Laursen methodology for analysis because this methodology was

expressed in terms which are generally recognized as important variables related to bed-

material transport. Dimensionless unit stream power was used with regression analysis and

nonlinear optimization techniques to improve the Laursen Equation. The modified Laursen

equation resulting is (variables are defined in Section 4.9):

V

76

a

log f *

τo '

D

VS

ω

- 110

C t = 0.01γ 50

50

(B.10)

d

τ

ω

c50

where the coefficient a is a variable related to mean bed material diameter as shown in Table

B.11.

Table B.11. Value of "a" in Equation B.10 for Various Sizes of Bed Material.

Bed Material

"a"

Gravel

0.0

Medium to very coarse sand

-0.2

Very fine to fine sand

0.078

Silt

0.06

In equations B.7 and B.10

Sediment concentration, N/m3 (lb/ft3)

=

Ct

Unit weight of water, N/m3 (lb/ft3)

γ

=

=

Fraction by weight of bed sediment mean size, Di

pi

Di

=

Bed sediment size with I percent finer, m (ft)

y

=

Mean flow depth, m (ft)

V

=

Mean veolcity, m/s (ft/s)

=

V*

gRS = τ′ / ρ ,m / s (ft / s)

o

ω

=

Particle fall velocity, m/s (ft/s)

S

=

Slope

a

=

Exponent given in Table B.11

τo′

=

1/ 3

ρV 2

D50

2

2

y , N / m (lb / ft )

58

Particle critical shear stress = ks (γs - γ) Di, N/m2 (lb/ft2)

τci

=

=

Shields parameter

ks

Unit weight of sediment, N/m3 (lb/ft3)

γs

=

Note that in the modified Laursen equation an exponent equal to log f(V*/ω50) is a significant

variable. This parameter can be determined referring to Figure B.8. Comparison of

modifications to the Laursen equation by Madden, Copeland, and Kodoatie et al. are

presented in Table B.12.

B.24

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