where:

=

Bed-load rate in weight per unit time and per unit width

qB

=

Water discharge quantity determining bed load transport

Qb

Q

=

Total water discharge

=

Depth of flow

yo

=

Energy slope

Sf

=

Dimensionless constants

B′, B

B′ has the value 0.047 for sediment transport and 0.034 for the case of no sediment

transport. B has a value of 0.25 for sediment transport and is meaningless for no transport

since qB is zero and the last term drops out. The quantities KB and Kr are defined by the

V

KB =

(4.15)

R 2 / 3 S1/ 2

f

and

V

Kr =

(4.16)

1/ 2

2/3

S′f

R

where:

=

Sf

Total energy slope

=

Part of the total slope required to overcome grain resistance

Sf′

=

Part of the total slope required to overcome form resistance

Sf - Sf′

Therefore

′

KB

fb

V

=

(4.17)

Kr

8

gRS f

from the Nikuradse pipe friction data with pipe diameter equal to four times the hydraulic

radius and Ks = D90. If the boundary is hydraulically rough, (V*D90/ν≥ 100), Kr is given by

26

Kr =

(4.18)

1/ 6

D90

where D90 is in meters.

Equation 4.14 is dimensionally homogeneous so that any consistent set of units may be

used. Equation 4.14 was converted to units generally used in the United States in the field of

sedimentation for water and quartz particles by the U.S. Bureau of Reclamation in 1960 and

is expanded here for application in SI units. This equation is

3/2

3/2

D 90

1/ 6

Q

qB = K u1 K u2 b

y o S f - 0.627Dm

(4.19)

Q

n

b

4.11

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