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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