Geoscience Reference
In-Depth Information
sediment, is a function of flow conditions and sediment properties. A variety of such
functions for bed load, suspended load, and bed-material load have been established
in the literature. Some of them are introduced in Sections 3.4-3.6.
3.4.1 Total transport rate of bed load
Many investigators — e.g., Duboys (1879), Schoklitsch (1930), Meyer-Peter and
Mueller (1948), Bagnold (1966, 1973), Dou (1964), Graf (1971), Yalin (1972),
Engelund and Fredsøe (1976), and van Rijn (1984a) — established formulas to cal-
culate the total transport rate of bed load. The following formulas are presented as
examples.
Meyer-Peter-Mueller formula
Meyer-Peter and Mueller (1948) related the bed-load transport rate to the excess grain
shear stress:
8
0.047 3 / 2
k )
3
/
2
(
k
/
γ
RS f
q b
s
gd m =
d m
(3.65)
γ)
γ
1
)
s
s
m 1 s 1 );
d m is the arithmetic mean diameter of the bed sediment mixture (m); k is the reciprocal
of the Manning roughness coefficient n of channel bed; k is the reciprocal of the
Manning coefficient n due to grain roughness, calculated by k =
where q b
is the bed-load transport rate byweight per unit time andwidth (N
·
d 1 / 6
90
26
/
; and R is
the hydraulic radius of the channel (m).
Bagnold formula
Bagnold (1966, 1973) related the sediment transport rate to the stream power
τ b U
and derived a bed-load transport formula:
log 0.37 h
nd
5.75 U
+ ω
ρ
b U
tan
τ
U
U c
U
s
s
ρ s ρ
1
q b =
(3.66)
α
U
m 1 s 1 ),
m 2 , tan
where q b
is
the friction coefficient of about 0.63, nd is the average height of acting force during a
saltation, d is the sediment size (m), and n
is by weight per unit time and width (N
·
τ b is in N
·
α
0.6 .
=
1.4
(
U /
U c
)
Dou formula
Dou (1964) also established an empirical formula for bed-load transport rate based
on the stream power concept:
K 0 ρ
U
g
s
U c )
q b =
ρ τ b (
U
(3.67)
ρ
ω
s
s
 
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