An adjustment factor related to the Froude number was utilized to modify the Laursen
equation by Madden as follows:
76
0.1616
τ′
V
d
0.904
o - 1f *
C t = pb i
(B.8)
F
ω
τ
d
r
i
ci
i
In addition, Copeland and Thomas (1989) proposed a modification of Laursen's 1958
concept. This methodology was formulated to be utilized in both sand-bed rivers and, to a
lesser degree, in larger gravel-bed rivers. The Laursen equation as modified by Copeland
and Thomas is:
V′
76
τ′
d
o - 1f *
C t = 0.01γ pi i
(B.9)
ω
τ
d
i
ci
i
The results of Copeland and Thomas' modification to the Laursen concepts are presented in
Figure B.6. The relation between V*/ωi and f(V*/ωi) for four sizes of sediment sizes and three
sizes of channels were plotted on the Laursen Graph and are presented on Figure B.7.
Many researchers have observed that more than one value of bed material transport can be
obtained from the same values of Q, V, Sw, Sf, and τo, see for example, Brooks (1958),
Simons and Sentrk (1992) and Yang (1996). Gilbert (1914) proposed the fact that different
values of transport can occur for the same hydraulic parameters.
silt-bed
v. fine to fine sand-bed
med to very coarse sand-bed
gravel-bed
Figure B.6. Modifications of Laursen's (1958) Graph.
B.22
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