54
R.H. Charlier and Chr. P. De Meyer
Eq. (1) is based on particle diameters in the range 3.17 to 28.6 mm. The dso is
used as the effective diameter for particle mixtures, while the dgo is used as the
effective diameter for grain roughness.
1.3
Prediction Method of Frijlink (1952)
The formula of Frijlink is essentially an approximation of the formulas of MeyerPeter and Miiller (1948) and of Einstein (1950), as shown in Fig. 1.
The formula, which is because of its simplicity given here, reads :
9b,c = 5 X/'~U * ds0 e027/(/~O)
(2)
~C
with : u*o = bed shear velocity.
The parameters are identical to those given in 1.2.
1.4
Prediction method of Bagnold (1966)
Bagnold (1966) introduced an energy balance concept and related the bed-load
U'ansport to the work done by the fluid (product of bed-shear stress and depthaveraged velocity). He explicitly incorporated the local bed slope in his bed-load
formula:
e b
qb,c =
~'b U
(3)
(Ps -- p)g(tan d~b - tanfl)
The bed-load transport rate is related to the overall bed-shear stress and not to the
grain-shear stress. Thus, the effect of the bed-forms is not taken into account,