and for trapezoidal channels is
Qb
1
=
(4.24)
3/2
Q
nw
2y o (1+ H )
2 1/ 2
1+
s
n
W
b
The Meyer-Peter and Mller formula (Equation 4.14) is often written in the form
qb = K(τ - τc )3 / 2
(4.25)
where:
3/2
1
12.9
≅
K=
(4.26a)
2/3
1/ 3
γs ρ
γ γs - γ
B
g γ
s
3/2
K B
Q
τ= b
γy o S f
(4.26b)
K
Q
r
τ c = B′(γ s - γ ) Dm
(4.26c)
An example of sediment transport calculations using the Meyer-Peter and Mller equation is
given in Section 4.12 (SI) and 4.13 (English).
4.5.2
Einstein's Method of Computing Bed Sediment Discharge
Einstein's (1950) method is included in detail because the formulation provides an excellent
discussion of sediment transport processes. The equations describe and incorporate the
physical processes of contact load and suspended load. The method computes a contact
load concentration and uses this concentration as the starting point for integrating the
suspended load as presented in Section 4.4. The method also incorporates the vertical
velocity distribution based on the roughness of the boundary.
The total bed sediment discharge is the sum of the contact load and the suspended load. As
mentioned earlier, there is no sharp demarcation between the contact bed sediment load and
the suspended bed sediment. However, this division is warranted by the fact that there is a
difference in behavior of the two different loads which justifies two physical equations.
Einstein's bed sediment discharge function gives the rate at which flow of any magnitude in a
given channel transports the individual sediment sizes which make up the bed material. This
makes his equations extremely valuable where it is necessary to determine the change in
bed material with time. Each size moves at its own rate. For each size Ds of the bed
material, the contact load is given as
4.13
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