Furthermore, Einstein suggested that

V / V*′′ = θ[ψ′]

(4.43)

where

ρ s - ρ D 35

ψ′ =

(4.44)

ρ R′ S f

b

The relation for Equation 4.44 is given in Figure 4.11. The procedure to follow in computing

Rb′ depends on the information available. If mean velocity V, slope S, hydraulic radius Rb

and the size of bed material are known, then Rb′ is computed by trial and error using

Equation 4.42 and Figure 4.11.

Figure 4.11. Friction loss due to channel irregularities, as a function of sediment

transport (after Einstein and Barbarossa 1952).

The procedure for computing total bed sediment discharge in terms of different size fractions

of the bed material is:

Calculate ψ* using Equation 4.33 for each size fraction

(1)

Find φ* from Figure 4.5 for each size fraction

(2)

(3)

Calculate iBqB for each size fraction using Equation 4.32

(4)

Sum up the qB across the flow to obtain iBQb

(5)

Sum up the size fractions to obtain Qb

4.20

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