V*D s

= 1.00

ν

In this region, the boundary is in a transitional state and δ/3 < Ds < 6 δ. For this region:

1 k s V*

ks

=

(3.36)

δ 11.6 ν

The Shields Diagram has a form similar to Darcy-Weisbach's resistance coefficient f versus

Reynolds number Re. Also, it is similar in form to the relation between the drag coefficient CD

and the Reynolds number Re for cylindrical bodies and to the relation between V*ks/ν and B =

f (V*ks/ν) proposed by Nikuradse (1933).

The minimum value of F* = τc/(γs - γ)Ds is 0.032 ~ 0.033 and the corresponding value of R* =

V*Ds/ν is about 10. If Ds is computed from these values of R* and F*, it can be seen that Ds =

0.0006 m = 0.6 mm = 0.002 ft. For larger diameter particles, ripples do not form; dunes form

on the bed.

In this region, the boundary is completely rough and F* is independent of Reynolds number

R* and is equal to

ρV*2

= 0.06

(3.37)

(γ s - γ)Ds

The upper limit of R* in Region 3 is subject to discussion. Some researchers have given

values as high as 1,000 for R*. Considering F*, Meyer-Peter and Mller (1948) suggest a

value of 0.047 instead of 0.06.

Experimental values of the Shields parameter for sand size (0.062 mm to 1.0 mm) bed

material range from 0.030 to 0.047. For coarser bed material (gravels, cobbles and larger)

the experimentally determined Shield's parameter ranges from 0.020 to 0.10. An average

value of 0.039 is a good compromise for all sizes (Fiuzat and Richardson 1983, Ruff et al.,

1985, 1987).

It is suggested by Simons (Simons and Senturk 1992) that collecting data on initiation of

particle motion under field conditions permits selection of a more precise value for the

particular channel. However, identifying initiation of particle sizes by utilizing observed

values or by trapping particles in motion over a range of discharges is extremely difficult. It

must be done with considerable care and with knowledge of channel geometry and hydraulic

conditions at the cross section and upstream of the selected cross section. This is

particularly true for gravel- and cobble-bed streams.

3.38

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