Recall that V*2 = τo/ρ. The relation between τo/(γs - γ) Ds and DsV*/ν for the condition of
incipient motion has been determined experimentally by Shields and others. As the relation is
determined experimentally, the relation considers viscous effects. In functional form the
relation (called the Shields relation) is as follows:
V*c D s
τ0
= f
(3.34)
υ
(γ s - γ) Ds
3.5.4 Shields Diagram
Many experiments have been conducted to develop an explicit solution of the Shields
relation. The earliest one is the graphical presentation given by Shields (1935). The concept
of the Shields Diagram (Figure 3.15) is widely accepted and τc/(γs - γ) Ds (often referred to as
Shields parameter) is widely used to determine the shear stress at beginning of motion. For
example, Gessler (1971) gave Figure 3.16 for the relation given in Equation 3.34.
Figure 3.15. Shields Diagram: dimensionless critical shear stress.
3.36
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