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Technical Note DOER-N4
May 1999
A method developed by Ackers and White (1973) is used to determine the water depth for initiation
of motion for a specified grain size, current condition, and wave condition. The original Ackers and
White relationships predict sediment transport and initiation of sediment transport as a function of
sediment grain size, depth, and depth-averaged current velocity. As stated previously, this method
was designed for current-only environments, and the above described effective velocity that
accounts for waves and currents will be substituted for the current velocity in all equations. The
equations were not developed for a single grain size, but rather for uniformly graded noncohesive
sediment with a median grain diameter in the range of 0.04 mm to 4.0 mm, assuming only a small
fraction (<5-17 percent depending on mineralogy) cohesive clays and fine silts (White 1972). Many
equations have been developed to describe noncohesive sediment transport, and the various
methods have been compared with multiple data sets (Brownlie 1981). These comparisons indicate
that the Ackers and White method performs as well or better than the other well-recognized
procedures.
The Ackers-White transport equations relate initiation of sediment transport to two dimensionless
quantities. The first, a nondimensional grain size Dgr , is defined as a function of the ratio of the
immersed particle weight to the viscous forces acting on the grain:
g (s - 1)
13
Dgr = D
(7)
υ2  
where
D = sediment diameter (i.e., D50), ft
2
g = acceleration of gravity, ft/sec
s = sediment-specific gravity
υ = fluid kinematic viscosity, ft2/sec
The value of Dgr is used to categorize the sediment as coarse or transitional, with the following
coefficients defined for the two sediment classifications:
a. Coarse sediments: Dgr > 60.
n = 0.0
A = 0.17
b. Transition sediments: 1.0 < Dgr 60.0.
()
n = 1.00 - 0.56 log Dgr
(8)
0.23
A=
+ 0.14
(9)
Dgr
3

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