FLOOD03637

• County: Statewide
• Basin: Statewide
• Title: Incipient Motion and Sediment Transport
• Date: 10/1/1973
• Prepared By: Journal of the Hydraulics Division
• Floodplain - Doc Type: Educational/Technical/Reference Information

1684 .

OCTOBER 1973

HY10

in which V,'r = the average critical velocity at InClplcnt motion; and VcJw
= the dimensionless critical velocity. Eq. 13 is the basic equation which specifies
the flow condition when a sediment particle is rcady to move on the bottom
of an open channel. The values of IV I' * 2' and *) have to be determined
from experiments. The roughness function, B, depends on whether the boundary
is in a hydraulically smooth, transition, or completely rough regime. If we assume
that Nikuradsc's roughness height can be replaced by sediment particle diameter,
the relationship between B and shear velocity Reynolds number U. dj v is shown
in Fig. 2. Herein, v = kinematic viscosity.
In the hydraulically smooth regime, B is a furtction of only the shear velocity
Reynolds number, U.djv, i.e.:

U.d
B = 5.5 + 5.7510g-,
v

U.d
o < - < 5 . . . . . , . . . . . . . . . . . . (14)
v

Thcn Eq. 13 bccomcs

[ D J
log-- I
d
+1
U,d
log ----;;- + 0.956

~................(15)
1jI, + <l<3

v
"

w

,
,

which is a hyperbola on a semilog plot between V cr/ wand U. d/ v. The relative
roughness, dj D, should not have any significant influence on the shape of
this hypcrbola in the hydraulically smooth rcgime,
In the completely rough regime, the protrusions reach outside the laminar
sublayer. The laminar friction contribution can be neglected, and B is a function
of only thc relative reghncss d/ D, i.e.

U.d
B = 8.5, - > 70 . . . . . . . . . . , . . . . . . . . . . . . . . . . . . (16)
v

~.
0:'
~,I
~"
~":
~. "
~,.
t
~f~
f'
'.'
,~'

then Eq. 13 becomes

V [IOg~-1 ]
~= +1
w 1.48

~...................(I7)
<l<, + 1j13

~""
,
~:"

Eq. 17 indicates that in the completely rough regime, the plot of V cJ w against
U. d/ v is a straight horizontal line. The position of this horizontal line depends
on the value of relative roughness, ~ l' ~2' and W 3"
In the transition regime with the shear velocity Reynolds number between
5 and 70, protrusions extend partly outside the laminar sublayer. Both the laminar
friction and turbulent friction contributions should be considered. As shown
in Fig. 2, Bdeviates gradually fromEq. 14withincreasing U.d/v. It is reasonable
for us to expect that, basically, Eq. 15 still is valid but with thc relative roughness,
d/ D, playing an increasingly important role as U. dj v increases.
The flow condition corresponding to the incipient motion depends more or
Jess on the investigator's definition of incipient motion. Data used in this paper
include Casey, Grand Laboratory, Thijsse, and Tison's "initial motion" (30),

t'....... .
"
.

f[
'..
t
h
f
~;

INCIPIENT MOTION .5
TABLE 1.-Flow Conditions at Incipient Motion
Particle Shear veloCity Dimensionless Number
size d, in Slope, Reynolds number, critical velocity, of data,
millimeters S RS6 = U. d/v Vc/w N
111 (21 (31 (4) 151
(a) Casey's Data
0.17 2.20 8.35 3
0.68 10.35 2.671 2
0.94 15.80 2.230 3
(b) Grand Laboratory's Data
IT 12.93 3.280 3
2.0 51.0 2.606 I
4.0 187.0 2.444 4
5.0 269.0 2.502 2
(c) Gilbert's Data
1.71 0.005-0.020 55.69 1.843 3
3.17 0.0100-0.0105 166.75 1.892 2
4.938 0.0105-0.0250 339.81 1.920 8
7.01 0.011 757.04 2.208 2
(d) Kramer's Data
0.51 0.00100 6.40 4.667 1
0.51 0.00125 6.55 3.656 2
0.51 0.00166-0.00168 6.66 3.550 2
0.51 0.00218-0.00228 6.76 3.577 2
0.53 0.00098-0.00101 7.34 3.781 3
0.53 0.00126 7.37 3.827 2
0.53 0.00165-0.00173 8.17 3.t20 2
0.53 0.00240-0.00246 8.34 3.206 2
0.55 0.00100 7.93 4.073 I
0.55 0.00125 8.14 3.869 2
0.55 0.00167 7.84 3.890 2
0.55 0.00250 7.53 3.557 2
(c) Thijsse's Data
0,28 I 3.04 7.010 6
(f) Tison's Data
0.15 1.61 12.583 6
0.25 2.64 7.385 5
0.3 3.43 6.268 4
1.0 19.33 2.913 4
2.0 65.00 2.573 I
(g) Vanoni's Data
0.102 L 1.50 27.673 4
(h) U.S. Waterways Experiment Stations's Data
0.2053 0.0010 2.47 8.165 4
0.2053 0.0015 2.67 9.005 2

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11

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