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

1682. OCTOBER 1973
7rd2 P 7f'dJ
C~--w' =-(p - p)g
4 2 6'

. .())

in which C~ drag coefficient at w; w = terminal fall velocity; and P, =
density of sediment particle. By substituting C~ with I.VI CD' and elirninatina

~,:

I
,
I
9----1
I
I
I
I
I
I
I

,
~
,

"

'0

fR

'5

, FIG.
,
.
,
,
, 11
I
.
, 10
t
! ~

1.-Diagram of Forces Acting on Sediment Particle in Open Channel Flow

3.5.5"5.751O<J~

.0..::: ::,:.
r,'"" "
"
'J
" ,
.: I
I
I
I
I
I
I

......:..
. ....~:. .
. ..1'......

. 9
o
~ II

"
~ 7
"

"
a'8.S t
I
I
I
I
,

tOMPLETElYROUGH

"

Sl'OOT~

TRANSITION

s
0.;: 0.4

1.0 1.2 1.4 1.5 1.8 2.0 2.2 2.4 2.6
lOGARITiIMOFSIl[ARVELOCITYREYNOLOSNUM8[R,10<J~

FIG. 2.-Relationship Between Roughness Function and Shear Velocity Reynolds
Number (Ref. 18, Fig. 20.21)

Cv from Eqs. 2 and 3. the drag force becomes

'TTd3
F D = --------;- (p ,- p)g V~ .. . . . . . . . . . . . . . . . . . . . . . . . . . (4;
61j1,w'

If we assume that the logarithmic law for velocity distribution (15) can be applied
in this case, then

INCIPIENT MOTION

.

v )'
. -L~ 5.75 log- + B.
U, d

. . (5)

in which V y =:: local velocity at distance y above the bed; and B :;;:: roughness
function. Then the local velocity at y = d becomes

V,= BU.

. (6)

The average velocity can be obtained by integrating Eq. 5 from y = E: to Y
== D with E -. 0

V~ U, [5,75 (lOg ~ - I) + B] . . . . . . . . . . . . . . . . . . . . . . . (7)
From Eqs. 4, 6, and 7

,

FD~ 1Td' (p _ P)g(V)' [ B ]' ........... (8).

6>1> ' ( D )
, w 5.75 log d - I + B

The lift force acting on the particle can be obtained by

,

F ~ C :'!... d' ~ V'
L L4 2 J

The relationship between lift coefficient eLand drag coefficient CD can be
determined experimentally. If we let tV2C L = CD' and follow the same procedure
as in obtaining Eq. 8, we have

. .. (9)

FL~ 6:d: (P'-P)g(~)'[ ;)]'
, , w 5.75 (lOg d - I + B

The submerged weight of the particle is

'ITdJ
W'~6(P,-P)g ..........,.................. (II)

. . . . . . . . . (10)

Then the resistant force becomes

F.=>I>3(W,-FL)

>l>1Td3 {I (V)'[ B ]'}
=-2--(p,_p)g 1-- - ... (12)
6 >1>, >1>, W (D)
5.75 log d - I + B

in which *) = the friction coefficient. Assume that the incipient motion occurs
..'hen F D = F R" From Eqs. 8 and 12

[5.75 (lOg D - I)
V" _ d
.. B

+I]~

1jI, + 1j13

. . . . . . . . . . . . . . (13)

,t,.

~-;--