sheilds
TRANSCRIPT
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A P P L I C A T I C N S I M f L A R I T V P R I N C I P L E S AND
TUR ULENCE RESEARCH TC BED LOAD M O V E M E N T
by
Dr . Ing. A. Shields
T r a ns l a t e d f rom:
Anwendung d e r Aehnlich keitsm echa nilr und
der Turbulenzforschung a d die
Geschiebe
bewegung Mittei lungen d e r Pr eu ss is ch en
Vers uch san sta l t fu r Nassexbau nd Schif fbau,
Ber l in ,
1936
by W I? Ott and J C van U chelen
Soil. Conservat ion Serv
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n~Ove~ ken2n P V & ~aze 1 inadequ.a@s nce:t~Bedgeo
the
procaeees,
and 23
the
caavoidable
maek
5 ~a:rnxiaaity a ^ ~ I Q ~ .qerimLcnt;3,
eo
bad-loa&
xckovezmeat n
r ivers, Mor,;vever, they-
-wad. not cover
LPP
bed-isad
prob1e:ms e n c o ~ ~ a t a r e dn hydrauA.ie en gins aria^^
$+* oreover, he ux~avstsidabls
- C l
aec nd
aec+Loa
caneiders p r i ~ ~ ~ a ~ ~ ~
zle
c s k ~ d ~ ~ ~ s n e
t
he
be-
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finds
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n &i %. i i~rm
l osev
t&e e
25
xist only
the f.r.i&iou
f o ~ c c a
pressure ,Qarcca
re@nl%%ng%ozfi he ~ d ~ i ~ h tf&be%.water,
~o n s e y a e n t l y , he
eonaponent
of
the weigh5 in the
direction 0 E f k v ~
a s t
e
equated to the total
slxeax*upon
the
perimeter::
with smaL1
d
sin c:-- tzwg@ slope,
-asregarding the fPicdtioa
o
air , nd v~rikfng:
&.eaf%agstress
; an
a : ~ e b a ~ @ d
-+;erthe
-wetted
peri:me&er, As
a ru le -
this
a
momentum
r ~ ~ e $e applied
to the
bottom s folPows:
bottom nd
perpendfeu1a.f
zo t11e
i s ~ v e ; ~
f he s t ream
Fig
2
shows
the
subdi~sion l
yeas.
fnee
khc
.si 3,g
areas
cu9
the iso~sels e-:peneicu%ar, there a r c c
shearing fopecs yaa . s fe r~edlona these asreas,
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What rex~-mias
a
e
de'kesmia&l
age thb2 oubdivisiiandl areas ad Aw.
f vv~s igae isn
a - -
of a
series
- f
isa\*ebs
shows -ih la
composite
cross-
pc r i r ~e teb -a
f u ~ i l o ~ p ~z irreg 4a.r
~ o u g b r ~ e s s ,
~ h., re
vd
a
l
1
d ~
.e
05
[see --age
6
nd
J-
page
10)
a
desired
a.9;.p.zi.oxbr?~;a;ee
=&
di%4s%ors%el:e ercas..seegion
can
agt;incd
y ~ - ~ ~ ~ ~ ~fmiddle and
arSgL~Ear
division Ilne
a ,
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k e r
*. --
B + , % u ~ , . 1- a t e of . a - the computed sub-
n
&visiana*l vo.e~scf$-Jes,
rhesa esmpu&aionsare
~a> It,ed..e h 0 ~ 8 M8f Z O V ~ P ,
eince t S J
~
qtzc.rfisn ~ ~ h c t h e ~
o ap~ibicat ian
6
the
resui ts o
cir~ul:? :r.-
---
COW &~$
elq~eri:msnb
s p:~ rn , fsible c,r
the
sub,divisional
cross
s e ~ f f n ~n
q ~ ~ e ~ t ~ , ~ a ,t advi.sable to
exnreae
the
mean
part-ve5oeities in relation to
the
cross .~ec&iona,i loci&v,
s n c e ;
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B rs%rativc ~aghaess ~s v ~ c l lsa g;4her f a a c e ~ ~ s ,
$ ~ ~ V ~ ~ . _ V C F .o
res&
gcaz;raS
cancluaiolln,
is
~ + e e e s a ~ r y-hat
he
q u ~ n t i l y - disc%-a&rgee a aawin3uim va:uc .
SJ- a
the latter being an a ~ ~ t ~ - a o i . a fequisi te, F s z a
h ~ % ~ L e d g e
f
the processes
involved,
vcPocity
mmacaur
emants
a r e
necae
sr
in order
tea
eonstruet
t he
isoval
patterns.
On he ather hand, since the canstruetion s complete
i ~ 6 v e I ateern requires Baborio~~s
ork
and
i s agtte.cnunnecessary,
t
i s
more przetics%to d e t e r r ~ i n e portion sf' be pattern,
Measurements n MI
open
channel
'8.Sitere
arried sut in the follo\z~%ng
anner:
A Pitot tube v ~ a , ~Eaced upon a kzidge in
such a
n ~ a r n e r ha h tube
could
be
moved horizantafiy across in he ci~a-mef,
A perpendicular velocity
as t r ibut ion
n
%e
m i d d l e
Bane
vvas
next
recorded,
order
to
deter ldnc
ta what wid & the uelocitiaa of he
zor,e: ecxtsnd~d, he Pitot tube wao
%en gradually .r;-.,o~~edcross the chanael ,
In this -aanner
the
region of
validity his
V~IOC~ ~;-
.
s ributBon
W ~ I
e8kabE8 ds
Thereupon
tsac~:'17e
farce
axqd r n i . 8 ~
scloeiPf
w e r 8
graphically
dete~x:ained,
ebis region
also
being dzciaive for bed-load.
I T I O V ~ ~ ~ ~ E ~ ~
The value
5 tbe tractive X Q P ~ ka th i s region
was
determined by She
level
of
he -maximum
vz,scitg,
As
Lsng
as
ekis
i%23.~~-mern
velocity
was
main-
tained
at
the
s~~.rt%acz,t
w a g
pc~ssfbfe O UPC the ~i iaiter epth fn t h i ~ O % ~ ~ U -
lation, Up to he
t ime
the bed was
cxees~ i vc2y
ev:delsged, re-cxaminatisa
of
the tractive force swsa pss sx i i ka ace no ~4laence as exercised
by
the
UI
vta14is, and the km:bBfez~e
COU
d.eveIop freeky, n a m
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siace
P=Til:uza2se',
veluc;: A : E, 8
ia
v d i d
8cg xalp*Per ta definite roughn ss
,
(see Pn$luanre sf Grain 6&3,pe), A -- provided
I 1s icx~ewn
could
be computed,
This rcauPted i n A .- va ues
-;thich
z agprax J z:~oteiy, O C s~nalieria,~
-a
&
d
&%
one
p ~ ~ t & ~ ~ ~ gjf --- against
Isg
An
the; g ~ k % c l ~ a l~'z$bb~.S,fngf
the bed., due
8 $e
6
- f s
0
d e w ~ ~ ~ p ~ ~ ~ . i . ~ t ~
~t :d
e dete;:rnrrtea
~y gstanxatic
dewiationa, The
m a g ~ d t ~ d cfA $OX
2h,e
~;esiaus kinds
sf r ~ ~ ~ g h n c s s
ith
quadreABc resistance
is
given by a q u s & i ~ ~
-i-3
an6
p
gs
4
a~ x d
5%ll,u&zz te tine
pi3Miag
0 2 u
agaiaat y a
logarithmic
f t9rm
* 9
far
variaus wszar d-.pt::l.,s W P G ~c m~ ta r~ tiope,
6
Hz obvious that the
friction
Ip
this
geckiwfi
t
jz s
been
S ~ B Q - ~ ~ P ; ~
&i,yc,*j
j e
sh,ear
~ - n &
s s ~ h & ~ g e
& a
e
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.
--
~ ~ ~ ~ f d e ~ i n g
he
grad3 s
k~:
;s
bad
~ f
~;r.~~~.rcr:::~~
5:~~~j.n
f.aes
tpbc
q ac:gtion
is .---
v , ?&~a&
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reppase. Lsa d e c i 3 i ~ ~ ezain area {i h
-again
d e p e ~ d i z g
olely up n ~ n c
-
grain
shape
[ a
/ x ~
n&icates tb, stagp-ation
pressure
o
a
crktieal
e
veIocieJj l
:zin. shape ),
~ y c 2 ~ 2 e R 8 y v L
I-irb eC.eqc..i3'ia.:iduL5.td~ecief;.'i.cient 2 the grain depends
upon both,
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ourth regicn, \:J;~:~
gre~kex*s*-d k~
alues th t
i s
cgioa
i 17
iP
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q - 5 8 balds ir8pap ;
u]ar
for
e w
-..-
--A .
,J.&,A ~.ne,,~si t sh ooting f3.o~~
since
4
al.1 s
Iacae \yJaF@
?:i
oQf;
i , e -v~ith
amka,'Jl
depths,
of
njovercank
sf m2zrtarL:t,
E.P
paaBPq
x i s c ~ 0 ~?iasiciiiik~rf:y 2 the
gsaia
a>apes,
i
sav9, ,'* vbr. ..rp 3 P
*=,,*
t :
*,,
; ~ c c g ~ ~ L c . A I BetaLai,~ .3ii,
bec use rixjs .TI
he
nand ~ K I ~ X ~ U ~ Se , ~~~;* rxs - ;
9
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8 i n e ~
>-- i s also valid fo r the inyrestigate4 type of broavn
coal
%
'3
bed
loadAi,
w e can
210:
the c o r r r s p o n d i ~ ~ goints in Fig. 6.
The
obvious
h
odorm mi ;^,,
together w$th
Lkc conformity of barite
and granite bed laad
.
=
ere he b r o v ~ n
exeeg.:
the
separat io:~
nd
cornenLnkisn o
f iner parzs lead to a sanirnewhat l%i@hercritical
i w, . A ~ Z G ~ ~
---P-~-e ---.p
urnishes
e-vidsnce
that the influence sf iweigkt upon t he
beginning sf
haa bean
ftelly
covered,
Influence
o
Grain
Sbape
-1Pw
The
grain.
shape
Tray
i n i i u c ~ c e
he beginning
af
movement
in
just as
many
respeces as tbc
-~ai.al=aeq
;ppe:-as-ing
in derivszisns of the aqusa kiongar
ha b eg i n a l ~ ~ g%~xoxren~ent ,
hey
we.+e
ae follov~s:
= in6Buence
of
grain
shape
upan p~%r $rsi ty
P
d z
=
ixifluznce of grain shape upor. bed- i r ic i iua
coefficient
@
i ~ f l u z n c e
f grain
shaglie
u p ~ n
r a i n
surface
3
Pa4 .Ge:r?rasses influence of grain s i ~ a p e pon
flow
cond ik io~s n
l t is evident
from. Fig,
6 $haitthese
131,
s a y
elczrt opposing in -
rounded
gr~a ins nd s h a ~ p - e d g e d r s i ~ sie
sor12ewl1.,at
higher
than
those
f o r
grain shape garan:etritaEly,
In
eat:er lo
llu&rw& thie
point,
@
muat
investigated
eeparatzPy,
The
g ~ r o s i t ~
,
:an
be 2asiI.y dekt~1~~4fLi~$d,
I
+
q may
'p 6siblg
be
d i t ~ r a l ~ n e d
y ~ r ? ~ i ~ r e i ~ ;
at is,
by
s-irt,usring
a ew
- .
erains on a beard
wli &-~
i3i i forzm.
+rsdna g;.iled an do IE* thzn
b y g r a d ~ ~ a l l y
n
= k*
#
clining the bsrArd vhile si-$?&l$ sl~a-icin.~j$;
4@sz~*&~~nding
~rbultgia $ZCI~~tu-
&e$cas),
un.tjl
the g2:ains
3-s)iil
of;,
xfi
&f
manne$f
~ g i $ i @ a l
l ~ p e
e
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used
by
Cdsey,
ix:,?gi:ther
% t i k d r ~ & %
ap ith he^^
;lave
zk:-,aJa
experit1~1.?n$c
n ; ,?~s
v i t i a aagular grai12.3 I ~ Q : X J ~ % ~ ~ F
q2eti'~ 1-tez.7r@9rl cbp x? c$aanncls
* i ~ l ~ 5 : 1
granite
f d i1gzxentsof
ar sh8-r.m ( t y ~ , ~
-3 IT? -;$ittiv e r y sharp edges
were
avail-
slbe
to
clea.2
u
:=his
point,
To
deskzr~mj-neefinitely
he
nfluence
of
the
grain shape requires
that
all
ather
variables mechanical. m d hydrhulic .-
- *
be ekim-icated,
k c ~ a r ~ n g l p ,
he axpe5.rncnts \
it11 gzanite gr ,~in- t yes
ere
made not only v ~ i t ? - ~hs s ~ x r ~ enif~>:~n-i~ a i n
i zes {d -.
0 , 8 5 mm, d -- 1-23mm,
d =
%,44
nxx and in same channel, bat also with
be
same slopes, and by
using the sams ewperiixeatsl technique as
sad
by Gasey in his
s a r ~ d xperime~:ts~
rzle ~iftzsuj. . fa:: grain sjzeg 3,
g 5
;m3yI a2.ltl
2,44 3 3s
Eire
very
cl-.,dractzr-
i ~ t i c
;mid
85 j3
d s p i& b
i g s u 9 and
lii:
> f
3
pja'kted agdas t f ie ,
il?ustri*';ion ehaivs ti2ni
kc
-values fo r
the
meny-edged gj:.;iils iie every
t ime
about
ten
pe:- ;.zent higher than hose
Isx
rounded sends
- i
e,
n
awguls-z
qrsie~ ;.o&~~,ces
p2a t e s c
~ I O ~ J Y
uesistzt~ee&aa
z-ounde2 one, Thus he --a
* A h n
velocity,
wit;. constar& 5 ,
i a
es w i t 3 fr g ~ ~ e n t a
b a . wit
sand,
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ff3Pnxaeio -' eel rLc ~ ~ s s U ~ &~asgi.::~@ ys oon :eache& Tl~tas,
ba
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The
3eroistenee 0. He
type
oi
moEfau
and Lhe t i m e required for
%t.sith
a
miovable bed this
3criad
indicates
he
pcrtiaeng
sea , for
bed-
3.4
Bsad ~mo ~ezx3.,ebfs. ,ee
Krey
t i m e scale
?OF thzt e~z;>zripn~nd9
1 : ; h
a t ~ a i g k t hannc ,
Eowevcr
results
ob%&ned
i~itk
-~i:fe~Trne~t&.Z
h a ~ a , z h areish
vahsbfe
facts
{barn-i,%g
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P*S;
inus
i r o ~ ;
i ~ e ebd-tivc
~ ~ ~ , . g 4 n c s s ,-:l~ce ,pa.~ii~bHe~re
a be
considered:
P PL
1
sne born?
of
the *&~ataauzface
2,
Tbe
w a t e r
depth
3
The bed
shape
A t the
present
state
61 seier t2Ae
i avea t ig~~t iont s practical&
*
iwlpossihte
0
Saifi 3
a?&,a,-
c*zy~f~ens--en&sn6
one
a*L.,us ie
oetisfied
w i t h
csas ide~ai ion be ?
shape
w: ..rdvpa ep
dep &*
It
~ ~ f i c e s
o design&%@%e
bed sh pe
xaerely by the
relation
oi
-
heigkk
to length,
nd
0%
bed
de~fe lsp~~e, r irsegulas:i&ies
d
LQe
b~etow-,
k CC c
d
thi
s
&he
extent
~ e d
de-:re%oprfie: ;:&Ci
3~Hichs 2
-.sq;.rea
sed
sLwmeneisn-.
l e s ~ l y
y
the relation
of the
hsEgh4 0%
he
ripples, dx..x~es,xe S OUT
holes to
the w a t e r
de;:-&,
&J'a
&p$l2e:c &e
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TL
s s a ~ ~ e z * -he
gs&n matzraa i ,
tnt
y :
2~&%9:jccn
eiabt
e2
an.d
%eae&$
of
bed
f s ~ ~ ~ ~ ~ i o n
ecpaeese~, ,.r>&e a fire
sarF,e
E fi2e -
as
s h o ~ l in
iT
g , 6 -
the
r31am3er
0 ed-load
r~~ovemze:18h a ~ ~ g e s
n
the fo elox:ring
sequeaee:
scaLe3,
g & ~ r ~ ~ ~ ~ ~ ~ ,
~ y q
ze,- ~
(f?:eq:ao-&H.br of &;2liqnz sl~.aupe)ntil
-~j&eahe
oalace v,
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&*
8 -
? +
IT d
#
,""*
*---
~ S and s k a ~ ~ e
ac&aps
nd
ally
ccsm~?,a?~t$sa
K
>rp
"
these raagaitudsa
rs analysi s pro~dsl;
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..-.
I1 pp
7 ;th
st ll
i;rijates
I{ l
-*>a] also for b =
; : S ~ . Q Q
coal i s
t rausgressed.
vev y
ngjl
v ~ B U C : ~
T- f ff,,-
_.y di g E ~ ~ Ffii~..
~ f i l g
b e smbes. hesl~kts
O 1 1 . 6
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-a
pee i g z
c
n
Grain .m
q gh
6 ~
*'* -?* Zq
u
s,dv~2d,3~a~~6. aa
diam.e er &~pe
y 7 ex
>-
: &- a
VJ ?
I L ~ ~ ~ z
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Fi g . 1
F i g .
2
F i g . 3 Rat io of hydraul ic ra d iu s to
dep th
a s
funct ion of depth width ra t io .
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Fig .
4.
Veloci ty d is t r ibut ion
c u r v e s f o r B a r i t e .
d 1 .52rnm S 1/500
Fig. 5. Velocity distr ibuti on
c u r v e s f o r B a r i t e .
d
2. .?6mm
S
1/380
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Fig.
6 .
Trac t ive fo r ce coeff i ci en t
Y ,
Y)d
a g a i n s t t h e
V4cd
Reynolds numb er of the gra in
Fig .
7. C r i t i c a l tr a c t i v e f o r c e r aga ins t we igh t
of
g r a i n l a y e r s ,
y
y d ,
the c u r v e s re ob ta ined f r om F ig . 6 a s s u m i n g
=
0.012 a n d =
1) .
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Fig 8
Cumulat ive mechanical
ana ly s i s cu rve and modulus
M
Af /A c of a bed m at er ia l
Fig 10 Res is tance coeff ic ient a s a funct ion
of the Reynolds nu mb er
Fig 11 Ge om etri c si m il ar i ty of two sta tes of flow
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Fig .
15.
Plo t of e m pi r ic al equat ion fo r
bed- load t ranspor ta t ion .
Fig.
16
Sieve ana lys i s squ a re mesh ) .
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