The action of submerged jets on moveable material

i 'j I '' .I ., . I r I • --~-· ·--,.-·-B10uo-r:R . Waterloopkundig. Labor~lo · Postbus 1n •

DELFT

TI!E ACTION OF SW..>ERGEl I JETS ON HOVE!i.BLE '!'lf1.TERT.iJ.,

by

FREDERICK ROY \~INDSOR CLARKE

D:.:ow.~tr.::\:l.n

·c

;rt

Ci t-il Eug5. 1es:-.1int;,

.: _·,t

;.1 -•. • .,,

"-I

~his work ~a~

done

in the ila~ksley Hydraulic □

of ~luid ~echanics _{ond hydraulic} , _in[ineerin[~

Au~hur ~ishes to expres8 his, $1ncere gratitude to

-

·

--~~~~

i5,

7

26

37

~ Rip..9J..c s ;

4

Diaaus~ion o~ results

1) Poser reiation

0 0 r

r 0 .

72

D~~criyticn

of

the scour process

E~laticn of r~:~tc of scour· . to . '

fcrcc of· je•;j

85

Lcfarithmic relation of leneth of

, ,

su~~~~~ed Vertical ~ater Jet

- - ~-""--=..,...,."t-:"~.~--...,..,._--1. _ ____ ....,~,.----v-.no....--...:,-.,._-•

r,,1"

...,.,_

RG Iat5.on bet·..-1(')c!1 volUJi'.e or hole and

i)

alter discontinuity 142 1i)bcfore diBcontinuity I to t:i..n1e Horizontal hir Jct Vel~city Diatribution

17··

• I t •/ _... l.;7

'.

'

.l, r· .!.J V =

=

= 1•0_{'>1r -'-}1_{1 O-"' 'Co,,-..,} v.·. (!', l,.l ). S • v .. l d.0::_;th Of SC0lE'

i'i1G.SS _{. •'-}Der· _. i.ll1J.. °t _{volu.me; of fluid}

( U.r

-

(:::,;·_{'_..,,} ·

.

..

_.

8ettlint-: velocity o:e ;~.rains in ai;:,, or Y,b.tE:r·

or

i J.:_ -· ·:. - - - -. I - · -·/ . 1 I -:---•.,. ... ,...,.,~ ~.•.-...,.-:-r~-~. -,,,,~ \ I ., , , ,_ -~ ,. ·'-\! .!.. ~J L t.., ... .!.,.J ~ t, "l = p ₌ =

I 1 !f

I

C

J

j

'

I

t.•• ~r '-' ..,

c

_·,

.

r< v,-. c. DC D s h -'-_t, H .i.T, 'L. .Li :::: == = = :::: ·-=

-

--constants d:i.e1,10tcr of cr·e r.-;t height of crest

-1L

t nne

rr~usured depth of sbour hole

.

.

.

.

.

.

.

= square root of slope of lines

.

.

.

.

_.

·

.

•

.. LlTRODUC'l'IC·H

Tl~c C.d~ord Dict:i.on::.i1~y defines the worcl ' to Ge-our_:

..

It

ie

used

t echnically by

. .

inv~sti~&tion, ·concnrncd as it is with the l a~s

rov~rnin3·the cutting u~ny of o sand bad by moving

r 2~t~iction conveni0ntly distin~uiuhe8 scour from the

s~~~ ~ind 0f action occurine when wat er ~eves seJimcnt

i'Y'Oi-:J. ::;. r:~ 1_{/c:.., bod \'.'lL!.uh h;}

c

ont:i.nuc

l

ly

_{r ei,,lel·d.uhcd by}

\

i nt ,3 rc1H.a.i.1£::e

for '.'.:hich ·:;110 term 1

• I

-

-3

,

.,

I

'-be m~ntioncd that the lin~

ot

d~markation

I.

_,

In the words . . .

6r s.

L~liaysky ' (2), -· .. '~ithii

the

limits

. /

:i;h0 dj :£°"'1'ererice; :In pri ncrple, b8tween 'the ·so lid

parti~les carried in

nus~eno1on,

·

ind

thos

i

'

transp

orted

. . . '. . . . . . ' .

'oy

tractic·n, is indeed obvious, •it· is _.al.m~rnt

impos::; i b J. ,~

th_e _most.

a.nd

----

'-4

• I

t.nd. crnp~ricism is still the ba_sic. tool: •. In viev; of

\

ti.1is ," i t is not k}tirprising th&t _ _one. mc.iY find. mr-\ey

ccnflictins ideas on_ the st~b.ject~· ·. ·on0 i:)a:i."~mount-··

. . .

ex2mµJ:0 ·m&y bG seen in t,ab·le .( ))

bf

H •. ··Rou.8e (L1.) ·

.

i .,,.

unC:.:-?r t;_~,~1 hs&.d1ng of 'l!:mp )rical · Formulae for· _Be_d Loc'.d.

' /

. .

T;.~c.nu ()Orte. ti on' , 'i:lwre . the difff)rent _{,. .} fo:c_. mo.l ce of

sev0n inveGtigators are listed. But it is -only by

. '

sdch worthy efforts t hat an .apJraisal of the _,, S;J.bj~ct:

Th,::; prP.09,nt _ study :le:ils· _spe_cific.:1J."1.y ·::i th tli0 . ·

-~ .

~h0no1i10i1::1 of sco1.1.r by tn1hrneI1•_ ed horj_zontal ~n6. v~~rt:J.cul

' . /

/

s0our h~G bean ~ubj~2ted -to 8UCh

t

ij□ali 2mount

oi

.

tWGtc:n..:.·tj_~\ study. · It W38 ·_-.-ith this- in ·viE',,'1 t )wi'. ·fr.,s:-:;1..:.

/

'I'l1 is

\ could be ot

~mportance: not ranly in est&blishin~ Ei □ il&ri~y

for model Bbudi AUr but·_alsc in giving a deeper

~nBight ihto the problems of rivoi h~~rrrulic~.

-_•,

I

··-1\s m'..'!!1t:i.oned, th0 li t\ erc::. .ture on simple fo:rm3 of

Gcour ts extrom<{ly_ limi teci, oni:l flB in · the more gc.aer•:.;.;l

ca~:.i·e of flow i-n ercidc:.ble ··channels, the Dl'eatmoo.t is

·,

usu2l ly en~irical.

i n the 0roccss is great, crid their i ' ter~l~tionship

co~9lc~, und ) t seem~ that ~ b~tter unders tGnding

, . . .

of the scour phcnqmenc can only be ~chieved ·if all

t'ne. c-1· _{,;::, t:,>},.,,,~ _{Ll .l .l ~}--=-~ .,, _,-n.:.. _I,

-uos:3 _{- .} i b le !'.",rn1.tfl: _~

-pt:;rumetero :-:-:re v.;ari~d over

t

:1e

I -The ;\

uth

o

r

hl?-S Ci ven in, tab '. e ( ·1 ') . . .

-

. . . . \" It is -only b~, the~ . .

t:hr-eclds o-J: info:emL.t:lo!1 can- be- unr.aveJ.l ed i'ror:1 a · :naze

and woven of knowlecl.ge. ' ' .,· \. ,,

F l uid VJ ate::.• Air

..

Ti~BLE ·l R A.NGJ~ OP V . ,\H I ABLgs COVE RJm Ei ~:E J;; PHI:.SEI·iT S'l'G)Y

-

---·--·

-

-·

--·

-

----·

-

-

'"'--·

-·--·

--·

-·

-

---.,,...-I

T-•l o• ; •, , le

I

dj_;.

i;ater

!

Se·'--'-· , i·, .-,. ,__ u v · -· . . 1 ,.

I

ve 1oc:L

ty

I

r

o.

238 --·j. 43

It,.

5-17. 5 e ms. cm/ cec. -Oo2_38-Colt-7 6 237 -7-io e ms. cm/ se c I Hej_s:ht o f Hater• ao .:lvc b8

a

.

Bi'i'l u.x veloeity

·

I

F or • ce ~ :i:' 2 j j e t ( 1j c1Il) ' : -6 . 2~ ?nd .

I

se.

5-1 _ ~:0 5 3660 -677000 . 1 -Jo O J . nc.ne s ! . c m/ si:::c

I

co

ver

usad

to detect i boundary

I

·

1nf'luence. · Resu:u negLlsible. 1 :

I

.

112050-26950

1

21aoo

-•

I

cm/sec · 87950 . · ·

I

i

!

I '

-

--+-

-•--•

~ l ~fo. t e1., Oo 238~·1 o

43

em s 406-17.5 c m/sec

I

I I

I

1

·

1

I

i

_

J

_

_____

.

_____

----·.

.

l

'i :-.; nor •i:-:iont a1 \ie.te:i." Jet. 2 = Uo~izontal A ir Jet

.

3'

= Ve1.~·uca l ~;ater· Je·t

I

.

Both nozzle :8 6-1430 and v1a · t;er

!

.

cm/ sec height kept

j

c onstant . . N . ~ . . .._ I oz .. ie 1gn1.1 ; =

5~

0 i::is~ : Wat er heigh t ! :-: t L O : lna . ' 1 715-165000 'I.

1 ime _{10-10,000 (minutes) 20-10800 (} seconds) 1

0 0-420001 1 ( seconds) , I 0)

. . . : ... ·. ,,.

.

....

.

I . I . J . OJ? _.. PJ\ST 'YORIC _._~---=no>~ ...

-'

rwu

~

:

:

J!:

(5) · 1_{showed tl-ult the} rel;;itive _motion

-

---

,

~--

..

' .

bct~oon ·sedj_ment ~nd wuter i i proportional to the normal

s ottlinf ~elocity o~ the ,i~dividual _, ~~nd ~f~ins~ ·and

I - I

b_y tl1e use of 'd)_mP.i1Sion::: 1 e-rn:dy.sis · express od . the

re J.u.ti ve dnp th of scour as .tl1e fo.llo~-/j_-ng · functj.on · of

. .

·,t i:-r10, m0Gn voloci ty of inflo"1,,, and the sediment

ch,:U',o c t.eria ti cs

..I"

a (

. VJt ~ V ,

-~

_a

·

·W

-:,·1 !1e~n 0 _{s = uepth of ~,cour,}

-a = .,eir:rht of _{nozzle from} tl1e

·i)Ot tom o·"' .l the ·hole, /

: _I

.. \'{' ::: s0"-ttJirw _vel,gqt

t,Y·_

\.

Qf

_t~fl

r

t; :i •J

l

t fJ ; ' I ~! = s·tnndsrd d"'v 1 •· tion · ,., J. G. ' '

-V'

·-

voJ,.oc:l ty of. _{efflux, und}

...

I.

cc r;c l ud.e,s: __,

·

-

'

· 8Co,2r r;nd timP- wi1ic.:h

I...

2j _1'he r'-:J. GB· of bcour i;:; ~ -fur,c ti,on of_ the ru tfo

or

·

,i

.!.he j ot ,,clocity ,to the .settlii:1g v0:l91

;i.cy~·

thr.·:~ ~h-"l .

' . / r-- -1' I 1•1 ••• ! .!.0-! i ;°! : ... .

j

~nu the rat~ of supply of matar~al to _thp· holQ.

. . ~·-::(: tion ic enl~r>geo.. I_ • ._ ,_ • "-. ,_..: ·,.•. , ::-. • I :" •• "' ·• ::.-, -·,.... t' ::-; ___ t:--:.!.,.~~/ ~:io--:,·cct ,:\·;~ ·1,_n.c µf..J.,_,;·.J 01 .1.11.~)-~~1f-1 .. 1.:-1:t1.~,."' · : "\ . . .

!j"'..JV:::-1:1:;;r:·i: :.):i.°1 p.~.:.~(t:J.e:t~~s r, .j .1r1_• ~.b.G (!J.'Cot· _\,1..~;!; t1a1"(lJ.~~ ilot ~.C8-

-•. '· - •-~ •., L:,.. ,;) ,··•,t=,~· •. •

no l, v\'<,!: ~- :,il,, c~ ·=··-- 1,:

l

l

!

t

.·. ·.' . ) .

. '

urwd ,to SUflt-1lY sc.ncl to _ the SC.:lU.:i." hole ut,

s m00surcd rute. ·

llis equ:., ti

on

_

for the e}: t,,nt ·of scou.r rcL _i:.i vcJ to

.. -·

thr.- lim:i.tinc extent,_-u.s a function _of --~~:nc, is ~.:.i~1~~n

. , X (.) ,...r.-;x..., ..., .1\.I

....

·-:;::; l og .wt:. a . ) l

_.

<;-n:.:

_-

·th lenrth \ ' of' .,

scour,

' ... _{l:l_m1. t.} -} >. ,:..t V = sottling vel-0city of ·"' ·. = = eJ~!~lu:~~~ -ve.loci Ls··~ J -/

l

_{, prD['..I'e~·;~·:Lon of _ ti1:w •} _.t •. . ·\ 2) .. ·.::~1.::r·e j_, l) I , () ~:! /)

,.IA

.

... _. ~--.Jr _ _..-,_ , . , b ;::: == t. ₌ -f • ) .. ·•.

equt tion_{, ,} . for cl8p·th &a:

. . V ( --- -.:.; 1 ) ,-1: \ ... ---1..'. .... '

,,

,,.. :

a~ttlin~ velocity

'ti.8P. of run•

. '

~ 0~0221:l

loer;I} ~.-co ur.

.· '\ .

• 1

From an·nnuli~is of t~e influence of

no~~10

n8~d

_

reiuired

t~

~~6d~da

~b8

. . ) .

of ucour holfi ve1ried inV;Jrse.ly , s· t:~e .

, '

V n

::..• .

mo:nentum of thu •jet L-: thJ

. . ' rlrn cf flux vtilocft,1 h:; ,.-r o,:op!;j_o1;

-r7rJ

-

.

= \., \ )·

,.:,

\ .

Ti1G1."ef'orc the rate.· of chEinf~ J>f·. momentum 1.s:

-. \.

' I

,

clincr:: the~ ,f'o_rc0 i G e'qui:l to thf! rate

of

C;\[_;nf.e

, o:r mo:ner.t u,11, D _{Ci. •} H O when ths i'or·ce is . n ---He·c;onclucted thc:1t' ·:::ien ' S ~) ;.10 ..

'lctt '"' :: t'l"' o·; · "JC: ro-.., ·o:t·· tJ1c.· c•c· our· ·10 1 •">

U • ., I \J C, ~; l. i:, , - C..• \.~ 1,1 ,.. J. . ••• ~ . ( .-.•

-

- . ' \ .

:,

I

I

:

I

.. ,

I

thst. tho time toien ·n~· ·the s8me fo~ .the S8m~ siz~ of

fr·om 60 ~o '120 mirtutcs.

cii~, iWtcr. of' r,cour &foinst .ti1::.e of

run

_is e;,-."r,mino~.

. .

incre: :;;ec~ .a;; f:i.r::;t very 1 .. aµic...ily '.rith ti.:1e, so tk1t .

wi~hin ubout ·one minute of the st&rt

tl!.3 r.un. ,0_{,·J"'"-1,n,·•} '1 :,1•i ,~. c·'n···rt ·''-'T·J

0

oc·l OJ.1.;1 inc··,.-,::,, ... P

.. . . ._,_ ' • --.\,,) t._) V . ~ , -.. ·. • _(.,..._,_. , , ' tl:1e

:.., i .y C, C... r• r0v ~•'1-,1-l,' ; C

0

0 l } ...,.. t,

-· .

ce:_co,r:{-;f. 1.;n .\;n,)c:s:;:::i.ble ;.:::i.::;l< tc obtain t:h0 ti:'.•,0 ;.:.t ::;h:\.ch

, .

t i-::.8 sccu.r, ~L•Jlt:r;:j r.pr:) cori:]t::11t.

to inc1.,~:tloe tn sj_xA fo~r mt:Dj' 1·1oi.tJ'S. iJ8inZ ~:. 2i.ib::1r:rf:~8G

'

'

(

l:i. r:our :coh~ tion~hi ~· Lo ·

~ilne

plotted on log. s·ca1.e·9

. .

Si:niJ.: .. ,:;_,ly ~ for e.1.per·i:11-'ints wj __ th u. sub_::1er£:1Sd hopi:.:;ont&}.

Cri the

. .

o·i;h0.:c hc:..n,:J., f'or 0;q)ori.,1cn_Ls ustnf.:; ·a:ir j,yts, · ~ll~·)ro s0erns

,.

• -. I ,

lc110 ii1 of tlw scour hole inc1-.{!~Gas line~:rly- •,;i th th<~

but quite_ 8oc.~ this,..rE')_,~tio11shif;

- ~ . r .

Dµ{JO& rs tc be ::;9µro.rchinf;

z.

-fin~~

· 'i'hG Lim~3 nccflss1..r·,y for thin vt;;rie~ ·::j th ti'ie fore::, o_f

' I •

of~ t~1c ~c-.11d.., c_\ ~11d _, ~~i"ics from

....

3 intnute;:,· to o ve:c

50

m5. nu. to::,.

\

• t

. \

' < I

. CrlA~TER 2

.I

'L'he 0xµ0rimonts were c:,ri'i~d out in a

parGp0x-sidcd flume \'l,5

ft

·deep,

3._7

ft wide~ ano.

--< ·. .

120:f f t long) with ~ro~i:-.:i~n for t1-~/o de.pths

'oi

l'iuter

\ . •.

lf;v·c1 . &bovc" the SHncl bed.: · one

·

11.

d-\nches

above the

. . (

l evelled S~.nd bed, ~nu th3 _ot.h~r:. 6.26"fnchG~j (i)l:...t~ ( ·j i (

A micromatsr potnt guuge mouhted ~bove

on a s0rveci to the contours of ti1e

. .

'.l'he ...-rn:::.nonotr-11'.' w1~;3 a dirnct;...rac.c.fin.5 rnei'cU.t'Y

d.j_:o:,1c·t.,··:-: of t-h~ gh,Gt'i °ti.\be in ·,1h:i.ei1 ·the :heifl1t of ·c.h1::

I.

ms l'<.: u.r~• co :i. u.i1: n 1 r, ni Oct8 Ui'':-· d • · · This t,y u 2 of ml:-nome ;·, r-, 1.~

The. volume of l iquid

. .

r:1:: n: :c-od to fi·lJ. the smc:

n.

glc,SG tv.b'3 i s ·3up:Jl iC(J f:com

'

SCHE.MATll D IAC.,RAM Of HORIZONT A L JE.T TO MA.NOME.TIE.I\ , -· TANI( WAT£.I'. LE.VIEL. / NOZZ.LC IN PLANE o, &EO Wl~R MNO ee:o OUTLET I I

--w

_FIG.

1

_., o·,

\

'· ..

.. / ..

1st d_,

I c.Uame tc~r of el&ss tube, · ·

di~meter of glusB _reservoir~·_

/

' r-~:0:1.,;_; ter•cd heirrht in .the -gl~ss 'tube; _and.

h,,. ,:;. = .,; fop -. . . of' rm;_0rvoir, ' I ( • • ) : h: 1 ( L) ~ -( 12

Y

2 ' . ; ; . ' . = . I _( th:::i"l; tiie droiJ '

Poi.~ tt10 ~n.LlJ.exi 11:,,:•ds 2. sL11pl-e wo.ter_ column ·.-::::,.s used.

r~o diffnrsni sonQs _of.Qu~rtz . . _{grai~s and of}

' ,

8 p oc i fj_ c er:i \~i t,y 2"

G~,

aJJ[-1 i'.'O.i:i m·a t e l:;r ·:,· ere _ UG

r-<,.

'-.

Sieve analysis

of

bbth si.ndri ~~s _C8rri

,·

_{ec1 out und·}

•

,

.

I

i

1 I t i

I

;

r

;

.

[ ... • • ,t ... ~;-,r -.;. ·.• -~ ... , .-.,_. . ,.. : . .

.

:• .... : ' ... _ ...

.

'

·

-·. .

.

. f

.. ·--. :

.

~...

.

.

..

..

..

:.· • l • •·• I l .. ., . , .. ,, I -• ~ I-. : : -.- ... · . ' • o- I _. • ::' • • Sand NQ 2 ~ & 2· 02 mm W . a 17 · 5 urt/SU,. &nd No 4

d:J

.

-

1· %.7 ,..,,., w • 12·5 Vf'/"4..._

SAtJDS USED lN SCOUR EXPERlMENTS · . . ' '

.

·.... . ..

:.

:-- . · .. . _.,. .. . -·.·•

..

.~ . ' -· -·

..

' ... , .• .. ' &lf\d No-1 d9 s o-62. "'"' ~ a 0++"'"1 w • 8-3

cm/.sc.&

-

w • + -i .:m • _s(.: ··'·

.

:· .

.

.,

~

-•-.·

.

.

.

. -j

;

l-

·

--::it.~~

~

i

!-

-

+

r

~

:

-

-

Tt

_

--t:+

Q<H

"""T,-

-

~r

_

-

~

-

➔

t

-

-

+

~

~

~

~

7-:-tt1:t-

~

r_1r

...

r

_

t~-1~if_1➔--t~-..r~1➔--T~-1r-rtr-i

:

Y:1:r]:]:J~t1:r:tJ[1-,-

--,.

-

,

_

-~r-L-4t_-

~

r

_

-:_r

... 1.~t._--..,_1.r~1_-4t_-~r~i-~t_-.._r ~;

.

-

-. I • -•·

;

i

.

.

·

-t

-t--i-.-++-M"+' 't .. -, ~

...

; I •

·

l

·

~ -r-• - "1 . r .. ·-· • I ;

\.!--~-!--i-++-H-+-M~-+ ... Mh--t-TtH-t-t-hlf'TJ ,1,_h+ -_;""'!-i_;J1--l-+-r.-~-;-+ri-+-+-t-H;"TIH1--+r. _..-._--:-,...1_r,--~--t-+----_:_t_1~-~-~t-.... ~

-[

l

'

:_..

·

·!-+-t-t-t--+-t-++-t ~ • ---L~

-~+-+-1-t(

..

~

'

: I ~. -~ +-..-,--t-+- t--1 I · :•-;-+-'-+ . I ... -,-~ --,-..-- -~ I .• ---~ \ . . . ;. -4---!---j- -i-: ; l •. • -r· I .. t . ' . i I ~ ! ... ' .l. I .. --,. - ~ +--.-~II--.-..-,-~ 'l . _:.. - ..

J

< :

.

.

:

-

,

·

•

-+-

--.-

...

~

l

-

-

-;

-,-F '-;-1, ; i -·. ~ ~ , __ ;_.L_ • 1 • • -~-:1 -"' .., '

-

t-

,

:...

I

r

. 1 ···--,~- -- +-~-+-+"--;---.-+-+++-+-H-+-+++-+-.._H-+-+..,...-H-+-++++-;--HMf'"'fJ~~--r-"!~..JC'--':..L+..:..._,..,..-'+-'-·"· .. ·_,_ ... _ _ ~•:_-:_.--:_·:;:,:_

•-;

l

:~ -·-

-

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. ! --_. · I · -I . ~ . . ... . . . . . , . . . ·-. ... . . . .. . . ' . : I .: . : : : .. ·• . . ·-. :_; .. :--r·..: -~ f ·""!· -~· 1 -i.:. : '."'

=~

:

..

.

-

---! . ·- •.• . ·- ·I-. -· . 1--i :: . -. . ' • I - I I •-""----..

-

-

-

-__ t .... t---·- . T-·,r:::'f"fj; ·-::-i ~-~:~ f4 ;·: f::_~..:. -+:f· !=~~

-

~

~-

~

1:

~f?~-.:--~

~:

~:.3=-==r=:

:--1.;..~-:-f,;; :, ; ~ ~..:t=.:c::-1 .. :·=-: "?:"

£7.;~:-r..:

·~

:-=-::·

:

,'

c,

·

.:.

"=::±f:i :..:...._:~ J ~

•

•

7

•

s J

-~

I

•

•

7

•

s

'

,

- ·-· ·t -···---. ~-:· i ,;:-;

+

~.C-;' ,:,; . . -•... - - - ·- -- ·-r·. ·• - -- . - ---~- - - a.

i:,=£f .. :t~-:;..-·i-:-· ·.,:::-=-=-.::=.,~-F. ·:;c~· ..:,;·.-·.u.r. ~~ ~~ci., ,

__ , ... ·o ; 'ii ,.::;:: <I) :·.t ~" 0· 1'~ T~~::f-~"- +::=--0.:f",° --~--:-~~~ ~~: =.f#f..~··1~·~ . ~-o~~ 1

-

~

-:=x.

~~f~-L~ ~::-: ~ ~-_:-::..:

~:-=

~

·

-=-

--==

I F ;:~T-.1 ; ; ""·· .i-:.f-=~-: ·i.:.~: ·J~h.._ ~~~ . .L-. :~.:--!.=:::.~ ::3 - ~ ~ - : - ~ ~ -:T:.:=-1-~--:·.::.!::: .. · - .. !-;-' c·: ~ .. _x:; -~ 1:~ ·\=h a 2-~E, C!·, :=t::;?.:f•.0 :~ : . : J:.~'-:f-'.:-: . . :·-:.. ~~-•-,;-=· .:c-=

::~:·:·~ i ~->~::::· ~~-~-~-~·y~-::==.r. ~ -~~

'°

:;:

:

~

·

:-:.

"

:,..:

~~

=-

-=

=

~7=--_

_

:_=E-,-:-_-

i~--· --·---·- -.. --·

.

- ·-·-·- ··- ···1 .... -··· .. •·

.

.

-, . --.

'

I

• _ ... ... -~ ... -.. ... . . ... ,. . •• --♦ - ~-.. -. , . _ _ • ~ · • • __. .. , PLAN OF 6COUR HOLE et -~

~

a·

a

•

R-.rvcr«!'ii. flow once 6tart~d 'c.ontinue.s throu9hout the run . (table (2)) b ~ R£rv<Z,r.5t-flow at all times. C = Ruvu-s~ . ' flow · at 011 tim«.6 . LONG,ITUDINAL. SECTl'ON OBSERVED REGIONS OF RE.VERSE FLOW IN SCOUR HOLE • -; . . .. · 6ond bad

__

_/_

... · · FIG. 15 ~ \J1 , .

46 . GCOi)ct. ·---

--..-·----

.

---

--

..

·-

··-

--

.

-·--.

·

-

·-

·

-

--~-

---•'

• ~ ("I,,.. '1 ·.·, , ... ,.· ... ,

'-.f-1:·:-)~:1 ·.·:i:::_~:~~1 ii: c,~11 be scsn t~1~ t th.or ...

'_• ' .... _·- Y' _{.... 'IJ} ~f

1·s::..,f_J ~c::.::; .. ~:(~ o.<: t•;_~-1~.1~, ~LD ·con;e ct., .. '3s fr•orn ·! . \J Ei1nv.~.e:;

'·

" _J·. _: J •_:

' o.f' tflf; :j:Jt delile,,.,-Je · .J.. • • !..~. :ty.; .~j:;_..,coe I "v·l:.·.,0.-v:·,,..,_,·,·1 _,..ll·,,·:· ', Jr--;' ' ,~1·~c1or.,·'1 1rr n,.,,-; • ,; U. U ~ •. • !..• .-_ ll,; ... '-.

L:·.-..; ~;i;c1:·t o·J7 v :,;_u.:·.:. t~Jc:··.:::)L :tc.1lo·;.:s clos81.)' tl11=

-

..

.!. 1,.J ., ..t\:ft:~~ f:JOL!H) ti?:l~! 1 no .,. \.._I,~,, -;~:; ... _. ,:~~ ~:...-:..1~i ... 1rr!ot_·~ r10··

1? 11o·l; u·~ r:i.f;i1t 1.::11elt:r,; OL;t ti0I;1::>-·

• I

:·,;::::~·~: ~)~"'\ C/.:! ,:.;,,-:. t~ ~:.,r:::.::~ 5.2· :-:-i··=I'l~:.'=?~~.~~' ),.1!)~:, ·t,p:2;~'i'i'lr,

'

occur1'ed :i.n th1.:: mJ .ar-.. 'J..-.... 1 t."' (?) - J

---

-

---

-

-

·r

---:---j

L:;~.-'.J'.~s

i,-

t\);

_~:

~

~}

~~:

i.

z

T

::

.r

r:

~

I ~ ! ();, ~.30-:!r!1 ·;

3-5

i -~ --,=,

9

;

:.

I 1.-·---· -j 5r.?~f.c, ~ I I I

I

1 I ! ₁ ~~5--~.C, ; j f ·I j I ~ ( ) ,,.,,

L

__

_

_j ___________

l_

~

.. = __ O_•._J _ _ __,_

j ' l . -·c.-'· , ] , ; V J.3 :-;uo-::e!•t:ed llor-L~t;nL:_.1 ..

_.

_..

,,

_.

-. .._. · '--:;-<> l , .l

-·:·, ~ ~-'

I

q ~ 0

-I

I

r1-::· !~ ~·.J. ·:: (~.:. :.,;~1:::-t. 1·-:-:.!"~3 ; ) \ .

,.,

V1 _,

5

.r. . l ~ii1erGv:d. \. ❖ G .2 :.: ~: .. ~ .n ~1

~L·:I: t1.;-~ ,! ~~loci tic:.; \1;· ·::ci

_> \ .,~ r> :C(:-!? I' e~ (; :::1.·L, t.11.-:=; ce:r,11'> :~ .. r1.:-:l '\ c,,; c.

I

l

: / . '"1" . - -, •• - lJ

I

--'

-·

·

.

-1 / ·-·---····---

---\/ l_r)f'_;· -~ - lo[: t 1 ' ... ,. \ . ··. ,-: . : :, r, :J.11, ,. v.-1.• . ., ; ,.,- · -r r·::, \~

<

.

:

:

..

-! t.i-:. ~-; ~ c_:: ~~ c~ .. ;·:;_ ~-~:.:· ;1 t. ( ~ ~r .. a:.:. t< o ~ ;~) to J _.,, .

.

I

• t

l

f

I

I

,

I

I

!

I

_j

::

:, ';,}f

}l

JY;~;~1~.!_:::1?t

~

:

t. ·'.

:

.

_·

·

.

•.

t

r:(~

.

.

. ·:; .. _ . .. , .. ·:>::.•~ .... : -~"',.· : .

nozzle Noo2, •'il}:len the ·three

larger

. . - ,,_ preosure heads of ,. -. . ·

- . .. . -. "'

• ,. .• • • -~--1 -: •· .. ·., . .• ,·- .

17 .93

·ems · of mercury

:

i

re

consiu~red·.

-. ·.' .. ,·. ,,.. ,

It is se·en :from

th

~

e.xp~rimental·_plottcd points· o:r· ... · ·

,.,.. ' . -.· . . . : .

. : ..

1·eneth

o

-

f

scour b&;n_- in~t .. timP.

-

o~

lo-t( o~~l;~.-that t~cre

. .. , ,,.

rir

e

·t .::o d~fini

t

e

S~0-~0El . fo~ {'!t;~h

rµn.-

:

a

trv.ns1

~i

_

o

·

n

.

·

.

.

_ ·

,

, .· - • -. -"r • . · . . •

I

. (

occurt

f

ng

~t

6pproxim

&

toly

_

100

.

mintltas

for th

~

:

thr

cio

··

·

-

;·

.r

. i" . . ·. . . ·: . ·-.. ... -, :. ·:.·- ... ... : .

runs . : On. the other ho.nd ~ 1'or ,-t·he'

0"10

sm~lle.r hea~&, .. -~ ... _

I , . . "

7;

9

3

ond

2

.

9

3

ems of m,~rcuri,•·thr?. lincs,,-t'epre8fHi't1ng --, ;

. -.;...

-

.. -

-

... . .

, - each run cart 'b<~ taken

as

a. s·irai'gh't. 11~~ .hn1r!bng' a

• • I •- _. • • • • .. , ~ ~ • ~ • • '

cons tunt slog~,' fig (9)...

.><;-

,~

_-.

• \ . ' •• • • a • , -.

The

·

r~te

•

of scour f'~r the _.. -

l

~

r

ge

r

pressure !~e~da··

. . ..:--• ' '\ .

-·

.

or for~o!3

durin

g

the fi_ro t; · ~ 00 mi~utes is grer, ter thnn

,,..

for t~n

rest· of. the

e~iends for as· much

~un,

-~

hich, indidentaily

,

·

aom

e

ti

rne

i

-·. • . - , CJ" - ' ... ! ...._ -

-as. 4t300 minutes. :Correl ut ion of

,I' - • • /

Sand_ No •. 1 ~ for- thc-1 entir~ run,. arid ·surid :--:o_.2,.-for t.hG

)

-fi'rs t 1

u

o

minutes g r·f!sui ts 'in ~n eQu~ tton which nu:,y'oe

g

iv

e

n

as:

.:,

L _. - L ₁

=

---

-

·

. / . .... ' • \ •• i: ... ·~ i • •• '.t... • • ·r1t.n~; OF IIHTIA°L<scouR .(t.·) -. .. ·- .: ._·;)·: _·: · .. - - - . 0

<

:-

,

..

·

_

·_

,

._

\

~~:

·

.

'

,

.

.

. ·'- -·; .

-~

--

... : -"~ . .

. It was expect'e-d -~hat ~o ( th'e -~p_othe_ticul

vo1u·~ or··t;ime :;;_t·

whicih,

.

L6

·

cbrdin1;

·

t

_

o

equ

~~

ion (

.

1_~.1-);

~ .:.

.

., ....

the

len

'l;:t~

of L1 VJOUld hn-~o

·

b

-

~ien

'

;e~o)

·

~

-

w6~:{d

OG a

.:

.

.

. sim~lc function.

of

the oth:~r µt.rani£?_. .teru; -·/,cc'or<lingJ.y, - .

.... . ( .

-• I • ,

-from

0C.i,UU

tion

·

(

4

·

o

1}

and figs

(

6-9),

vc1-lue~..,

of

t

·.rnre

/ . ·. ,, . . . . 0

cul'cuicted ·and pi-o t ted-· agaihn

t

the: force o.:f the j~~ t

. ·. . . .

. / "

. for the two sands 6nd th(l lihre(i

nozzlcrn

p ··1.5_nd . t,·hc

r0s·ul t, fig ( ·1. 9)., ahows-· that~ the_.-p.oint~, ·ror -the di ffercn t

• • .:::. • • j -

-nozzlA the : TC1S ults for ..

S:::.nd.s

No .1

li.

:

nd

i::o. 2 ~pp.eur uS

'

.

and

appo:::r to br. !_)Ul,t

.

of

a· rainily .

or'

curven

in ~-;hich

. . . ,.

tha vcirious ·ctirvcs_--azte displaced v·ertically occoi'•dine.

. . . . ...

-.to. the diamotere of the no·z~lP.t:; end th0, is1ze cjf . the

I

.

I

' .

. \ .,

....

'

--:-- . .-\ .... . .

-. ', Gnnds. . · . But, the ~ tihif ~ bet·.·.-·een·· thh' 'cu'rves uf ( .1)

·- .. ..

. ·. "

and .(,2) ;-· repras··rmt:i __

ng

_no:6~les. X:10 .1 ~n·~ !fo ;2

.

r:c,s~e

-

cti

vely ,~

:... . . . ~ ·. ._ ·., . . : ,-

-is greater t\1~.n th::,t

e>

-

f

.

curv~·s ·(2)

.antl

(3),

re9re3::ntirif· · -;_·.

• :.:..., • • , •• J ·•• • • ~ ,.

. ... - . ,... .

· nozzTen :{o;2 ~nd

r.fo

..

.}.

..The

rat

:

io

of_ the noz<'·-le .,,

.. .

-·

.-

., . .

.-.Tne sj. ~n'if'icunc~ of this 1s- tha-t .t.he·r~ 1~ :;.6.1nh-Br::-nt

.

\ ,.

dep

e:

m

a

1nce

of

t \ - . . ..

611 th0 nozzle -dismeter and th0 sand- :, ·

. . 0

.,.... • c: r J t ,

( . . ,

of t , ss r~p;E'isentnd:

by

'

th

e

\;9i•l-ici::.l shift beti·1ecn ...

·- - 0 . , ,.

• • ~ • , I \ • • • • • • • ,

the curves .of __ thc th~e-~. noz_~le~, . ..'fig_ ( ·19), ·_tnken ut . .. ; ,. .

. <, . . . ~ . 1 . ~ -- . • ;

'. bclact,3d values

of

_P, :\-~ere

plot~sd

arrainut. th0_ diamete~ ·

. .· .

.

·_ ) .. .

-

--

. :

'

of _.

trt~¾

·nozzl_{, ·} cfo ( t _o . _{, · )7_,.} .d ) •_n. . - Tl11s _. plot _. ·1s _{. _}

neen

·

in fi1~ ~2(,?), and -the points do not s·00m to o'bey rJny

... .,_ .

,;:hich v_{. .} alues _. of' t ₀ are ·_.-ulo ttcd ac--ainnt_{. .. . _., . ' .} ·· the JJn~rtri.1c _.

-. . . . . ... . .

.

.

ores~ur e h~ad on.the nozzle,·which r~oreGPn·ta the

-. ' .. . .

.

•

.veJocity. o:f the jet~ _since. · ·: __ ... .- .

~

>

)

· . . . V

. ·. n = C

n

~ ✓

12cif,

7t:,U

·

··

·

. (

• • • ' ,. 1

·~here U • dynamic head

or

the nozzle~

.· 1.·

.

.,

\..,.

l

l (

1

j

I : . ;:; · .. •: ··· , .... .... •·

.:

;

,I

. ' ' 5 ···

.e

.j: .,

,,

,o

..

her,d c;re&,ter th1.:?n 17.

5

Cri!S of t:nercur"y, · as denoted by

(a) ,. thc:.-6 ·oe~!'i1G to. be some· c_onut~:n~y in the ·vultHH,· '

.

'· .,,,,.

of · t _O• . In oihcr . \','Or<ts ·, in' t~s

f

;g

ion

.

·

t~' sc~ms -~·o bs

1nd.0pendent of 'bo·th r,>?ci ::. ure •.head · Jn'u noz~le ::!1.:: -~e ter ₁

• • • • I \ ·, • • • • • • \,.

as tho po into for ~l

i

nozzles can- bc-,,, repr~:.,ent_a<l ~by

.... . . .. .

.

'

a struiebt iine ,·~hich is

hor

i

zoritbi~

·

·

u~

~cvcr

,

f

6r

/ , / ;'

. '

pro~rn ure h0.uJs l esG tht.n i

7

.)

ems of marcury; rot;i o~

.·

(b), the points for e&ch ·no~~le aiameter lie on. s0parate

. .

curves, \'ihich fare not. horizon't:-.!l , -inu.ic:::.'tin[ that i n

this· resion 'there ·i.s

:£

~

J.e1J~ndence of

t

0

·

on

no.zzl e

diameter and pressure heu_d •. I. The na.ture

of

the de·penclence

. . "'

i s obscure. . One _mu.,y

?ri~

~

co_nclud~ th£1t ·-the rcu ul ts

. ~

• I ••

·of thcec exp9riment~ do sugg0s~ that tha time.of initial

. - . .

SCOUI'

ft

₀

)

i~ in some way d~pend.ent on: .these pG.rt:meters;

·, .

which me2ns that 'in attempti~i to estub_.

.

lish _.

~

·

l

i

m~

-sc3l e the nozzle. diam~ter i s a significcnt pn:1'.'s. :et er.

-'

\ .

!I0i.''3Ycr, f rom thsoretical -consideration, the

l . . .

origin

or

a j et is intle~c~dent of the noi zie diamet ~r.

Schlicht:l.nf!. ( 9) and oth""r~,

in

cqnsider-lng the .

.:...

' ,, __, _{. .}

.

...

. : . . \ ' . . , ... . ., ._•I, .. • ... .-

..

.

, . . . '

diffusiori

o~

freely

dispG~a~nrr

.

;eta;

~ave_~~o~n

ih~~,

'

·

~

··

' . . . ,.. . .

ri.ft~1 .. a . dis t~nc8 of

e1ppr~ximE,t(!];y

6 .di ninet{;"rG

<.iowi'l-s tream·, or b0y,oncl thB "f,9gion oi' t"he ·p,otentiel core,.

·-: • • ✓ •

,

. .

the · jct cherac·ter~ct_ic is ·int'.iep0t1d_ent of th~ origin;

thut iB9 the l~ni th of the $COUr hole iE ipdopendcnt

of the diametnr of Lhe nozzle ~qr v; luea of L

»

d,

'

.

.

'\

:- v1hnr0 L

=

length of.scour.· _{But, for the ce~e :}

-. ' •.

· of occur _{~Y ~u~~arg0d}

_jeti,.wh~re

_"

_th;

_{initial time of} -,

• • . . • l . : , ". • l . - •. ~ . • •

tµ1cler considc~rc::tion; ·the_ 'thoore•ticol r38Goning,

~ . . ... __ . :~ ·"· .

-~cour

_-

'i s

'

bused

on

·fre-~ly dispersing jet_s wi:th un·constrict0d ,

' . .

bou;11darics, mc.y not 'oe applicabl~.

... I

Ins te&d, one 1s

faced wi.th

a

'

much

:no;e

·comµlica~·cd ~c.rn·~ a q-isperoing

•. • : • • • • _v • - > •

. . , -· . .

j et on

u

snnd ,bed·, where th0 bo'undary' ceomet:cy is .

. continously , ~han... ging with.

tho

.

flow and ~ith time, and

. : .. .

the flow in tµrn, 1s affected: by thelle change:-:i.

! .

I ,

,

✓ -In consi(lerj_ng the history of a run, . . the time

interv::.J. between the start and-fully established .flo·.-;

.

.

.

is

t~~metl the 'time

6f

flo~ es~abliahmaat', Albertson

(10)- r0fers to the 'zone' o.f'flo;;; establishment._

The ;n1t1i1 etHfC of sc6ur i~·prob&bly the mqnt

.difficult-to analyse...because of the short'

timo

tc:lrnn

. . : . (. .

for flow establiohm~nt, and bec~uie th~ scour hole ana

. .

-· flow prittt,rn muy• n~t be simili:;.r .to that (!_b_tEineu l cter;i.

In vi9v1 of' th0 in~_er0·nt diff'ic.ul ty and un·c0r.tc1inty

of. obtLd. qing the f"u11c

tfon~r

-

relati

·

on~~ip

b~tvie_en

t

0 ·

I • • - •

and thP othnr

v

~

~inble~,

--

as d~acribed ~&rlicr,-a ·

. . . ·: . . °' ✓ .... '"\ .' • . ,

-• I . J . ·.

aimpl0r

_.

0mpiri·cc,l· oqur.1 tion for ·tho scour phenomena

. .. "'\. ~, .

, .

'

.

.

.

. r12s_ derived. ··r1ie _p0rt~.icnt Vt.:.risbl<:Hi: involved in

.

.

. . \

-· the scour ph0nbmena muy be \~ri tte.n·

a

s

..

. ·

·

.

·

-•

. I

..

,

.

f, ( V

_.

_n'

-1,

_.

,

·

t ,

·

_.

er)

== ~ 0

\

~

.

~

and non-dimenG ions I croupi ni~s cc.n ·be· formed,

thr

ee

~

(-Lb

V wt ( f·

_;,

_.

_{- )}

_{0 •••• ( L~ o 5)} 2 ~

,

_.dn V ' V

, The_- , gronninF, _{•. ,._} -_'/J , tlrn r&tio of eff:J,.ux veloci t·y to

oettlint velocity of··the erai_ns, hr::s bc::::n aho'.·in bj'

~ou~e(5) to be a significant ~Hlr'~~'.,tf-lr •. ·_ ·us_-;Gho;;,s

thut the. r&te of' ucour is a . .r·u~ction of t)w r,-.tio of

ihe jet velocity to ~he scttlin~ yeloci~y -ot the

Wheh

!

= 1, und that the s16pes of.the lines are

\'/

I >