D1
AN EZPERI&ENT IN BTRATMPZD MLW
by
MARTMA
CARl
8.M. L~ The George 1asha1gtcp Unvraty
(19")
BUBMITYSD IN PARTIAL FWUI=TL~'
DllORBK OF MASER OF
ATUTi
ABAOWBSET
It4STZITJ
*s.INST. tc,
OF ThRKLOX
may 1966
iIBSR ARY
LINDGREN
BlnatUft Of
AMth@W~;uW*
r*
V~~art~~~jt3
Accpt"dby....(
Mamteaqwfy
166
....
C
*..
. on
D% rtmmtal Can mtft
Grafate Ntuadents
An
xperifant in Stratifted Flow
Martial
Car
Submitted to the Department of Mateorolog on
May 0. 19ff in partial tuftillamet of the requirements for the degre of Master of S lence.
ABSTRACT
A theoar
it developed 4bich predicts the des1tIe
of outflow
of a stratifted fluid as it flos out of a tsmk. lbe geometry of
the tank is oes
occur in the team.
sch that several diftermet but related flows
These diffteret
to eah other are discaused.
mws and their relateonhip
An esperimet. was performed to check
the theory and the results are diasLused.
Thesis Supervisor: iik MUloaeChrstensm
Title: Professor ot Meteorolega
The author Is deeply Indebted to Professor Norma
Phillips tor bhi
sugi~ston of the probles and hi
during the course of this study.
'Lw
author e
thanks to Profseor Erik Mollo-ChrItease
estiag and helptul Ouggestion.
maUsm
work.
wipt.
A.
gSuidanoe
oxpreese
his
for several Inter-
Mrs. Jane MtNabb typed the
The author thanks them all for their ecellent
TABLE OF COINTJT8
is
INTRODUCTION
1
Il.
PHSICAL DESCRIPTION OF TM FLOW IN THE TANK
6
II.,
THlI2E0TICAL DISCUSSION (F WE FLOW IN THE TANK
11
1.
11
2.
3.,
4.
S.
IV.
Instantaneous density and presre
but aon
Deftalf
the mix4 IYol r
Detfing p
Relationshp betvw n h l and h 2
Density of outflow
dlstrl-
12
14
16
17
EXPERIMENT
20
1.
Demoription of the tank
20
2.
3.
Method for filling the tank
Method for measuring height of the ained re-
20
25
gion
V.a
EXPERIMENTAL RESULTS
31
APPENDIX A
43
APPENDIX B
44
BIBLIOGRAPHY
47
1,
i1MRODUCTION
The pupos@ of this operiMet 19 to develop and test a theory
which predicts the density o outfalow, of a stratified1fluLd
of a tank wth a given geoatry.
o'At
The geamtry consisted of a see-
tanglar tank In which a partition was intrcduod which did not
ztiMd to the bottoM of the teak.
An outlet sas placed on the slde
of the tank at a height above %e bottom of the partition.
geometry
as chosen so that a
This
the fluid flowed cut of the tank,
several ditterent but related flows ocourrte
in the tank.
These
difterent flows and their relationship to each other will be dis-
cussed as well as the experimental repalts.
In the flow of an Inciwpresdble
d A iwisold fluid, difterences
An density of the fluid Intfluence the flow In t wo wy.
Firat, a
change of density al
s involves. a proportlonal cheane of the inertia
of the tid.
a density change always invelves a change of
Seo=4
body forces per muit volume in a gravittional field.
If we consIder only the
ntatia efects, Y h showed that In the
absence of a gravitatelnal field, the steady flow of an ~a
sageus
l1 id li identical to that of a bhecoeneous fluid under sltilar boundary
coadtitons.
Only the velocity is differebt.,
This type of flow (absee of gravitatioal field) cra
be obtainad
If the flow is entirely hoiaontal, or it the flow is so rapid that
tbe gravity effects are neglisible.
For very weak
sttion to catio ly ditfernt.
teay woticn, the
The efftect of gravity Is to inhibit vertical wotion and horlontal
gradients oampletely.
Thus the flow It8
iconned to the lev*l at
whi h the dLsturbance oma"sng the motion Is situated.
In order to
observe both the inertia and gravity effects, the discharge of a
stratified fl£ud Into a line sink is ltvestigated.
The mathematic.l solution for the
-dimmesional proble
of a
stratified fluid in a horamtal channel flowng sato a lie
ank
was discusosed by YAh.
The de6sity variatoa In the cha il ftar
m~atro the s k is con-
sidered to be linear and of the for
epoo:
P - ji
pa
density at the bot
P. & density at the top
SInce the dORiS ty 1w26&'
constant sTngD
0
Upe 4AJFP
C' treSt1-a1l6
O
The ccmtinuty equaton may be written
9o
the usual form
and the use of the strem function IE, such that
Ylh simplitfis the equation of motion by Introducing a now streem
function
The equation of motion sa
.r.
Her
be written as
is a fUnction that mUst be deteranIed.
originates from a larg
The equation. of mtion becomes
+
the fluid
reserva
l
r anO flaows horiontlly into the
channel, then
v z
If
-~ f
YIh solvs this equation by the
vethod of sEpartion of varlables
and obtains
--
where
L
"
.3
solution In Walid as loag as
O's
It
reac ed that when the Froude nsuber to greater tha
Is
sieo
Is
tipossible to separate parts of the fluid in
process.
avabrs less than
Thus, tor.Froud
regions.
divides Iato two distnct
motionless, amd a lower region In which all
concentrated.
As the FrwAoe wmber is
of tUhs region of discharge,
fige
variation (Debbler)
d
,
is
the discharge
tJ., the flow pattern
an upper region.compowed
There Is
of fluid that does not flow Into the sik
mtal
ca'Theo>00 1%
and
aeich remains relatively
of the discharge fluid Is
decreased to '
also reduced to 0.
the heightThe epert-
of dr with the Froude number to given in
2 wtich shows the epeoriantal critical Froude number to be
approximately
28.
dI
1
. ..
,(6~1I
~'I
8
4-
In the tat
sink aes disesd
which me u±sed, th . fluid
d not flow into a line
by Y15 and Dabbler but rather into a polut
Looking down an the tnk, the stream linos in the horia
ink.
tal plane
vould not be parallel as in the case of the line slnk
Stk
P61M%
LwSlle*
But, even with this difference, the Froude number In the point
sink arrangement Is
til
an Indication of whether or not the flow
will separate* UsIng a varlation of densty of *2 and a flow rate
of 40 oc/seo, the Froude number for the expri.Mnt is 8 x 10 3.
Since th4a is very rmnu
smaller than 1/T = . 18, then it is
reasonable to .isct that the flow
outlet.
In fact, the Froude number
eoh density surface as being
ill be oncentrated only at the
So
so mall that one can Imagine
d*11
off one at a time at the outlet.
Il.
PHiSYICAL DESCRIPTION OF THE VLOW IN TZE TANK
severOl different flows
*opesned
Whn the outlet of the tank Bs
occur.
In order to describ
the total flow, the flow in each region
will be discssesd eparately.
tqgion I I
the eaoaiest region to explaln since it
As was shown, the Fwroad
contact with the outlet.
ex~eriment is
m=ch less than 1/1
that the flow in
h~
in contact with the outlet l
that an lnterface Is
face is
this
Is rasounable to assume
of region 11 falls, each density surface
slid out
moe at
time.
The result is
This lnter-
produced at the level of the outlet.
the dividing line between region II
1
number In
direct
concentrated only at the Outlet.
this region is
Therefore, as the height
and thus it
to in
and nXgion III.
2
3
Fi5 4
11 falls,
From fig. 4 we can see as the height of region
the density
outlet decrease with ti~a.
of the surfaces which are removed through the
Since
must be the swoe,
the pressure across the bottom of the partition
the drop in height in
partition.
region II
causes a flow aross
the bottom o. the
off at the
Thus, here again, density surfaces are slid
bOttom of Vezgin I , end a
region I and th
taant
econd iace
real"on.
is produced betress
The dsity
of 1ho Surftaic
are removed at the bottom of reglen 1 decrease
height f
vci-h
with tlmo as the
u.
The flow 2rom ragian I to vegion II pro ces aei
a mixzed
which I have called region IV.
rginca builds up,
As the flow otatinues1 this azed
Ittil It finally readhes the outlet.
A, Mhi
itxed regiont builds up, It tende to force the still straUt-fed roigonl
wh(ih I have called region III, to riset.
TiMh,
t
e mixed region
my be cozwidered as a piston which forces region XL to rise .
Th
dnsity surfaces %Iobh are slid off reion III increase as thivs rogiq
as
forced upward.
Thus,
wrnm fg. 8 it lo csparent that the flud
whioh leaves the outlet I made up i1 part of the fluid In rogion
where the -density surfaces which
e alid oft doerease with ti~e,
xf;
and
in part of the fluid in region III, where the density surfaces wbich
3MO cknSlidofooff~ncr
e with
!, ti
.
Pto. CpOS.
___
de.id4
(O
, O
bf..t
surj4ges
tUve.
by 'wpd ao
sS
8.
Once
Is
vaply
the rEned region reaches the cutlet,
-lited boyamty to t
the fluic from region I
t
heh .tlt,tsbog the_
polrt LtiLamed with the flow from region Ig.
-tom
R.
6
gl. 6 shows the fow In the tak
reache
the outlet.
moce the miwd ragian has
This correposge to then rgio
The three diumasoal view of th
comblned tlom are show
MI
in
igt. s.
III goes to 0.
tank is shown In fig. 7.
Tho
i
.1
79
i
OVTL9T
D%-O'st y %mh-."14c-e
L
-
IFI
DQ^%$
%Mkyiqft
Al
-I
OUTiC
LT
-)c
(wm
Ixeci)
(CQ)
-H
'~~flA1 ~A&M~C
~eaiNA'%
%n&mk 'Ri
I
I
Cxo
SAVAII
j*%O
ro
l~ft
IEANyS
1&
o
F'
-~
i.
@A
v~.") ~
aWC
At.
Os$o ,ns
lWfPSIOfA
C~A'A'I,~
tows
l.L
?LJoW IN TE TANK
THEORETXCAL DISCUSSION OF 11
Il.
The InItial d~isity distributtia in the ta~* ir
umi d to
be iear
a density of fluid at bottom of the tasn
whee
bange of density frm bottom to top of the tank
ha
As the level Is the tank begnSe to fall, region I and II
by a distance
H1- (H
O
:h-
Rand
(H
t X.)
are lowered
respectlvely.
The instantaneous densities In region 1 and U are obtalned by translating the initial density distrIbution by the amount each level falls.
ex
. 3Ieek6Wois AeI
.
*
Ustan
ye
4
sdamsa
Sta
i
tj
ee
kt P
'it
$*
the same procedure, the mnmtantaneou
and IR
1-4) Po*9.Q(I*.raV
preasures at height 'A
Are
i lurtSRiC
esssue sk6*48$..$
R,.xsineamos
PL4.
L ?($9
12.Y
Sinice the pressures on both saides of the bottom of the partition
are eJqual
2 0
z ed
(Bore
then
to n e
a
d ,at
0 afto
P
rhEg
1e IVy e
n4
e
j3
$ 4)
udpe
tlo
()
3. Dettatasz the Nimed layer
Befor, the mixed sone IV
xtends up to
lI
, the denity sur-
fames In region III aMunst be ascnding at the rate:
(.)X. Mfte,..
* A% d%
due to the 4dded volume of fluid frea region I to regon 11.
on this constant volum
assDmO aton wa can determine a relation between
the height of the mixed region
Ar (I3-
Based
U-
)
ad
Ax
(aRs.phn
the height of-the uixed region can also be deftned in a different
and more realistie manner.
regiso
IV ftro
Siaoe the density of the fluid, entering
region I, I* decreasing we may expect the top of the
Ixed layer to have a density alset
This a shaoa in fig
9.
equal to
(
Yo
1$ ,
qI
h
In region III eah Qemslty awsnofamb
A~ Ax
tb
PmAPo t
1Xrd4 reglci Is
Om CLPC*
l-- i
- 'is-
4~
/t~5las~)r
Thus by OwUatfgt
.04
ver-On
.
(t
A4
In
region I Isr
aet
N (4aI,)
for tho height of the m
q
-
po
The ILntntamem5 4ultY at heght
4". tr
44
~tOUGO O
k4$- kl')1
dna1ty at em top of the
4imsv at tap 4mlyk vl%
UP Z di
UW64 Pn
Ma
/I--
,
w
iam sox
dla
1a4ry
Ax'(7P)
140
In the co=tant volume assumptions tb
wll
top of the aizad region
reach the outlet whim
a =-
Ai
(-
H)
On the other hand, In the constant deisity aweamption (eq.
6) the
top of the atred region will reach the outlet when
- Am
t AiA
.
(r9)
At + ATL
It wo equate equation (8) and equation (*), we obtaint
Am -t Ar
(10)
=R AX
A
Thb,
~ram equatlO
variattio
assumptie
A-4Por
(10) it to clear that ther does not exist any
of the given tank ,geomtry for Thich the costant
and the o0nstant deMsity
masumtion
olume
Ill1 be the same.
S. D.bIzmiaae
P nws detiaed earlier as the mean
IV,
Until the mixing region extends up to
lsity in volume III and
Iz
, the change of
is caused by the fluid entering and leaving region III and IV. 8ince
the volume of region III and IV remains the same, then the emount of
fluid entering this reion maet equal the amount leaving.
Drnsty of ftbgd enteIft rglmQ
I I and IV Is.-
Density of fluid lea itg region III amd IV Is:
e
%1A
The efatiOfln
S- %AZ-
acOPftltfg the
jam (.w~
where
F
px (3 ,0,)
Is the t1ow rate into the rqicni
wiL
k-
(12)
tA3 IFLALAI
Integated
ThiS equation oa"a
aR ( euI r
In region IIaIac IV In
aaft* of
(" a- L A c 43X it rvxx I = A-
~i
'i
ZIt(FCt4a)
.
[(A%
145
vibere
60)
t~~o3
14,v
;CC
ly
i
P
~f~
UtU,
pr J;3 ;
iLH
+ Am TI
14
L'Ar tA)(
~3)-
AIz41~}c:
(Axt Ar)
t Axht Ar \A2
A. U%'t)
Thus~
(2-4
- LP As
3-%-. iA)
PO)z Po +
-VriUiV
tL~kpkl)( I-
(13)
fo (4+iy
4.
lelatl~oR~p botwm
a,
=i
prosoure. at
The lustent aonou
.W" derived as
It ums also derived am
44
.t.]I p
(13v- 1*)
equating ftese tw. eapreolons md jut.oicn
wo obtain a quaadrottle rolatloa bteat
Lp
it fl- 't YX
9
the emUaton for
ancl
'y AP & +
A B
14.
2A
X
(A:
-W
A
ALbl4
A%)-(k4A3) * AIAr 1.kzj
0
outlet.
Oin(e the b~eght of the Mned~ regla
heirght$ then equMtio!
AS
(14) Is not vaV.d
cmcathe a1zed reglon reachats the outlet., the
on
VOC0
Sm Mntined earllvr
the SIUid fro!M
ifted tnaoyantly -to tho hlght of the*outlet.
I is
determine the relationship betv "-a'k,
8
Md
the QM30utt
eglo
Thu 1 , In order to
the amgunt of
mixing thich the boyrant set Umdergoes ulie ri.%ng Is neaded.9
thIle Is very difficult o
the enperlcntal
obtai,
and k?
glue*
113.1
be used In jeternl5 ag the deneity of outflow once the mixId region
has reached the outlet*
Before tUs aixed region has reached the OutletO the outlet atve=
is
of 2 paxrts:
ed
oompe
region III*
FIt
and
the flow frm rnegion 1L and the flow frcsm
Rluxsout
fw
are Isve
Of r~e on,
11 ad III rspoctIvey, the eQuation for the donlty of autfloir Is:
Thus
p~ ~
113
PeeE
- (,H F, -t 1 za
f~9
dt;
F.=
where
-xOa
Ar k
In order to eliminata
from the equation, dividing
e te
. by F
yields
/= Azs
dthdt . A
WE
I4L dt /dk
Tho density of outtlow become
We a
k% and
, .
outlet streasm
antly lifted fr
fron the qadratSc relation between
dJ/d,
compute
After the mized region has reached the outlet, the
s agan composed of 2 parts;
the flldd which ts buoy-
ragion 1, end the flow from region II
Itf
t to
assumed, as previoualy stated, that the buoyant j t does not aix w1th
the now stationary mixed region, than the equation for the density
outflow is
s
+
c z
By eliminating tim frm the equation, the density of outflow
becames
lov
(djr
( +rfAL
where
andih
In
}
I
( 17)o
cm1mlated tra te. &V'riwatanly cdowlv" 42.
206
1.
IDespqrition of the teak
The exsperimntal
glass to k.
The tank was 46 am
15 am daep and 90 cm hlgh,
54. cn
from the bottom of the
The partition me placed 30 am from the left
and left
:j
0s
MeBthod for tilMing th
tasu
Tioomethode wre used to 1ll
gradient.
edge of the tas
a gap of 18.6 on from the bottom of the teak.
:
2.
tbde
area wa
The round outlet .18 oain
tank,
carried out In arectangular pztq-Y
wrh was
In the firt
vater, each withb
metho
d,
the tank with a Inear donsity
disttact layes
.of 1000
o of malt
difeort desity, were super-wlposed on each othar.
The densmdt solution was frst.
added to the tek
lighter layer was floated on the proviou
oeam.
and then each succeeding
In order to obtain
ditfferent donitte
i vtereac
1ayr, a know
aleount of trerh
measured in a 1000 cc greaduated Cy11ndear and sal
P
wva
ated salt ~ator,
1*2, Was then added to obtain 1000 cc of salt solution.
Tho
solution was than thoroughly niaed.
The arount of fresh water ji
added in each 1000 cc of solution is
given in Table 1.
oc
The apparatus used for the floatation process Ib shom below
in Fig. 11.
to sUpport
SiRtL
fwpovatus aor
Cf.tcluse spo
it
h this floating board,
e
the lighter fluid floated on top of
the heavier fluid aith almost no dieturbance of the liquid interfact.
A period of about 24 hours was used to permit the diffuston proces
to smooth out the abrupt density diffterences I
the adjacent layers
and thereby producing a linear density gradient.
A second method of fillng
bet
n 6 and
hours to fill
the tank was tried because it
the tank
tk
b the layering nethod.
by
In this second method, a liquid of density
slowly at a rate of flow V1
liquid of density
zo
.
took
Inateo a
o
was introduced
ixing vessel containiag a seond
At the same time, the liquid In the mixng
vessel. me transferred to the tak
at a volume rate
Va
.
22.
TAMBL
1
Amount of fresh water In 1000 co of satwrated s1lt water fresh water
Layer
3
4
6
7
9
10
11
12
13
14
15
18
of tresh
0
18.87
31.7
47.6
83.8
19.4
98.2
127.0
80
21
t2
3
24
26
28
27
2a
29
30
31
82
33
34
cc of Fresh
Water
412.7
428,0
444,4
480.3
478.2
492.1
807.9
8238
539.7
142.0
174.6
190.8
206.3
222.2
23.1
37
38
269.8
301.6
317.8
40
41
42
43
44
48
349.2
3865.1
881.0
380.7
47
4.
49
80
17
1
Layer
No.
slture
$71.4
887.3
603.2
419.0
634.9
680.8
066.7
682J.
698.4
714.8
730.
74040
777.8
793.7
Layer
SI
62
53
54
5
87
88
89
00
61
88
83
cc o Fresh
-Water
828. 4
873.0
888.9
904,68
920.6
93M8.
982.1
98.3
984.1
1000,8
The ditferet1al euatio s decoribl9gJ
the above arrangeat awe:
4t
where
V1.
is the volum of liquid I
volume setcun ated In the tank, and t
the mintag veswM,1
represents tae.
V is
The solu-
tion to these eq~ations is:
The
nitWal condtions ares
For the casewhere
Lt
2
A
* eqAawtion
a)
ecomes
Which desribes a linear gadlent In the tank.
The aethea used to construct such a linear denalty gradient in
the tank ias to use pumps to control the flow rate in and out of
the a.2mng vessel.
11q4d traisfer proes,
the liquid In both vese.1s ga1ls at the
sam rate, then
Two pumps wre ueed
one to pump the liquid Into the aIuIng
vessel, and the other to pp
needle Va1
the sixed liquad lnto the tansk.
A
was used to control the flow sumch that the levels i n
both the vessels reinated the
ia.
A annmter on eacW vessel u8
uwrd to check that the levals in each vessel
up Is Illustrated itn fig. 12
a the emS.
TIs aot
L-L
soat C.Ai-ev
26 .
3.
Method for
itsuria tho height o
h
mied re Ion
In the provias dlscussion, tw*o dfferest defaiitslos
in doeaibing the height of the vixed regBi
.
In one ea~a,
iere give
a con-
stant volume relationship eas assumed and in the othsr, an equal
density relationehlip was asumed.
To doteine which rlattleship the fluid obeyed beat, a sail
speago soaked to mthyblue was plaed at the bUotto
As the fluid pesed aeross the partitioua
blue color, and the height of the
coaUd be deterdzned.
n ble
1't
it
of the
WtItttt.o.
picked up a charactewrist~
mixed region as a function of height
This it aoun in fig 134
----------
=
.7'
FI.13
4.
athMd for seasnaesthe dmittr tradet
The first sad easest method used to ueasu e the density gradiat
was to obtain amples of flud at given podtioneA
there elste pepoolk
at the bottom and near t .
of the tank.
Since
ddle of the tank,
mall samples we. removed and their densities Ieasured with a
hydrometere
.
A sall Msaple was also obtained fwe
tank. -A straight line ws drlaa frJe
the top of the
these points and the density
J7
as calculated.
gricat
This Is aboy
In fig. 14.
I
I
---The seand method whioh m
the densty gradient
used to obtei
we to fill ping-pong balls with a solutico
deasit3r
,-
,
water of known
of sat
am to measure the height at which they floated IJ the ta3k~
This method ms mly approximate because of the weight of the balls.
Also, due to the sase of the balle, it
bthheight at which they floated.
eo ----
Ps diffic alt to deteralne
This is shon in fig* 15.
-- -- -P,, - ,
P.P.0g
In order to o"rmame the problems assolated with I
A list of the
small drops of tasoluable orgaloecopound s ere used.
e oeepods tiSd he demsity range of 1.0
%nsoluable arg
given in table
f elt
.
UMntortunastel,
balls,
1.8 is
mest et these coapo0nds are d1f-
to obtain and are very eopensve.
The case
bich were
ouovnpfeu
"wtsm
owelmrsa
ounmd *acr
almITOOTo TFqse
omago
TPZLE 2
ALLY &CeUt04t O
Amyl A 'fuy1.orY1t.
Bawl Gaotate
BMWl .5140i
Bousyl blityrat*
besyl cyanide
Bgmayl eIthor
Bssyl gozste
8oasy1 pnrptste
Ssmql pVpwtdino (2) (a)
Bawly salloytate (j)
u)1077
Rutyl furoato (a)
Butyl 3-turylaorylate
Butyl ndtralto (ISO)
Mhoro butywmitrIts
Chiozo etia
nsu (0)
Chioraoethylbnus" Ca)
bty1 2-cooo-4 tort buatyl, 4w-2,11)
CMoro
- bha~o Ca)
Chioro styzen. Ca)
Chioro styrone C)1*110
Chioro tolune
Dially oxalate
PlAMYl pbalat.
DIawy1 tawtwate
Dtabloro poutane (1,5)
Dichlore pestano (M,)
Wdethyl acetyl suclmate
Diethyl allyl Maoat
Dletbyl busyl "mlosto
Diethyl, gltaoosate
Edethyl aslsato
DI9thyl omaoto mIlaftts. "etr
Diethyl
0hhlt
(0)
1*losl
eater
Otethyl phtbalato (a)
DIetwy
iont
oiethyl Isoftsuaclato
Difloro 1.1 dlobloroethane
D"iathyl adlpat.
!imethy]l assacemste
DIftww wptaadne
1
(a)
Dimethy ugphtbyle"nne (1,4)
Dipropyl sulfite (a)
1.180
10032
10057
1.006
1.443
1.018
1.036
1.081
1.036
1.05S4
1.056
1.048
1.015
1.102
1.055
1.045
1.149
1*194
1*102
1*082
1.055
1.022
1.003
1*094
1.003
100
1.000s
1.077
1.050
1.070
1.131
1.121
14*13
1.040
1.6031
1.494
1.003
14121
1.0042
1.010
1.030
30.
Ethyl
1c0tla1oyat157
Ethyl a
seate
(P)
Ethyl beawyl acetoacetate
Bthyl a-chloraoproplonate
1.103
1.e38
1.08?
Ethyl cumsate (trans.)
1.049
Ethyl hydro slnn4sate
Ithyl Methyl saeto-acetate
Ethyl L-naphthylamine
Sthyl phsaylaetate
Ethyl pyrua te
Sthyl saliOate (0)
Ethyl tuluate (0)
Ethyl tuluate (a)
Ethyl tulauate (P)
f wfuryl acetate
Gluoos (a) pentapreplanate
Glyeawyl tributyrate
Glyoerly trivalerate
a4e.ic attrite
haUthyl saloylate
Methyl P-ansyl
Methyl befoglacetate
Methyl diphenylamine (N)
Methyl ethyl Sucotate
Methyl pheaylaoetate
Methyl toltate (0)
Methyl toluate (a)
Nitro ethylbenmene (0)
itro ethylbeno e (P)
Nitro propens (3.1)
Nitro 0-Qlene (3;1,2)
Nitro a-cylene (2;O,3)
Nitre a- lene (4;1.3)
Phemyl ethyl alcohol (a)
Phg
Yl tso-thLtcyanate
Pheayl toluene (a)
Propyl besocate (n)
Pzopyl p-*tluUe culonate
Yhiophena
TUbutyl ttrate ()
Triethyl citrate
1.018
1.019
1.060
1.033
10.60
1.135
1.03
1.030
1.024
1.118
1.181
1.032
1.030
1.124
1.04
1.071
1.173
1.048
1.093
1.044
1.073
1.06
1.120
1.124
1.051
1.147
1.112
1.125
1.019
1.138
1.031
1.021
1.144
1.070
1.046
1.137
313,
V.
It
ISMULTS
EXPIER1IMNTAL
is apparent grom the theoretical equations, in order to achieve
agreement between the theory mad the experAimet , thua the orta~ia
dew ty gradient aat be aeourately determined.
Fig. 16 describes the density of overy fifth layer ldch w~a
as a fu otie
in filling the ta
Fig
used
of the height of the free surface.
of the free
1.7 describes the density of the fluid as a fuctiona
s rface as the sae tank was emptied very slowly Irm the botton.
aince ahe flow rate out of the tank was very sall,
it
ts again assumed
that the fluid flowing out of the opetaig was rouved one density layer
at a tie,
and should therefore represent the density structure before
the tank was emptted.
a
fig. 17, abshows that thee tw
oates that very little
aiag
the deuity gradif
imsr4na
gradients are
t in fig. 16 and
nearly the same
Shich indi-
occurred between each deasity leor.
aof-l3aearity of the density gradient at the betto
The
of the tank in
fig. 18 to a result of leVtaig the teak set over night in order to
smooth out the origial density layers'
Fig. 18
desorlbes the density gradient obtained by usaig ts setod
of controlitag the flow rate in a"
to fig. 12.
obtained.
out of a miag vosse1 as explained
Using this method, &aach smaller donsaty gradient to
Also,
the pointa an the graph show a greater spread than by
fSlling the tank with layers of difftrent layers.
The density gradent
in this case was determined by uslag filled ping-pong balls.
The results from two represntative eporimentes
ill now be d1scuesed.
401
10
600
4A'4
50
200
10'404-.
PO
1
0
(p
Fil.Ck
o~t%10.elr
A10
J~t-
t
20
13
A
&
1
s
oht
WGAC#l cnollvno
4L01
0 Avswo(3
(I-
4a
0t
oc
:
C-0-
Fr
0
-4,
to'
bo
c,
lo--
SO --
40
io+
0
ro0
10
9
so
Ila
10
I
DO
l
1c
(e-O 3
Den'ly svxatervA obtavnc(
lq 0
Ki
11T
0
.)SIM)c
1(00
110
frL
lO4
The tbe
B.
brfeered -to ao e
iand
erimnts w
rlment
The in1tial conifderatos of is.eriament A are:
dality gradiaent
=
2.19 x
de"sity variation
=
.18
0"
c
= 84.0
UH e
nltial height in t ank
cm
The initial cor~ltions of .zpriment B are
denaety
radieat
dnasity variation
Initial height In tak
=
1.4a x 10 -
n
.126
a
8
Com
= 88.68
In the theoretieal analysis, two relations were derived for the
Equation (0) w.a based on a constant
height of the wmied region.
volume asamption Uad equation (7) ws baed o
assumption.
a constant devsoty
m
In fig. 19, both equation (6) and equati
are
(7)
plotted along with the .xperimemtally derived hsoght of the mlxed
region.
Frem fig
19 It
Is obvious that the height of the ximed r~gion
to govermed by the onstant volume ausmption:
In experiaant'A the theoretical height
reached the outlet
fro
the IN
the theretimoo
was 53.80
versus
as
at which thet
ned aregio
1. 38 dS. The experimental height obt"Qap
c urve was 583.40 cm.
In eperimet B
helght was 63.12 am ~iile the experisental Wtight
Thu,
T.
equation (7) agObre
from fNi.
19 and the just mentioned reosuts,
very %11lwith the experimental results.
d
36.
/noiwIno
*~v~.ov%~cAL ec~v~1 ~
e~. 7
t
O
A
/
C--
F15. 19
Hi~~o
V%~4V~av
37,
p
In quat1on (6)
gIaS
III and IV.
between
Iantrod
This quantity
t- and k1
PFIs
.
range of
msxed ret
W
as Introduced so that a relation
a theoretial relation betwee n
20 and PiEg
curve and the esperimental
respetivelyl
and kL
21 show the theoeteial k
i v
The theoretieal
e
.
for. a given
esperten tal value.
In
curve for oexperI
.
A and B
to
the
The theorettcal reeaIts in erxpert
pimetal remts.
the theorettcal value of
,
,w
, sioe the theory i Only valid until the
lose
ory
I
audl b
urve does not extend for th. total
ngIreaches the outlet.
mant A are vet
inaw density in ro*
could be derived.
gy solving equation (14),
is deteramied.
edotas the
In eaperiment B,
In
HoMver, the theoretical slope
lowar than the
of theh
,
A
e
8eportmen
B
does agree with the .aperimental slope.
F gs. 22 and 23 desrtbe the theoreteal and asperiaenta
aitts of outlow as a
respectIvely.
nott
o
for experImental A and
denB,
the reion of the theorettal ourwe whth abows the
density inoreasing I1 plotted from eqnation (18),
of the theoret al cUrve "i b sabho
from equation (1).
equation (16) ae
For a given
thhedensity decreaesag Is plotted
,
b
the densettes derived tfrm
lower than the esperimetally derived densitieS
exaperlant A ad higher or experment B.
related to the fat
the region
0le
that the dsity
larger thaM in experiment B.
for
This disorepe ey may be
variation aper
ALso. for a given
t A mr
, the densAites
derived fm equation (17) are lowr than theoperimetal derived
denties for both exe5riment A and B.
This bou14d be espOeted snce
38.
the equtatin does not take Into accaunt misLgagi
Although the theory and experiment
Is enough slailarity betw
vn
Is adequate.
In factt, t
o not exactly agree, there
th~a to augg.t thhat the
more linear and exzact density gradIet
oul4d bo achieved, then the theory and the
closely agree.
xperls
iporlmeat vould more
I as led to this conclusion by the fact that the
ntal valuasaa,
such as height of mixed rsgion, vhich are not
a function of the density gwradimeat were vry close to the observed
values.
39.
0-
ro
40
s
w ev,;cnL
A
40.
-C
40
70
60
F%. .
40
h,
Uersehl.
Foe
41.
0x
.. 1;
eus4Jtues
A- Horrub
04W\e&
aD
8ot
1o
to
a.
50
ed4y
at saj
40
eo
ipyw'
A
42o
v - rlyt~vo*mt
a
0
S110.
a
-
f%3.?.3
0
u
s,e
430
APPENDIA
A
Data fros3 xrapwment A
R3
o
84.98 a
3
1.010
4
=
.186
60.35
5.15
30.46
278.180
*2.40
25.40
23.70
223.10
20.80
19.00
17.80
160.00
14.70
13.30
12.00
10.70
9.i0
8.20
7.00
5.75
4.00
3.40
00.0
67.46
53.06
62:s
4.80
47.00
40.45
44.80
43O,10
41.95
40.90
3.900
310m
2*40
1.30
.00
1.080
1.084
1.086
1.088
1.001
1.101
1.103
1.110
1.107
1.108
.104
1.102
1.100
1.098
1.097
1.008
1.093
1.124
440
Dmai
fwor~F
esr~
3 =
P=
nt ai
86.658 c
1.051
p W
88.00
33.15
30.15
84.70
63.25
61.60
28.30
58.80
66.65
50.15
88.8
53.85
52.20
50.78
49.35
47.00
a125
26.60
24.78
22.90
21.10
19,10
17.30
16,.25
14.7
13o25
11.78
10.30
9.00
4.60
4.760
43.8
41.30
358.6
3.55
3.20
.8
1.093
1.009
1,102
1.105
1 100
1.111
1.113
1.117
1.11
1.117
1.110
1.114
1.112
19111
1.109
1.107
1.100
1.108
1.103
1.104
45.
APPatDIX B
1.
Cal3ulatite
of Foud* number
voluatric flow nrate/ ut
%
F~
~
L'g1
Sa=
dpth of water to outlet
*, dnsity at outlet
P
3.
daesity at tfree surface
Calculation of height of aied region
Constant vo~um
relatonaaip
09.85
20
62.35
30
S8
40
45
s0
58
67.35
84.5
8.35
Constant daeltty relationabip
670.8
20
66092
64.2
60.98
87.56
65.02
30
35
4.
60
sof
width
3.
:from VIt
Calcuation of
Bxp*riMent A
06.0
03.0
000
37.0
56.0
30.5
23.0
190.8
17.8
Experimet B
4
Caoloulatic
67.0
64.0
338.5
30.0
6.0
21.0
of density of outflow
3eprimena
A
06.0
038.0
00.0
5.0
80.0
60.0
47.,6
45.3
44.3
43.1
40.9
1.083
1.094
1.097
1.089
1.08S
1.078
1.076
1.073
1.006
1.066
iperi
07.0
4.0
600
50.0
82.20
49.3
44.0
41.3
38.0
ent B
1.100
1*104
1.110
1.110
1.100
1.105
1.101
1.007
1.004
1.000
47.
BIBLIOGRAPUY
Crays, A., 1949:
Recberches theoriques sur l'e'"oulment do coauhes
s
es
superposees de fluides de demt
otaIlle Blanche.
ditfferentes.
La
Jan-Feb, 44-5.
Debleor, W. R., 1959: Stratiftd flow into a line sink. Journal
of the Engineera I
Mechanics Divisioa. Proceediags of
the American Soiety of CiVi Englasers. July, 61-65.
Gariel, P., 1949: Recherchee Ezperimmtal s sur 1'e'culemet do
coauohes superposees do tluidee d ddonsetes dfferentes.
La Noulle Blanckhe
Jan-Feb., 58643.
Lag, R. R., 1953; Some aspects of the flow of atratitted fluid.
UniverJohns 3Opka;i
D partmat of Civil Eloggineeria
sity.
Oster, G.,
Terbtcal Report 2.
Density Gradients.
solentific American.
Aug., 70-78.
Oster, G., and u. Yamaoto, 1963: Dnasity Gradient Techniques.
Chemical Reviews, Vol. 88, No. 3, 27-288.
Yh.e Ce-S., .19:
Effect of density variations on fluid flow.
Journal of Geophysical Research, Vol. 64, No. 12,
2219-2223.
Yih, C,8S., 1958: On the flow otf tratified Fluid. Proo.
Third Nat'l. Congr. Appl. Mechsaios. $57-861.