reducing mixing effects in water storage tanks using calming inlets
TRANSCRIPT
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Redu c ing Mixin gEffec t s In Wat erS t o r a ge T a n k sD. Brett Man son
EDAT Year Fou r
Final Year Project 2000
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SUMMARY
Clean drinking water is becoming more and more of a world wide problem,
particularly in developing countr ies . Rain water harvesting is a technique
which is creating growing interests as it is decentralised, locally
manageable and relatively cheap to implement. However one barrier to its
widespread use, is the issue of health, part icularly with regard to bacteria
wash ed in from th e roof. There is su bsta ntial evidence th at th is b acteria die
off after a period of storage in dark conditions so it is advisable to add
water to one pa rt of a t an k a nd take i t from a noth er , while not a llowing th e
water to m ix.
This report looks at the methods of mixing in water tanks and describes
experiments performed on a cylindrical model tank with a negatively
bu oyan t water source d ischarging throu gh var iou s inpu t ar ra ngements .
Mixing was foun d to be confined to the b ottom of th e tan k with th e h eight
of the mixing front proportional to the product of the Froude number and
the inlet diameter, the constant of proportionality changing with different
input ar rangements . Recommendat ions are made regarding input and
output ar rangements based on these resul ts and on observat ions made
du r ing th e exper imen ts .
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CONTENTS
1 . INTRODUCTION 1
2 . BENEFITS OF RESIDENCETIME 3
3 . CAUSES OF MIXING 7
4 . EXPERIMENTS 22
5 . CONCLUSIONS AND RECOMMENDATIONS
FOR FURTHER WORK 42
BIBLIOGRAPHY 48
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1. INTRODUCTION
THE NEED
Water is one of the p rimary n eeds of hu ma n beings. The b ody is over 60%
water and needs over two l i tres a day to maintain good health. Water is
also the universal solvent and is used for washing. According the World
Health Organisation, each person needs at least 10 l i tres a day of potable
water for drinking, cooking and dish washing purposes . New sources of
water supply, however, are rare and old sources are drying up or are
becoming contaminated.
Rainwater harvesting (RWH) is an age old technique that is experiencing a
resu rgence of int erest . This is not only du e to the a ppa rent sh ortcom ings of
various other techniques being used but due to i ts convenience. Water is
collected where it is used so long trips to the well are avoided. and
expensive piping u nn ecessary.
One of the prima ry concern s , h owever, is t ha t of contam ina tion. The water
fall onto a surface such as a roof and is then diverted to a s torage tank.
The surface itself also provides a place for falling vegetable matter, dust
and faeces from birds and animals to sett le. When the rain fal ls , this
matter is washed into the system along with the water . Fil ter ing can
remove the larger debris and various first flush systems have been
promoted to remove the worst of the conta m ina tion b u t sm aller debris su ch
as s i l t and micro-organisms such as faecal coliforms are not so easily
disposed of.
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Th ere is stron g colloquial evidence to su ggest th at s imply storin g wat er in a
dark environment can reduce pathogens s ignif icantly as without l ight,
photosynthesis cannot take place and the organisms soon die off . This
m ean s th at , ideally, new water sh ould enter a t one en d of a ta nk while old
water should be drawn from the other without al lowing the water in the
tan k to mix. Water in th e tan k sh ould also be kept s t i ll to al low su spen ded
m atter to sett le to the bottom of th e tan k.
AIMS AND OBJ ECTIVES
This project aims to investigate the phenomenon of reductions in
pathogens through s torage. The work can roughly be divided into
an swering four m ain ques tions:
1 . What e ffect s does s torage have on pa thogen nu mbers?
2 . What a r e the s to rage t imes fo r pa thogen d ie off and s uspended
solid sett lement?
3 . What e r e the cau ses of flu id mix ing in wa te r s torage t anks?
4 . Can m ixing effects be redu ced s ignificant ly, and what m ethods
can be adopted in the design of tanks, inlets , outlets etc. to
achieve this?
Th e work itself can be divided rou ghly into th ree sta ges:
1 . Des k Res ea rch
H ea lt h b en e fit s of s t or a ge
Ca uses of m ixin g
Qu an tifica tion
2 . E xp erim en ta tion
3 . Recom m en da tion s
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2 . BENEFITS OFRESIDE NCE TIME
Storage is one of the most effective methods of wastewater treatment.
Commercial waste reduction ponds boast a removal rate of up to 99.8%1 ,
a l though the res idence t ime tends to be measured in weeks ra ther than
da ys. Die-off, sedimenta tion an d pr edation are th e ma in factors .
2.1 BACTE RIA DIE-OFF
Typical die off behaviour for micro-organisms in water follows the pattern
of a s hort period where nu m bers rem ain const an t followed by a exponential
decline in numbers . Adverse environmental factors outs tr ip supportive
factors due to removal of organisms from their natural environment.
Somet imes there may be a shor t term increase in numbers as the micro-
organ ism s ta ke u p residence. The m ain factors for the decline a re:
Algae d ie off from lack of sun ligh t
Com p et it ion for food in c rea s es
Pr ed a t ion i n cr ea s e s re du c in g th e p r ey m ic ro-or ga n is m s a n d
u lt im ately s ta rving out th e predators
floc cu l a tion a n d s e d im e n t a t ion r e m ove s om e b a c te ria
These factors tend to be lumped together into a die off rate (k) which is
u sed in the equat ion 2
1 Gray p276
2 Dros te p172
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d c
d t= k c (2.1)
Where:
c is th e concen tration
t is tim e
Bacterial decay tends to follow an exponential curve, so an appropriate
rewritin g of equ at ion 2.1 is:
c = c0ek t
(2.2)
Where:
c0 is the initial concentration
This in tu rn ca n b e rewrit ten in term s of t:
t =
lnc 0
c
k(2.3)
Th e t90 value is a typically published figure. It is the time required for 90%
of th e ba cteria to die off. equa tion (2.3) can be th u s rewritten :
t90 =ln10
k(2.4)
Som e typical valu es ofk a n d t90 are sh own in ta ble 2.1
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TABLE 2 .1 VALUES OF k AND t90 FOR VARIOUS WATER BOD IES1
Type k (h r -1) t9 0 (hr)
Oxida t ion pon d 0 .1 21
Wa s tewa ter la goon 0 .008 0 .029 79 276
River wa ter 0 .17 0 .23 10 90
Storm wa ter 0 .03 72
There is considerable variat ion and the rates are very dependent on
temperature (high temperatures = more die off), UV radiation (more UV =
more die off but more algae) etc. Actual rates of die off will have to be
determ ined b y experimen t on s i te. Fu rth er work could u ncover a ra nge of k
that corresponds with certain roof types, climate, time of year etc. These
results together with the init ial concentration and health data can be used
in equation (2.3) to determine the residence time necessary for die off to
bring the concentration down to a safe level or an appropriate level for
seconda ry t rea tm ent .
2.2 SEDIMENTATION
water will also arrive with a load of sediment. While not usually unhealthy,
th is s edim ent can discolour an d f lavou r th e water wh ich can in itself affect
th e wat ers accept ab ility. Sedim ent will u ltim at ely settle ou t of water if it is
left still . Particles fall by gravity but are held up by buoyancy and drag.
Each particle will find some velocity where these factors balance and will
fall at this rate (the terminal velocity). The time it takes for this to happen
1 Based on da ta from Dros te p 172
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depen ds u pon th e sur face area an d dens ity of th e part icles an d th eir height
ab ove the bottom.
For sph erical pa rticles a t low Reynolds n u m bers (>0.1) th e term ina l velocity
is given by Stokes Law1 :
u t =
gdp
2 p ( )18
where:
u t is th e term ina l velocity
g is gravity (9.8 m s-1)
dp is the diameter of the particles
pis the d ens ity of th e par ticle
is th e den sity of water (1000 k g m-3
)
is th e viscos ity of wat er (9.4 x 10 -4 kg m -1 s -1)
As p art icles fal l at different ra tes , th ey run u p a gains t each other a nd form
clumps of particles. This process is called flocculation and results in larger
particles that fall more quickly. Flocculation results in a reduction in
pa thogen levels a s th ey can be tra pped in th e clu m ps of fal ling sett lement
and the method is often used in waste s tabil isation ponds where
coagulants are add ed to the water .
1 Perry p 6-50
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3. CAUSES OF MIXING
Th ere a re five fact ors a ffecting th e m ixing of water in a closed t an k:
Ve loc ity o f the incoming s t r eam a nd i ts subsequen t k ine t ic energy
Bu oya n cy of t h e in com in g s tr ea m
Diffu sion
C on ve ct ion c a u s ed b y c h a n ge s in ou t s id e t em p e ra t u r e a n d
rad iation of su nlight on th e tan k walls .
3 .1 VELOCITY OF THE INCOMING STREAM
Wh en t he wa ter ent ers th e tan k i t will have kinetic energy gained from th e
fall from the roof. A jet of water results which stirs the water in the tank
cau sing mixing. This tu rbu lent m ixing by us ing a jet of water is often u sed
by the water industry to maintain even chlorine dis tr ibution in s torage
tanks . Ros sman and Grayman 1 have shown that the mixing t ime can be
foun d by
m =k V
2
3
M
1
2
(3.1)
Where:
m is the mixing t ime defined as the t ime necessary to achieve 95%
uniformity
1 Rossman and Grayman JoEEp 758
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k is a cons tan t
V is th e volu me of th e tan k
M is th e mom entu m flu x; the produ ct of discharge an d velocity
FIGURE 3.1 TYPICAL TANK CONFIGURATION
Water level
Sludge
Water inlet
Water outlet
Gut ter
Roof
h
do
SludgeSludgeSludge
In a typical tank configuration (figure 3.1), the water simply falls freely
under gravity from a gutter or delivery pipe and therefore has a vertical
component of velocity that is a function of the fall from the inlet of the
downp ipe to its out let (h ) given by th e u n iform acceleration equ at ion ;
u 0 = 2 gh (3.2)
Where:
u 0 is the velocity on im pa ct with th e water s u rface
The horizontal component will be much the same as the output velocity
from th e gutter or pipe.
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The area (A 0) of the jet will depend on the discharge (Q) and u 0.
Cons ervation of volu m e leads to:
A0 =Q
u 0(3.3)
Th erefore, if th e jet is rou n d, th e diam eter (d0) will be given by:
d0 =4Q
u 0(3.4)
The velocity decay of the jet is a key factor. Any means possible to lower
th is will lim it the overall circu lation . Wh en a jet en ters a s ta tionar y fluid, it
entrains the f luid around i t and gains in volume. Conservation of
momentum means that the velocity must therefore fal l . There has been
some work on decay of falling jets, mainly from the point of view of erosion
from dam outfall. Ervine and Falvey1 derived a n express ion for th e velocity
deca y of a falling circu lar, n on a era ted jet:
u m a x 4u 0d0L (3.5)
Where:
u m ax is th e velocity at th e axis of th e jet
L is the depth beneath the su r face
If the jet penetrates to the bottom of the tank, i t wil l dis turb the s ludge
and, if the velocity is sufficient, circulate up into the higher water bringing
th e s ludge with it . Thu s n ot only will the dir t an d ba cteria from the rainfall
1 Ervin e , D, A. an d Fa lvey, H. T . Behaviour of tu rbu lent water jets in the
atm osph ere and in plu nge pools (Proceed ing of th e Ins titution of Civil Enginee rs,
19 87 , Vol. 83 (2)) qu oted in Boh rer et a l
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and roof mix throughout the tank, but any sett led matter will be s t irred up
an d m u st s ett le back ou t again. Falling jets a lso entra in a ir as th ey develop
which will cause further mixing as the air bubbles out of the jet as it falls
below the surface.
If the jet is submerged (figure 3.2) , the water will fill the downpipe to the
level of the water in the tank. When rain falls, the water will rise in the
downpipe unti l the difference in pressure head is enough to overcome the
pipe friction .
FIGURE 3.2 SUBMERGED J ET ENTRY
Water level
Sludge
Water inlet
Gut te r
Roof
SludgeSludgeSludge
d0
The path of the jet impinges on the opposite wall and causes eddies and
circulation upward, s ideways and downwards. The downward circulation
causes eddies and s t irs the s ludge but will remain mainly below the outlet
due to the barr ier of the jet . The s ideways and upward circulations cause
mixing of the new and old water and s teps should be taken to avoid them,
particularly the upward circulation as i t mixes the oldest water from the
top of th e tan k.
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In this case d0 is the inlet diameter and u 0 will be derived from this, so
equation (3.4) will read:
u 0 =4Q
d02 (3.6)
An empirical relation for the fall in velocity of a jet along its principle axis
was found by Rus hton 1
u x
u o= 1.41Re 0.135
do
x
(3.7)
Where
ux is th e velocity at a point a lon g the cen tre lin e of th e jet
x is th e dis ta nce to tha t point
3 .2 CONVECTION OF THE INCOMING STREAM
When water enters the tank i t wil l almost certainly have a different
temperature to the water already in the tank. Kincaid and Longly2 have
done modell ing that suggests that evaporation causes the temperature of
raindrops to approximate the wet bulb temperature of the surrounding air .
This temperature is dependent on humidity but is below the dry air
temperature .
There is l i t t le exchange of air between the top of a water tank and the
surrounding atmosphere so the air above the water surface in a tank will
1 Rus h ton The axial velocity of a s u bm erged axially sym m etrical fluid jet
(AIChE J 26, pp 103 81041) Qu oted in Perry
2 Kin c a id a n d Lon g ly
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quickly reach saturation and no further heat transfer will then take place
by this means, Thus the water temperature will be related to a more
general heat balance and will usually be higher than the wet bulb
temperature of the surrounding air mainly due to absorption of solar
radiation, Rainfall is also often associated with a drop in air temperature
and a cor responding drop in wet bulb temperature . This means that the
temperature of the s tored water will be higher than the temperature of the
ra in .
A shorter term effect is the temperature of the roof. If the roof has been in
su nlight i t wil l be warm er tha n t he s u rroun ding air . When th e rain fal ls on
the roof i t wil l be heated and could be warmer than the water in the tank
until the roof cools. This effect corresponds with the wash down of the
majority of debris and so this water is often disposed of via various first
flu sh m echa nisms .
The temperature of the rainwater will affect the flow in the tank by
cha nging th e bu oyan cy of th e incoming jet .
FIGURE 3.3 DENSITY OF WATER VS. TEMPERATURE
990
991
992
993
994
995
996
997
998
999
1000
15 20 25 30 35 40 45
T em pera t u re (C)
Density(k
gm-3)
Ca lcu la ted Actu a l
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Water changes density with temperature as shown in f igure 3.3. Fit t ing a
cu rve to the da ta yields th e equa tion;
= 0.005T2 0.0049T + 1000.3 (3.8)
which holds 0.005% between 15C and 45C. A temperature difference of
5 will result in a change in density of 1 2 kg m -3
If a fluid of one density is introduced into a fluid of another, the change in
den sity will give rise t o a r edu ced gra vity given b y:
g = g f a( )a (3.9)
Where:
g is th e redu ced gravity
g is the a ccelera tion d u e to gra vity
f is th e den sity of th e feed water
a is th e dens ity of th e am bient water
A temperature difference of 5 will result in a reduced gravity of 0.008
0 .02 m s -3 and he jet will either rise or fall according to this reduced
gravity. Factors t h at will affect th is motion a re:
Fr ic t ion caus ed by free viscos ity on the su r face of the je t . This will
fall as th e jet gains in size
Re du c t ion in t e m p er a t u r e d u e t o c on ve ct ion o f t h e s u r r ou n d in g
flu id an d entra inm ent with th e sur roun ding flu id
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The principle measure of the buoyant effects on a jet an unconfined or
semiconfined body is the densimentr ic Froude number. This is a non-
dimen siona l ra tio of a jets inertia to its bu oyan cy and is given b y:
Fd = u g d(3.10)
Where:
Fdis th e dens imentr ic Frou de nu mber
u is th e velocity of th e incomin g strea m
d is th e diameter of the incoming s trea m
When a buoyant jet water is discharged into ambient water , the upwards
m oment u m of th e jet will, at some p oint be defeated b y the bu oyan cy of th e
tan k water . Fischer et a l.1 foun d th at th is h eight is given by:
h = k Fd d (3.11)
Where:
k is a cons tan t u su al ly between 0 .5 an d 0 .7
If a jet is introduced into a closed body such as a tank, it will ultimately
impinge on some surface, I t wil l then change direction and in some cases ,
r ise against the reduced gravity and so will at tain a s imilar maximum
height. Rossman and Grayman have used equation (3.11) to plot ei ther
1 Fisch er , H, B. , Lis t , E . J . , Koh l , R. C. y . , Imber ger , J . and Brooke s , N. H.
Mixing in Inland an d Coas tal Wa ters (New York: Academic, 1979) Quoted in
Rossman and Grayman JoEE
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stratified or fully mixed behaviour in enclosed tanks with horizontal and
vertical inlets. k was foun d to ha ve a ra nge (between 0.8 a nd 1.5).
3 .3 DIFFUSION
Th e diffu sion of pa th ogen s th rou gh wat er is driven by two effects
Move m en t of b a c te ria b y fla ge llu m
Br own ia n m ovem en t of t h e flu id
A ready value for this sort of diffusion is unavailable and diffusivities of
liqu ids a nd gasses a re us u ally foun d by experiment.
DIFFUSION BY BROWNIAN MOVEMENT
Th e volu m etric diffu sivity of th e pa th ogens can be fou n d by cons iderin g the
problem statistically. If a particle moves randomly, a so called random
walk it will be likely to move a distance equivalent to1 :
s = 2Dt (3.12)
Where
s is the distance travelled
t is th e t im e taken
D is a diffu sion consta nt
1 ht tp:/ / www.genevue.com/ A_Diffu s/ Diffu sMain_1.ht ml
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If the particle is moving in a fluid, D can be foun d by the S tokes / Eins te in
equation 1 :
D =RT
N
1
6r(3.13)
Where
R is th e gas cons tan t (8314.41 J kg -1 K-1)
T is th e tem pera tu re (K)
N is Avogad ros n u m ber (6.0 2 X 1026 m olecules kg -1 m ol-1)
m is th e viscos ity (kg m -1 s -1)
ris the ra diu s of th e par ticle (m )
A pa thogen can be considered as a p art icle with some a verage radius . Sizes
of some comm on pa th ogens a re in t able 3.1:
TABLE 3 .1 SIZES OF PATHOGENS2
Typ e Exa m p le Size (a p p rox.)
Ba cter ia Ch olera 1 40 m
Viru s Sm a llpox 200 n m
1 Eins te in p75
2 Data from Droste
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FIGURE 3.3 MOVEMENT OF PATHOGENS BY BROWNIAN MOTION
0 .0
1 .0
2 .0
3 .0
4 .0
5 .0
6 .0
0 10 20 30 40 50 60
Days
Millimetres
Virus
Bacteria
The average movement is plotted against time in figure 3.3. It proves to be
very small but is based only on the effects of Brownian motion, therefore it
will not be a ccura te when flagellu m movemen t is taken into a ccou nt .
BACTERIAL MODATION
Most bacteria are capable of movement. This is usually accomplished by
movement of flagellum (see figure 3.4) but sometimes by other means such
as slithering or corkscrew rotation.
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FIGURE 3.4 MODATION BY FLAGELLUM MOVEMENT1
POLAR FLAGELLUM PERITRICHOUS FLAGELLUM
Speeds attained are far in excess of those from simple Brownian
movement. For example Escherichia coli which is peritrichously flagellated
moves at 16.45 m s -1 . Polarly flagellated micro-organisms move about five
times fas ter. Som e exam ples of th e flagellation of pa th ogens is in ta ble 3.2.
TABLE 3.2 FLAGELLATION OF PATHOGENS
Dise a se Ge n u s2 Flagel la t ion 3
Typh oid Sa lm on ella typh i per itr ich ou s
Ch olera Vib ro Ch olera e Pola r
Ga s troen tr it is Esch erich ia coli
Salmonella
Cam pylobacter jeju ni
Yersinia entercolitica
Peritrichous
Peritrichous
Polar
Peritrichous
Bacteria, h owever dont m ove in a s tra ight l ine. Ea ch ru n ends in a tu rn ing
motion called a twiddle. Twiddles are random movements and could
result in the next run being in any direction result ing in l i t t le net
1 from Brock et al . p 41
2 Data f rom Cairncross & Feachem p260
3 Data from Brock et a l .
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movement. A typical pattern of modation is pictured in figure 3.5A. If an
at t rac tan t su ch as a food source is present , then the ru ns become longer in
th e direction of th e attra ctan t an d sh orter in oth er directions res u lt ing in a
movement towards the attractant. Similar ly, if a repellent chemical is
present the runs will become longer away from the repellent as in f igure
3.5B. This process is called chemotaxis.
FIGURE 3 .5 ; MOVEMENT OF B ACTERIA
A, NORMAL
Ru n
Twiddle
B, WITH CHEMOTAXIS
Chemotaxis results in swarming, where bacteria toward or away from
stimu li en m a s s th is movemen t is clear ly seen in figu re 3.6 .
FIGURE 3 ,6 STROBOSCOPIC PHO TOGRAPHS OF BACTERIAL
MODATION
A. WITHOUT CHEMOTAXIS B. WITH CHEMOTAXIS
In a wat er tan k, n ew water will be at tractive an d old water repellent a s th e
older water will be depleted of nu tr ients . The n et resu lt sh ould be th at a ny
ba cterial movem ent will favour t h e newer water a n d m ay even p lay a role in
depleting the older water.
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3 .4 CONVECTION BY CHANGES IN OUTSIDE
CONDITIONS
Changes in outs ide temperature can cause f lows in the water . I f the water
in the bot tom of the tan k is made warm er than the water in th e top , then
the s tructure becomes unstable and convection occurs causing mixing. If
the water a t th e top is warm er than the water in the bot tom then the water
is s table an d th ere is n o movemen t. Heat gain will be ma inly in th e form of
solar radiation; mostly on the top of the tank and heat loss will be mainly
from convection with the outside air from the tank sides. In itself this
should help create a s table temperature gradient from the bottom to the
top of th e tan k wh ich will increa se th e sta bility.
There are also a number design s trategies that can be followed to
encourage s tab le temperatu re gradients
Pa in t t h e ta n k b la c k on t op t o e n cou r a ge sola r h e a t ga in a t t h e
top of th e tan k
G row t r ee s a r ou n d t h e t a n k p er im e t er t o s h a d e th e b ot t om o f t h e
t a n k
This temperature gradient can also posit ively enhance the buoyant effects
of th e incom ing s tr eam by increa sing the r edu ced gravity as th e jet r ises in
the t ank .
Heat exchange can also have a negative effects if one side of the tank is
heated by the sun. Bnard convection will result which will churn the
water in th e tan k cau sing mixing. This sh ould be a fair ly sma ll effect as th e
temperature difference should not be too great and the cellular nature of
the convection will localise mixing effects. Reducing solar radiation on the
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s ide of the tank with appropriate paint or tree shading should reduce this
problem.
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4. THE EXPERIMENTS
The principle area wh ere design can influ ence res idence t ime is in th e area
of turbulent mixing by jet momentum. The principle way this can be
reduced is nozzle placement and design. Larger diameters will reduce the
velocity and reduce mixing, however this can only be pursued to a limited
extent. Other strategies could involve different nozzle configurations such
as manifold designs and designs that encourage certain f luid behaviours
such as horizontal rotation. The experiments were designed to exploit
bu oyan t s trat ification to investigate thes e ideas .
4 .1 NON-DIMENSIONAL PARAMETERS AND SCALING
Recall, The ma xim u m height of a b u oyan t jet is p roportional to th e produ ct
of th e jets Frou de n u m ber a n d its diam eter (equ at ion (3.11)). Th is can b e
writ ten non -dim ens ionally as :
Fd = k
h
d(4.1)
In a closed tank, a mixing front is formed where the jet reaches i ts
m aximu m height, This h eight can be m easu red for jets of differ ing Frou de
nu mbers a nd a value for k can be found . At the sa me Froude nu mber , the
resul ts are scaled as :
h m
dm=
h p
dp(4.2)
Where the subscripts m a n d p refer to the model and prototype
respectively.
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The tes ts use salt as a medium to raise the density of the jet . This al lows
good control over the buoyancy and also allows bouyancies to be made
much greater than those in the real world which in turn allows higher
velocities for closer dynamic similarity as F d =u
g d
. Velocity ca n be
increased so long as the reduced gravity is also increased. This technique
was developed by Linden at al. for studies of natural convection in
buildings. Larger bouyancies also reduce the tes t t imes and are more
toleran t of m easu ring errors an d cha nges in tempera tu re. Full dynam ic
similar i ty was not obtained as the large amounts of salt needed were
difficult to mix thoroughly resulting in some errors. The tests times also
became so short that measurements were diff icult to take. A balance was
struck at 60 ml salt to 10 l of water which provided a reduced gravity of
-0.052.
Buoyancy was a product of both temperature and sa l t content . The
calculated densit ies of the fresh tank water and feed water as well as the
sa lt content were u sed to calcu late g u sing equ at ion (3.9)
The dens i ty o f s a lt was foun d by weigh ing a known quan t ity.
Each ml of salt into 10l of water added 0.1325 kg m -3 (it was
as su med t ha t th e salt com pletely dissolved)
Th e t em p e ra t u r e of t h e ta n k w a te r a n d fe ed wa t er we re m ea s u r e d
at regular intervals and equation (3.8) was used to f ind the
density
Th e d ye h a s a ve ry s im ila r d en s it y t o wa t er , s o it wa s a s s u m e d to
play no extra part in th e dens ity calculation
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4 .2 APPARATUS
All experim ents u sed a scale model of a wat er tan k m ade from a clear pipe
with a movable base made from Styrofoam. The overall apparatus is
pictured in figure 4.1. Dyed water was stored in a reservoir which was
placed at a height of 1.6m above the tank model. The dyed water was fed
down a flexible tube a nd thr ough a nozzle int o the ta nk . A screw down gate
valve regulated the f low and a ball valve was used to s top and s tar t each
trial. A light s h eet was m ad e u sing a s lide pr ojector with a s lotted s lide.
FIGURE 4 .1 TES T APPARATUS
Flexible tu be
Dyed water
Clear acrylic p ipe
Movable base
Clear wa ter
Gate valve
On/ off ball valve
Ruler
Slide projector
The nozzle arrangement was a s tandard plumbing f i t t ing into which either
different sized inserts or a number of different nozzle configurations made
from copper pipe cou ld b e fit ted. Measu remen ts were taken by s i t ing a cross
two ru lers an d each tr ial was t imed with a s topwatch .
4 .3 METHOD
Food dye was added to the feed water as an indicator as well as a
predetermined amount of salt to give it negatively buoyancy. At the start of
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each s et of tr ials th e tempera tu re of the feed water an d th e tan k water were
noted .
Most trials started with the tank filled with fresh water to a level of 10 cm .
The dyed feed water was discharged into the model and the height of the
dyed water mixing front (h d; see f igure 4.2) was measured for each cm of
change in water level (h w ). The trial ended when the water level reached
15 cm. Several tests were also done with an initial level of 7 cm and final
level of 12 cm to test the sensitivity to water level.
FIGURE 4.2 MEASURED QUANTITIES
Mixing fron t
Mixed water
Clear water
Dyed water
hw
hd
Water level
Each tes t was t imed and the total volume discharge (A hw ) was divided by
the tes t t ime to obtain the velocity of the jet . The temperatures and salt
quanti t ies were used to calculate the buoyancy. The densimetr ic Froude
nu mber was then calcula ted from th ese values an d th e je t d iam eter .
Early in the tes ts , i t became apparent that as the water level rose, i t was
possible for the mixing front to r ise a t th e sa me rate (hw = hd).This effect
is shown in the unity s lope at the end of each l ine of the graph in f igure
4 .3 .
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FIGURE 4.3 RISE IN WATER LEVEL VS. RISE IN DYED WATER LEVEL
0
5
10
15
0 5 10 15h w
h
d
If this was the case, all mixing would be occurring well below the mixing
front and there would be no further mixing of clear water as the height of
th e clear water (h c) would remain constant (see figure 4.4). , For this reason
the height of the water level was subtracted from the height of the dyed
water mixing front, leaving only the height where actual mixing was taking
place (h m).
FIGURE 4 .4 DETERMINATION OF ACTUAL MIXING HEIGH T
hc
hw
hw
hm
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Measurements were then only taken at the end of each tr ial when h c h a d
sta bilised. Th e calculat ed hm was then divided by the nozzle diameter and
plotted against th e calculated den simetr ic Froude n u m ber for the tes t .
The gate valve was then set to a different discharge and the experiment
repeated .
4 .4 HORIZONTAL INLET
INTRODUCTION
The first set of experiments were to determine the relative effects of
buoyancy and momentum in the mixing behaviour of the tank wi th a
s tra ight h orizon tal inlet . Wh ile Rossm an an d Gra yman ha d p lotted m ixed
or not mixed results based on a known height tank and f i t ted a l ine
between these results 1 , these experiments at tempted to derive the l ine
directly by plotting the ratio of mixing height to inlet diameter against
Froude number. Three nozzle diameters were tr ied and three quanti t ies of
sa lt . Thes e are detailed in ta ble 4.1
TABLE 4 .1 EXPERIMENTAL VARIABLES
Nozzle Dia m e t e r s Sa lt Qu a n t it ie s
6 .7 m m 20 m l
8 .0 m m 40 m l
10 .5 m m 60 m l
1 Rossman and Grayman JoEEp759
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RESULTS
The jet had two means of impingement on the far wall . I f the Froude
number was low enough, the jet fell to the floor, moved along it and then
climbed the wall . This can be seen in the series of photographs in f igure
4.5. If the Froude number was high, the jet impinged the far wall directly
and followed the pattern in figure 4.6. In both cases, the jet would climb
the wall for a short distance before falling back and filling the bottom. As
the jet f i l led the bottom of the tank, i t would again attempt to cl imb the
walls. It was t h is second clim b th at form ed th e bu lk of th e mixin g activity.
FIGURE 4 .5 PROPAGATION J ET FALLING TO BOTTOM
FIGURE 4 .6 PROPAGATION OF J ET IMPINGING THE FAR WALL
When plotted , all results fall on a straight line through the origin with a
gradient of -0.91. This is in reasonable agreement with Rossman and
Grayman who found the coefficient to be -0.8. The results are plotted in
figu re 4 .6.
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FIGURE 4 .6 FROUDE NUMBER VS. MIXING HE IGHT/ INPUT DIAMETER
STRAIGHT H ORIZONTAL INLET
h m = -0 .91 Fr d d
0
2
4
6
8
10
12
-14 -12 -10 -8 -6 -4 -2 0
Fr d
hm
/d
d = 6 .7 ; s a lt = 6 0 m l d = 8 ; s a lt = 6 0 m l d = 1 0 .5 ; s a lt = 6 0 m l
d = 6 .7 ; s a lt = 2 0m l d =6 .7 ; s alt = 4 0m l d = 1 0.5 ; s alt 4 0m l
This relat ion appears robust against changes in diameter , discharge,
bu oyan cy an d water level so th e resu lts s hou ld be s caleable.
4 .5 CIRCULATING INLET
INTRODUCTION
The major cause of upward movement with a horizontal inlet is the jet
impin gin g on t h e far wa ll. If th e water is des ign ed in su ch a way as t o avoid
this, it is possible that the mixing height will be reduced. One way of
ach ieving th is is to encou rage the inlet to circu late a roun d th e perimeter of
th e tan k a s in figure 4.7. This sh ould both a void direct im pingemen t on th e
wall but should also provide a surface on one part of the jet to slow the jet
down more quickly and with less mixing than with free turbulence.
Circulation also has a natural stratifying effect.
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FIGURE 4. 7 CIRCULATING INLET
RESULTS
The jet performed much as expected. There was no impingement and the
jet sim ply fell gradu ally to th e bottom a s it circu lated a rou n d th e tan k. As it
h i t the bot tom i t spread out and behaved in much the same manner as
with a s traight jet .
FIGURE 4 .8 PROPAGATION OF CIRCULATING J ET
The resu lts from the circu lating jet a gain fell on a s tra ight l ine t hr ough th e
origin but the coefficient of stratification of 0.65 was significantly lower
th an a s traight horizonta l jet . The r esu lts a re plotted in f igure 4.9.
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FIGURE 4 .9 FROUDE NUMBER VS. MIXING HE IGHT/ INPUT DIAMETER
HORIZONTAL CIRCULATING INLET
h m = -0 .65 Fr d d
0
2
4
6
8
10
12
-20 -15 -10 -5 0
Fr d
h
m
/d
Straight horizontal inlet
4 .6 DOWNWARD POINTING VERTICALINLET
INTRODUCTION
Another option to avoid impingement on the sides is to simply aim the jet
downwards as in figure 4.10. the jet will then first impinge on the floor and
only then move up the sides. This is a very different situation to simply
dropping the water in from the top as the diameter of the inlet is
controllable and all air will float out before the water is introduced into the
tan k. it will, however, dis tu rb th e s ludge on th e bottom of the ta nk , bu t, as
the water needs to be left for pathogen die off, this should also provide
ample t ime for sedimentation to take place. I t is also possible that
sedimentation could reduce the necessary res idence t ime through
flocculation.
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FIGURE 4 .1 0 DOWNWARD POINTING VERTICAL INLET
x
Tests were made with the inlet at several heights above the base (x),
centra lly and near to the tan k wal l
RESULTS
The jet moved outward s along the bottom of th e tan k an d th en climb ed the
walls with a s imilar p attern as h ad b een n oted with t he s t raight jet .
FIGURE 4. 11 PROPAGATION OF DO WNWARD POINTING VERTICAL J ET
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Once again the results fell on straight lines however the coefficients of
s trat if ication ranged as the height of the nozzle changed. The resultant
coefficients are in table 4.2. The actual results are graphed in figure 4.12
The results for central positioning and positioning next to the wall fall on
th e sa me line. So m ixing ap pears ins ensit ive to the h orizonta l placem ent of
th e jet .
FIGURE 4 .1 2 FROUDE NUMBER VS. MIXING HEIGHT/ INPUT
DIAMETER
DOWNWARD POINTING VERTICAL INLET
h m = -0 .47 Frd d
h m = -0 .41 Fr d d
h m = -0 .51 Fr d d
h m = -0.59 Frd d
0
2
4
6
8
10
12
14
16
-40 -30 -20 -10 0
Fr d
h
m
/d
x=5m m x=5m m (a t s ide)x=17m m x=35m mx=57m m Stra igh t h orizon ta l in let
TABLE 4 .2 COE FFICIENTS O F S TRATIFICATION FO R
DOWNWARD POINTING VERTICAL INLET
x k
5 m m 0.41
17 m m 0.47
35 m m 0.51
57 m m 0.59
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The results for k were charted against the height of the nozzle which was
non-dimensionalised by dividing by the diameter of the tank. They also fall
on a s tra ight l ine a s sh own in f igure 4.13
FIGURE 4. 13 STRATIFICATION COE FFICIENT VS. VERTICAL INLET
HEIGHT
k = 0 .5 x / D + 0 .4
0
0 .1
0 .2
0 .3
0 .4
0 .5
0 .6
0 0 .1 0 .2 0 .3 0 .4
x/D
k
4 .7 E XTENDED HORIZONTAL INLET
INTRODUCTION
These results beg the question of how much effect the dis tance before the
jet impinges upon the far wall makes. To this end several tes ts were done
with differen t length s of extens ion to th e h orizon ta l in let (see figure 4.14 ).
FIGURE 4.1 4 EXTENDED HORIZONTAL INLET
x
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RESULTS
the results fel l on the same l ine as those from the other horizontal inlet
tests. Mixing height appears to be completely independent of distance from
th e impinging wall.
FIGURE 4 .1 5 FROUDE NUMBER VS. MIXING HEIGHT/ INPUT
DIAMETER
STRAIGHT HORIZONTAL INLET
0
2
4
6
8
10
12
14
-20 -15 -10 -5 0
Fr d
h
m
/d
x=10m m x=70m m Stra igh t h orizon ta l in let
4 .8 STRAIGHT HORIZONTAL MANIFOLD
INTRODUCTION
One way of increasing the total cross sectional area of inlet and
consequently lower the velocity is to use a manifold design such as that
shown in f igure 4.16. Each jet will have a Froude number and a
consequent terminal height, however the total height should be less than
for a s ingle jet of the same cross section as each jet has a much smaller
diameter. The calculation of the manifold considered the effects of each jet
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in the manifold individually and divided the discharge by the number of
jets cons equ en tly redu cin g the velocity.
FIGURE 4 .1 6 STRAIGHT HO RIZONTAL MANIFOLD
RESULTS
The horizontal manifold gave a poor performance with a coefficient of
str at ificat ion s ome four time h igh er th an for a sin gle jet.
FIGURE 4 .1 7 FROUDE NUMBER VS. MIXING HEIGHT/ INPUT
DIAMETERSTRAIGHT HORIZONTAL MANIFOLD
h m = -3 .60 Fr d d
0
10
20
30
40
50
60
70
-40 -30 -20 -10 0
Fr d
hm
/d
2 2 x 1 .5 m m 2 2 . 2 .5 m m Stra igh t h orizon ta l in let
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4 .9 MODIFIED STRAIGHTMANIFOLD
INTRODUCTION
The p romising resu lts of circu lating inlets prom pted tr ials with a n u m ber of
configura tions of m an ifold in an attem pt t o ascerta in wheth er proximity to
th e tan k wall ha s a ny s ignifican ce,
FIGURE 4.18 MODIFIED STRAIGHT MANIFILDS
CONFIGURATION
ONE
CONFIGURATION
TWO
CONFIGURATION
THREE
RESULTS
The results are fairly inconclusive, All configurations gave a better result
th an th e longer m an ifold bu t worse resu lts th an a s tra ight inlet . The a ctua l
gradients are within a small range and favour configuration two. The
improvement is probably due to the lower number of jets interfering with
each oth er h owever, th e lack of overa ll prom ise of th e str aight con figu ra tion
does n ot really warran t furth er investigation.
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FIGURE 4 .9 FROUDE NUMBER VS. MIXING HE IGHT/ INPUT DIAMETER
MODIFIED STRAIGHT MANIFOLD
h m = -1.3 Fr d d
h m = -1 .58 Fr d d
h m = -1 .47 Fr d d
0
10
20
30
40
50
60
70
-40 -30 -20 -10 0
Fr d
h
m
/d
2 2 . 2 .5 m m 8 x 2 .5m m (con fig 1 )8 x 2 .5 m m (con fig 2 ) 8 x 2 .5 m m (con fig 3 )Stra igh t h orizon ta l in let Stra igh t m an ifold 22 h oles
4 .10 RADIALMANIFOLD
INTRODUCTION
Manifolds can also originate from a central point. This should result give
less interference between each jet. Trials were made with a radial manifold
with twin jets in opposite directions from a central position and one with
four equally spaced jets.
FIGURE 4.20 RADIAL MANIFOLD
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RESULTS
All results fall on the same line. This line has a gradient within 1% of that
for a straight inlet which is what is to be expected if the jets have no
contact with each other . The difference is almost certainly due to
measurement er rors .
FIGURE 4 .2 1 FROUDE NUMBER VS. MIXING HEIGHT/ INPUT
RADIAL MANIFOLD
h m = -0 .92 Fr d d
0
5
10
15
20
25
30
35
40
-40 -30 -2 0 -1 0 0Fr d
h
m
/d
2 x 2 .5 m m h oles 4 x 2 ,5 m m h oles
Straight input
4 .11 HORIZONTAL MANIFOLDWITH COLLISION
INTRODUCTION
An oth er poss ible geom etry is to h ave th e jets collide with each other .
FIGURE 4 .2 2 COLLIDING MANIFOLD
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RESULTS
Th e resu lt from t h e colliding in let a re slightly better th an th ose for a s imple
straight manifold. They are, however s t i l l much worse than those for a
s tra ight inlet a nd could s imply be du e to the lower nu mb er of jets .
FIGURE 4 .2 3 FROUDE NUMBER VS. MIXING HEIGHT/ INPUT
COLLIDING MANIFOLD
h m = -1 .92 Fr d d
0
5
10
15
20
25
-15 -10 -5 0Fr d
h
m
/d
14 x 2 .5m m sp lit ma nifold Stra igh t h orizon ta l in pu t
PLUNGING J ET
INTRODUCTION
For compa rison, several tests were done with th e in let ab ove th e water level
as in a tr adit ional tan k configura tion
RESULTS
The velocity gain due to the fall from the inlet meant that the cross section
of th e jet was less t ha n 3m m by the t ime it h it th e su rface of the ta nk . The
jet also had a great deal of entrained air which was released below the
surface. This effect was even seen with quite clean jets that had not
developed int o droplets. The effect can be clearly seen in figu re 4.2 4. At th e
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small scale of these experiments , surface tension was more of an issue
than would be the case on a larger scale so the resul ts may not be
completely accurate, however most turbulent jets will have entrained air
an d d roplets a s they develop. It was imp ossible to create a s tra t ified resu lt
at the scale of these trials due to the dropletting of the jet as it fell, the
sm all cross section an d su rface splash ing.
FIGURE 4. 24 PLUNGING J ETS
DEVELOPED DROPLETTING J ET UNDEVELOPED CLEAN J ET
SUMMARY OF RESULTS
TABLE 4.3 COEFFICIENTS OF STRATIFICATION
In le t t yp e Coe ffic ie n t o f s t r a t ific a t ion
Horizon ta l 0 .91
Circu la t in g 0 .65
Ver t ica l 0 .41 0 .59
Stra igh t m a n ifold (22 ou tlet) 3 .6
Modified m a n ifold (8 ou t let ) 1 .31 .47
Ra d ia l m a n ifold 0 .92
Collid in g m a n ifold 1 .92
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5. CONCLUSIONS ANDRECOMMENDATIONS FOR
FURTHE R WORK
GENERAL DESIGN RULES
Some general design ru les h ave emerged from th is work
Pla c em e n t of t h e in p u t is b es t u n d e r th e s u r fa c e of t h e wa t er
Ma k e t h e in p u t a s la rge a s pos sib le
The bes t configu ra t ion fo r the in let is h o rizon ta lly downward
followed by along th e ta n k wa ll to en cour age circulation
Ma n ifold s ca n b e u s e fu l b u t s h ou ld b e ra d ia l n o t lin e a r
O u t p u t s h ou l d e it h e r b e floa t in g or a t s u ch a h e igh t t h a t on ly
water that h as been depleted can be drawn
When a h o rizon ta l in let is u s ed , the bes t p lace fo r a fixed ou tpu t
is on the same s ide as the input as the mixing height is higher at
th e opposite s ide
SCALING AND EQUATIONS FOR CONTAMINATION
HEIGHT
Th e ta n k will con sist of three layers.
On the top will be fu l ly aged fr esh wa ter fo rming a bu ffe r
Undernea th the re will be wa te r tha t i s age ing wh ich will have
been a dded in a nu mb er of discreet s torm events . Its qu an tity,
however will depend on the longer term rainfall over the period
need to age the water
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At the bot tom is the mixing front which forms the floor of the
ageing water . Water b elow this is s u bject to m ixing an d can not b e
considered as h aving s ta r ted ageing
FIGURE 5.1 LAYERS IN A WATER TANK
Fresh water
Mixing water
Agin g wat er
The height of the ageing water is determined by the prevailing rainfall
which forms the basis of the upward velocity. Practically, the average
ra infall can be u sed to find t h e average velocity.
v =4AroofR Cr
D 2(5.1)
Where
v is the average velocity
A roof is th e roof ar ea
R is th e average rainfall
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Cr is th e ru n off coefficien t
D is th e tank d iam eter
The height will be determined by the t ime n ecessary to a ge the water . This
will depend on the die off coefficient and initial and safe concentrations.
Equ ation 2 .3 provides th e necessa ry t im e.
t =
lnc 0
c
k
Comb ining equa tions (2.3) an d (5.1) finds th e height
h =
4A roofR lnc 0
c
D 2k(5.2)
The mixing height i s an ins tantaneous phenomenon which is found by
u sing equ ation (3.11)
h = k Fd d
As Froude number is dependent on velocity, diameter and buoyancy, an
equation can be developed by combining equations (3.8), (3.9), (3.10) and
(3.11) along with the rainfall intensity and the roof area. When this is
simplified and insignificant terms are removed we obtain:
h = 182 k IACrd
3
2 Tt2 Tf
2 + Tt Tf( )1
2
(5.3)
Where:
h is th e height
k is the con sta n t of str at ificat ion
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Iis the rainfall intensity
A is th e roof ar ea
Crid th e ru n off coefficien t
d is th e inlet diam eter
Tfis the feed tem pera tu re (in C)
Tt is th e tan k tem peratu re (in C)
This equation is rel iable 0.5% between 0 and 50C and depends only on
the highest expected rainfall intensity, tank and rain temperatures and
kn own ph ysical factors .
SOME EXAMPLES OF APPLICATION
Early indications from field work indicate that a 4 5 temperature
difference is fairly reliable. and short term rainfall intensities of
4m m/ minu te are common. We can u se th is data to ca lcula te the mixing
height in some real tanks su ch a s th ose in ta b le 5 .11
TABLE 5 .1 SIZES OF WATER CATCHMENT SYSTEMS
Roof Ar e a Ta n k
C a p a c i t y
T a n k
D i a m e t e r
m 2 m 3 m
Botswa n a "ALDEP" ca tch m en t 40 11 2 .7
Th a i h ou seh old ja r 100 2 1 .56
1 From Gould an d Nissen -Petersen
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TABLE 5.2 MIXING HEIGHTS FOR TANKS
Mixing Height (m )
1 1 0 m m
Inlet
2 5 m m
Inlet
1 1 0 m m
Bent
In le t
1 1 0 m m
v e r t i c a l
in le t
Rad ia l
Manifold
6 x 2 5 m m
"ALDEP" ca tch m en t 0 .80 7 .35 0.57 0 .44 1 .22
Th a i h ou seh old ja r 1 .99 18 .37 1.42 1 .09 3 .06
When the heights are greater than the tank height, total mixing will take
place, however with judicious choice of inlet, both types of tank will gain
some benefit f rom stratif ication. Larger tanks such as those found on
public buildings in Africa have very large roof areas and require large and
complex inlets to achieve stratification. For example a typical school set up
in Botswan a 1 with a 1 300m roof area a nd two water tan ks requires a ra d ia l
system of 6 150 mm pipes to achieve s tra t ification at 1 .35m or a downward
inlet of 30 0 m m to ach ieve a m ixing heigh t of 1.58 m .
FURTHER WORK
WEATHER
The height of the output above the input is dependent on several local
factors:
Ra in fa ll in ten s ity
D et er m in e s d is ch a r ge a n d velocit y
Ra in fa ll tem pera tu re
1 Gou ld a nd Nissen-Petersen p210
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Ta n k tem pera tu res
Determ in e bu oya ncy
MICROBIOLOGY
The r esidence t ime is a lso relian t on a n u m ber of u nk nown local factors :
Th e m a xim u m c on c en t r a t ion r ec om m e n d e d b y loc a l h e a lt h
authorit ies
Th e in it ia l con cen t ra tion
Th e d ie off ra te
At pres ent, th e lat ter t wo of th ese m u st b e foun d b y local sa mp ling. Furt her
work could yield guidelines according to roof type, tank size, rainfall
int ens ity etc.
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BIBLIOGRAPHY
BOOKS
Abram ovich , G. N. The Theory of Turbulent Jets (Cambridge,
Ma: MIT Press , 19 63)
Avallon e, E. &
Ba u m e i s t e r , T .
Marks Standard Handbook for Engineers
10 th Ed ition (New York McGraw Hill, 1997)
Brock, T. D. , Smit h , D.
W. & Mad igan , M. T.
Biology of Micro-organ ism s 4th Ed ition (New
J ersey: Prent ice-Hall, 1979 )
Cairnc ros s , S . &
F e a c h e m , R . G.
Environmental Health Engineering in The
Tropics (Chichester: Wiley, 1983)
Dros t e , R. L. Theory and Practice of Water and
Wastewater Treatment (New York, Wiley,
1997)
E in s t e i n , A Inv es tigations into The The ory of Brow nian
Motion (New York: Dover, 1956)
Fox, J . A. An Introduction to Engineering Fluid
Mechanics 2nd Edition (London:
Macm illan , 19 77)
Gould , J . &
Nis sen -Pe t e r s en , E .
Rainw ater Catchmen t Sy stem s for Domes tic
Supply (London, Intermediate Technology,
1999)
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Gray, N. F. Water Technology: An Introduction for
Scientists and Engineers (London: Arnold,
1999)
Greenspa n , H. P . The Theory of Rotating Fluids (Cambridge:
Cambridge University Press, 1968)
H o lm a n , J . P. Experimental Methods for Engineers 6th
Edition (New York: McGraw Hill, 1994)
H o lm a n , J . P. Heat Transfer 8th Edition (New York:
McGra w Hill, 199 7)
Massey, B. &
Wa r d -S m i t h J .
Mechanics of Fluids 7th Edition
(Cheltenh am : Cha pm an & Hall, 1998)
McCabe , W.L. &
S m i t h , J . C.
Unit Operations in Chemical Engineering
(New York: McGraw Hill, 1995)
Perry , R. H. &
Gree n D. W. (Eds .)
Perrys Chemical Engineers Handbook 7th
Edition (New York: McGraw-Hill 1997)
T r it t o n , D. J . Physical Fluid Dynamics 2nd Edition
(Oxford: Oxford University Press, 1988)
White, F. M. Fluid Mechanics 4th Edition (Singapore:
McGra w Hill, 199 9)
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KEY PAPERS
Bohrer , J . G. , Abt , S . R
& Wit t ler , R . J .
Predictin g plu n ge pool velocity deca y of free
falling, rectangular jets ( Journal of
Hy d rau lic Engineering 1998 Vol. 24 pp 1043
1048 )
Kinc a id an d Long ly A water droplet evaporation and
temperature Model (Transactions of the
ASAE, 1989 Vol. 32, pp 457 463)
Linden , P . F . Th e Fluid Mecha n ics of Nat u ra l Ven tilat ion
( Ann ua l Review of Fluid Mecha nics, 1999,
Vol. 31 p p 20 1 23 8)
Lind en , P . F . ,
Lane -Ser ff, G. F. &
Sm eed , D. A.
Emptying Filling Boxes The Fluid
Mechanics of Natural Ventilation (Journal
of Fluid Mecha nics , 1990 , Vol. 212, pp 309
335)
Rossm an , L. A. &
Graym an , W. M.
Scale Model Studies of Mixing in Drinking
Water Storage Tanks ( Journal of
Environm en tal Enginee ring , 199 9, Vol. 25 p p
755 761
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