reducing mixing effects in water storage tanks using calming inlets

8/9/2019 Reducing Mixing Effects In Water Storage Tanks Using Calming Inlets

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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.

D. Bret t Ma n son 1


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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



28/54

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.



34/54


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



37/54

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.


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



39/54

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.


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



40/54

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.



41/54


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



42/54

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 .


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 .


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



44/54

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



46/54

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



47/54

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



48/54

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



49/54

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



50/54

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.



51/54

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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reducing mixing effects in water storage tanks using calming inlets

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