Development of a compact air-regulated siphon for use in storm sewage overflows.

MILROY, Charles J. A.

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MILROY, Charles J. A. (1988). Development of a compact air-regulated siphon for use in storm sewage overflows. Masters, Sheffield Hallam University (United Kingdom)..

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DEVELOPMENT OF A COMPACT AIR-REGULATED SIPHON FOR USE IN STORM SEWAGE OVERFLOWS

by

CHARLES J A MILROY BSc CEng MICE MIWEM

A thesis submitted to the Council for National Academic Awards in partia l fu lf i lm en t of the requirements for the degree of Master of Philosophy.

Sponsoring Establishment

Collaborating Establishment

Department of C iv il Engineering Sheffield City Polytechnic

Dumfries and Galloway Regional Council

August 1988

DEVELOPMENT OF A COMPACT AIR REGULATED SIPHON FOR USeIN STORM SEWAGE OVERFLOWS

by

CHARLES J A MILROY Bsc CEng MICE MIWEM

SYNOPSIS

An air regulated siphon has been developed to operate as a storm water overflow. One of the main requirements has been that a siphon of compact design can accommodate high discharges for relatively small increases in upstream level thereby preventing the possibility of surcharges in the sewer upstream of the overflow.

The s-shaped siphon was chosen for development as it has, by virtue of its natural shape, an efficient priming system. The downstream leg of the s-shaped siphon is returned beneath the crest so that a vertical wall of water formed shortly after first spill thereby effecting a seal which ensures priming.

A sectional perspex model was used to determine the effects of inlet lip length, inlet lip elevation, tailwater level, siphon width, upstream channel width, vortices at inlet and revised outlet configurations.Results were compared using a dimensionless plot of the ratio of priming head and throat depth (hi/d) against co-efficient of discharge (CD). The curves obtained for all the differenct configurations are useful as design aids for the design of a compact air regulated siphon for use in storm sewage overflows.

CONTENTS

Page

L is t of contents ( i )L ist of figures ( i i )Acknowledgements ( i i i )

Chapter One INTRODUCTION 11.1 Introduction to siphons 21.2 Uses of an a ir regulated siphon 111.3 Air regulated siphons, advantages and disadvantages 151.4 Types of flow regime in a ir regulated siphons 191.5 Siphonic hunting 24

Chapter Two STATE OF THE ART REVIEW 252.1 Siphon shapes 262.2 In le t configuration 292.3 Outlet configuration 312.4 Vortices at in le t 342.5 Siphon materials 36

Chapter Three THE THEORY AND DESIGN OF AIR REGULATED SIPHONSINCLUDING THE SIPHON MODEL 38

3.1 Dimensional analysis 393.2 Siphonic discharge theory 463.3 Low head a i r regulated siphons 493.4 Modelling technique 523.5 Aspects of s im ila r ity and scale effects 56

Chapter Four THE AIMS AND PROCEDURES OF EXPERIMENTATION 604.1 Objectives of experimentation 614.2 The experimental apparatus 634.3 The experimental procedure 64

Chapter Five DISCUSSION OF RESULTS 685.1 Order of analysis 695.2 Effects of in le t l ip elevation 715.3 Effects of in le t l ip length 825.4 Effects of ta ilw ater level 935.5 Effects of siphon width 965.6 Effects of upstream channel width 1065.7 Effects of vortices a t in le t 1115.8 Effects of revised ou tle t configuration 1135.9 Dimensional analysis of the optimum siphon configuration 113

Chapter Six CONCLUSIONS 1176.1 Comments and conclusions 1186.2 S u ita b il i ty for use in a 'combined sewer" overflow 122

Appendix A L is t of references Appendix B Laboratory sheets

( i )

FIGURES

Figure 1

Figure

FigureFigure

FigureFigureFigure

Figure

Figure

Figure 1 Figure 1

Figure 1

Figure 1 Figure 1 Figure 1 Figure 1

Figure 1

Diagramatic section of a simple siphon tube.Typical head/discharge characteristics for a blackwater

siphon and an a ir regulated siphon.Methods of a i r entrainment.Typical arrangement of a trad itiona l siphon overflow on combined sewer.

Siphon spillway straddling a dam crest (Spelga Dam).

Siphons incorporated into a bell mouth dropshaft spillway

A low head a ir regulated siphon as a river/canal level regulator.Typical head/discharge relationship for an a i r regulated

siphon.Types of flow regime in an a i r regulated siphon.Methods of submerging siphon o u tle t .Effect of l ip length on the low head priming

characteristic .Effects of l i p elevation on the priming characteristics

of the low head siphon.

Effect of ta ilw ater level on priming characteristics. Diagram showing in le t geometry of siphon.Schematic diagram of the apparatus.Side e x it type s t i l l in g basin - plan and section.

Graph of ^1/^ against CQ.

ACKNOWLEDGEMENTS

The author would l ik e to acknowledge Dr D J Balmforth for his help and guidance in producing this document. Thanks are also due to the Director of Water and Sewerage, Dumfries and Galloway Regional Council, Mr K Holliday and Miss H Jordan who assisted in various stages of this work.

( i i i )

CHAPTER ONE

INTRODUCTION

1.1 Introduction to siphons

1.2 Uses of an a ir regulated siphon

1.3 Air regulated siphons, advantages and disadvantages

1.4 Types of flow regime in a i r regulated siphons

1.5 Siphonic hunting

- 1 -

1.1 Introduction to siphons

The simplest form of siphon is the U-tube siphon ( f ig 1) as

used by the Greeks as fa r back as 1500 BC. The siphon may be

of iron, lead, glass or plastic tubing, generally c ircu lar in

section, primed by applying suction at the downstream end.

This type of siphon, once primed, transfers water from a

higher level to a lower level by gravitational means.

However, a l l the a i r has to be removed f i r s t and the act of

removing a ir is termed priming.

The U-tube siphon was f i r s t used, in conjunction with

aqueducts and open channels, to transfer water fo r domestic

and ir r ig a t io n purposes over long distances and d i f f i c u l t

te rra in . However, the main requirement for the development

of hydraulic structures came with the Industrial Revolution.

Industry required water not only for manufacturing purposes

but also for canal navigation. Dams, docks and canals were

b u i l t , a l l requiring some form of level control. At this

time weirs and spillways were the main form of overflow

arrangement but gradually in the la t te r part of the 19th

Century and the beginning of the 20th Century siphons were

developed as an a lternative means of level control.

In i t i a l l y the siphon used was the blackwater siphon and the

problems experienced with some of these siphons made

engineers wary of siphons in general. In broad terms the

Blackwater siphon is an inverted U-tube where the saddle is

-2 -

SIPHON THROATPRIMING HEAD

CROWN

CREST

WORKING HEAD

Fig1. A DIAGRAMMATIC SECTION OF A SIMPLE SIPHON TUBE

set well above the intake ( f ig 2a). I t can be primed

a r t i f i c i a l l y by closing o f f the ou tle t and f i l l i n g the

downstream leg with water from a remote source to a level

higher than saddle lev e l, but more usually the upstream level

is allowed to r ise until the flow over the saddle in i t ia te s

priming, whereupon fu ll-bore discharge takes place. The flow

is v ir tu a l ly constant, being determined by the tota l head

across the structure and not by the inflow to the structure.

Full-bore discharge continues until the upstream water level

is drawn down s u ff ic ien tly to admit a i r , which breaks the

siphon column, thus causing sudden and total cessation of

flow. The process repeats i t s e l f i f the inflow to the in le t

continues.

This mode of operation is c learly i l l - s u i te d to natural flow

situations where a control structure w ill usually be required

to accommodate a wide range of discharges. In such

circumstances a blackwater siphon w ill tend to 'hunt' ( ie

alternately prime and deprime) unless there is a particu la r ly

large body of water for i t to draw on immediately upstream,

or unless the inflow to the siphon is more or less constant

at i t ' s design capacity, neither of which is l ik e ly in a

r iv e r , canal or in a storm sewer. In fact this type of

siphon is rarely used except as part of a storm-water

overflow ie incorporated within bellmouth dropshaft

spillways. The head-discharge relationship for a typical

blackwater siphon is given in f ig 2a.

-4 -

V>*

*-o>k.VM»tr

Siphon discharge

Throat area APrim inglevel

Normal range of water level

Breakflowlevel

FIG 2(a) BLACKWATER SIPHON AND ITS TYPICAL HEAD/ DISCHARGE CHARACTERISTICS

Priming level

Normal range

of waterlevel"^

Crest length L

Breakflow level

Q =KLh

Siphon discharge

FIG 2(b) AN A IR REGULATED SIPHON AND ITS TYPICAL HEAD/DISCHARGE CHARACTERISTICS

The cycle of priming and de-priming is not satisfactory for

level control and therefore an improvement to the blackwater

siphon was sought. I t was found that blackwater flow may be

readily arrested by the admission of atmospheric a i r into a

low-pressure region of the siphon. K e n n ^ , by plotting

a ir flow against corresponding water flows found that as the

a ir flow is increased, by admission into the siphon hood, the

discharge is reduced, i n i t i a l l y almost l in e a r ly but f in a l ly

at an increasing rate. Therefore, an e ffec tive method of

control had been found where flow rate was determined by the

volume of a ir admitted.

Two main types of a ir in le t were developed for use in

siphons. The f i r s t , and most successful, took the form of a

s lo t in front of the siphon hood. The size and shape of this

slot has a great e ffec t on hydraulic performance. The

optimum s lo t configuration was found to be a shallow s lo t

extending the fu l l width of the siphon. This configuration

produced fine control of the upstream water level with

minimum flow in s ta b i l i ty . However, in the region where the

a ir demand increased with increasing discharge, a form of

in le t such that the rate of a i r entry was not d irec tly

dependent on the reservoir level was preferred. The

provision of a l ip over the s lo t , through which a i r and water

could be drawn to produce a local drawdown curve, was found

to be an effective solution.

-6 -

The second type of a i r in le t arrangement, as sometimes used

in sewerage overflows, introduced a i r , by means of a pipe,

into the crown of the siphon. This method of a i r admittance

proved unsuccessful as a method of a ir regulation as

dispersion of a i r over the width and depth of flow was found

to be inadequate and hunting resulted. This emphasised the

importance of introducing a i r both near the entrance of the

siphon and over i ts fu l l width.

Development of siphon design continued resulting in the

air-regulated siphon. The e a r l ie s t recorded air-regulated

siphons are believed to be the Renal a siphons in India,(21designed by E S Crump and completed in 1922

The trad itional a ir regulated siphon spillway resembles a

weir over which an a ir t ig h t hood has been placed ( f ig 2b).

Part of the intake is a t a higher level than the saddle, or

crest, thereby allowing very low discharges to be passed as

normal weir flow before the siphon primes. Priming occurs

gradually as the flow builds up; the r is ing water level seals

o ff the hood from the atmosphere, and the internal pressure

drops as entrained a ir is carried away a t the downstream

end. The internal head, and therefore discharge, increases

as the hood pressure is reduced. Unlike the blackwater

siphon, however, the a ir regulated siphon does not

immediately prime to fu l l bore flow, for as the discharge

increases a ir is drawn in at the intake and the hood pressure

-7 -

is stabilised as the a i r entrained into the hood from in le t

is equal to that taken out of the hood by the flow through

the siphon. Air is e ither introduced by vortex induced(31entrainment or a form of gulping1 ' under the in le t l i p ,

both forms of entrainment draw a i r under the in le t l i p .

The head-discharge relationship for this type of siphon is

i l lu s tra te d in f ig 2b. From this figure i t can be seen that

the flow characteristics in general are smoother, resulting

in a uniform increase and decrease in siphon discharges,

which closely re la te to the flow quantities offered to i t .

There are two main types of a i r regulated siphon employing

d iffe ren t methods of self-priming. The original design ( f ig

3a) was that of a saddle shape with a ramp or "ski-jump"

deflecting water onto the outer face of the downstream leg

thereby creating an e ffective seal. This type of siphon was

mainly used for dam spillways and r iv e r regulators. For

situations where space is restric ted the siphon has to be as

compact as possible and an S-shaped siphon was developed ( f ig

3b). The S-shaped siphon has b u i l t into i ts natural shape an

e f f ic ie n t priming system. The downstream leg of the 'S'

siphon is returned beneath the crest so that a vertica l wall

of water formed shortly a f te r f i r s t s p i l l thereby effecting a

seal which ensures e f f ic ie n t priming.

-8 -

FIG 3A SKI JUMP DEFLECTOR METHOD OF AIR ENTRAINMENT

FIG 3B FALLING NAPPE METHOD OF AIR ENTRAINMENT

- 9 -

(a) The ski-jump method of air-entrainment

At low discharges, water passing over the crest takes o f f at

the "ski-jump" ( f ig 3a) and strikes the hood near i ts t a i l ,

creating a turbulent region which entrains a i r and passes i t

downstream with the flow. In i t i a l l y , the crest acts simply

as a weir, since an ample supply of a i r can enter under the

l ip . As the discharge increases, causing the upstream level

to r is e , the supply of a ir is restr ic ted and the entraining

mechanism becomes more powerful. A partia l vacuum is

created, raising the internal water level and increasing the

discharge through the siphon until equilibrium is again

reached. At higher discharges separation occurs a t the

crest, and the a i r pocket contracts until eventually i t is

swept out of the siphon, the a i r then passing through the

siphon as a chain of b u b b l e s T h i s chain of events

removes the a ir from the siphon, thereby priming i t , allowing

fu l l bore flow. This method is usually used in the case of

dam spillways where the downflow leg has to slope away from

the in le t , ie down the dam face.

(b) The fa l l in g nappe method of a i r entrainment

By a lter ing the actual geometry of the siphon, without the

inclusion of any ski-jump mechanism, and by sloping the

downflow leg towards the in le t the f lu id a t weir-flow

discharges fa l ls onto the opposite wall producing the same

priming e ffec t. This priming e ffe c t is shown in f ig 3b.

- 1 0 -

1.2 Uses of an a i r regulated siphon

Air regulated siphons are most commonly used in the following

roles - overflows, spillways and level regulators.

(a) Overflows

Air regulated siphons used as overflows are in essence

smaller scale siphon spillways, the only difference being

that they have d iffe ren t requirements. The type of siphon

used in this situation are known as low head siphons, ie with

a working head of up to 3m. This low head v ir tu a l ly ensures

that cavitation w ill not occur.

The most widely used low head siphon overflow system is the

storm water overflow system which determines the amount of

sewage flowing into a works, the residue is passed for

storage or disposal. A typical arrangement of a trad itiona l

siphon overflow on a combined sewer is shown in f ig 4.

Siphons have been found to be particu la r ly suited for use on

storm water overflows and a ll tests carried out for this

report are based on a storm water overflow configuration.

The requirements of such a siphon are as follows:

( i ) I f overflow water is to be discharged into receiving

waters then the level of the overflow should be such

that s u ff ic ien t d ilu tion has been achieved. This

dilution has tra d it io n a lly been 6 x dry weather flow

(6xDWF).

- 1 1 -

to□

2OCQ

* ---I\-*

-12

-

FIG A TYPICAL ARRANGEMENT OF AN AIR REGULATED SIPHON

OVERFLOW ON A COMBINED SEWER

( i i ) The overflow should operate with an effic iency such

that undue surcharging of the system does not occur,

nor surface flooding.

(b) Spillways

The most common type of siphon spillway is one straddling the

crest of a dam, f ig 5. This type of siphon is termed a "high

head" siphon due to large differences in upstream and e x it

levels which may exceed 9m. The results of high heads are

large velocities which cause low pressure especially in the

crest. Because of cavitation which may cause structural

damage, negative pressures must not be allowed to approach

9m. The answer to this velocity c r ite r io n is the use of some

flow re s tr ic to r , the most generally used one being converging

outlets. To provide an adequate seal to allow priming to

occur (the e x it is open to the atmosphere) a ski-jump

arrangement has to be used. In some cases (Spelga Dam) a

second ski-jump was proposed near the e x it , the object of

which was to form an additional pocket in order to increase

air-pumping effects and oppose the ingress of a i r from

downstream. Using the "two ski-jump" type of arrangement on( 5 )the Spelga Dam, Northern Ireland 1975v 7 they have a

working head of 8.5m, the level was raised by lm so causing a

phenomenal increase in storage capacity of 22%,

-13-

MAX.WL. 343-20

343-97

34298

7 9 60

1-220 1 220 1-220

230230 860

SECTION A-A

FIG 5 -SIPHON SPILLWAY STRADDLING DAM CREST(SPELGA DAM)

PQSKITT AND ELSAWY JUNE 1976

- 1 4 -

Another type of spillway siphon is the combined use of one or

more siphons with a bell mouth dropshaft spillway. A number

of siphons are arranged rad ia lly within the bellmouth

spillway structure, f ig 6. The siphons regulate flow into

the dropshaft and supress turbulence.

(c) River and canal level regulators

Low head a ir regulated siphons f u l f i l th is role and are used

in cases where the maximum upstream levels are to be closely

controlled such as r iv e r and canal control devices. Flood

water is discharged through the siphon to keep river/canal

levels below maximum values in order to prevent flooding. A

typical low-head a ir regulated siphon acting as a r iv e r flood

regulator is shown in f ig 7.

1.3 Air regulated siphons, advantages and disadvantages

When considering other spillway or overflow devices which are

usually weirs, an a ir regulated siphon has many advantages.

(a) Even though discharges may vary greatly , upstream

levels are regulated within a very small range. Weirs

require large upstream level variations for s im ilar

discharges.

(b) A siphon u t i l is e s the fu l l working head between

upstream and downstream levels whereas a weir discharge

is governed by the re la t iv e ly small head over i ts

crest. Thus siphon crests can be placed higher than

weir crests and s t i l l be capable of discharging

-15-

Profile of an

open spillway

FIG 6 SIPHONS INCORPORATED INTO A

BELLMOUTH DROPSHAFT SPILLWAY ■ ■■■■ ■ =

- 1 6 -

ACKERS & THOMAS

onzQ_ »-—«U1

□

ZDIDLUq :

<CD2

i/)<CD

>cr

LU uOLU

LUO

cc*— I <

LU

O _I<ir-

ID

<23crLU>

- 1 7 -

AS A

RIVE

R/CA

NAL

LEVE

L RE

GULA

TOR

equivalent flows. This is the case of reservoir

overflows and w il l allow an extra storage capacity for

a given dam height.

(c) A siphon can prime quickly to fu l l capacity without

large increases in upstream leve l.

(d) Because of th e ir re la t iv e ly small size, compared to

equivalent crest lengths of weirs, siphons may be

accommodated within smaller confines where other

devices may not even be contemplated.

Conduits are more l ia b le to blockage than most open

structures but this can be avoided by the provision of

g r i l le s and screen arrangements in front of the siphon

entrance. Where consequences of to ta l blockage are

unacceptable an emergency weir spillway may be provided a t a

higher level to avert th is danger.

The cost of construction of siphons would be s ign if icantly

reduced i f they became more commonplace structures. This

would be especially the case i f , for the common roles, siphon

requirements could be standardised and a range of such

siphons detailed. However due to th e ir v e rs a t i l i ty some a ir

regulated siphons w ill always need to be designed

specifica lly and therefore w ill always be re la t iv e ly

expensive items. Nevertheless, the a b i l i ty of a i r regulated

siphons to exactly su it the requirements should compensate

for the extra expense. The close constructional tolerances

-18-

which they impose require accurate and expensive construction

and considerable falsework for re la t iv e ly small quantities of

materials. They do however, appear to o ffe r a means of

economically increasing storage in many existing reservoirs(51which have weir type overflow structures' ' . Another point

to consider is that design costs are generally small compared

to constructional costs.

1.4 Types of flow regime in a i r regulated siphons

Fig 8 compares the typical Head/discharge relationship fo r an

a ir regulated siphon with those of a conduit and a weir. The

terms h-j and H are defined as follows:

h-j (priming head) = reservoir level (above crest leve l)

H (working head) = difference between in le t tank level

and o u tle t tank level

There are four c learly defined flow regimes for an a i r

regulated siphon, weir flow, sub-atmospheric weir flow, a i r

partia lised flow and blackwater flow, represented by 0-A,

A-B, B-C and C-D in f ig 8.

(a) 0-A, Weir flow ( f ig 9a)

In this phase the siphon acts as a normal rectangular weir.

The upstream level is below the in le t l ip and the a ir above

the crest is a t atmospheric pressure, as there is an a i r

passage under the in le t hood. The siphon is only open to the

atmosphere via the in le t as the nappe fa l l in g on the fa r wall

-19-

PUM

PING

HE

AD

(hi)

a

WEIR FLOW Q *h

0DISCHARGE (Q)

/ CONDUIT

FIG 6 - TYPICAL HEAD/DISCHARGE RELATIONSHIP

FOR AN AIR REGULATED SIPHON

-20-

WOR

KING

HE

AD

(H)

i

FIG 9A-WEIR FLOWWEIR aow

FIG 9B-SUB ATMOSPHERIC

FIG 9C-AIR PARTIALISED FLOW FIG 9D-BLACK WATER FLOW

FIG 9 - TYPES OF FLOW REGIME IN AIR REGULATED SIPHONS

-2 1 -

seals the ou tle t. In this flow regime air-entrainment has no

effec t. The flow follows the weir equation Q oc h3/2_

The siphon has been shown to pass a very small proportion,

perhaps 5% of i ts total flow in this way before moving onto(21the next flow regime .

(b) A-B, Sub-atmospheric weir flow ( f ig 9b)

With a flow increase the a i r space in the siphon becomes

sealed o f f as the reservoir level has risen to a level above

that of the in le t . The flow entrains a i r from this a ir space

causing a partia l vacuum. This vacuum has the e ffec t of

water being drawn up into the siphon so increasing the flow.

But to compensate for this air-entrainment, a i r is drawn

under the in le t l ip to maintain the a ir a t a constant

pressure, even though i t is below atmospheric pressure.( 2 )Headv 7 termed this flow regime induced weir flow under

sub-atmospheric pressure, however sub-atmospheric weir flow

appears to be a more compact phrase retaining the accuracy of

meaning.

(c) B-C, Air partia lised flow ( f ig 9c)

As the inflow into the reservoir increases and the reservoir

level r ises, the flow in the siphon also increases and the

a ir space is reduced until i t is removed altogether at the

commencement of a ir -p a r t ia l is e d flow. This means that there

is a fu ll-depth flow at the weir crest. Air is s t i l l drawn

under the l ip e ither by a gulping e ffe c t or by vortex induced

-22-

a ir entrainment. This represents the largest and most useful

flow regime of the a ir regulated siphon and for a well

designed a ir regulated siphon th is phase w ill be extensive ie

covering a large range of flows. Air partia lised flow

produces a mixture of water and a i r bubbles distributed

throughout the siphon with no large stationary pockets

(d) C-D, Blackwater flow ( f ig 9d)

When the in le t l ip is to ta l ly immersed and no a i r is admitted

to the siphon (by gulping or vortex action), the siphon w ill

be running fu l l bore without a i r bubbles being passed through

the siphon. The siphon in this stage is acknowledged, by a l l

sources of information, as being fu l ly primed. This can only

be achieved by raising the water level by increased flow. As

opposed to a i r partia lised flow, the blackwater flow regime

produces re la t iv e ly small flow increases for increases in

upstream levels . The discharge relationship for a siphon

running under blackwater flow conditions is the same as that

of a closed conduit where Q ^ h ^ .

From th is information i t is possible to see the trans ition in

flow type. Sub-atmospheric weir, a i r partia lised and

blackwater flows as being analagous to weir flow transforming

to conduit flows. When looking a t the head-discharge curves

the transition should be smooth for a well designed siphon.

-23-

1.5 Si phonic hunting

Si phonic hunting (sometimes termed overrun) occurs generally

at low inflow rates into the upstream reservoir which cause

priming to commence but i t is in su ff ic ie n t to build up and(4)maintain blackwater flow. But Harrison had the

following to say on hunting with respect to his research

work. I f the water level in the upstream reservoir is well

below the siphon crest when a flood occurs (flow increasing

into the reservoir) i t is possible that the water level could

be approaching i ts l ip level as the flood inflow reaches i ts

peak. When the upstream level rises rapidly and hunting

occurs, ie the water level rises above i ts equilibrium level

for the given inflow discharge in the time that the siphons

take to prime. The siphon then discharges more than the

inflow discharge until the upstream level has been drawn down

to i ts equilibrium position. This additional discharge is

temporary blackwater flow and when the upstream level reaches

i ts former equilibrium le v e l, a i r is admitted breaking

si phonic flow. The cycle of priming and depriming

recommences with the upstream level osc il la t ing and surges

and lu l ls in discharge.

-24-

CHAPTER TWO

STATE OF THE ART REVIEW

2.1 Siphon shapes

2.2 In le t configuration

2.3 Outlet configuration

2.4 Vortices at in le t

2.5 Siphon materials

-25-

2.1 Siphon shapes

Setting aside the primitive yet practical U-tube type siphon

as shown in f ig 1, two siphon shapes have dominated

publications. The "saddle" shaped siphon which is mainly

used for dam spillways and r iv e r level regulators and the "S"

shaped siphon which is generally applied to situations where

space is restricted and the shape has to to be kept as

compact as possible

Design of the "S" siphon depends mainly on the radius of

curvature of the crest and the lower bend to ensure that

separation immediately a f te r the crest does not occur.

Modification and optimisation of th is curvature s ign if ican tly

improves the discharge capacity of the siphon. The saddle

shaped siphon requires an a r t i f i c ia l aid to complete th is

seal as there is no natural seal formed by the water in the

downstream leg as is apparent in an "S" shaped siphon.

Designers and researchers have included deflectors, which

deflect the flow on the downstream leg of the siphon onto the

upper surface so achieving th is seal. Ackers and Thomas

described the problems of priming in saddle siphons and

methods required to ensure that e f f ic ie n t priming may occur.

Their conception of the problem and how to achieve a solution

is la id out as follows.

-26-

Except for the a ir intake, the design of an a i r regulated

siphon is generally sim ilar to that of a blackwater siphon.

The essentials are that in the priming stage i t must be

capable of exhausting the a ir from the crown, by entrainment,

so that the siphon may flow f u l l , the difference being that

a fte r priming whereas a blackwater siphon w ill flow fu l l of

water, an a i r regulated siphon w il l carry an a ir-water

mixture. The aim is generally to achieve priming with a

smooth trans it ion , at the minimum possible depth, the priming

depth being measured as the height of mean upstream head

above siphon crest level when the siphon f i r s t becomes

capable of extracting enough a i r to flow continuously with an

air-water mixture.

Before the a ir in the crown can be evacuated, the waterway of

the siphon must be sealed upstream and downstream so that the

pressure drop in the crown can be maintained. The upstream

seal results from the submergence of the a i r intake by the

ris ing head water. The downstream seal may be provided

either by submerging the ou tle t in the ta i l water as in f ig

10a or by deflecting the flow in the form of a detached nappe

to form the other as in f ig 10b.

Submergence of the outle t below lowest t a i l water level is

generally completely e ffec tive and i f necessary the t a i l water

level can be maintained by providing a ta i l weir or a bucket

as in f ig 10a. In some cases th is is not feasib le , and

-27-

Air inlet

Head water- pool Air extract ion

Nappe -

Sealing bucket

10(a) SIPHON WITH SEALING BUCKET

Ducksbill Air entering

Head wate r pool

ju mp

Doubl-e cur ta in seal Air w a t e r -

mixture

Priming s tage Fully primed

10(b) SIPHON WITH DUCKSBILL, SKI JUMP PRIMING & FREE OUTLET

FIG 10 METHOD OF SUBMERGING SIPHON OUTLET

- 2 8 -

ACKERS & THOMAS

reliance must be placed on the deflected nappe. A single

seal at the ou tle t may then not be perfect and i t is

desirable to provide a second seal higher in the downstream

leg by deflecting the flow from the inner to the outer wall

as in f ig 10b.

In the Plover Cove s ip h o n ^ submergence of the ou tle t was

by using an ou tle t bucket as the dam's siphons would not be

drowned a t any stage of priming and a divergent ou tle t could

not be used to increase the discharge. A second ski-jump was

proposed near the e x it of each siphon as shown previously in

f ig 5 the object of which was to form an additional pocket in

order to increase a ir pumping effects and oppose the ingress

of a ir from downstream.

2.2 In le t configurations

Charlton and P e rk in s ^ defined two parameters whose

re la tive values a ffec t the priming and performance of a

siphon based on e a r l ie r work by Crump and Ackersv .

The two parameters are as follows:

a = height of a i r in le t above the crest

p = equivalent head of water above the crest required

to provide a discharge at which the rate of a i r

entrainment is ju s t s u ff ic ie n t to evacuate the a i r

from beneath the hood and cause priming.

-29-

The evacuation of the a ir in le t may be selected while the

priming level is dependent upon the efficiency of the a i r

entrainment system within the siphon, and on the effic iency

and type of outle t seal.

When a < p, at the level of potential priming the a ir in le t

is submerged and thus sealed. Air may be entrained and

removed causing the siphon to prime. The reservoir level is

then drawn down below priming level to permit a i r to enter.

This is an unstable condition and the siphon may de-prime

p articu larly i f appreciable drawdown occurs. When the

reservoir has a large surface area this is less l ik e ly and

stable performance could resu lt. However in a storm water

overflow de-priming is l ik e ly to occur.

When a > p, a t the potential priming level the a i r in le t is

open, and priming may be delayed. As the discharge and

upstream water level increase more a i r is evacuated and more

is drawn through the a i r in le t which is ultimately th ro tt led

as the water level continues to r is e . Sub-atmospheric weir

flow develops which gradually changes to a ir partia lised flow

with l i t t l e in s ta b i l i ty . Avoiding a sudden change from one

mode of flow to another reduces the possib ility of drawdown

which, were i t to occur, could be tolerated since the

pre-priming conditions are stable.

-30-

19 )Elsawy and Ervine1 ' realised not only the importance of

in le t l ip elevation but also in le t l ip length and in le t

depth. They recognised that short l ip lengths require larger

upstream heads for a required discharge, compared to a lower

head for longer l ip lengths required for same discharge.

They attributed this to a function of the specific energy at

a section ju s t a t the upstream end of the in le t l i p . The

variation of flow through the siphon a t each l ip length used

by Elsawy and Ervine is shown in f ig 11. The lower portion

of the graphs refers to the sub-atmospheric weir flow phase,

and the upper portion to the a i r partia lised flow phase. The

longest l ip length has a very small a i r flow a t the onset of

priming, resulting in in s ta b i l i ty and hunting. With regard

to in le t l ip elevation f ig 12 shows the e ffe c t of each l ip

elevation on the priming characteristics of the siphon. The

lowest l ip elevation produced the steepest priming curve and

the highest l ip elevation produced the shallowest. Hunting

was found to be greatly reduced a t the highest l i p elevation.

2.3 Outlet configurations

Various authors have covered the effects of d if fe re n t ou tle t

configurations. Charlton and P e rk in s ^ found that o u tle t

conditions a ffec t the priming, a i r entrainment and the

s ta b i l i ty of the siphon. The most e ffec tive seal occurs when

the ou tle t is submerged. Providing a basin at the o u tle t ,

however, may be inadequate i f the basin is so shaped to

permit the water to pass smoothly through i t before shooting

-31-

V-O

JQCL

o

roto

CO

U sCL

cn IT) CL o a

inC"Jro

'4-O C

COo

cvj’60 1

o

oCO oinC" CD

o(ddAiojaid) uu jsajD js/vo pr»q jjOAjasaj

00ooooo

a.

u

—I*L_aiCJot_O

J=LJ

CJci

tdIOailJ Z l

0aj

co

CJIcQJ

uai

LU1

onlUI

FLSAWY AND ERVINE

- 3 2 -

k

-i 1------------ 1----1-------1------- 1 i •

O C3 O Q O Q Q o o O4040JCI) UJ 4 S0 J D J0AO pD9 q JIOA J3S3 J

-33- ELSAWY IERVINE

head

sip

hon

clear of the structure. The water level must back up within

the basin and cover the l ip of the o u tle t , preventing the

entry of a i r . Under such circumstances a small step in the

ou tle t leg, to provide a temporary curtain seal and entrain

a ir at the lower stages of flow, is required. This has the

advantage of in terfer ing l i t t l e with the flow a t higher

stages, and having only a s lig h t e ffe c t on the coe ff ic ien t of

discharge.

Elsawy and Ervine went one stage further. They showed the

e ffe c t on the priming characteristics for d iffe r in g t a i l water

levels to be quite pronounced ( f ig 13). At higher t a i l water

levels the in i t i a l stages of the priming characteristic are

largely unaffected, but near fu l l flow the head/discharge

curve becomes much steeper and gives a lower maximum flow as

expected due to the reduced head. For higher t a i l water

levels an increased ta i l water level on the siphon produces a

marked drop in a i r flow but a t the expense of poor control at

certain flows. I t is c learly an advantage having a decreased

a ir flow at higher t a i l water leve ls , provided the a ir control

and regulation is not seriously affected.

2.4 Vortices at in le t

Reddy and P ic k fo rd ^ ^ described the factors affecting the

production of vortices a t in le t and th e ir physical e ffects on

hydraulic machinery. This is of great importance to the

siphon designers when considering in le t conditions. Vortex

-34-

x7th scale low head siphon priming characteristics and tailwater riseddAiojoid

(sajpuj) ;sojd

j&so

poaq j»OAJas

jELSAWY AND

ERV1NE

-35-

Fig 13- Effect of tailwater level on priming ch a ra c te r is t ic s .

induced a ir entrainment is considered a disadvantage as the

vortices tend to make the siphon flow unsteady therefore

producing a varying upstream leve l.

I f the depth of water above an intake is low, a i r entraining

vortices develop and these adversely a ffec t the e ffic iency of

the hydraulic machinery by reducing flow rate and by giving

extra swirl to the f lu id , in addition to causing vibration

and noise. In shallow reservoirs wave action develops an

unstable boundary layer (depending on the wave length to

c e le r ity ) and this is generally responsible for the change in

v o rt ic ity which leads to formation of a i r entraining vortices.

Their main recommendation is to try and s t i l l the wave

formation around the in le t by use of (several) ba ff le boards.

2.5 Siphon materials

K e l ly ^ ^ suggested that there may be a relationship

between tube material and bubble emergence and to confirm his

suspicions carried out various tests on the following

materials: mild s tee l, polyethelene (high density), copper,

perspex and glass. He also proposed that i t is the number,

size and shape of "pores" or traps in the surface of the

material that enables bubbles to form. Ho satisfactory

explanation of the mechanism of origination of gas or vapour

bubbles in a l iqu id has ye t been found. Any bubbles that

-36-

appear spontaneously w i l l again vanish immediately unless

considerable heating or high tensional stresses occur or

unless the l iqu id is highly supersaturated with gas.

However, the pores provide bubble "factories" that can

continue to obtain gas by diffusion from the liq u id and

release streams of bubbles. These factories only operate for

particu lar bubble sizes, which means that as the pressure

decreases at higher elevations within the siphon d iffe re n t

size bubbles w il l emerge. Kelly concluded that the

m aterial's surface roughness determines the bubble

formation. Even the comparison of s l ig h tly rusted steel with

new steel is radical and the comparison of steel with perspex

is s ta rt l in g . No bubbles formed in the f lu id , a l l bubbles

formed on the material surfaces during these tests. Thus

siphon performances cannot be modelled in one material to

forecast results on a project using a d if fe ren t m aterial.

Kelly 's conclusions do not apply to a l l stages of siphon

discharge as i t can be readily appreciated that a ir

entrainment in the a i r partia lised flow regime would

completely swamp the processes described above.

-37-

CHAPTER THREE

THE THEORY AND DESIGN OF AIR REGULATED SIPHONS

INCLUDING THE SIPHON MODEL

3.1 Dimensional analysis

3.2 Si phonic discharge theory

3.3 Low head a i r regulated siphons

3.4 Modelling technique

3.5 Aspects of s im ila r ity and scale effects

-38-

3.1 Dimensional analysis

To enable meaningful 1 comparisons of results a dimensional

analysis of the terms affecting siphon discharge is

required. The analysis applies to the siphon running fu l l

and therefore relates to the a i r partia lised and blackwater

flow phases. With reference to f ig 14, which is a cross

section of the siphon model, i t can be seen that the

discharge of a siphon running fu l l is dependant on the

following variables:

Q = f I b, H, hp h2, R2, L, Lt , g,p , d V a ]

where Q = Volume discharge rate

H = Working head

h-j = Priming head

h2 = Elevation of underside of in le t l ip above siphon

crest

f* 2 = Outside radius of upper bend

L = In le t l ip length, measured from siphon crest

l j = Siphon length, measured along centre l in e of

siphon section

g = Acceleration due to gravity

f = Density of f lu id

d = Siphon throat depth

= Surface tension

M = Dynamic viscosity

Va = Velocity of approach to siphon in le t

and f I ] = Function of

-39-

Section A-A

UPSTREAM TANK

- / -

DOWNSTREAMTANK

FIG 14 DIAGRAM SHOWING INLET GEOMETRY OF SIPHON ~ .......

- 4 0 -

Taking the repeating variable p , g and d.

term

'T r i = pa gb dc b

= (mL- 3 ) a (L^2) b (L )c L

for m : 0 = a

T : 0 = -2b b = 0

L : 0 = -3a + b + c + 1

= 0 + 0 + c + 1 . *. c = -1

1 = d" x b

_ b 1 d

and as dimensions of b, H, h-j, 1^, L, and L

the same we can write

= Hi 1 2

h-3 " T

h9i t V h:

t f = R2_ 5 cT

- r f = L2 l6___3_

i f = L j" 7 cT

-41-

-j- are

' t f o term

'T f „ = f a gb dc Q

(mL'3) a (LT"2) b (L )c (L3T_1)

for m : 0 = a

L : 0 = -3a + b + c + 3

0 = 0 + b + c + 3

T : 0 = -2b - 1 b - - XSubstitute in L equation

0 = 0 + ( - X) + c + 3

c - -2 1 = - 5 c - d j - ?

iT n = g '1/2 d - | Q8 - a u i

- Q_8 T / S T

iT g term

-rr gi f , = Pa 9b dc e r

= (mL"3)a (L T '2) b (L )c (mT-2 )

for m : 0 = a + l a = -1

L : 0 = -3a + b + c = 3 + b + c

T : 0 = -2b - 2 b = -1

c = - 2 t f a = e rp d 2 g

i f l O term

< 1 0 " ? “ ^ d<>= (mL’ 3)a (L T '2)b (L )c (mL_1T_1)

-42-

for m : 0 = a + l . ’ . a = -1

L : 0 = -3a + b + c - 1

= 2 + b + c

T : 0 = -2b - 1 b = - 12

also 0 = 2 + b + c

. . . T f10 = f' g-V2 d-3/2

M d Vgd"~ 7 T r e 7 r ' r

t n i term

' t f 11 = f a gb dc V.

= (mL'3) a (L T '2) b (L )c (LT-1 )

for m : 0 = a

L : 0 = -3a + b + c + 1

= 0 + b + c + 1

VaVgd" /g J

from original expression

Q f 5 b H hl h2 R2 L LT < r M Vm - M d* d> d’ ~H‘ ~ S ' d* d> gd2p > d3/2d ^

-43-

We now need to derive a lte rn a t ive forms o f the Froude number,

Reynolds' number and the Weber number using th is analysis.

f f 3 may be re -w rit ten by combining with and

J H/ d to gi ve

Qd o J g H

since — Q_ _ y (where V, = mean ve lo c ity through the siphon) do z z

f ig becomes Vt thus TTq becomes a form of the Froude number

w

S im ila r ly 1^10 = d Jg d and is a form of the Reynolds' numberV

and tT 0 = o" which may oe inverted to y

eg d

f g d^ which is a form of tne Weber number <r

the re su lt of th is analysis may be more meaningfully

w r it te n as:

Equation 3.1

Q . f f b H nl h2 R2 L LT d Jgn f gd2 Va bd^(gH) T £ d ’ d’ d ’ d ’ d ’ d ’ d < r ’

Froudenumber

Reynolds number

Webernumber

The variables which are being studied are contained in

equation 3.1 and are H, h-j, h^, b and L.

- 4 4 -

From equation 3.1 there are two tT* terms which can beu

combined to y ie ld /h-j

ie 4- Equation 3.2

For the purpose of our testing work we can assume that Va

?is small and therefore V becomes negligible. This

a

assumption allows us to ignore the effects of upstream

velocity . I t would not be possible to make this assumption

i f the siphon was fed by a narrow, shallow channel of s im ilar

dimensions to the siphon.

Comparing equation 3.1 and 3.2 with Q = Cp bd J 2gH (where

Cp is the coeffic ien t of discharge) i t can be seen that

Equation 3.3

- _ a 5 b hl H h2 R2 L LT d /ih" f g d 2 ZD ” r (. d’ d * h , ’ ds d’ d* d* y ’ «r )

Therefore meaningful study may be made by comparing the

following:

d TgiT egH2 H hl , H D’ Y ’ <r ’ cT’ '3 TTT"

Thus dimensionless graphs may be plotted as follows:

W, H, 1 & H against Cne cT “a- TTJ- D

where R0 = Reynolds' number

and W = Weber number

-45-

3.2 Si phonic discharge theory

The flow regime in the upper bend (Section A - A, f ig 14) in

the siphon is approximately that of a free vortex. This flow

regime is apparent where the velocity (V) is inversely

proportional to the radius (R) ie

V 1 R

Thus, the smaller the rad ii the faster the velocity . The

region of maximum velocity and hence the region of lowest

pressure occurs to the flow passing round the crest. Also

the product of the velocity and the radius is constant,

ie

k = VR where k = constant

The working head H, may be considered to be the sum of the

velocity head losses for various parts of the siphon as well

as including the head loss due to the conversion of

velocity. Knowing these factors i t therefore is possible to

derive an expression for the discharge of the siphon. The

tota l head loss in the siphon h may consist o f : -

ht = hv + hl + h2 + h3 + h4 + h5

which since the tota l head is expended in producing velocity

of flows and overcoming these resistances (hv , 1-5) then

h = the working head H where

H = working head

h = total head loss in siphon

-46-

h = head loss due to conversion of velocity

h-j = head loss a t entry

h2 = head loss due to top bend

h = head loss due to f r ic t io n

h = head loss due to bottom bend

hg = head loss due to kinematic head at ou tle t

Assuming that each of these losses is proportional to the

square of the velocity of flow V a t the throat then

expressing in terms of velocity heads:

Equation 3,4

V 2H = t (kv + k] + k2 + k^ + k^ + k^)

■ £ <

where:

Vt = mean velocity at throat

k(v !_ 5) = empirical coeffic ients covering the

various energy head losses

Rearranging equation 3.4

y = V2gH_______ 1

' < * K(v , l -5 ) )7

The discharge through the siphon:

Q = At vtwhere A = constant cross-sectional area of siphon along

length except for entry and e x it sections.

-47-

Thus:

At <[ZgH 1 Equation 3.5

or Q = CQ At yfzgH Equation 3.6

where

CD = — ^---------------- 1 = c oe ff ic ien t of discharge for the

siphon running fu l l and can be determined

d irec tly i f k coeffic ients are known.

For a newly designed siphon i t is unlikely that these k

coeffic ients w il l be known due to the complexity of flow and

to the very wide variations in velocity and pressure across

various sections, thus making coeffic ients based on more

conventional types of flow incompatible. Therefore a

practical solution must be found to overcome th is problem. A

method of taking a series of ca libration runs on the siphon

measuring working heads for a series of discharges w i l l give

an accurate solution to this problem, but the discharge

expression equation 3.5 w il l only determine the overall

coeffic ien t of discharge, CQ and not the individual

empirical coeffic ients.

The coeffic ien t of discharge CQ w ill be found to vary

greatly with flow rates up to a i r partia lised flow. This is

because the discharge equation and the coeff ic ien t calculated

is derived from a blackwater flow condition and calculations

should be restricted to flows above sub-atmospheric weir flow.

-48-

From equation 3.6 ie Q = CQ JzgH, i t is apparent that

a siphon has sim ilar discharge characteristics to those of a

sluice gate. A sluice gate u t i l is e s a sim ilar working head

to a siphon and i ts discharge expression is of the same

format.

3.3 Low head a i r regulated siphon design

At th is date the most logical sequence of design devised has(91 11?)been by Elsawy and Ervine' ' and Charlton' . This

technique makes use of the in i t ia l requirements to determine

the basic siphon dimensions and then refine such geometric

features such as the in le t and ou tle t configurations as well

as the upper and lower bends.

The known factors, i n i t i a l l y , are the maximum discharge

required and the available working head. An approximate

determination can be made of the mean velocity a t maximum

(blackwater) flow, by assuming a typical value of the

coeff ic ien t of discharge and using a modification of

equation 3.6 ie V = CQ JzgH as V = By reducing

this velocity by between 10% and 15% blackwater flow w i l l be

avoided and the resultant velocity used to determine the

required cross-sectional area of the siphon. This procedure

determined the following, maximum flow and corresponding

velocity , working head and cross-sectional area.

-49-

The next stage in design now centred on the upper bend,

determining the values of the two rad ii R-j and R£, the

throat depth d and width b. Charlton showed:

Equation 3.7 where k = constant of free vortex flow.

i ) k = R, R-> / 29-7 R1 + R2

Equation 3.8 Equation 3.9

/ ri + r2 A ( + r2R1 = h y - T 5 R2 = v i / - T g ^

Equation 3.10

V + V^..j) y _ 1 2 This expression provides ant p

approximate value of mean

velocity V .

But these expressions are based on the assumption of free

vortex flow in the throat and a required neutral pressure

gradient between the crest and the crown to assist mixing of

a ir and water.

(13)Although not c r i t ic a l Ervine' ' recommended that the ra t io

of width/throat depth should be in the region of 1:5.

Bearing in mind the required cross-sectional area and theL

ra tio a t r ia l procedure using equations 3.7 - 3.10,

may be used to achieve satisfactory values of R-j, R2, d

and b. The bottom bend may be taken as the same

configuration as that of the top bend but washout could occur

-50-

at higher flow rates and so impede the required higher

discharge, therefore, care should be taken to ensure that i t

is not too rounded ie of too large a radius. Washout is a

term used for a case where the flow tends to cling to the

lower surface as a high speed j e t , which in th is situation

may even empty the lower sealing pool. The problem could be

overcome by the use of 2 adjacent siphons (especially

applicable in a bellmouth dropshaft) and arrange them so that

th e ir discharges are directed against each other. However

this would resu lt in a reduction of downstream ve loc ities and(14)the siphons w ill surcharge. Charlton 7 suggests making

the lower bend of an angular design to eliminate this problem.

The in le t configuration of an a i r regulated siphon is of

c r i t ic a l importance as i t effects the entire range of flow

characteristics. The in le t geometry forms the most delicate

design area. Model tests are required on which to form a

design basis and i t is th is which forms the substance of th is

report. There are three variables in in le t geometry:

( i ) In le t l ip elevation above the crest, which

determines the in i t i a l priming head and hence

the nappe thickness fo r a i r entrainment.

( i i ) In le t l ip length, which affects the

characteristics of a ir-regula tion and the head

discharge relationship in the a i r part ia lised

flow regime.L

( i i i ) Aspect ra tio - ra tio 7^.

-51-

3.4 Modelling Technique

I f the results obtained from a model are to be transferable

to the prototype i t is necessary for the two flow systems to

be hydraulically s im ilar. This entails (a) geometric, (b)

kinematic and (c) dynamic s im ila r ity .

(a) Geometric s im ila r ity

This basically is s im ila r ity of shape. The ra tio of any two

dimensions in the model is the same as the corresponding

ra tio in the prototype, or

(L-j)m _ (L-j)p m = model p = prototype L = length

(L2)m (L2)p

Thus i f the linear scale of the model is 1 :x the scalar2 3relationship for area is 1 :x and for volume 1 :x .

(b) Kinematic s im ila r ity

This is the s im ila r ity of motion, thereby introducing the

vector quantity and time factor. The la t te r is of importance

in problems involving unsteady flow. The velocities (and

accelerations) a t homologous points and a t homologous times

in the two systems have the same ra tio to each other. Also

the corresponding directions of motion are the same. Thus

(V-j)m = (V^p and (a-j)m _ (a-j)p V = velocity

(V2)m (V2)p (a2 )m (a2 )p a = accelerat1on

-52-

(c) Dynamic s im ilar ity

This is the s im ila r ity of forces a t homologous points in the

two systems which have the same ra tio to each other and act

in the same direction. Thus

( F-j )m = (F-j)p

(F2)m (F2)p

The component forces acting on any element of incompressible

f lu id may be due to pressure, gravity , viscosity or surface

tension. The conditions for dynamic s im ila r ity can thus be

expressed algebraically as

(Fp )p _ (Fg)p _ (Fy)p = (FST)p

(Fp)m (Fg)m (Fy)ra TF^jTm

When considering these forces with respect to a model

accurately scaled to a prototype, geometric and kinematic

s im ila r it ie s are both achieved, true dynamic s im ila r ity is

impossible to a tta in .

To i l lu s t ra te this phenomenon le t us consider the Froude and

Reynolds' laws.

(a) Froude law

Gravity is the predominant factor influencing f lu id motion

wherever a free surface gradient is present. The Froude

-53-

number represents the ra tio of in e r t ia to gravity forces, and

is given by

F = V7C F)

where

F = Froude number g = acceleration due to gravity

V = mean velocity L = length, taken to be the depth of flow

For compliance with the Froude law of scaling, the

corresponding ve locities must be so related that

1 /2V _ (g L ) ' _ 1/2 V = mean velocity of prototypeY~ T T I t A rn a m Vm = mean velocity of modelm J

Lp = depth of flow, prototype

= depth of flow, model

x = geometric scale factor

between model and prototype

(b) Reynolds1 law

All real flu ids possess viscosity and the poss ib ility viscous

shear drag requires consideration in the planning stage of

every type of f lu id model investigation. The Reynolds'

number represents the ra tio of in e r t ia to viscous force, and

is given by R = VL/V where

R = Reynolds' number L = length, taken to be the depth of

f l ow

V = mean velocity ^ - viscosity

-54-

For compliance with Reynolds' law of scaling the

corresponding velocities must be so related that:

H * H

V„ L_ 1

P - P y m = 1 P V " x L X 7 ~m m p m

1 'Vp _ -j when water is used in model andv • w~ Y

m prototype.

From these analyses i t can be seen that the velocity cannot 1 1/2satisfy and X ' and in the same model ie fu l l

dynamic s im ila r ity is physically impossible

For a siphon, the most s ign ificant forces results from

gravitational and in e r t ia l e ffects . The model is therefore

based on s im ilar ity of these forces. The forces are due to

the transference of water from a higher level to a lower

level (gravity e ffec t) and the f a i r ly high velocities

together with considerable changes in the direction of flow

( in e r t ia e f fe c t ) . Therefore, a Froudian model is most

suitable and would accurately simulate the flow dynamics for

gravity and in e r t ia . The scale ratios fo r the Froude law of

scaling are shown in table 3.1

-55-

Table 3.1 Scale ratios for Froude law of scaling (a f te r

Weber^ ^ )

Quantity Dimensions Froude law natural (scale 1 :x)

Geometric

Length L X

Area L2 X2

Volume L3 x3

Kinematic

Time T x1 / 2

Velocity L/T x1 / 2

Acceleration L/T 2 1

Discharge l 3/ t5/2X

Dynamic

Pressure M/LT2 f rx

Force ML/T2„ 3 prx

Energy ml2 / t 2 prx 4

Power ml2 / t 3 Prx 7 / 2

3.5 Aspects of s im ila r ity and scale effects

Model/prototype conformity is good for the fu l l discharge

condition, but i t is not possible to reproduce correctly the

priming and de-priming processes, which are complicated by

virtue of a i r entrainment. The priming action demands an

absolute velocity su ff ic ien t to entrain and transport a i r

bubbles and therefore does not lend i t s e l f to scale

-56-

reduction. Consequently, priming in the model w ill occur at

a re la t iv e ly la te stage and higher upstream level than in the

prototype.

The functioning of a siphon necessarily depends on the

existence of sub-atmospheric pressures, and under these

conditions great care in measurement and in terpretation of

model pressures is required. For instance i t would be quite

conceivable for a model siphon to continue to operate whereas

the prototype would have ceased to do so.

During priming the bubbles of a ir which are entrained are

approximately the same size (5mm diameter) in the model as in

the prototype. This non-scaling of bubble sizes and bubble

rise velocities gives r ise to the non-scaling of the rate of

evacuation from a siphon model. Models involving velocities

in the range of the bubble r ise velocity may not be capable

of removing entrained a i r from the siphon barrel.

Other scale effects include the non-scaling of surface

tension forces a t the siphon hood in le t , often resulting in a

restr ic tion of a ir inflow in the smaller models, and the

greater expansion of a ir within the fu l l-s c a le siphon often

producing a larger ra tio of a i r to water.

Also another surface tension e ffec t occurs at the l ip of the

siphon, where in the model the size and frequency of the a i r

-57-

bubbles entering the siphon are determined by the rate of

making and breaking of the surface tension film between the

water surface and the l ip . This e ffec t w il l be no greater in

the prototype where, consequently, a steadier stream of

smaller bubbles is to be expected. This suggests that the

fluctuating forces imposed on the hood may be less severe

than the model indicates, but th e ir frequency w i l l be greater.

M 51Ali and Pateman1 ' tested 8 models of a siphon, a ll b u i l t

to the same design, a t scales ranging from V-|q to

^240* determine(* that the smallest model

^ 2 4 0 ^ sca^e) was dominated by surface tension forces.1 1 1 The larger scale models ( / - j 7 6 and / 1Q)

exhibit the conventional form of head-discharge curve for an

a ir regulated siphon. The Vg^ g scale shows d if fe re n t

behaviour (the Vyg g, ^ 1 0 0 and ^133 3 scale

models were similar) but Ali and Pateman merely state that

small-scale models do not work correctly . They also tested

models of Ervine's siphon at scales of V -|q 9 V 2 5 and

VgQ and found that the two smaller models displayed the

anomalous behaviour already mentioned; the largest model/ 1 c \

behaved conventionally

From work carried out on several d if fe re n t scale models ( 18)Gibson concluded that the viscous effects became

negligible when the product of the mean throat velocity

-58-

pand the th roat, d, exceeded 0.167m /s . A tentative choice

of scale of V 4 fu l l s ize, y ie lds a model throat depth of

75mm. Thus the required velocity to avoid viscous effects =

v = M § Z . = 2.39 m/sz 0.075

Hence a required flow rate in the model,

Q = vt At

= 2.39 x 0.0752 x 103

= 13.44 L/s

t ] g\From previous work carried out by Smith1 ' i t was known

that discharges of up to 15 L/s would be encountered, hence a

scale of V 4 would not incur viscosity scaling effects of

the flow. Using the scale 1:4 and the table 3.2 we can draw

the conclusions:

Table 3.2 Table of scalar relationships for models

Parameter Model Prototype

Length 1 4

Area 16

Volume 1 64

Velocity 1 2

Discharge 1 32

Time 1 2

-59-

CHAPTER FOUR

THE AIMS AND PROCEDURES OF EXPERIMENTATION

4.1 Objectives of experimentation

4.2 The experimental apparatus

4.3 The experimental procedure

-60-

4.1 Objectives of experimentation

Because of restrictions on space in prototype in sta lla t io n s ,

and the need to keep excavation to a minimum, the siphon

geometry was kept as compact as possible. An S-shaped siphon

was chosen with a rectangular section, not unlike the e a r l ie r

types of blackwater siphon. The downstream leg of the siphon

was returned beneath the crest so that a ve rtical wall of water

formed shortly a fte r f i r s t s p i l l , which effected a seal and

ensured e f f ic ie n t priming. The radius of curvature of the

crest and lower bend was increased from that of e a r l ie r designs

which suffered from severe separation immediately a f te r the

crest. This modification s ign if icantly improved the discharge

capacity of the siphon. Particular attention was paid

observing the effects of varying the following parameters ( f ig

15) on the siphon's performance:

(a) In le t l ip elevation over the crest (h2)

(b) In le t l ip length (L)

(c) Tail water level ( ie working head H)

(d) Siphon width (b)

The aim was to produce an optimum in le t geometry configuration

together with the most effective working head to provide the

siphon with the required characteristics peculiar to a

stormwater overflow.

-61-

FLOW VAU/E

LU —1

> £

O O

CL

QLU

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oO

QO(N

(N f»)

70Z

cc

- 62-

FIG 1 5 - SCHEMATIC DIAGRAM OF THE EXPERIMENTAL APPARATUS.

The e ffe c t of variations of the above parameters were analysed

by consideration and comparison of the d if fe ren t head/discharge

relationships of those parameters shown to be of importance in

dimensional analysis.

Another important part of th is work was to determine the e ffec tL

of a i r entrainment on the values of CQ and 1 /^ .

4.2 The experimental apparatus

The major components of the r ig were two galvanised steel tanks

at d if fe re n t levels (higher tank for inflow and lower for

outflow) which were connected by the model siphon, f ig 15.

Water was delivered by a centrifugal pump through a 100mm

diameter PVC pipe from an underfloor sump tank via a control

valve to a diffuser in the bottom of the in le t tank and the

opposite end to the siphon in le t feed. This provided a

'uniform' flow across the tank through the siphon. To vary the

outlet water level three weir boards 'x ' , ' y ' and ' z ' were

placed in the centre of the downstream tank. The flow was

returned to the underfloor reservoir by a 300mm PVC pipe flange

bolted to the tank base downstream of the weirboards.

To measure the discharge a venturi meter was incorporated into

the 100mm delivery pipe. The venturi pressure d i f fe re n tia l was

measured using two types of manometer and the discharge was

found using a calibration curve. A water manometer was used to

-63-

measure flow rates up to 3.1 L/sec and a water over mercury

manometer for flow rates between 3.1 L/sec and 15.5 L/sec,

which corresponded to the manometer's maximum reading.

By taking tappings from the base of each tank and connecting

them via two p lastic tubes to a multitude manometer, the

upstream and downstream levels were determined. Fourteen of

the sixteen pressure tapping points were also connected to this

manometer, the other two tappings were connected to a U-tube

water manometer and connected to each as required. A separate

U-tube manometer was used as the pressure tappings in the crown

of the siphon were often subjected to sub-atmospheric pressures

in the a i r space. Because a i r was l ik e ly to enter the tube and

result in inaccurate readings the tappings were unsuitable for

use with a continuous water manometer.

4.3 Experimental procedure

Three siphons were used in the tests , each of identical through

section but with d if fe ren t widths. Siphon Nol was of 0.75mm in

width, siphon No2 125mm and siphon Mo3 100mm. The siphons were

constructed so that d if fe re n t in le t inse rt pieces could be

interchanged easily to fa c i l i ta te changes in in le t geometry.

Wooden in le t insert pieces of various thicknesses were made,

i n i t i a l l y to the longest required for testing (5d), and then

cut down in length as the testing proceeded. The variation of

in le t l ip elevation was achieved by varying the thickness of

the inse rt piece.

-64-

The in le t configurations tested for siphon 2 were:

(a) In le t l ip lengths, lengths of 5d, 4d, 3d, 2.4d

(where d is the throat depth).

(b) In le t l ip elevations above the crest, of 30,

2 0 and 1 0 mm for most l ip lengths in (a).

A series of three tests were carried out for each in le t

configuration and by alte ration of the ta i l water level using

d iffe ren t height weirboards the working head was altered for

each run. A test run consisted of 14 or 15 increments in flow

rate from zero to the maximum possible. For each increment in

flow, manometer readings were recorded to determine the siphon

discharge and by use of the multi tube manometer the upstream

and downstream levels were recorded to determine the working

and priming heads. The flow regime and any physical factors

noted were recorded in a comments section.

The results obtained from siphon 2 were used to determine the

optimum l ip length and the above procedure was repeated fo r 3d

and 2.4d on siphon 1.

Having completed these tests, further work was carried out on

optimising the in le t geometry of siphon No2 and the following

in le t configurations were used to achieve this aim.

(a) In le t l ip lengths, lengths of 4.2d, 4.0d and 3.8d

(d = throat depth)

-65-

(b) In le t l ip elevation above the crest, h2 of

15mm, 10mm and 5mm fo r a ll in le t l ip lengths in

(a) above.

Siphon No3 was then tested to investigate the e ffec t of siphon

width more thoroughly.

Finally tests were carried out on a revised outlet

configuration ( f ig 16) and the results compared to the

straightforward downstream weir at ou tle t. This revised

configuration incorporated a side e x i t from the s t i l l in g basin

instead of an outlet e x it over ta i l water weirs. The downstream

wall of th is revised chamber was removeable and several

positions at r igh t angles to the direction of flow were tested.

-66-

•»

460

AL

OVERFLOW PIPE

SIPHON CREST

155

SIDE EXIT

PLAN

155

SECTION A -A

SIPHON OMITTED FOR CARRITY

FIG 16-S ID E EXIT TYPE STILLING B ASIN-PLAN & SECTION

- 6 7 -

CHAPTER FIVE

DISCUSSION OF RESULTS

5.1 Order of analysis

5.2 Effects of in le t l ip elevation

5.3 Effects of in le t l ip length

5.4 Effects of ta i l water level

5.5 Effects of siphon width

5.6 Effects of upstream channel width

5.7 Effects of vortices at in le t

5.8 Effects of revised outlet configuration

5.9 Dimensional analysis of the optimum siphon configuration

-68-

5.1 Order of analysis

The effects of t a i l water le v e l, l ip length and l ip elevation

were i n i t i a l l y investigated using siphon No2. Comparisons were

la te r made with siphon Nos 1 and 3 which were used for

investigations of upstream channel width (siphon Nol) and

outlet configuration (siphon No3).

(a) Using siphon No2 investigation into the e ffe c t of l ip

elevation was carried out using a l ip length of 2.4d

and elevations of 10mm, 20mm and 30mm above crest

leve l. Although a ll tests were carried out using

d iffe re n t ta ilw ate r leve ls , ta ilw ate r level ' Y1 (281mm)

was used for analysis and was considered as giving the

optimum seal a t th is stage. From analysis of the

results the optimum in le t l i p elevation was determined.

(b) Using th is optimum l ip elevation sections of d if fe r in g

length were used: 2.4d, 3d, 4d and 5d - the 4d in le t

l ip length was found to give the best performance, as

discussed la te r .

(c) Having determined two c r i te r ia in (a) and (b) the

variation of ta ilw ate r level was thoroughly

investigated and the most effective level determined.

-69-

(d) Having determined generally the optimum in le t l ip

length and elevation further work was carried out to

determine those parameters more precisely. As in (a)

and (b) above ta ilw ate r level 'Y 1 was used for the

following configurations.

In le t Lip Length In le t Lip Elevation

3.8d 5mm3.8d 1 0 mm3.8d 15mm4.0d 5mm4.0d 1 0 mm4.0d 15mm4.2d 5mm4.2d 1 0 mm4.2d 15mm

During the above tests a l l in le t inserts were tested using side

plates to avoid the effects of side vortices and to represent

prototype in sta lla t io n deta ils more accurately (see section

5 .7 ) .

(e) To complete testing and to determine the e ffec t of

siphon width, further tests were carried out on siphon

No3 (100mm width) using the same configurations as in

(d) above with ta ilw ate r level 1 Y1 (281mm).

-70-

To demonstrate the effects of d if fe re n t in le t configurations

f ive basic graphs have been plotted.

I Working head (H) Vs discharge (Q)

I I Priming head ( h-j) Vs discharge (Q)

I I I Coefficient of discharge (CQ) Vs discharge (Q)

IV Ratio of working head/throat depth (^V^) Vs

coefficient of discharge ( Cp)

V Ratio of priming head/throat depth ( / ^) Vs

coefficient of discharge (CQ)

Note: IV and V have dimensionless axes.

However, for accurate investigation into optimum in le t

configurations, effects of side plates etc only graph V was

used as this graph is indicative of the siphon's performance

and is easily interpreted. Further to these graphs three other

dimensionless graphs are to be considered.u

(1) Ratio of working head/priming head ( /h-j) Vs

coefficient of discharge (CQ)

(2) Reynolds' number ( R0) Vs coe ff ic ient of

discharge (CQ)

(3) Weber number (W) Vs co e ff ic ien t of discharge

<cD)

5.2 Effects of in le t l ip elevation (graphs 5.1 - 5.9 refers)

Air pa rtialised flow is the flow phase the siphon is required

to operate in. I t can be seen from graphs 5.1 - 5.3 that

during a i r pa rtialised flow, the higher in le t elevations ( ie

-71-

GRAPH-5 1 GRAPH OF WORKING HEAD (H) AGAINST DISCHARGE IQ)

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id

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-74-

the higher the underside of the in le t l ip inse rt compared to

the siphon crest) require greater working and priming heads to

produce equivalent discharges. However, a t the onset of

blackwater flow the priming head/upstream ratio is almost the

same for a ll in le t l ip elevations (graph 5 .3 ). I t can also be

seen that the s ta r t of blackwater flow occurs at a lower

discharge (and therefore head) for a lower in le t l i p elevation.

From graph 5.2 a transition or 'humped' zone can be seen3 -3between 9.0 and 11.5 m /s x 10 . This is probably due to

vortex action at in le t and this phenomena is explained more

fu l ly in chapter 6 with specific reference to f ig 17.

Graphs 5.4 and 5.5 p lot coe ff ic ient of discharge (Cq) against

discharge (Q). The coeffic ient of discharge is greater fo r a

given discharge as the in le t l ip elevation decreases. As

blackwater flow increases the coefficients of discharge rapidly

level o ff to constant values as discharge increases. The

highest l ip elevation gives the highest coe ff ic ient of

discharge for this flow phase, probably due to less contraction

at in le t . Graphs 5.6 - 5.8 i l lu s tra te s the same

characteristics as above.

Graph 5.9 confirms that the above results are not pa r t icu la r to

any one in le t l ip length and i t would appear from th is graph

that an in le t l ip elevation of 5mm would be the optimum.

However, an in le t l ip elevation of 10mm is considered the

-75-

GRAPH 5-4 - GRAPH OF COEFFICIENT OF DISCHARGE (C n ) AGAINST DISCHARGE (Q )

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-76-

Discharge Rate Q (mVs * 10

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-77-

GRAPH 5 6 -GRAPH OF RATIO OF WORKING HEAD AND THROAT DEPTH (H/d) AGAINST COEFFICIENT OF DISCHARGE (Cn l FOR VARYING INLET LIP ELEVATIONS

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GRAPH- 5-7 GRAPH OF RATIO OF PRIMING HEAD AND THROAT DEPTH (hi/ctt

AGAINST COEFFICIENT OF DISCHARGE (CpI FOR VARYING INLET

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-79-

GRAPH- 5- 8 GRAPH OF PRIMING HEAD AND THROAT DEPTH (h,/dV

AGAINST COEFFICIENT OF DISCHARGE (C.) FOR VARYING'

Coefficient of O ischornelGn)

GRAPH- 5 9 GRAPH OF RATIO OF PRIMING HEAD AND THROAT DEPTH fh./d)

AGAINST COEFFICIENT OF DISCHARGE FOR VARYING

£LU_I

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-81-

Coefficient of Discharge (Cn)

optimum value as an in le t l ip elevation of 5mm hunts up to

approximately 0.4CD and is therefore unsuitable as an optimum

value. Also, too low an in le t l i p elevation inh ib its priming

and reduces CQ due to contraction. To produce a more

accurate optimum value of in le t l ip elevation further tests on

in le t l ip elevations of between 5 and 15mm would prove

. valuable.

5.3 Effects of in le t l ip length

Due to fluctuations in upstream level during the hunting cycle,

flow could not be evaluated so that the s ta r t of the plots in

graph 5.10 represents the end of the hunting cycle. For

tailw ate r level 1 Y1 (281mm), siphon No2 and in le t l ip elevation

10mm, a l ip length of 4d causes hunting for flows up to 25% of

the range to onset of blackwater flow. This hunting stage

increases the sub-atmospheric flow regime and hence shortens

the region of a i r pa rtialised flow. An in le t length of 5d

results in increased hunting of up to 35% of the range to onset

of blackwater flow, a characteristic to be avoided due to

priming d i f f ic u l t ie s . In le t l ip lengths greater than 4d resu lt

in increasingly severe hunting and therefore an in le t l i p

length of 4d is the maximum desirable.

With reference to graphs 5.10 and 5.11 i t can be seen that

working heads remain approximately constant (graph 5.10) until

blackwater flow is approached (graph 5 .11), when they suddenly

-82-

GRAPH-5-10 GRAPH OF WORKING HEAD (H) AG AIN St DISCHARGE RATE (Q)FOR VARYING INLET LIP LENGTHS

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COoo

(UJ) pDdH D

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-83-

Discharge Rate (mVs xIOM

GRAPH- 5-11 GRAPH OF WORKING HEAD I H) AGAINST DISCHARGE RATE (Q)FOR VARYING INLET LENGTHS

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a.

a>

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Discharge Rate Qt nMxI OM

increase. Lip lengths above and including 3d were observed as

requiring reduced working heads.

The lower the value of l i p length the greater the required

priming head. From graph 5.27 we can see in le t l i p lengths of

3d compared for siphon Nos 1 and 2. These curves are

dimensionless and should be the same, y e t in a certain region

of flow there are large discrepancies. Work was carried out to

determine why th is tran s it ion zone was only apparent with

siphon No2 and i t was found to be due to the weir crest being

j o f f level and vortices forming a t the higher

in le t side. See conclusions for comments on f ig 17.

For siphon Nol the optimum configuration is 3d but fo r siphon

No2 (graph 5.12) 3d is c lea r ly not the optimum configuration.

In fact 4d would seem to be the value of in le t l i p length

producing the smoothest discharge curves. Lip lengths above 4d

show f la t t e r discharge characteristics which a t 5d and above,

tend towards pure blackwater flow characteristics.

As shown in graph 5.13 the c o e ff ic ie n t of discharge (CD) is

. l inea r ly proportional to discharge rate (Q) for a l l in le t l ip

lengths. For a given flow the longer in le t l ip lengths give

higher values of co e ff ic ien t of discharge. As was experienced

with siphon Nol, as blackwater flow was approached these curves

diverge. In increasing blackwater flow conditions, the

-85-

GRAPH- 5-12 GRAPH OF PRIMING HEAD (hi) AGAINST DISCHARGE RATE (Q)

FOR VARYING INLET LIP LENGTHS

-36-

Discharge Rate (m'/s xlQ1)

GRAPH-5-12q GRAPH OF RATIO OF PRIMING HEAD (hi) AND THROAT DEPTH Id) AGAINST

COEFFICIENT OF DISCHARGE 1C.) FOR VARYING INLET LENGTHS

*

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Coefficient of Discharge Ci

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coeff ic ient of discharge rapidly levels o f f and even shows a

peak with a s lig h t f a l l - o f f following. This peak value is

especially prevalent with non-optimum configurations.

Graphs 5.14 and 5.15, ratios of working head/throat depthH h( /p) and priming head/throat depth ( 1/^) against

coeffic ient of discharge ( CQ) corroborate the findings of

graphs 5.10 and 5.12 , which correspond to the study

of effects of working and priming heads on l ip length. In

graph 5.14 i t is d i f f ic u l t to discern the two categories of l ip

length but th is is not so for graph 5.15. 4d and 5d are in one

category whilst 2.4d and 3d are in a category depicting uneven

priming characteristics.

To summerise the e ffec t of increasing l ip length, in

pre-blackwater flow phases, increased l ip length results in:

(a) Increased hunting phase.

(b) Reduced working and priming heads necessary fo r a

pa rticu la r flow rate .

(c) F la tte r priming head/discharge relationships

tending towards blackwater flow characteristics.

(d) Increasing coefficients of discharge for a given

flow rate.

For siphon Mol a l ip length of 3d was found to be optimum for

good a ir regulation. For siphon Mo2 (graph 5.16) 4d, instead

of 3d, was found to be the optimum in le t length. For siphon

-89-

GRAPH- 514 GRAPH OF RATIO OF WORKING HEAD AND THROAT DEPTH (H/dl AGAINST COEFFICIENT OF DISCHARGE I Cr.) FOR VARYING INLET LIP LENGTHS

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GRAPH 5-16 GRAPH OF RATIO OF PRIMING HEAD AND THROAT DEPTH (hi/d) AGAINST

COEFFICIENT OF DISCHARGE (C.) FOR VARYING INLET LIP LENGTHS

>

-92-

i\lo3, 4d was found to be the optimum in le t l ip length. This

leads to the conclusion that for a square siphon section 3d is

the optimum in le t l ip length and fo r obvious rectangular

sections 4d is the optimum in le t l i p length. For a rectanguler

section, 4d gives the best priming characteristics, exhibiting

a gradually inclined, stable priming head/discharge

relationship. I t incurs reduced priming and working heads than

lesser in le t l ip lengths whilst being in the category giving

higher coefficients of discharge.

5.4 Effects of ta ilw ate r level

As can be seen from graph 5.18 the main e ffec t of increasing

tailw ate r level is to reduce the a ir pa rtialised flow range.

The higher the ta ilw ate r level the less the working head for

any given value of discharge. For a ll three ta ilw ate r levels

shown in graph 5.17 the working head reduces in the in i t ia l

flow stages of increasing discharge. Also, from graph 5.18, i t

can be seen that up to blackwater flow the higher the ta ilw ate r

level the greater the priming head necessary for a pa rticu la r

flow. For a particu lar discharge the required head is

maintained and also the increased resistance due to the greater

submergence of the e x it is overcome.

From graph 5.19 i t can be seen that coefficients of discharge

( Cp) are lin ea r ly proportional to discharge rate (Q) for each

ta ilw ate r leve l, as before. For a given flow ra te , the highest

ta ilw ate r level results in the highest coe ffic ient of discharge

-93-

GRAPH-5-17 GRAPH OF WORKING HEAD IH) AGAINST DISCHARGE RATE'IQ)

oo

(ui]H

PDaH 6

ui>ijo

m

-94-

Discharge Rate Q [mVsx10%)

0 0 7 - GRAPH-518 GRAPH OF PRIMING HEAD (hi) AGAINST DISCHARGE RATE (0)

FOR VARYING TAILWATER LEVELS

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-J’

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Discharge Rate Q (m V sxlfl)

and vice versa. As the working head is a component of the

coeff ic ient of discharge the coeffic ient of discharge

compensates for the working head ie a lower working head

requiring a higher discharge co e ff ic ient. As can be seen from

graph 5.19 the approach of blackwater flow produces a leve lling

o ff producing a peak value. The highest ta ilw ate r level

produced the highest maximum value of discharge co e ff ic ient.

When examining graphs 5.20 and 5.21 o f, ratios of workingu

head/throat depth ( /^) and priming head/throat depth

(^ 1 / 4 ) against coeffic ient of discharge, confirmation of

the a ffec t of tailw ate r level va riation, on working and priming

heads and the maximum discharge coefficients is apparent. Up

to 0.45Cq equivalent priming heads produce equivalent

coefficients of discharge.

With reference to graphs 5.17, 5.18 and 5.19 (especially graph

5.18) blackwater flow transpires a t an e a r l ie r flow rate for

higher ta ilw ate r levels and i t was noticeable that the two

lower ta ilw ate r levels commenced blackwater flow at

approximately the same point.

5.5 Effects of siphon width

Up to 9 L/s flow, siphons Nos 1 and 2 have sim ilar patterns of

working head and priming head/discharge relationships (graphs

5.22 and 5.23). I t w i ll be noticed that the wider siphon

produces lower heads compared to those of the narrower siphon.

-96-

GRAPH-519 GRAPH OP COEFFICIENT OF DISCHARGE (C.) AGAINST DISCHARGE RATE (Q)

FOR VARYING TAILWATER LEVELS

*

(#3) e6joip

sja }.ue(Oj jjeoQ

-97-

GRAPH S-20 - GRAPH OF RATIO OF WORKING HEAD IH1 AND THROAT DEPTH (d) AGAINST COEFFICIENT OF DISCHARGE (Cp ) FOR VARYING t m l w At e e . l e v e i -S

om

wn

-98-

C o e f f i c i e n t of discharge (Ch)

GRAPH 5 2 1 -GRAPH OF RATIO OF PRIMING HEAD Ih.) AND THROAT DEPTH (d) AGAINST

COEFFICIENT OF DISCHARGE ICn ) FOR VARYING INLET IIP LENGTHS

-99

-

After 9 L/s the heads for the narrower siphon increase rapidly

with the onset of blackwater flow. Due to lim itations of

equipment i t was not possible to te s t the wider siphon under

blackwater flow conditions. However siphon No2 was compared to

siphon No3 and as expected the wider siphon (No2, width 125mm)

produced lower heads than the narrower siphon (No3, width

100mm) as seen on graph 5.24.

Comparing siphons Nos 1 and 2 for a given discharge the

coeffic ient of discharge is less for the wider siphon (siphon

No2) than the narrower siphon (siphon Nol) and th is is

attributable to the larger cross-sectional area of which the

coeffic ient of discharge is a function (CQ = Q wherebd \/2gh

bd is the cross-sectional area).

Comparing siphon Nos 2 and 3 (graph 5.26) confirms the fact

that the wider the siphon the lower the co e ffic ien t of

discharge for a given discharge rate.

For siphon Nol the coeffiecient of discharge is l in e a r ly

proportional to discharge rate ie CQ << Q until blackwater

flow is reached and at this stage the coe ffic ient of discharge

value levels o ff in the blackwater flow phases. For siphon No2

CpoCQ until the beginning of the transition range previously

mentioned, the same being true of siphon No3.

-100-

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- 1 0 2 -

46

GRAPH 5 -2 4 -GRAPH OF WORKING HEAD (H) AGAINST DISCHARGE (Q)

W

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On inspection of graph 5.27, the ra tio of priming head/throat

depth(^1/^jagainst coeff ic ient of discharge (CQ) is

almost constant up until approximately 0.45CD (siphon No2).

Above 0.45Cq the effects of this transition phase arei_

apparent. The ra tio for the wider siphon, of (graph

5.27 and 5.28) exceed the ra tio fo r the narrower siphon but theu

same is not true of (graphs 5.29 and 5.30). This is

because the working head contributes l i t t l e to the transition

phase previously mentioned.

Effects of upstream channel widths

This work was completed using siphon Nol where the upstream

channel width was altered using aluminium sheets and dexion

framework. The upstream tank's width was reduced and the

effects studied.

Siphon No2 was tested using an upstream tank width of 43cms.

I t was postulated that by using a channel width proportional to

siphon width, siphon Nol, with adjusted upstream channel

conditions, would produce sim ilar results to siphon No2.

Siphon Nol width = 75cms - channel width to be determined = Xcms

Siphon No2 width = 125 cms. Channel width = 43cms

GRAPH 5-27 GRAPH OF RATIO OF PRIMING HEAD AND THROAT DEPTH (h,/d) AGAINS

-107-

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- 108 -

Coe

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GRAPH 5- 29- GRAPH OF RATIO OF WORKING HEAD TO THROAT DEPTH ( H/d) AGAINST

EE

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-109-

o efficien t of Discharge

GRAPH 5-30 -GRAPH OF RATIO OF WORKING HEAD AND THROAT DEPTH (H/d)

a

-110-

Coefficient of Discharge ( C p)

Using a channel width of 25 cms for siphon Nol and p lotting the

results on graph 5.27 i t can be seen that the original siphon

Nol plot has moved closer to the siphon No2 plot by this

variation in approach conditions. This of course is a

dimension!ess approach.

Again at approximately 0.45 x CQ the curves diverge due to

the transition of flow in siphon No2 but i t is possible to see

that even in this region the a lte ration of channel width

produces marginally more comparible results.

The point again must be made that a two-dimensional approach

has been made ie no consideration was given to reducing

upstream tank depth. This non-scaling of depth and also

experimental error probably causes the discrepancies between

siphon No2 and siphon Nol with altered upstream channel width.

5.7 Effects of vortices a t in le t

With reference to graph 5.27 i t is possible to see the

previously mentioned 'hump'. This is probably due to a

'depressed nappe1 flow phase which is not apparent in the

smaller of the two siphons or due to increased flow resistance

(increase in priming head). Using Reddy and P ic k fo rd s ^ ^

work and refe rr ing to Ali and Patemans'^^ papers i t would

be more sensible to adopt a 3-dimensional approach to a ir

entrainment. Looking at the laboratory sheets in Appendix B

- 1 1 1 -

th is characteristic commences at a point where a i r entrainment

is in a transient stage ie from gulping of a i r under the in le t

to vortex/side vortex induced a i r entrainment.

To apply Reddy and Pickfords' work on vortices, the depth of

water above the intake, low air-entraining vortices develop,

and these adversely a ffec t the efficiency of the hydraulic

machinery by reducing flow rate and by giving extra swirl to

the f lu id , in addition to causing vibration and noise.

In shallow reservoirs wave action develops an unstable boundary

layer (depending on the wave length and c e le r i ty ) and th is is

generally responsible for the change in v o r t ic ity which leads

to the formation of a ir-entraining vortices.

Applying this in a sectional sense i t would be a feasible

suggestion that vortex formation is a function of siphon width

and this is borne out by the observations made on the

laboratory sheets. With siphon No2 side vortices were more

obvious and conclusive proof that vortices are instrumental in

producing the transition zone could be given in a number of

ways. Physical prevention of vortex formation could be

achieved by (1) introduction of ba ff le boards to regulate flow

into in le t , (2) a lte ration of upstream tank depth and (3)

attachment of tr iangular side plates to siphon mouth and in le t .

- 1 1 2 -

The attachment of aluminium side plates greatly reduced the

e ffec t of vortices on siphon flow and therefore improves th e ir

efficiency ( f ig 17 re fe rs ).

5.8 Effects of revised outlet configuration

To investigate the e ffec t of ou tlet conditions a revised outlet

configuration was set up in the downstream tank of the

apparatus. The new configuration incorporated a side e x it to

the outlet chamber and a moveable downstream chamber wall as

shown in f ig 16. Tests were carried out for each of the six

chamber wall positions. As can be seen from graph 5.31 this

variable produced no s ign ificant change in siphon performance.

5.9 Dimensional analysis of the optimum siphon configuration

(Lip length 4d, l ip elevation 10mm, ta ilw ate r level 'Y'(281mm)).

Reynolds1 number and Weber number

From graph 5.32 i t can be seen that both ratios follow

identical trends to that of the working head for variations in

flow rate and coeff ic ient of discharge. This is a resu lt of

both expressions of Rg and W being functions of working

head. As such they reveal l i t t l e . However, the Reynolds'

number is d irectly influenced by velocity of flow which varies

l i t t l e in the a ir pa rtialised flow regime but rapidly increases

with the approach and development of blackwater flow. This can

be construed as being related to the proportion of a i r flow.

- 1 1 3 -

GRAPH 5-31 - GRAPH OF RATIO OF PRIMING HEAD AND THROAT DEPTH (h i/d) AGAINST COEFFICIENT OF DISCHARGE (Cn) FOR REVISED

OUTLET CONFIGURATIONS.

-114-

Coefficient of Discharge (Cn )

GRAPH 5 -3 2 -GRAPH OF REYNOLDS' IRa) AND WEBER (W) NUMBERS

01 x on spjouXsa

- 115-

The Weber number is at i t ' s lowest value in the a ir pa rtia lised

•flow regime, remaining reasonably constant. This indicates

that in th is phase of flow, surface tension effects are l ik e ly

to be greatest. Once blackwater flow occurs surface tension

effects become neglig ible. This may appear to validate the

concept of Froudian models not accurately portraying the a ir

p a r t ia lised flow phase. However, to put this matter into

perspective, although the effects of surface tension are

greater in the a i r p a r t ia lised flow regime than in blackwater

flow, surface tension effects are s t i l l neglig ible.

Siphon No 1 produced a transition region, as indicated between

points A and B on fig 17, where a higher upstream level is

required to produce an equivalent discharge. This transition

region was initially thought to be produced by the action of

vortices at inlet reducing the effective cross-sectional area of

the siphon and therefore increasing the upstream head to achieve

the same discharge. Side plates, forming the shape of a hood,

were added to siphon insert pieces and tests completed to

confirm.the origin of this transition zone.

-116-

\

trt

.m

a

ut

-11

7-

FIG 17 GRAPH OF hv« AGAINST C,

CHAPTER SIX

CONCLUSIONS

6.1 Comments and conclusions

6.2 S u ita b il i ty fo r use in a combined sewer overflow

-118-

6.1 Comments and Conclusions

The general geometry of the siphon gave good flow

conveyance, minimising the risk of flow separation at the

bends and giving a good coefficient of discharge for

blackwater flow of between 0.75 to 0.80.

The optimum inlet configuration for Siphon No 1 was jlnlet

lip length 3d and inlet lip elevation 10mm. For Siphon

No 2 the optimum configuration was found to be an inlet lip

length of 4d and an inlet lip elevation of 5mm above crest

level. The optimum inlet configuration for Siphon No 3 was

found to be 4d and an inlet lip elevation of 5mm.

Therefore, an aspect ratio of 1:1.3 or greater produces

consistent optimum values of inlet geometry. Aspect ratios

of less than 1:1.3 would require individual assessment and

testing if they were to be used in a working prototype.

The optimum bend ratio, r1 and R2 (fig 14) were found to bein)

0.5d and 1,5 d respectively. These optimum dimensions

produced the best flow conveyance for all flow phases.

As can be seen from sections 5.2 and 5.3 the inlet lip

configuration determines the priming and depriming

characteristics of the siphon and especially the range of

the hunting cycle. However variation in tailwater level

had little effect on the fundamental characteristics of the

air-partialised flow phase apart from higher downstream

levels curtailing the range of this flow regime. Also the

working head and initial priming head requirements were

affected as well as the pressure regions in the siphon.

-119-

The following conclusions may be drawn from the results in

Chapter 5.

(i) The effect of siphon width produces increased

discharges.

(ii) The optimum lip length previously thought to have

been a function of siphon width may now be a

function of shape.

(iii) The effect of upstream channel width is that a

proportional channel width/siphon width will produce

similar results to another siphon model with the

same channel width/siphon width on a dimensionless

plot.

(iv) The width of the chamber into which the channel is

fitted has little influence on discharge.

(v) The revised outlet configuration produced little

change to the hydraulic characteristics of the

siphon•

(vi) Although the air-mixture in air-partialised flow is

not precisely scaled using a Fruode Law of scaling

previous research by Ali and Pateman^O) has shown

that model scales no smaller than 1 to 10 do not

suffer significantly from scale effects. Indeed,

the prototype performance can be expected to be

marginally better than the model. Thus the

dimensionless results given above could be applied

-120-

with confidence for siphons discharging up to 4m3/s,

although at the higher flows a bank of smaller

siphons might be more effective due to restrictions

on sewer levels^l).

The optimum design for each of the three siphons gives

rapid priming, little tendancy to hunt and a progressive

discharge characteristic with little rise in upstream water

level up to blackwater flow making it an excellent choice

for a storm sewage overflow device. A conclusion which

will be dealt with in section 6.2.

The S-shaped siphon has been successfully constructed on

site using preformed permanent formwork surrounded with

mass concrete. This formwork can be of steel, glass,

reinforced plastic or any other material able to withstand

the rigours of vibro compaction of concrete around it and

also produce a permanent, smooth finish on the inside face.

With further developments in materials, especially

plastics, it is not inconceivable to consider an S-shaped

siphon being replaced unprotected in the ground and

backfilled like any other pipe fitting.

-121-

6.2 S u i t a b i l i t y fo r use as a combined sewer overflow

From resul ts previously discussed i t may now be seen tha t an

air- regulated siphon is idea l ly suited fo r use as a storm water

overflow. I t may oe designed to operate under low head

condit ions with coe f f ic ien ts of discharge of around 0.75. I f

the inve r t level downstream of the overflow is re s t r ic ted to

some minimum value then low worKing heads are held to be

pa r t i c u la r ly advantageous, especia l ly in deep sewers, or i f

sewers are in close proximity to the r i v e r in to which the

overflow is to be passed.

For tn e i r size siphons discharge large quant i t ies in re la t ion

to other overflow devices and hence th e i r compactness is a

d i s t i n c t advantage in the r e s t r i c t i v e nature of sewer systems.

For re la t iv e ly small increases in priming head a large range of

discharges are achieved, th is is benef icial fo r two reasons:

(a) High discharges are accommodated fo r with re la t i v e ly

small increases in upstream levels thereby preventing

the p o s s ib i l i t y of surcharges in the sewer upstream of

the overflow.

(b) Whilst maintaining the a b i l i t y to discharge equvalent

flows the crest level may be positioned higher, ie a t a

higher elevation than fo r other devices. This increase

in level in the sewer before overflow occurs increases

the d i lu t in g e f fec t and thereby reduces the po l lu t ing

e f fe c t and also reduces the frequency and volume of

s p i l 1.

- 1 2 2 -

Due to space requirements preventing use of a s u ff ic ie n tly

large/wide downstream weir arrangement d i f f ic u l t ie s may arise

in achieving the required elevation of ta ilw ate r leve l. High

downstream velocities must be avoided as they are associated

with scouring problems. With the provision of two siphon exits

i t would be possible to eliminate the high downstream<K

velocities and achieveAs u ff ic ien tly high ta ilw ate r le ve l. I f

the two siphon effluxes were arranged so that they were

directed against each other the resu lt would be an effective

dissipation of the high velocity energies by conversion to a

head of slower moving water. The simplest way to achieve such

an arrangement would be to position two smaller siphons side by

side and for th e ir bottom bends to be in a plane perpendicular

to the plane at the top bend, so that the two exits faced each

other. For a single siphon the flow may be divided in the

downflow leg or in the bottom bend and for a double e x it

arrangement to be provided, again facing each other.

Considering a ll these factors and solutions, downstream weir

arrangements could be dispensed with, scour problems eliminated

and increased compactness achieved. This crite r io n was not

used in the sectional models but may be a va lid source of

research in the future.

-123-

REFERENCES

(1) "An experimental study of the control of siphonic water flow

by atmospheric air" M J Kenn. JIWE, 1957.

(2) "Siphons in r ive r engineering" C R Head. Symposium on design

and operation of siphons and siphon spillways. BHRA, 1975.

(3) "A Partial siphon of compact design" G D Manley & E Markland.

Symposium on design and operation of siphons and siphon

■ spillways. BHRA, 1975.

(4) "Hydraulic model investigation of a siphon bell mouth" A J M

Harrison. JIWE Vol 20 p269-285, 1966.

(5) "Air regulated siphon spillways a t Spelga Dam" Poskitt &

Elsawy. JIWE Vol 30 No 4 p i77-190, June 1976.

(6) "Design and operation of a i r regulated siphons for reservoir

and headwater control" P Ackers & A R Thomas. Symposium on

design and operation of siphons and siphon spillways. BHRA,

1975.

(7) "The behaviour and design of a i r regulated siphon spillways"

F G Charlton & J A Perkins. Symposium on design and

operation of siphons and siphon spillways. BHRA, 1975.

(8) "An experimental investigation into the performance of a

siphon spillway" E S Crump & P Ackers. Report INT 22

Hydraulics Research Station, Wallingford, 1961.

(9) "The design and model analysis of a low head a i r regulated

siphon spillway" E M Elsawy & D A Irv ine. Symposium on

design and operation of siphons and siphon spillways. BHRA,

1975.

(10) "Vortices at intakes in conventional sumps" Y R Reddy & J A

Pickford. Water Power, 1972.

(11) "Effect of tube material on siphon performance" A G Kelly .

Symposium on design and operation of siphons and siphon

spillways. BHRA, 1975.

(12) "The design of a ir controlled spillway siphons" J A

Charlton. JIWE Vol 25 p325-336, August 1971.

(13) "The behaviour of siphon spillways with pa rticu la r reference

to a i r entrainment and model scale effects" D A Ervine. PhD

thesis, Queens University, Belfast, 1974.

(14) "A study of a self-priming saddle siphon, with a special

reference to means of admitting a ir" F G Charlton. JIWES Vol

20 p251-267, June 1966.

(15) "Ali and Pateman. Discussion on the design and modelling of

a ir regulated siphon spillways" D A Ervine. Proceedings ICE

Part 2 Vol 63 p237-242, March 1977.

(16) "Some scale effects in modelling a i r regulated siphon

spillways" D A Ervine & E M Elswy. Symposium on design and

operation of siphons and siphon spillways. BHRA, 1975.

(17) "Fluid mechanics for c iv i l engineers" Webber. Chapman & Hall

Ltd, 1971.

(18) "Experiments in siphon spillways" A H Gibson, P H Aspey & F

Tatte rsa ll . Proceedings ICE, 1931.

(19) "Model investigation of a storm-sewerage overflow siphon" T A

Smith. Sheffield City Polytechnic, Sheffie ld , April 1975.

(20) "Theoretical and experimental investigation of a i r regulated

siphons" Ali & Pateman. Proceedings. In stitu tion of C ivil

Engineers, London Part 2 Vol 6, March 1980.

(21) "Development of a compact a i r regulated siphon fo r storm

sewerage overflows" D J Balmforth, C J A Milroy & E J

Sarginson. Proceedings of the f i r s t International Seminar

for Urban Drainage Systems, Sept 1982.

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