Chapter 1 – Introduction by sdsdfqw21

VIEWS: 8 PAGES: 113

									 AN EXPERIMENTAL INVESTIGATION
   INTO THE PRESSURE-LEAKAGE
RELATIONSHIP OF FRACTURED WATER
              PIPES

                                       by
                         BRUCE GREYVENSTEIN
                              909802067

A dissertation submitted to the Faculty of Engineering and the Built Environment in
                   fulfilment of the requirements for the degree


                      MAGISTER INGENERIAE

                                       IN

                         CIVIL ENGINEERING

                                   AT THE

               UNIVERSITY OF JOHANNESBURG




                 STUDY LEADER: PROF J.E. VAN ZYL

                                      2007
                                                                              Summary



SUMMARY


The aim of this investigation was to determine the N1 value in the relationship
between pressure and flow for different types of water reticulation pipes with different
forms of fractures. The relationship is defined as:
                                   Q = Cd A 2 g H N1
Once these N1 values are established, they can be used as an indication for better
pressure management in water reticulation networks. This investigation was limited
to three types of pipe with diameter 110 mm and wall thickness of 4 mm:
   •   uPVC
   •   Cast iron
   •   Steel

And three different forms of failures:
   •   Round holes
   •   Longitudinal splits
   •   Circular cracks

Pressure step testing was used to obtain experimental data. During analysis of the
data, Cd was calculated from the initial area of a fracture and kept constant thereafter.
Conclusions could be drawn about similar type pipes with similar fractures and
comparisons could be made between all the samples as well as previous studies.
Generally it seems that longitudinal splits lead to the most excessive leaking, followed
by round holes and then the circular cracks. A summary of typical N1 exponents
found is shown below:


   •   uPVC pipes with round holes                                           0.48 - 0.49
   •   uPVC pipes with longitudinal splits                                   0.89 - 1.26
   •   uPVC pipes with circular cracks                                       0.31 – 0.48

   •   Cast Iron pipes with round holes                                      0.43 – 0.44
   •   Cast Iron pipes with longitudinal splits                              0.42 – 0.46
   •   Cast Iron pipes with circular cracks                                  0.41 – 0.43

   •   Steel pipes with round holes                                          0.42 – 0.44
   •   Steel pipes with longitudinal splits                                  0.39 – 0.45
   •   Steel pipes with circular cracks                                      0.38 – 0.48


                                              i
                                                                          Opsomming



OPSOMMING


Die doel van hierdie ondersoek was om die N1 waarde te bepaal in die verhouding
tussen druk en vloei vir verskillende tipe waterpype met verskillende tipe falings. Die
verhouding is beskrywe soos volg:
                                   Q = Cd A 2 g H N1
As hierdie N1 waardes bepaal is, dan kan dit gebruik word as ‘n indikasie vir beter
drukbeheer in waterverspreidingsnetwerke. Hierdie ondersoek was beperk tot drie
tipes pype met ‘n diameter van 110 mm en ‘n muur dikte van 4 mm:
    •   uPVC
    •   Yster
    •   Staal

En drie verskillende soorte falings:
   •    Ronde gate
   •    Lengtekrake
   •    Omtrekkrake

Drukstaptoetse is gebruik om die eksperimentele waardes te bepaal. Tydens die
analise van die data, Cd was bereken met die begin area van ‘n faling en was konstant
gehou daarna. Gevolgtrekkings is gemaak tussen soortgelyke pype met soortgelyke
falings, en vergelykings is gemaak tussen al die pype as ook voorige studies. Oor die
algemeen lyk dit asof die lengtekrake die meeste gelek het gevolg deur dieronde gate
en dan die omtrekkrake. ʼn Opsomming van die N1 eksponente gevind word hier
onder aangetoon:


   •    uPVC pype met ronde gate                                           0.48 - 0.49
   •    uPVC pype met lengtekrake                                          0.89 - 1.26
   •    uPVC pype met omtrekkrake                                          0.31 – 0.48

   •    Yster pype met ronde gate                                          0.43 – 0.44
   •    Yster pype met lengtekrake                                         0.42 – 0.46
   •    Yster pype met omtrekkrake                                         0.41 – 0.43

   •    Staal pipes met ronde gate                                         0.42 – 0.44
   •    Staal pipes met lengtekrake                                        0.39 – 0.45
   •    Staal pipes met omtrekkrake                                        0.38 – 0.48


                                          ii
                                                                    Acknowledgements


ACKNOWLEDGEMENTS


I would like to thank the follow people for the role they played in the completion of
this investigation.


    •   God Almighty for the opportunities He has afforded to me.


    •   Prof. JE van Zyl for providing me with guidance and knowledge.


    •   Mr. Giel Vermeulen for his technical assistance.


    •   Incledon DPI (Pty) Limited for donating pipes for research purposes.


    •   Rand Water, ILIFA Africa Consulting Engineers, Infraconsult and the NRF
        THRIPP programme for financial assistance.




                                          iii
                                                                                                                             Table of Contents



                                                 TABLE OF CONTENTS


SUMMARY ............................................................................................................................................. I 
OPSOMMING ....................................................................................................................................... II 
ACKNOWLEDGEMENTS ................................................................................................................ III 
TABLE OF CONTENTS .................................................................................................................... IV 
LIST OF TABLES ............................................................................................................................... VI 
LIST OF FIGURES............................................................................................................................ VII 
LIST OF SYMBOLS ............................................................................................................................. X 
1.       INTRODUCTION......................................................................................................................... 1 
      1.1.       BACKGROUND ........................................................................................................................ 1 
      1.2.       AIM ........................................................................................................................................ 2 
      1.3.       OBJECTIVES............................................................................................................................ 2 
      1.4.       SCOPE OF INVESTIGATION ...................................................................................................... 3 
      1.5.       OVERVIEW ............................................................................................................................. 4 
2.       LITERATURE REVIEW............................................................................................................. 5 
      2.1.       INTRODUCTION....................................................................................................................... 5 
      2.2.       WATER BALANCE .................................................................................................................. 5 
      2.3.       WATER LOSSES....................................................................................................................... 8 
      2.4.       LEAKAGE ............................................................................................................................. 10 
      2.5.       PREVIOUS INVESTIGATIONS ................................................................................................. 14 
3.       METHODOLOGY ..................................................................................................................... 17 
      3.1.       DESIGN................................................................................................................................. 17 
      3.2.       THE PIPES ............................................................................................................................. 24 
      3.3.       CALIBRATION ....................................................................................................................... 25 
      3.4.       PROCEDURE ......................................................................................................................... 27 
      3.5.       POSSIBLE PROBLEMS ............................................................................................................ 32 
4.       RESULTS .................................................................................................................................... 33 
      4.1.       UPVC 6 MM ROUND HOLE ................................................................................................... 34 
      4.2.       UPVC 8 MM ROUND HOLE ................................................................................................... 35 
      4.3.       UPVC 10 MM ROUND HOLE ................................................................................................. 36 
      4.4.       UPVC 12 MM ROUND HOLE ................................................................................................. 37 
      4.5.       UPVC 8 MM ROUND HOLE – LONG PIPE ............................................................................... 38 
      4.6.       UPVC 12 MM ROUND HOLE – LONG PIPE ............................................................................. 39 
      4.7.       UPVC 50 MM LONGITUDINAL SPLIT ..................................................................................... 41 
      4.8.       UPVC 100 MM LONGITUDINAL SPLIT ................................................................................... 42 
      4.9.       UPVC 150 MM LONGITUDINAL SPLIT ................................................................................... 43 
      4.10.      UPVC 200 MM LONGITUDINAL SPLIT ................................................................................... 45 
      4.11.      UPVC 40 MM CIRCULAR CRACK .......................................................................................... 47 
      4.12.      UPVC 80 MM CIRCULAR CRACK .......................................................................................... 48 
      4.13.      UPVC 120 MM CIRCULAR CRACK ........................................................................................ 49 
      4.14.      UPVC 160 MM CIRCULAR CRACK ........................................................................................ 50 
      4.15.      CAST IRON 6 MM ROUND HOLE ............................................................................................ 51 
      4.16.      CAST IRON 8 MM ROUND HOLE ............................................................................................ 52 
      4.17.      CAST IRON 10 MM ROUND HOLE .......................................................................................... 53 
      4.18.      CAST IRON 12 MM ROUND HOLE .......................................................................................... 54 
      4.19.      CAST IRON 50 MM LONGITUDINAL SPLIT ............................................................................. 55 
      4.20.      CAST IRON 100 MM LONGITUDINAL SPLIT ........................................................................... 56 
      4.21.      CAST IRON 150 MM LONGITUDINAL SPLIT ........................................................................... 57 

                                                                            iv
                                                                                                                      Table of Contents

      4.22.      CAST IRON 200 MM LONGITUDINAL SPLIT ........................................................................... 58 
      4.23.      CAST IRON 40 MM CIRCULAR CRACK .................................................................................. 59 
      4.24.      CAST IRON 80 MM CIRCULAR CRACK .................................................................................. 60 
      4.25.      CAST IRON 120 MM CIRCULAR CRACK................................................................................. 61 
      4.26.      CAST IRON 160 MM CIRCULAR CRACK................................................................................. 62 
      4.27.      STEEL 6 MM ROUND HOLE ................................................................................................... 63 
      4.28.      STEEL 8 MM ROUND HOLE ................................................................................................... 64 
      4.29.      STEEL 10 MM ROUND HOLE ................................................................................................. 65 
      4.30.      STEEL 12 MM ROUND HOLE ................................................................................................. 66 
      4.31.      STEEL 50 MM LONGITUDINAL SPLIT ..................................................................................... 67 
      4.32.      STEEL 100 MM LONGITUDINAL SPLIT ................................................................................... 68 
      4.33.      STEEL 150 MM LONGITUDINAL SPLIT ................................................................................... 69 
      4.34.      STEEL 200 MM LONGITUDINAL SPLIT ................................................................................... 70 
      4.35.      STEEL 40 MM CIRCULAR CRACK .......................................................................................... 71 
      4.36.      STEEL 80 MM CIRCULAR CRACK .......................................................................................... 72 
      4.37.      STEEL 120 MM CIRCULAR CRACK ........................................................................................ 73 
      4.38.      STEEL 160 MM CIRCULAR CRACK ........................................................................................ 74 
5.       DISCUSSION .............................................................................................................................. 75 
      5.1.       UPVC ROUND HOLES ........................................................................................................... 75 
      5.2.       UPVC LONGITUDINAL SPLITS .............................................................................................. 77 
      5.3.       UPVC CIRCULAR CRACKS ................................................................................................... 79 
      5.4.       CAST IRON ROUND HOLES ................................................................................................... 81 
      5.5.       CAST IRON LONGITUDINAL SPLITS ....................................................................................... 83 
      5.6.       CAST IRON CIRCULAR CRACKS ............................................................................................ 85 
      5.7.       STEEL ROUND HOLES ........................................................................................................... 87 
      5.8.       STEEL LONGITUDINAL SPLITS .............................................................................................. 89 
      5.9.       STEEL CIRCULAR CRACKS ................................................................................................... 90 
      5.10.      ALL ROUND HOLES .............................................................................................................. 93 
      5.11.      ALL LONGITUDINAL SPLITS ................................................................................................. 95 
      5.12.      ALL CIRCULAR CRACKS ....................................................................................................... 97 
6.       CONCLUSIONS ......................................................................................................................... 99 
      6.1.       RESULTS OBTAINED ............................................................................................................. 99 
      6.2.       CONCLUSIONS .................................................................................................................... 100 
      6.3.       RECOMMENDATIONS .......................................................................................................... 101 


Appendix A………………………………………………………..……..……........103
References.……………………………………………………….….…..……...…..263




                                                                         v
                                                                                                 List of Tables



LIST OF TABLES


Table 1 IWA Standard Water Balance (Modified from Greyvenstein, 2004) ............... 6 
Table 2 N1 Results (Greyvenstein, 2004) .................................................................... 14 
Table 3 N1 Results (Cassa, 2006) ................................................................................ 15 
Table 4 N1 Results (Coetzer, 2007) ............................................................................. 16 
Table 5 N1 Results (Buckley, 2006) ............................................................................ 16 
Table 6 Conversion from bar to meters ....................................................................... 25 
Table 7 Example of processed data ............................................................................. 29 
Table 8 Information sheet for a sample ....................................................................... 31 
Table 9 Results of all uPVC round holes ..................................................................... 76 
Table 10 Results of all uPVC longitudinal splits ......................................................... 77 
Table 11 Results of all uPVC circular cracks .............................................................. 80 
Table 12 Results of all Cast iron round holes .............................................................. 81 
Table 13 Results of all Cast iron longitudinal splits .................................................... 83 
Table 14 Results of all Cast iron circular cracks ......................................................... 85 
Table 15 Results of all Steel round holes..................................................................... 87 
Table 16 Results of all Steel longitudinal splits........................................................... 89 
Table 17 Results of all Steel circular cracks ................................................................ 91 




                                                        vi
                                                                                                      List of Figures


LIST OF FIGURES
Figure 1 Leakage Management Activities (Thornton and Lambert, 2005) ................... 9 
Figure 2 Efflux from a tank through an orifice ............................................................ 10 
Figure 3 Contracta of an opening................................................................................. 11 
Figure 4 Cd vs. Reynolds numbers ............................................................................... 12 
Figure 5 End section with pressure transducer ............................................................ 18 
Figure 6 End section with water supply pipe ............................................................... 19 
Figure 7 Alternate setup ............................................................................................... 20 
Figure 8 Steel rods and PVC flanges ........................................................................... 20 
Figure 9 50 to 25 mm reducer ...................................................................................... 21 
Figure 10 The flow meter ............................................................................................ 22 
Figure 11 Test in progress............................................................................................ 23 
Figure 12 The pipe samples ......................................................................................... 24 
Figure 13 Adjustment curve for pressure readings ...................................................... 26 
Figure 14 Example of raw data .................................................................................... 28 
Figure 15 H-Q relationship for uPVC 6 mm round hole ............................................. 34 
Figure 16 Change in area for uPVC 6 mm round hole ................................................ 34 
Figure 17 H-Q relationship for uPVC 8 mm round hole ............................................. 35 
Figure 18 Change in area of uPVC 8 mm round hole.................................................. 35 
Figure 19 H-Q relationship for uPVC 10 mm round hole ........................................... 36 
Figure 20 Change in area of uPVC 10 mm round hole................................................ 36 
Figure 21 H-Q relationship for uPVC 12 mm round hole ........................................... 37 
Figure 22 Change in area of uPVC 12 mm round hole................................................ 37 
Figure 23 Comparison of H-Q relationship for uPVC 8 mm round holes ................... 38 
Figure 24 Comparison of area change of uPVC 8 mm round holes ............................ 38 
Figure 25 Comparison of H-Q relationship for uPVC 12 mm round holes ................. 39 
Figure 26 Comparison of area change of uPVC 12 mm round holes .......................... 39 
Figure 27 H-Q relationship for uPVC 50 mm longitudinal split ................................. 41 
Figure 28 Change in area of uPVC 50 mm longitudinal split...................................... 41 
Figure 29 H-Q relationship for uPVC 100 mm longitudinal split ............................... 42 
Figure 30 Change in area of uPVC 100 mm longitudinal split.................................... 42 
Figure 31 H-Q relationship for uPVC 150 mm longitudinal split (run 1) ................... 43 
Figure 32 H-Q relationship for uPVC 150 mm longitudinal split ............................... 44 
Figure 33 Change in area of uPVC 150 mm longitudinal split.................................... 44 
Figure 34 H-Q relationship for uPVC 200 mm longitudinal split (run 1) ................... 45 
Figure 35 H-Q relationship for uPVC 200 mm longitudinal split ............................... 46 
Figure 36 Change in area of uPVC 200 mm longitudinal split.................................... 46 
Figure 37 H-Q relationship for uPVC 40 mm circular crack....................................... 47 
Figure 38 Change in area of uPVC 40 mm circular crack ........................................... 47 
Figure 39 H-Q relationship for uPVC 80 mm circular crack....................................... 48 
Figure 40 Change in area of uPVC 80 mm circular crack ........................................... 48 
Figure 41 H-Q relationship for uPVC 120 mm circular crack..................................... 49 
Figure 42 Change in area of uPVC 120 mm circular crack ......................................... 49 
Figure 43 H-Q relationship for uPVC 160 mm circular crack..................................... 50 
Figure 44 Change in area of uPVC 160 mm circular crack ......................................... 50 
Figure 45 H-Q relationship for Cast iron 6 mm round hole ........................................ 51 
Figure 46 Change in area of Cast iron 6 mm round hole ............................................. 51 
Figure 47 H-Q relationship for Cast iron 8 mm round hole ........................................ 52 

                                                           vii
                                                                                         List of Figures


Figure 48 Change in area of Cast iron 8 mm round hole ............................................. 52 
Figure 49 H-Q relationship for Cast iron 10 mm round hole ...................................... 53 
Figure 50 Change in area of Cast iron 10 mm round hole ........................................... 53 
Figure 51 H-Q relationship for Cast iron 12 mm round hole ...................................... 54 
Figure 52 Change in area of Cast iron 12 mm round hole ........................................... 54 
Figure 53 H-Q relationship for Cast iron 50 mm longitudinal split ............................ 55 
Figure 54 Change in area of Cast iron 50 mm longitudinal split ................................. 55 
Figure 55 H-Q relationship for Cast iron 100 mm longitudinal split .......................... 56 
Figure 56 Change in area of Cast iron 100 mm longitudinal split ............................... 56 
Figure 57 H-Q relationship for Cast iron 150 mm longitudinal split .......................... 57 
Figure 58 Change in area of Cast iron 150 mm longitudinal split ............................... 57 
Figure 59 H-Q relationship for Cast iron 200 mm longitudinal split .......................... 58 
Figure 60 Change in area of Cast iron 200 mm longitudinal split ............................... 58 
Figure 61 H-Q relationship for Cast iron 40 mm circular crack .................................. 59 
Figure 62 Change in area of Cast iron 40 mm circular crack ...................................... 59 
Figure 63 H-Q relationship for Cast iron 80 mm circular crack .................................. 60 
Figure 64 Change in area of Cast iron 80 mm circular crack ...................................... 60 
Figure 65 H-Q relationship for Cast iron 120 mm circular crack ................................ 61 
Figure 66 Change in area of Cast iron 120 mm circular crack .................................... 61 
Figure 67 H-Q relationship for Cast iron 160 mm circular crack ................................ 62 
Figure 68 Change in area of Cast iron 160 mm circular crack .................................... 62 
Figure 69 H-Q Relationship for Steel 6 mm round hole .............................................. 63 
Figure 70 Change in area of Steel 6 mm round hole ................................................... 63 
Figure 71 H-Q Relationship for Steel 8 mm round hole .............................................. 64 
Figure 72 Change in area of Steel 8 mm round hole ................................................... 64 
Figure 73 H-Q Relationship for Steel 10 mm round hole ............................................ 65 
Figure 74 Change in area of Steel 10 mm round hole ................................................. 65 
Figure 75 H-Q Relationship for Steel 12 mm round hole ............................................ 66 
Figure 76 Change in area of Steel 12 mm round hole ................................................. 66 
Figure 77 H-Q Relationship for Steel 50 mm longitudinal split .................................. 67 
Figure 78 Change in area of Steel 50 mm longitudinal split ....................................... 67 
Figure 79 H-Q Relationship for Steel 100 mm longitudinal split ................................ 68 
Figure 80 Change in area of Steel 100 mm longitudinal split ..................................... 68 
Figure 81 H-Q Relationship for Steel 150 mm longitudinal split ................................ 69 
Figure 82 Change in area of Steel 150 mm longitudinal split ..................................... 69 
Figure 83 H-Q Relationship for Steel 200 mm longitudinal split ................................ 70 
Figure 84 Change in area of Steel 200 mm longitudinal split ..................................... 70 
Figure 85 H-Q Relationship for Steel 40 mm circular crack ....................................... 71 
Figure 86 Change in area of Steel 40 mm circular crack ............................................. 71 
Figure 87 H-Q Relationship for Steel 80 mm circular crack ....................................... 72 
Figure 88 Change in area of Steel 80 mm circular crack ............................................. 72 
Figure 89 H-Q Relationship for Steel 120 mm circular crack ..................................... 73 
Figure 90 Change in area of Steel 120 mm circular crack ........................................... 73 
Figure 91 H-Q Relationship for Steel 160 mm circular crack ..................................... 74 
Figure 92 Change in area of Steel 160 mm circular crack ........................................... 74 
Figure 93 Comparison of uPVC round holes ............................................................... 75 
Figure 94 All studies results of uPVC round holes...................................................... 76 
Figure 95 Comparison of uPVC longitudinal splits ..................................................... 77 
Figure 96 All studies results of uPVC longitudinal splits............................................ 78 
Figure 97 Comparison of uPVC circular splits ............................................................ 79 

                                                    viii
                                                                                          List of Figures


Figure 98 All studies results of uPVC circular cracks ................................................. 80 
Figure 99 Comparison of Cast iron round holes .......................................................... 81 
Figure 100 All studies results of cast iron round holes ................................................ 82 
Figure 101 Comparison of Cast iron longitudinal splits .............................................. 83 
Figure 102 All studies results of cast iron longitudinal splits ...................................... 84 
Figure 103 Comparison of Cast iron circular cracks ................................................... 85 
Figure 104 All studies results of cast iron circular cracks ........................................... 86 
Figure 105 Comparison of Steel round holes .............................................................. 87 
Figure 106 All studies results of steel round holes ...................................................... 88 
Figure 107 Comparison of Steel longitudinal splits .................................................... 89 
Figure 108 All studies results of steel longitudinal splits ............................................ 90 
Figure 109 Comparison of Steel circular cracks .......................................................... 91 
Figure 110 All studies results of steel circular cracks ................................................. 91 
Figure 111 Comparison of All round holes ................................................................. 93 
Figure 112 Comparison of N1 values of round holes .................................................. 94 
Figure 113 Comparison of All longitudinal splits ....................................................... 95 
Figure 114 Comparison of N1 values of longitudinal splits ........................................ 96 
Figure 115 Comparison of All circular cracks ............................................................. 97 
Figure 116 Comparison of N1 values of circular cracks ............................................. 98 
Figure 117 Summary of leakage exponents ................................................................. 99 




                                                     ix
                                                             List of Symbols



LIST OF SYMBOLS


Q       =   Flow rate (m3/s)
H       =   Pressure head (m)
N1      =   Leakage Exponent
uPVC =      UnPlastified polyvinyl Chloride
VJ      =   Viking-Johnson
m       =   Meter
s       =   Second
l       =   Litre
mm      =   Millimetre
    2
R       =   Pearson product moment correlation coefficient
min     =   Minute
g       =   Unit gravity (m/s2)
Cd      =   Coefficient of discharge
Cc      =   Coefficient of contraction
Cv      =   Velocity coefficient
A       =   Area (m2)
b       =   Width (m)
D       =   Diameter (m)
R       =   Hydraulic radius (m)
V       =   Velocity (m/s)
Re      =   Reynolds number
ν       =   Kinematic viscosity (m2/s)
NRW =       Non revenue water




                                         x
                                                                              Introduction



                               1. INTRODUCTION

1.1.    Background


‘Only 1.5% of the available water in the Upper Vaal Water Management Area was
not allocated in 2000. With virtually no more water to allocate, the achievement of
the national growth objectives can only be achieved through more productive use of
the existing water, or through increasing the available water.’ (Claassen, 2006).


Water is a scarce resource and should be managed extremely carefully. Leakage in
water infrastructure is a world wide problem and prevents careful management of this
precious resource. If the mechanisms behind water leakage are better understood, it
could help to better preserve water.


Presently municipalities and specialists analyse minimum night flow to estimate water
loss through leakage. Measures are then implemented to reduce this loss but it does
not bring us closer to understanding leakage holistically.          An equation relating
pressure to flow could lend to better understand of the mechanisms involved in
leakage. This is the orifice equation and appears as follows:
                                    Q = Cd A 2 g H N1
If pressure (H) is varied, it is not only flow (Q) that is affected but also the area of the
fracture, the discharge coefficient and the N1 value. Furthermore one must consider
pipe material and wall thickness as well. These are the mechanisms mentioned above.
The relationship between pressure and flow is therefore a complex one.


If many of these variables are known and as few as possible assumptions are made, it
may be possible to determine a N1 value for each specific set of parameters. Having
this knowledge at hand may then assist in the design process of water infrastructure
and possibly even in the manufacturing process of water pipes and fittings.


Due to the complex nature of this relationship, the solution is easier said than done.




                                             1
                                                                             Introduction


1.2.       Aim


The aim of this investigation is to determine the N1 values within a set of known
parameters within the relationship between pressure and flow. The known parameters
are:
       •   Material type
       •   Diameter
       •   Wall thickness
       •   Type of failure


An assumption made was that the discharge coefficient will remain constant for each
pipe tested. Using the original area of a fracture the Cd valve was calculated. Now
for each value of H there will be an associated Q and A value which will lead to a N1
value.



1.3.       Objectives

   •       Prepare a literature review
   •       Prepare 38 pipes for testing.
   •       Design and build setup – Improvements to previous methods were made and
           new problems were overcome.
   •       Measure leakage flows under pressure – All the different pipes were tested.
   •       Obtain relationship between pressure and leakage – Results were processed
           and comparisons were made between the samples.




                                             2
                                                                          Introduction


1.4.    Scope of investigation


This investigation would like to see how the N1 value of different pipes exhibit water
losses and then compare the results obtained to that of previous investigations.
Questions to be answered would be:


   •   What is the relationship between pressure and leakage?
   •   Is the size of the fracture important?
   •   Is the shape of the fracture important?
   •   Is the type of material important?


This investigation is limited to three types of pipe, all 110 mm in diameter and with a
wall thickness of 4 mm:


   •   uPVC pipes,
   •   Cast iron pipes,
   •   Steel pipes.


And three different forms of failure:


   •   Round holes,
   •   Longitudinal splits,
   •   Circular cracks.




                                            3
                                                                          Introduction


1.5.    Overview


This report consists of the following chapters:


Chapter 1 contains the introduction to the report. The problem is defined here. The
aim, objectives and scope of this investigation are also stated.


Chapter 2 contains a literature review. It will brief the reader on water losses in
general followed by an in depth discussion of leakage specifically from fractures.
Then similar studies or investigations are reviewed for comparison. It also includes
brief explanations of some general terms and definitions associated with water and
materials.


Chapter 3 includes the planning and design of the experimental setup. Potential
problems as well as the procedure are discussed within. The method of processing the
data obtained is also discussed.


Chapter 4 contains the results obtained from testing. Each pipe that was tested being
discussed and general comments are made.


Chapter 5 discusses the results from the previous chapter. Comparisons are drawn
here between different types of pipes and different types of fractures.


Chapter 6 contains a summary of work done with the main conclusions.


Appendix A contains raw and processed data of all the tests done.




                                            4
                                                                        Literature Review



                          2. LITERATURE REVIEW

2.1.    Introduction


First it is important to understand the various aspects of the water balance from input
to revenue generated. This will enable the reader to understand where water losses fit
into the bigger picture. This will in turn lead to an explanation of leakage in specific.


Previous studies are also listed with their assumptions and findings.

2.2.    Water Balance
This section will explain what happens to all the water that is input into the water
infrastructure allowing the reader to see where water losses occur in the process.


Water supply: Although we live on a water planet, only 2.5% is fresh water, 97.5%
being salt water. Of this fresh water, 68.9% is tied up in icecaps and snow and a
further 30.8% is ground water. Much of this water is either too deep or the volumes
are just too small to be extracted. This leaves only about 0.3% of fresh water for
human consumption, which is 35 billion km3 (Shiklomanjov, 1999).


Water resources in South Africa were able to meet the demands put on them in the
nineteenth century.    Sustainable use, in the higher rainfall regions, and nomadic
subsidence, in the drier regions, ensured that water was not a limiting resource.
Modern agricultural practices, coupled with rapid population growth, industrial and
mining development in the 20th century has further increased the demand on this finite
resource (Claassen, 2006). Previously shortages were addressed by capturing a larger
portion of the hydrological cycle to meet amplified demands. It soon became clear
that conventional engineering solutions in terms of supply were not sustainable.
Improved efficiency and demand management has become the new focus.

The water demand of the 1995 increase in the South African population of about 1
million people, projected to the year 2015 when the newborns reach adulthood, is
conservatively estimated at 638 ml/day or about 23% of the average daily water


                                            5
                                                                      Literature Review


supply of Rand Water, at the time, indicating the tremendous pressure on resources
(Schutte and Pretorius, 1997).


To summarize, water supply is the total volume of potable water input into the
infrastructure whether it be locally treated or imported.


Authorized Consumption: This is the portion of water supplied that is authorized
for consumption whether it is paid for or not. The remained of the water supply is
then water losses which are expanded upon in the following section.


Table 1 IWA Standard Water Balance (Modified from Greyvenstein, 2004)
                              Billed        Billed Metered Consumption      Revenue
                           Authorized
                                                                             Water
            Authorized   Consumption      Billed Unmetered Consumption
          Consumption       Unbilled       Unbilled Metered Consumption
                           Authorized
                         Consumption Unbilled Unmetered Consumption
                            Apparent        Unauthorized Consumption
 System                      Losses              Meter Inaccuracies
  Input
                                           Leakage on Transmission and        Non
 Volume
                                                  Distribution Mains        Revenue
                                                                             Water
          Water Losses                       Leakage and Overflows at
                         Real Losses                  Reservoirs

                                          Leakage on Service Connections
                                                   up to meter




Billed: This is the portion of authorized consumption that is paid for by the
consumers.    When consumption levels are excessive, the cost per unit of water
increases, thereby regulating water use. This fact also discourages waste such as
leaving taps dripping, watering excessively, etc. Revenue is received for this portion
of water whether it is metered or not.



Unbilled: This is the portion of authorized consumption that is unpaid for by the
consumers. There are some water uses that are subsidized with water by government,
such as fire fighting water, street cleaning, parks, etc. Such instances are referred to
as Non revenue water (NRW).




                                            6
                                                                      Literature Review


In July 2005, DWAF introduced the free basic water campaign. The criterion was as
follows (Besseling, 2007):

   •   Quantity:              25 l/day/capita (now 200 l/day/household)
   •   Cartage:               200 m
   •   Availability:          10 l/min
   •   Assurance:             Secure supply
   •   Quality:               Minimum accepted standards
   •   Upgradeability:        Future house connections


Revenue water vs. NRW: The remaining portion of NRW is water losses. As the
proportion of water loss decreases, the proportion of non revenue water (NRW) will
also decrease. The proportion of revenue water would remain constant. This implies
the following:


   1. More funds would be available to maintain the existing system.
   Funds are required for activities such as:
         •        Replacement of old pipes/controls
         •        More/better leakage detection equipment
         •        New equipment for pressure management
         •        Better wages as incentives for better workmanship
         •        Research into improving techniques across the board
   2. A possible decrease in water costs.


A combination of the above factors would be most favourable; however the water
supplier would have to evaluate these measures individually.




                                            7
                                                                         Literature Review


2.3.    Water losses
Now that water losses have been defined in terms of the water balance, a further
explanation of how water losses are composed of can be defined in two aspects
namely apparent losses and real losses.

Apparent losses: These losses are those which are difficult to measure such as water
theft, meter inaccuracies, evaporation and secondary losses (Bends, valves,
restrictions in the system, etc.). That is to say all water that is lost not due to leakage.

Real losses: This is all water lost due to leakage of some form.                  The IWA
recommends four strategies to control real losses as shown in Figure 1. (1) With
pressure management, the losses will reduce with decreased pressure applied to the
system. (2) Speed and quality of repairs will reduce current losses with quicker
response times to reported leaks and improved workmanship. (3) Asset management
refers to criteria such as material selection, installation techniques, maintenance,
renewal and replacement of the system components. (4) The last activity is active
leakage control and is encompassed by various methods such as noise mapping
surveys. This is done by using acoustic equipment and/or digital noise correlation
methods.    With constant feedbacks, say twice per year, problem areas can be
identified and prioritized and maintenance teams can work according to this schedule.




                                             8
                                                                      Literature Review



                                      Pressure
                                     Management




                                   Unavoidable
                                   Annual Real
         Speed and                Losses (UARL)
                                                                     Active
         Quality of         Potentially Recoverable Real           Leakage
         Repairs                        Losses                      Control
                            Current Annual Real Losses
                                       (CARL)



                                      Asset
                                    Management




       Figure 1 Leakage Management Activities (Thornton and Lambert, 2005)

To address all the above aspects, suitable training programs could be introduced based
on IWA methods of water loss and management (Dickinson, 2007). The following
topic areas could be included in such a program:


   •   Practical field training – materials management, construction methods and
       quality, equipment selection and utilization.
   •   Water audit methods – mapping a water balance, validate all water
       components, assess and prioritize problems.
   •   Water loss intervention strategies – Selection and utilization of testing
       equipment, conduct leakage detection program, maintain interventions.




                                           9
                                                                        Literature Review


2.4.       Leakage
In this section leakage is discussed at greater length as it is the only component of real
losses. An orifice is defined as a hole where the ratio of the diameter to the depth is
less than 2. A tube is defined where this ratio is larger than 2 but less than 3. A pipe
is defined where this ratio is larger than 3. Therefore, for all leaks in a water system
we can use the orifice definition since the depth of a fracture is often insignificant to
the diameter thereof. (Consider an overflowing reservoir or burst in transmission
main). A mathematical derivation describes the flow from an orifice and is shown
below.     Thereafter the properties or occurrences associated with leaks are high
lighted.


Derivation of orifice flow:


If we consider a portion of a stream tube in a steady, incompressible and non-viscous
flow, involving mechanical energy only (no heat transfer, no internal energy changes),
the following energy equation would apply where 1 and 2 is the beginning and end of
the stream tube respectively. This is known as Bernoulli’s equation.



                                V2 ρ1      V22 ρ2
                                 1
                                   + + z1 = + + z2                                    (1)
                                2g γ       2g γ

The use of Bernoulli’s equation is illustrated with the following example. Figure 2
shows a large tank with a well-rounded and small opening as an outlet. The dotted
line is used as the datum level and H is indicated.

                                    1


                                     H


                                                       2




                       Figure 2 Efflux from a tank through an orifice


                                            10
                                                                      Literature Review



This flow is not steady flow since H is changing constantly (decreasing), however
with an enormous tank this change in H will be so slow that it can be ignored. The
flow is thus quasi-steady. Also density is constant and there is no friction.


Inserting known values into Bernoulli’s equation, i.e. V1 is zero and z1 is H. The
pressures at 1 and 2 are atmospheric, and V2 is the velocity of the efflux jet of water.
The following equation is obtained.


                         ρatm     V22 ρatm
                              +H = +                                                 (2)
                          γ       2g γ
Simplifying leads to:

                                  V2 = 2 gH                                          (3)


Now we can include losses through the orifice by using a velocity coefficient Cv. This
is the velocity coefficient and accounts for losses such friction on the side walls of an
opening. The value is usually no smaller than 0.98 for well rounded openings.


Also there will be contraction of the water jet as it leaves the opening. Water cannot
abruptly bend around a corner, which leads to a water jet, A1, which has a smaller area
than the actual fracture A0.



                                               A1




               Wall thickness                  Water
                                                Jet

                                                  A0

                               Figure 3 Contracta of an opening




                                             11
                                                                     Literature Review


The original area of the jet of water expelled is A0 and is measured at the beginning of
the fracture. The final area of the jet of water is A1 and is measured where the jet
streamlines are parallel to one another. Thus the coefficient of contraction id defined
as follows:



                                                                                     (4)


In this study, Cc will be used as a tool to compare various results. This is because Cc
was not constant since the area of the fracture was not constant. The values for Cc are
usually 0.6 for sharp edge outlets and 1.0 for well rounded openings. The Vena
contracta is defined as the minimum jet diameter where the jet stream lines become
parallel (Prandtl, 1952).


Cd is the coefficient of discharge; Cd   =   CvCc. The Figure below shows the typical
behaviour of Cd values in relation to the Reynolds number.




                       Figure 4 Cd vs. Reynolds numbers


Equation (3) now becomes as seen in equation (5). Note that V2 = Q/A.


                                   Q = C d A 2 gH                                    (5)


In this investigation it was this Cd value that was calculated from the original area of
the fracture and assumed to remain constant thereafter.




                                             12
                                                                   Literature Review



Properties or occurrence associated with leaks:


The objective of dealing with a fracture is to decrease or eliminate water loss. To
achieve this however, the properties of leakage and its associated impacts need to be
understood. Some of these properties are as follows:


   •   Water loss
   •   Saturated ground
   •   Velocity change
   •   Vibration of rupture
   •   Noise of vibration
   •   Frequencies of noise levels
   •   Type and shape of orifice
   •   Water pressure difference
   •   Pressure related changes at each side of a leak
   •   Pipe material
   •   Potential deterioration and failure of pipes
   •   Viscosity changes
   •   Diurnal changes
   •   Different materials at joints
   •   Depth of pipe
   •   Material surrounding pipe
   •   Visibility on surface
   •   Temperature


Many of these factors do not cause a leak but should be considered to develop best
practice methods (Waldron, 2005).




                                          13
                                                                             Literature Review


2.5.        Previous Investigations


If equation (5) is rewritten to appear as equation (6) below, then the power of H is
referred to as the N1 value. It is these values that will be compared to each other in
the following section. However, the previous investigations did not all use the same
set of parameters such as wall thickness and pipe diameter therefore making it more
difficult to compare results.                 These differences are pointed out with each
investigation.
                                              Q = CdA 2 g H N 1                            (6)



B. Greyvenstein: In an earlier investigation by the author (Greyvenstein, 2004), it
was found that the N1 value varies with the type of pipe and the nature of the fracture.
The method used in that investigation was the same used in this study (see chapter 3).
The results of that study which are relevant to this study are shown in the summary
below.


Table 2 N1 Results (Greyvenstein, 2004)
 Material        Fracture             Size             Pipe ø     Wall Thickness   N1
 uPVC            Round hole           12 mm            110 mm     3 mm             0.52
 uPVC            Longitudinal split   0.3 x 50 mm      110 mm     3 mm             1.51
                                      0.3 x 100 mm     110 mm     3 mm             1.48
                                      0.3 x 150 mm     110 mm     3 mm             1.84
 uPVC            Circular crack       1 x 90 mm        110 mm     3 mm             0.41
                                      1 x 170 mm       110 mm     3 mm             0.50
 Steel           Round hole           12 mm            110 mm     4 mm             0.52



Notice that the longitudinal splits led to the highest N1 values followed by the round
holes and then the circular cracks.




                                                     14
                                                                             Literature Review


A. M. Cassa: This method uses finite element analysis to analyse different pipe
failures. Below is a table of the results obtained (Cassa, 2006). Note that is was not all
the results, only the samples relevant to this study were included. From this table we see
that circular cracks had the highest N1 value followed by longitudinal splits and then
round holes.

Table 3 N1 Results (Cassa, 2006)
 Material      Fracture             Size           Pipe ø (OD)   Wall Thickness   N1
 uPVC          Round hole           6 mm           110 mm        3 mm             0.5089
                                    8 mm           110 mm        3 mm             0.5072
                                    10 mm          110 mm        3 mm             0.5076
                                    12 mm          110 mm        3 mm             0.5081
 Cast Iron     Round hole           6 mm           105.206 mm    0.603 mm         0.5009
                                    8 mm           105.206 mm    0.603 mm         0.5011
                                    10 mm          105.206 mm    0.603 mm         0.5013
                                    12 mm          105.206 mm    0.603 mm         0.5017
 Steel         Round hole           6 mm           104.628 mm    0.314 mm         0.5011
                                    8 mm           104.628 mm    0.314 mm         0.5013
                                    10 mm          104.628 mm    0.314 mm         0.5017
                                    12 mm          104.628 mm    0.314 mm         0.5029
 uPVC          Longitudinal split   2 x 50 mm      110 mm        3 mm             0.7834
 Cast Iron     Longitudinal split   0.5 x 50 mm    105.206 mm    0.603 mm         0.6616
 Steel         Longitudinal split   1 x 50 mm      104.628 mm    0.314 mm         0.7236
 uPVC          Circular cracks      0.5 x 40 mm    110 mm        3 mm             0.5578
                                    2 x 150 mm     110 mm        3 mm             1.1543
 Cast Iron     Circular cracks      0.5 x 40 mm    105.206 mm    0.603 mm         0.5136
                                    1 x 150 mm     105.206 mm    0.603 mm         0.9460
 Steel         Circular cracks      0.5 x 40 mm    104.628 mm    0.314 mm         0.5195
                                    1 x 150 mm     104.628 mm    0.314 mm         1.0170



Within these results, it can be seen that the round holes resulted with N1 values
similar to that of theory. Longitudinal splits showed higher values than that of the
round holes but curiously enough the circular cracks showed the highest exponent
values instead of the lowest.




                                                  15
                                                                               Literature Review


A. J. Coetzer: An investigation was carried out (Coetzer, 2007) which was mainly
concerned with the effect of soil around a 1 mm round hole. Only the results of uPVC
pipes with round holes are shown here.


Table 4 N1 Results (Coetzer, 2007)
 Material       Fracture         Size                  Pipe ø       Wall Thickness   N1
 uPVC           Round hole       1 mm                  110 mm       3 mm             0.47
                                 2 mm                  110 mm       3 mm             0.48




These results for the N1 value were similar to that of theory.


R. S. Buckley: An investigation was carried out (Buckley, 2006) which was mainly
concerned with the material properties of a pipe and what happens to the material
under pressure.


Pressure tests were done on a number of pipes. Pipes similar to those used in this
investigation are shown in the table below.


Table 5 N1 Results (Buckley, 2006)
Material          Fracture              Size               Pipe ø   Wall Thickness   N1
uPVC              Round hole            6 mm               110 mm   3 mm             0.5110
                                        8 mm               110 mm   3 mm             0.5246
                                        10 mm              110 mm   3 mm             0.5140
                                        12 mm              110 mm   3 mm             0.5091
uPVC              Longitudinal          1.2 x 40 mm        110 mm   3 mm             0.8413
                                        2 x 60 mm          110 mm   3 mm             0.7570
                                        1.7 x 90 mm        110 mm   3 mm             0.8579



Compared to the studies discussed above, the results for round holes correlate to those
obtained elsewhere and hence to the theoretical value. Longitudinal splits were also
higher than that of round holes




                                                      16
                                                                         Methodology



                             3. METHODOLOGY


In this chapter, the physical tests on various failed pipes that were carried out are
discussed.    The same setup was used in an earlier investigation by the author
(Greyvenstein, 2004). In this investigation, two pipes were tested in an alternative
setup to compare the accuracy of the original method. This section includes:


    • A detailed design of the experimental setup, (as well as an alternative setup for
          comparison)
    • The pipe samples that were tested
    • The calibration of the measuring equipment.
    • The procedure that was carried out to ensure consistency and data processing
    • Any possible problems that could be encountered.



3.1.      Design


The aim of the experiments was to be able to obtain a range of pressure values versus
flow values. To do this a fractured pipe is connected to a water source and allowed to
leak through the fracture only. This must be done in a manner so as to be able to
measure the flow of the water coming into the system and the water pressure in the
system.


The apparatus used is divided into four parts:
   •   End sections
   •   Joining end sections to sample pipe
   •   Keeping the setup together under working conditions
   •   Water supply




The end sections described here were manufactured for 110 mm diameter pipe. First
two sections of class 9 uPVC pipes with outside diameter 110 mm of length


                                          17
                                                                        Methodology


approximately 400 mm were fitted with saddles. These saddles have an inside
diameter of 110 mm and a 25 mm nozzle to allow water in/out of the uPVC sections
(Figure 5).




                      Figure 5 End section with pressure transducer


Figure 5 shows the class 9 uPVC pipe with a saddle firmly bolted onto the pipe.
Beneath the 25 mm nozzle of the saddle, a hole is drilled into the pipe. One end
section will have a pressure transducer connect to the nozzle as seen in Figure 5 and
the other end section will have a water supply pipe connected to the nozzle as seen in
Figure 6.


End caps were fitted to one end of each of these end sections and sealed water tight
with uPVC glue.




                                           18
                                                                          Methodology




                        Figure 6 End section with water supply pipe


Also seen in Figure 5 is a Viking-Johnson coupling. Inside the Viking-Johnson
coupling (VJ) are rubber seals. When two pipes are fitted into the VJ from either side,
in our case an end section and the sample pipe, it is tightened by pulling the bracketed
ends of the VJ together by means of bolts and nuts. In tightening the VJ, the rubber
seals seal any leak between the end section and the pipe sample. VJ’s were used to
connect both end sections to the sample pipe.


With the high pressures used in the experiments, the Viking-Johnson system was not
able to keep the joined pipes together. It was therefore decided to support the end
sections with a system of steel rods.


Twelve mm galvanized steel rods were used to constrain the setup by passing them
through the Viking-Johnson’s. This ensured that the pipe sample would be secure but
the end sections might still come apart. For this reason, uPVC flanges were
manufactured to fit onto the ends of the setup, supporting the end sections.




                                            19
                                                                        Methodology


A slightly different setup was used on two pipes, namely 8 and 12 mm (long) round
holes in uPVC. Instead of inserting the sample into a setup, the sample itself was the
setup. A uPVC pipe of 2 meters in length was fitted with end caps and saddles directly
as seen in Figure 7.




                                Figure 7 Alternate setup


Figure 8 shows how the pipe sample is fitted in between two Viking-Johnson
couplings which have end sections attached. On the ends of the end sections, one can
see the uPVC flanges and the setup were kept together by steel rods with nuts and
washers.




                           Figure 8 Steel rods and PVC flanges


                                           20
                                                                        Methodology


To allow water into the system, a clear hose was connected from the water supply to
the inlet saddle. However, the supply line is fitted with a 50 mm outlet therefore a
reducer was used at this outlet, see Figure 9, so that a 25 mm hose could be used (the
saddle has a 25 mm nozzle). Within the 50 mm outlet of the supply line was a lever
ball valve. The flow was controlled via this valve. A clamp was used to keep the
hose firmly in place. The insulation tape beneath the clamp was to ensure that the
clamp could be tight enough to seal well.




                              Figure 9 50 to 25 mm reducer


The other end of the hose was connected to the saddle in a likewise manner, except
that no reducer was necessary. Again, one can see the clamp and the insulation tape
below it in Figure 9.


Before the 50 mm outlet along the water supply line, a flow meter was installed seen
in Figure 10. This flow meter had a bypass meter seen on the left and the main meter
on the right. A logger could be connected to both meters as seen below to measure
the total flow going into the sample.




                                            21
                                                                         Methodology




                                 Figure 10 The flow meter


A pressure transducer was fitted to the other saddle (after the sample pipe) via the 25
mm nozzle. The transducer was also connected to the logger to measure the pressure
in the system. This can be seen in Figure 6.


The testing was done in a concrete basin so as to collect and drain water from each
test. Also, the sample was placed horizontally so that the pressure registered at the
transducer would reflect the pressure at the fracture.


Because it was still unknown how much leakage would occur, a plastic drum was
fitted over the sample to ensure that the water from the leak will remain in the basin.
These aspects can all be seen in Figure 11. This drum was later replaced with a
rubber mat.




                                           22
                             Methodology




Figure 11 Test in progress




           23
                                                                          Methodology


3.2.     The Pipes


Three types of pipes are used specifically uPVC, cast iron and steel. All the samples
are 500 mm in length. And all the wall thicknesses were 4 mm.


Each of these pipes then had different fractures manufactured into it, namely round
holes, longitudinal splits or circumferential splits. These fractures are of different
sizes:


Round holes:           6 mm                     Longitudinal splits:       50 mm
                       8 mm                                                100 mm
                       10 mm                                               150 mm
                       12 mm                                               200 mm
L round holes:         8 mm                     Circumferential cracks:    40 mm
                       12 mm                                               80 mm
                                                                           120mm
                                                                           160 mm


This gives a total of 38 sample pipes. Seen in Figure 12 is an example of each pipe
and fracture.




                                Figure 12 The pipe samples


Top is a uPVC pipe with a round hole.
The middle is a cast iron pipe with a longitudinal split.
The bottom is a steel pipe with a circular crack.

                                           24
                                                                             Methodology


3.3.      Calibration


The combination flow meter was tested to confirm its accuracy using a simple
method. Water was allowed to flow into a vessel ensuring that either the main meter
or the bypass or both meters were running. The valve was controlled to ensure
different flow rates. The meter readings were taken before and after this was done
thereby giving the volume of water registered by the meter. The volume of water in
the vessel was then measured physically. The volumes were then compared to each
other to ascertain the accuracy of the meter. The results were as follows:


                Reading                  Measured               Meters         Accuracy
Sample 1:       0.0139 m³                13,920 ml              Both           -0.14 %
Sample 2:       0.0135 m³                13,500 ml              Both           0%
Sample 3:       0.0100 m³                9,960 ml               Both           +0.10 %
Sample 4:       0.0076 m³                7,610 ml               Bypass         -0.13 %
Sample 5:       0.0050 m³                5,000 ml               Bypass         0%


It was therefore safe to assume an accuracy of ± 0.15 % which, for the purposes of
this investigation were negligible. At extremely low flow values, i.e. when the pipe
does not flow full, there was inaccuracy and therefore these values will be excluded
from any analysis. These are values ≤ 0.00015 m³/s.


The accuracy of the pressure transducer was checked using a Budenberg gauge.
The pressure (in bar) read on the logger display is shown in Table 6. This reading
contained an error which is shown as actual bar. The actual bar was then converted to
meters.


Table 6 Conversion from bar to meters
 H (logger bar)    H (kPa)        H (m)      H (actual bar)   H (kPa)     H (m)
           0.03             3           0.31              0           0      0.00
           2.02           202           20.6              2         200     20.39
           4.02           402           41.0              4         400     40.77
           6.01           601           61.3              6         600     61.16
           8.00           800           81.5              8         800     81.55
          10.00         1000          101.9              10        1000    101.94




                                              25
                                                                                 Methodology


The results from the above table are shown graphically in Figure 13.



                   120

                   100

                   80
           H (m)




                   60
                                                           y = 10.226x - 0.297
                   40                                               2
                                                                    R =1
                   20

                    0
                         0       2         4         6          8       10       12
                                               H (logger bar)

                         Figure 13 Adjustment curve for pressure readings


The following linear equation was found, y = 10.226x – 0.297.


The value of x was then the reading from the logger (refer to Table 7, column 6:
Pressure H (bar)).


The value of y was then the pressure in meters including the correction of the
transducer (refer to Table 7, column 7: Pressure H (m)).




                                               26
                                                                          Methodology


3.4.    Procedure


The first thing to be done was to fill the system with water by slightly opening the
lever ball valve. Once the system was full of water and the air was expelled, the valve
was opened more to create the first test flow rate. From here on the valve was opened
in small increments to obtain data points for an increase in pressure (step up) and then
closed in a like fashion to obtain points for step down pressures.


This process was repeated up to three times in succession for each sample. The valve
was opened and closed with best judgment to ensure that the data points gathered for
all three runs were well dispersed.


From here on it was just a matter of changing the sample once a test was finished.
This involved the reconnection of the hose and pressure transducer.


A logger, Cosmos Data Logger from Meinecke, was used to take pressure and flow
measurements. Input to the logger was via flow sensors and a pressure transducer as
discussed above. The logger recorded pressure in bar every 0.5 seconds and the flow
is recorded in l/s at every pulse. A pulse was set to 1 l/s. All measurements by the
logger were then downloaded to a software program, CDLWin 3.42 from Invensys.


Data for all the tables and graphs was obtained from the results of the logger, an
example of which is shown in Figure 14.




                                           27
                                                                         Methodology




                             Figure 14 Example of raw data


The flow meter sent a digital pulse to the logger. The pulse rate for the main meter
was every second and for the bypass meter every 0.2 seconds. The logger then
calculated, by the amount of time that has elapsed between two pulses, the flow.
Thus the flow is an average for that time. The pressure transducer sent an analogue
signal to the logger every 0.5 seconds and thus these readings are instantaneous.


Fifteen to sixty seconds intervals were chosen from the graph in Figure 14 for each
step up or down in pressure and the corresponding flow rates were located. Refer to
Table 7 where each pressure step was recorded with a start time (column 1) and an
end time (column 2). For each step two readings were obtained for flow, one being
from the bypass meter (column 3) and the other from the main flow meter (column 4).
These readings were summed and converted to total flow in m³/s (column 5).


The pressure at each step was recorded in bar (column 6) and converted to meters.
Specifically the reading was multiplied by 100 and divided by 9.81. Once the reading
was in meters, the calibration correction was met. Specifically the reading was
multiplied by 10.226 minus 0.297 (column 7).




                                          28
                                                                                           Methodology


This gave a pressure and a flow for each step. Because the test was run on each pipe
three times there resulted three sets of data of each pipe. The exponent for each run
was recorded as seen in the example shown in Table 7.


Table 7 Example of processed data
Processed data for uPVC, 6mm hole - run 1
                                Ave Flow for      Ave Flow for      Total Flow   Pressure H   Pressure H
 Start time      End time     small meter(l/s)   large meter(l/s)    Q (m³/s)      (bar)         (m)

  10:51:24       10:52:32         0.0000             0.1258          0.0001       0.2421       2.1783
  10:52:53       10:53:41         0.0000             0.2842          0.0003       1.3375       13.3803
  10:53:47       10:54:20         0.0000             0.3594          0.0004       2.1747       21.9415
  10:54:26       10:54:58         0.0000             0.4245          0.0004       3.0539       30.9322
  10:55:20       10:55:53         0.0000             0.4472          0.0004       3.3982       34.4530
  10:57:10       10:57:30         0.0000             0.4319          0.0004       3.1610       32.0274
  10:57:56       10:58:22         0.0000             0.3391          0.0003       1.9438       19.5803
  10:59:06       10:59:46         0.0000             0.1472          0.0001       0.3393       3.1722



Q = 0.00008*H0.4815          R² = 0.9998

Processed data for uPVC, 6mm hole - run 2
                                Ave Flow for      Ave Flow for      Total Flow   Pressure H   Pressure H
 Start time      End time     small meter(l/s)   large meter(l/s)    Q (m³/s)      (bar)         (m)

  10:59:06       10:59:46         0.0000             0.1472          0.0001       0.3393       3.1722
  11:01:02       11:01:32         0.0000             0.2089          0.0002       0.7067       6.9294
  11:02:02       11:02:34         0.0000             0.2576          0.0003       1.0894       10.8432
  11:02:44       11:03:16         0.0000             0.3773          0.0004       2.3988       24.2331
  11:04:00       11:04:40         0.0000             0.4515          0.0005       3.4610       35.0952
  11:06:10       11:06:40         0.0000             0.4059          0.0004       2.7957       28.2918
  11:07:34       11:08:02         0.0000             0.3700          0.0004       2.3132       23.3578
  11:08:36       11:09:42         0.0000             0.3491          0.0003       2.0516       20.6827
  11:10:16       11:11:00         0.0000             0.2721          0.0003       1.2264       12.2442

Q = 0.00008*H0.4744          R² = 0.9999

Processed data for uPVC, 6mm hole - run 3
                                Ave Flow for      Ave Flow for      Total Flow   Pressure H   Pressure H

 Start time      End time     small meter(l/s)   large meter(l/s)    Q (m³/s)      (bar)         (m)

  11:12:58       11:13:36         0.0000             0.2523          0.0003       1.0461       10.4004
  11:14:04       11:14:38         0.0000             0.2931          0.0003       1.4300       14.3262
  11:16:36       11:17:08         0.0000             0.3298          0.0003       1.8166       18.2796
  11:17:52       11:18:08         0.0000             0.3893          0.0004       2.5700       25.9838
  11:18:58       11:19:18         0.0000             0.4881          0.0005       4.0715       41.3382
  11:20:58       11:21:16         0.0000             0.4623          0.0005       3.6217       36.7385
  11:21:36       11:22:06         0.0000             0.3916          0.0004       2.5913       26.2016
  11:22:26       11:22:56         0.0000             0.2452          0.0002       0.9840       9.7654



Q = 0.00008*H0.4781          R² = 0.9999



                                                  29
                                                                            Methodology


Another table was setup using Q and H to calculate other variables such as Cd, area
and the Reynolds number. The data that was excluded was strike off (see Table 8).
Using the second data point in this table as an example, the following values were
found.


   •     Q = 0.00028 m³/s (column 1)
   •     H = 13.3803 m (column 2)

   •              = 16.2025 (column 3) was calculated by inserting the value of H.
   •     CdA = 0.00002 (column 4) would then be column 1 divided by column 3.



   •     Now area (column 5 and 6) was calculated from CdA. Start by assuming a
         value for Cd (say 0.65). Then draw up a graph of H versus A. Fit a linear
         trend line to this graph with an equation in the form of A = mH + A0. Now
         knowing the initial area of the fracture, A0 = 28.27 (that is to say when H = 0),
         Cd can be adjusted until A (y axis cutting point) = A0. Cd was found to be
         0.63. This value would then yield the value for A = 27.84 mm²
   •     The diameter d = 0.006 m, in the case of round holes, and breadth b, in the
         case of longitudinal splits and circular cracks was calculated in column 7.
   •     The hydraulic radius, R = 0.001488 (column 8) was calculated using the
         wetted area divided by the wetted perimeter.



   •     Velocity, V = 10.2076 m/s (column 9) was calculated using Q divided by A.



   •     The Reynolds number, Re = 53,311 (column 10) was finally calculated using 4
         times the velocity times the hydraulic radius divided by the kinematic
         viscosity (ν) of water at 15°C.




                                            30
                                                                                            Methodology

Table 8 Information sheet for a sample

  Q (m3/s)   H (m)     (2g)0.5HN1    CdA       A (m2)     A (mm²)   d (m)       R       V (m/s)    Re

  0.00013     2.1783    6.5375      0.00002   0.0000305    30.53    0.0062   0.001559    4.1186   22,527
  0.00028    13.3803    16.2025     0.00002   0.0000278    27.84    0.0060   0.001488   10.2076   53,311
  0.00036    21.9415    20.7483     0.00002   0.0000275    27.49    0.0059   0.001479   13.0714   67,838
  0.00042    30.9322    24.6351     0.00002   0.0000274    27.35    0.0059   0.001475   15.5201   80,345
  0.00045    34.4530    25.9994     0.00002   0.0000273    27.30    0.0059   0.001474   16.3796   84,716
  0.00043    32.0274    25.0675     0.00002   0.0000273    27.35    0.0059   0.001475   15.7925   81,745
  0.00034    19.5803    19.6001     0.00002   0.0000275    27.46    0.0059   0.001478   12.3481   64,050
  0.00015     3.1722    7.8891      0.00002   0.0000296    29.62    0.0061   0.001535    4.9701   26,775

  0.00015    3.1722     7.8891      0.00002   0.0000296    29.62    0.0061   0.001535   4.9701    26,775
  0.00021     6.9294    11.6600     0.00002   0.0000284    28.44    0.0060   0.001504    7.3458   38,775
  0.00026    10.8432    14.5857     0.00002   0.0000280    28.03    0.0060   0.001493    9.1890   48,153
  0.00038    24.2331    21.8049     0.00002   0.0000275    27.46    0.0059   0.001478   13.7371   71,255

  0.00045    35.0952    26.2406     0.00002   0.0000273    27.31    0.0059   0.001474   16.5316   85,516
  0.00041    28.2918    23.5603     0.00002   0.0000273    27.35    0.0059   0.001475   14.8430   76,829
  0.00037    23.3578    21.4075     0.00002   0.0000274    27.43    0.0059   0.001477   13.4867   69,916
  0.00035    20.6827    20.1443     0.00002   0.0000275    27.51    0.0059   0.001479   12.6909   65,881
  0.00027    12.2442    15.4994     0.00002   0.0000279    27.87    0.0060   0.001489    9.7646   51,021
  0.00025     10.400    14.2848     0.00002   0.0000280    28.04    0.0060   0.001494    8.9994   47,166
  0.00029     14.326    16.7654     0.00002   0.0000277    27.75    0.0059   0.001486   10.5622   55,072
  0.00033     18.280    18.9379     0.00002   0.0000276    27.64    0.0059   0.001483   11.9309   62,086
  0.00039     25.984    22.5788     0.00002   0.0000274    27.37    0.0059   0.001476   14.2246   73,654
  0.00049     41.338    28.4790     0.00002   0.0000272    27.20    0.0059   0.001471   17.9418   92,625
  0.00046     36.739    26.8479     0.00002   0.0000273    27.33    0.0059   0.001475   16.9142   87,523
  0.00039     26.202    22.6732     0.00002   0.0000274    27.42    0.0059   0.001477   14.2841   74,031
  0.00025     9.765     13.8419     0.00002   0.0000281    28.12    0.0060   0.001496   8.7204    45,768




              Date:    19/02/2007
              Cd =        0.63
               v=       1.14E-06
               g=         9.81
              D=          0.006
              N1 =         0.5
              A0 =        28.27


For each pipe tested, the results are shown in appendix A. First the raw data is shown
where pressure is the grey line, the main flow meter is the black line and the bypass
meter is the dotted black line like that of Figure 14. That data was then processed
and shown as a table like that of Table 7. Further information concerning that pipe
was then set out on an information sheet as shown in Table 8. This table also showed
general information for each pipe such as the initial area, Cd value. The last graph
shown is the Reynolds number versus pressure.



                                                          31
                                                                           Methodology


3.5.    Possible problems


On this setup there are ample opportunities for leaks to occur where they are not
suppose to. On the end sections, the end caps where glued to stop small leaks from
occurring with PVC glue. With the first test more glued had to be applied and the end
cap no longer leaked. The saddles where bolted onto the end sections firmly and no
leakage occurred here.


In keeping the setup together, the nuts on the steel rods where tightened, in other
words the Viking-Johnson’s were tightened, until leaking stopped. The PVC flanges
were tightened afterwards to ensure that none of the sections in the setup could come
apart under pressure.


The hose was clamped to nozzles as previously mentioned and this proved adequate to
stop leaking. The nozzles as well as the transducer were fitted in place with plumbers
tape. No leakage occurred from these connections.


Another obstacle was to ensure that there was no air in the system. The 25 mm hose
was chosen to be clear so that one can visible check that no air is entering the system.
Once the sample was lying horizontally, the setup could be manoeuvred to expel air
that may be caught beneath the transducer or any other crevice inside the setup.


Because the same hose with a steel nozzle had to be used for all the tests, it was
unclear what repeated reconnection would cause to the plastic saddle. The 25 mm
connection for the pressure transducer raised the same question. It was seen that the
plastic saddles lost their tread toward to completion of the tests, and if further testing
was to be done, these connections would undoubtedly leak.




                                           32
                                                                               Results



                                  4. RESULTS


In each of the following sections, the heading briefly describes the pipe tested. A
graph of flow versus pressure then shows all the data points used. A power curve was
fitted to the data to reveal the N1 exponent. This graph also shows the consistency
and repeatability of the test.


Then the values of N1, Cd and Re are reported.


A graph of area versus pressure then follows. For all these graphs the cutting point on
the y-axis is the initial area of the fracture as can be seen in the associated linear
equation


All other results are shown in appendix A. These include the raw data from each
sample, the processed data, and a calculation sheet showing various factors such as
the hydraulic radius as wee as a graph of Reynolds numbers versus pressure.


The following chapter will compare the results amongst each other.




                                          33
                                                                                              Results


4.1.   uPVC 6 mm Round Hole


                                0.0010


                                                       Q = 0.00008H0.4768
                                0.0008
                                                          R² = 0.9999

                                0.0006
                  Flow (m³/s)




                                0.0004



                                0.0002



                                0.0000
                                         0        10      20                 30   40     50
                                                               Pressure (m)


                                Figure 15 H-Q relationship for uPVC 6 mm round hole


The following values were found:
N1     = 0.4768
Cd     = 0.63
Re     40,000 – 100,000



                                30


                                25


                                20                                  A = -0.03H + 28.27
                  Area (mm²)




                                15


                                10


                                 5


                                 0
                                     0       10          20              30       40     50
                                                              Pressure (m)


                                 Figure 16 Change in area for uPVC 6 mm round hole




                                                              34
                                                                                                 Results


4.2.   uPVC 8 mm Round Hole


                                0.0014


                                0.0012


                                0.0010
                  Flow (m³/s)


                                0.0008

                                                                        Q = 0.0001H0.4878
                                0.0006
                                                                           R² = 0.9949
                                0.0004


                                0.0002


                                0.0000
                                         0          20         40             60            80
                                                          Pressure (m)


                                Figure 17 H-Q relationship for uPVC 8 mm round hole


The following values were found:
N1     = 0.4878
Cd     = 0.62
Re     50,000 – 160,000



                                60


                                50


                                40


                                30                       A = -0.01H + 50.27
                  Area (mm²)




                                20


                                10


                                 0
                                     0         20             40              60            80
                                                         Pressure (m)


                                 Figure 18 Change in area of uPVC 8 mm round hole




                                                         35
                                                                                            Results


4.3.   uPVC 10 mm Round Hole


                                 0.004




                                 0.003
                                                      Q = 0.0003H0.4920
                                                        R² = 1.0000
                   Flow (m³/s)




                                 0.002




                                 0.001




                                 0.000
                                           0    20       40            60   80       10 0
                                                             Pressure (m)


                           Figure 19 H-Q relationship for uPVC 10 mm round hole


The following values were found:
N1     = 0.4920
Cd     = 0.73
Re     120,000 - 250,000



                                 100


                                  80


                                  60
                  Area (mm²)




                                  40                 A = -0.01H + 78.54

                                  20


                                   0
                                       0       20       40            60    80       10 0
                                                          Pressure (m)


                                 Figure 20 Change in area of uPVC 10 mm round hole




                                                         36
                                                                                                 Results


4.4.   uPVC 12 mm Round Hole


                                0.004


                                                    Q = 0.0002H0.4820
                  Flow (m³/s)   0.003                 R² = 0.9996


                                0.002



                                0.001



                                0.000
                                          0             50                   100           150
                                                              Pressure (m)


                           Figure 21 H-Q relationship for uPVC 12 mm round hole


The following values were found:
N1     = 0.4820
Cd     = 0.47
Re     80,000 - 240,000



                                140


                                120


                                100


                                 80
                  Area (mm²)




                                                             A = -0.03H + 113.10
                                 60


                                 40


                                 20


                                  0
                                      0       20   40         60      80       100   120   140
                                                              Pressure (m)



                                Figure 22 Change in area of uPVC 12 mm round hole




                                                              37
                                                                                                   Results


4.5.   uPVC 8 mm Round Hole – Long pipe


                                0.0014


                                0.0012       Regular sample
                                             Q = 0.0001H0.4878
                  Flow (m³/s)   0.0010         R² = 0.9949

                                0.0008


                                0.0006


                                0.0004                                Long sample
                                                                    Q = 0.0001H0.4497
                                0.0002                                R² = 0.9994
                                0.0000
                                         0              20          40              60        80
                                                                Pressure (m)


           Figure 23 Comparison of H-Q relationship for uPVC 8 mm round holes


The following values were found (* = regular sample):
N1     = 0.4497                               (0.4878)*

Cd     = 0.59                                 (0.62)*

Re     50,000 - 130,000                       (50,000 – 160,000)*




                                80
                                                                     Regular sample
                                70                                  A = -0.01H + 50.27
                                60

                                50
                  Area (mm²)




                                40

                                30                                     Long sample
                                                                    A = -0.09H + 50.27
                                20

                                10

                                 0
                                     0       10         20    30         40    50        60   70
                                                              Pressure (m)



                Figure 24 Comparison of area change of uPVC 8 mm round holes




                                                              38
                                                                                                        Results


4.6.   uPVC 12 mm Round Hole – Long pipe


                                0.004


                                                Long sample
                                0.003         Q = 0.0003H0.4538
                                                R² = 0.9981
                  Flow (m³/s)




                                0.002



                                                                          Regular sample
                                0.001
                                                                          Q = 0.0002H0.4820
                                                                            R² = 0.9996

                                0.000
                                          0                     50                  100           150
                                                                     Pressure (m)


          Figure 25 Comparison of H-Q relationship for uPVC 12 mm round holes


The following values were found (* = regular sample):
N1     = 0.4538                                  (0.4820)*

Cd     = 0.62                                    (0.47)*

Re     60,000 - 200,000                          (80,000 – 240,000)*




                                140                                         Regular sample
                                                                          A = -0.03H + 113.10
                                120


                                100


                                 80          Long sample
                  Area (mm²)




                                          A = -0.20H + 113.10
                                 60


                                 40


                                 20


                                  0
                                      0         20         40        60      80       100   120   140
                                                                     Pressure (m)


             Figure 26 Comparison of area change of uPVC 12 mm round holes




                                                                     39
                                                                                 Results


For both the long pipe samples, the N1 value was lower than its regular sample
counterpart. However then Cd value was lower in the 8 mm hole of the long pipe than
the regular pipe and the Cd value was higher in the 12 mm hole of the long pipe than
the regular pipe. The Reynolds number remained in the same order.


In both cases, the regular sample was able to attain higher flow rates and higher
pressures. This implied that the fracture of the long samples were somehow limited.
Also from Figure 23 and Figure 25 it can be seen that the sample with the higher N1
value did not result in a higher flow rate (at a given pressure). This implied that a
higher N1 value would not necessarily result in a higher flow and thus a higher degree
of leakage.


From these results it is inclusive what the effect of the setup might be. Further tests
could produce enough data to better understand the effect of the setup with regard to
the stresses created around a fracture.


For the purposes of this study, all samples will be restricted in a similar fashion, that
of the regular setup. Note that all pipes would experience restriction of some kind
once buried anyway whether it be from the soil and/or from one pipe being joined to
another. Refer to recommendations for further work.




                                           40
                                                                                             Results


4.7.   uPVC 50 mm Longitudinal Split


                                0.0020



                  Flow (m³/s)   0.0015




                                0.0010




                                0.0005                           Q = 0.00002H1.0070
                                                                    R² = 0.8440

                                0.0000
                                         0        20        40         60    80       10 0
                                                             Pressure (m)


                Figure 27 H-Q relationship for uPVC 50 mm longitudinal split


The following values were found:
N1     = 1.0070
Cd     = 0.72
Re     40,000 - 60,000



                                70

                                60

                                50
                  Area (mm²)




                                40

                                30                               A = 0.38H + 25.00
                                20

                                10

                                 0
                                     0       20        40            60     80        10 0
                                                        Pressure (m)


                   Figure 28 Change in area of uPVC 50 mm longitudinal split




                                                            41
                                                                                Results


4.8.   uPVC 100 mm Longitudinal Split


                                0.005



                                0.004         Q = 0.0001H0.8935
                                                R² = 0.9658
                                0.003
                  Flow (m³/s)




                                0.002



                                0.001



                                0.000
                                          0    10          20         30   40
                                                       Pressure (m)



                Figure 29 H-Q relationship for uPVC 100 mm longitudinal split


The following values were found:
N1     = 0.8935
Cd     = 1.05
Re     15,000 - 70,000



                                160

                                140

                                120

                                100
                  Area (mm²)




                                 80

                                 60

                                 40                 A = 2.32H + 50.00
                                 20

                                  0
                                      0       10          20          30   40
                                                      Pressure (m)


                 Figure 30 Change in area of uPVC 100 mm longitudinal split




                                                     42
                                                                                       Results


4.9.    uPVC 150 mm Longitudinal Split



                               0.008


                                               N1 decr = 1.1483
                               0.006
                                                 R2 = 0.9985
                 Flow (m³/s)




                               0.004



                               0.002                                N1 incr = 1.5648
                                                                      R2 = 0.9975
                               0.000
                                       0   5       10          15        20       25
                                                     Pressure (m)


            Figure 31 H-Q relationship for uPVC 150 mm longitudinal split (run 1)


Here it is important to discuss the behaviour of the first run of this experiment. As the
pressure was increased, the fracture increased in area as expected with a N1 value of
1.5648. However as the pressure is decreased, the N1 value was 1.1483 which would
imply that the area did not return to its original size. After physically inspecting the
pipe, no change in area could be observed. An explanation could be that the pipe was
deformed when subjected to pressure for the first time due to its ductility or plasticity.
After a few moments though (time taken to reveal the fracture for inspection), the pipe
would return to its original state.


Run 2 and 3 did not exhibit this behaviour. This could imply that the material became
accustomed to the deformation and could take place more readily. The average N1
value of run 1 was 1.2649 and will be used for further analysis.




                                                     43
                                                                                                       Results



                               0.008

                                               Q = 0.0001H1.2626
                               0.006             R2 = 0.9537

                 Flow (m³/s)   0.004



                               0.002



                               0.000
                                           0       5        10             15      20        25
                                                                 Pressure (m)


              Figure 32 H-Q relationship for uPVC 150 mm longitudinal split


The following values were found:
N1     = 1.2626
Cd     = 0.667
Re     20,000 - 80,000



                               600


                               500


                               400
                 Area (mm²)




                               300


                               200


                               100                                      A = 19.28H + 75.00

                                 0
                                       0           5        10              15      20            25
                                                                 Pressure (m)


                  Figure 33 Change in area of uPVC 150 mm longitudinal split




                                                                 44
                                                                                    Results


4.10. uPVC 200 mm Longitudinal Split


                             0.008

                             0.007
                                         N1 decr = 0.9370
                             0.006
                                           R2 = 0.9943
                             0.005
               Flow (m³/s)




                             0.004

                             0.003

                             0.002                          N1 incr = 1.2817
                             0.001                           R2 = 0.9979
                             0.000
                                     0   2     4     6        8     10   12    14
                                                     Pressure (m)


           Figure 34 H-Q relationship for uPVC 200 mm longitudinal split (run 1)


Here we see similar behaviour as in § 4.9 for the first run. A weighted average of N1
value of 0.9495 was used for further analysis.


Figure 35 shows something quite different though. The third run was noticeably
different from the first two. Although the flow rate at a given pressure was much
lower for the third run, the N1 value was much higher.


Figure 36 shows that the initial area of the fracture could not be 100 mm² and
therefore permanent deformation has taken place. Only the results from run 1 and 2
will be used as this deformation can not be explained.




                                                      45
                                                                                                         Results


                              0.008
                                                Q = 0.0006H0.9475
                              0.007               R2 = 0.9647
                              0.006

                              0.005

                Flow (m³/s)
                              0.004

                              0.003
                                                                               Q = 0.0002H1.1421
                              0.002                                              R2 = 0.9928
                              0.001

                              0.000
                                           0          5        10              15             20   25
                                                                    Pressure (m)
                                                               Run 1&2        Run 3


                Figure 35 H-Q relationship for uPVC 200 mm longitudinal split


The following values were found:
N1     = 0.9475
Cd     = 1.32
Re     10,000 - 60,000


                                 400           A = 19.82H + 100.00
                                 350

                                 300

                                 250
                    Area (mm²)




                                 200

                                 150

                                 100                                                A = 9.67H + 45.70
                                 50

                                  0
                                       0              5        10              15             20    25
                                                                    Pressure (m)

                                                              Run 1&2                 Run 3


                   Figure 36 Change in area of uPVC 200 mm longitudinal split




                                                                    46
                                                                                             Results


4.11. uPVC 40 mm Circular Crack


                               0.00008


                 Flow (m³/s)   0.00006


                               0.00004


                               0.00002
                                                            Q = 0.000009H0.4423
                                                                R² = 0.9991
                               0.00000
                                         0        20        40         60     80      10 0
                                                             Pressure (m)

                   Figure 37 H-Q relationship for uPVC 40 mm circular crack

The flow rates for this pipe were too low and could therefore not be considered. The
following values were found though:
N1     = 0.4423
Cd     = 0.084
Re     1,000 - 3,000



                               25



                               20



                               15
                  Area (mm²)




                               10                                A = -0.03H + 20.00

                                5



                                0
                                    0        20        40            60      80       10 0
                                                        Pressure (m)


                          Figure 38 Change in area of uPVC 40 mm circular crack




                                                        47
                                                                                            Results


4.12. uPVC 80 mm Circular Crack


                              0.0020

                                                 Q = 0.0001H0.4771
                              0.0015
                Flow (m³/s)
                                                   R² = 0.9966
                              0.0010


                              0.0005


                              0.0000
                                             0     20      40        60     80        100
                                                            Pressure (m)


                         Figure 39 H-Q relationship for uPVC 80 mm circular crack

The following values were found:
N1     = 0.4771
Cd     = 0.73
Re     10,000 - 25,000



                                    50


                                    40


                                    30                           A = -0.02H + 40.00
                       Area (mm²)




                                    20


                                    10


                                     0
                                         0        20      40         60      80       100
                                                           Pressure (m)

                              Figure 40 Change in area of uPVC 80 mm circular crack




                                                            48
                                                                                             Results


4.13. uPVC 120 mm Circular Crack


                                0.0020




                  Flow (m³/s)   0.0015



                                0.0010


                                                                  Q = 0.0004H0.3073
                                0.0005
                                                                    R² = 0.9690

                                0.0000
                                          0        20    40           60    80        100
                                                             Pressure (m)


                Figure 41 H-Q relationship for uPVC 120 mm circular crack

The following values were found:
N1     = 0.3073
Cd     = 0.87
Re     10,000 - 20,000



                                70

                                60

                                50
                   Area (mm²)




                                40

                                30

                                20                  A = -0.25H + 60.00
                                10

                                  0
                                      0       20        40           60     80        10 0
                                                         Pressure (m)


                       Figure 42 Change in area of uPVC 120 mm circular crack




                                                         49
                                                                                             Results


4.14. uPVC 160 mm Circular Crack


                                0.0020



                  Flow (m³/s)   0.0015



                                0.0010



                                0.0005                           Q = 0.00005H0.7667
                                                                    R² = 0.9780

                                0.0000
                                         0        20        40         60   80        100
                                                            Pressure (m)

                Figure 43 H-Q relationship for uPVC 160 mm circular crack


The following values were found:
N1     = 0.7667
Cd     = 0.29
Re     5,000 - 20,000



                          160

                          140

                          120

                          100
                  Area (mm²)




                                80

                                60                               A = 0.58H + 80.00
                                40

                                20

                                 0
                                     0       20        40           60      80        10 0
                                                        Pressure (m)



                       Figure 44 Change in area of uPVC 160 mm circular crack




                                                        50
                                                                                                                Results


4.15. Cast Iron 6 mm Round Hole


                                    0.00008




                                    0.00006
                      Flow (m³/s)


                                                                                 Q = 0.00001H0.4818
                                    0.00004
                                                                                    R2 = 0.9997

                                    0.00002




                                    0.00000
                                              0        10        20        30         40        50    60   70
                                                                           Pressure (m)


                       Figure 45 H-Q relationship for Cast iron 6 mm round hole

The flow rates for this pipe were too low and could therefore not be considered. The
following values were found though:
N1     = 0.4818
Cd     = 0.081
Re     5,000 - 15,000


                               35

                               30

                               25
                  Area (mm²)




                               20                                               A = -0.02H + 28.27
                               15

                               10

                                    5

                                    0
                                        0         10        20        30         40        50        60    70
                                                                      Pressure (m)


                               Figure 46 Change in area of Cast iron 6 mm round hole




                                                                      51
                                                                                                       Results


4.16. Cast Iron 8 mm Round Hole

                                0.0014


                                0.0012


                                0.0010
                  Flow (m³/s)
                                0.0008


                                0.0006
                                                                              Q = 0.0002H0.4343
                                                                                R² = 0.9989
                                0.0004


                                0.0002


                                0.0000
                                         0        10        20    30           40    50     60    70
                                                                      Pressure (m)


                       Figure 47 H-Q relationship for Cast iron 8 mm round hole

The following values were found:
N1     = 0.4343
Cd     = 0.74
Re     80,000 - 170,000



                                60


                                50


                                40
                  Area (mm²)




                                30                                        A = -0.09H + 50.27

                                20


                                10


                                 0
                                     0       10        20        30          40      50    60     70
                                                                 Pressure (m)


                                Figure 48 Change in area of Cast iron 8 mm round hole




                                                                 52
                                                                                            Results


4.17. Cast Iron 10 mm Round Hole


                                0.0020




                                0.0015
                  Flow (m³/s)



                                0.0010


                                                                   Q = 0.0003H0.4425
                                0.0005                               R² = 0.9981


                                0.0000
                                          0    10    20     30       40    50    60    70
                                                            Pressure (m)


                    Figure 49 H-Q relationship for Cast iron 10 mm round hole

The following values were found:
N1     = 0.4425
Cd     = 0.64
Re     70,000 - 170,000


                                 90

                                 80

                                 70

                                 60
                  Area (mm²)




                                 50                       A = -0.15H + 78.54
                                 40

                                 30

                                 20

                                 10

                                  0
                                      0       10    20     30       40     50    60    70
                                                           Pressure (m)


                            Figure 50 Change in area of Cast iron 10 mm round hole




                                                           53
                                                                                                           Results


4.18. Cast Iron 12 mm Round Hole


                                      0.0020




                                      0.0015
                        Flow (m³/s)



                                      0.0010



                                                                      Q = 0.0003H0.4400
                                      0.0005
                                                                        R² = 0.9984


                                      0.0000
                                               0   5        10   15         20       25    30   35    40
                                                                      Pressure (m)


                    Figure 51 H-Q relationship for Cast iron 12 mm round hole

The following values were found:
N1     = 0.4400
Cd     = 0.64
Re     50,000 - 170,000



                               140

                               120

                               100
                  Area (mm²)




                                      80

                                      60                          A = -0.39H + 113.10
                                      40

                                      20

                                       0
                                           0           10              20                 30         40
                                                                 Pressure (m)


                           Figure 52 Change in area of Cast iron 12 mm round hole




                                                                 54
                                                                                           Results


4.19. Cast Iron 50 mm Longitudinal Split


                                0.0010


                                0.0008


                                0.0006
                  Flow (m³/s)




                                                              Q = 0.0001H0.4410
                                0.0004
                                                                R2 = 0.9967
                                0.0002


                                0.0000
                                         0        20         40             60        80
                                                        Pressure (m)

                Figure 53 H-Q relationship for Cast iron 50 mm longitudinal split

The following values were found:
N1     = 0.4410
Cd     = 1.16
Re     15,000 - 30,000



                                30


                                25


                                20
                  Area (mm²)




                                15                          A = -0.05H + 25.00

                                10


                                 5


                                 0
                                     0       10   20   30       40     50        60   70
                                                       Pressure (m)


                 Figure 54 Change in area of Cast iron 50 mm longitudinal split




                                                       55
                                                                                                   Results


4.20. Cast Iron 100 mm Longitudinal Split


                                0.0020



                  Flow (m³/s)   0.0015



                                0.0010                                  Q = 0.0003H0.4596
                                                                          R2 = 0.9874
                                0.0005



                                0.0000
                                         0        10         20             30      40   50   60
                                                                    Pressure (m)

            Figure 55 H-Q relationship for Cast iron 100 mm longitudinal split

The following values were found:
N1     = 0.4596
Cd     = 1.17
Re     7,000 - 30,000



                                70


                                60


                                50
                  Area (mm²)




                                40


                                30                     A = -0.05H + 50.00
                                20


                                10


                                 0
                                     0       10         20             30          40    50   60
                                                                  Pressure (m)


                Figure 56 Change in area of Cast iron 100 mm longitudinal split




                                                                  56
                                                                                               Results


4.21. Cast Iron 150 mm Longitudinal Split


                                0.0020



                  Flow (m³/s)   0.0015



                                0.0010


                                                                    Q = 0.0005H0.4219
                                0.0005
                                                                      R2 = 0.9907

                                0.0000
                                         0       5        10         15         20   25   30
                                                                Pressure (m)

            Figure 57 H-Q relationship for Cast iron 150 mm longitudinal split


The following values were found:
N1     = 0.4219
Cd     = 1.30
Re     5,000 - 20,000

                                90

                                80

                                70

                                60
                  Area (mm²)




                                50

                                40                   A = -0.57H + 75.00
                                30

                                20

                                10

                                 0
                                     0       5       10             15         20    25   30
                                                               Pressure (m)


                Figure 58 Change in area of Cast iron 150 mm longitudinal split




                                                               57
                                                                                          Results


4.22. Cast Iron 200 mm Longitudinal Split

                                    0.004



                                    0.003

                      Flow (m³/s)

                                    0.002


                                                               Q = 0.0006H0.4438
                                    0.001
                                                                 R2 = 0.9838

                                    0.000
                                               0    10   20            30    40      50
                                                              Pressure (m)

            Figure 59 H-Q relationship for Cast iron 200 mm longitudinal split

The following values were found:
N1     = 0.4438
Cd     = 1.22
Re     7,000 - 30,000



                               140.0


                               120.0


                               100.0


                                    80.0
                  Area (mm²)




                                    60.0                       A = -0.30H + 100.00

                                    40.0


                                    20.0


                                     0.0
                                           0       10    20           30     40      50
                                                          Pressure (m)


                Figure 60 Change in area of Cast iron 200 mm longitudinal split




                                                         58
                                                                                           Results


4.23. Cast Iron 40 mm Circular Crack

                                0.0012


                                0.0010


                  Flow (m³/s)   0.0008


                                0.0006

                                                       Q = 0.0001H0.4299
                                0.0004
                                                         R2 = 0.9973
                                0.0002


                                0.0000
                                         0        20        40           60   80    10 0
                                                               Pressure (m)


                Figure 61 H-Q relationship for Cast iron 40 mm circular crack

The following values were found:
N1     = 0.4299
Cd     = 1.22
Re     30,000 - 40,000



                                25



                                20



                                15
                  Area (mm²)




                                                               A = -0.02H + 20.00
                                10



                                 5



                                 0
                                     0       20           40           60     80    10 0
                                                            Pressure (m)


                  Figure 62 Change in area of Cast iron 40 mm circular crack




                                                            59
                                                                                       Results


4.24. Cast Iron 80 mm Circular Crack

                                0.0010



                                0.0008



                                0.0006
                  Flow (m³/s)



                                                              Q = 0.0003H0.4107
                                0.0004
                                                                R2 = 0.9980

                                0.0002



                                0.0000
                                         0       5    10             15   20      25
                                                          Pressure (m)


                Figure 63 H-Q relationship for Cast iron 80 mm circular crack


The following values were found:
N1     = 0.4161
Cd     = 1.30
Re     7,000 - 20,000



                                50


                                40


                                30
                  Area (mm²)




                                20                        A = -0.32H + 40.00

                                10


                                 0
                                     0       5       10           15      20      25
                                                      Pressure (m)

                  Figure 64 Change in area of Cast iron 80 mm circular crack




                                                      60
                                                                                              Results


4.25. Cast Iron 120 mm Circular Crack

                                0.0020



                                0.0015

                  Flow (m³/s)

                                0.0010



                                0.0005
                                                         Q = 0.0003H0.4228
                                                           R2 = 0.9911

                                0.0000
                                          0        10    20         30         40   50   60
                                                               Pressure (m)


                Figure 65 H-Q relationship for Cast iron 120 mm circular crack

The following values were found:
N1     = 0.4228
Cd     = 0.98
Re     9,000 - 25,000


                                70

                                60

                                50
                   Area (mm²)




                                40

                                30                              A = -0.18H + 60.00
                                20

                                10

                                  0
                                      0       10        20         30         40    50   60
                                                              Pressure (m)

                 Figure 66 Change in area of Cast iron 120 mm circular crack




                                                              61
                                                                                         Results


4.26. Cast Iron 160 mm Circular Crack

                                0.0025



                                0.0020



                                0.0015
                  Flow (m³/s)


                                                               Q = 0.0005H0.4119
                                0.0010
                                                                 R2 = 0.9878

                                0.0005



                                0.0000
                                         0        10    20           30    40       50
                                                            Pressure (m)


                Figure 67 H-Q relationship for Cast iron 160 mm circular crack

The following values were found:
N1     = 0.4119
Cd     = 1.17
Re     8,000 - 24,000


                           120

                           100

                                80
                  Area (mm²)




                                60

                                40                             A = -0.39H + 80.00
                                20

                                 0
                                     0       10        20           30     40       50
                                                        Pressure (m)

                 Figure 68 Change in area of Cast iron 160 mm circular crack




                                                        62
                                                                                           Results


4.27. Steel 6 mm Round Hole


                              0.00008




                              0.00006
                Flow (m³/s)




                              0.00004


                                                             Q =0.000009H0.4878
                              0.00002                           R2 = 0.9993


                              0.00000
                                        0         20          40            60        80
                                                       Pressure (m)


                               Figure 69 H-Q Relationship for Steel 6 mm round hole


The flow rates for this pipe were too low and could therefore not be considered. The
following values were found though:
N1     = 0.4878
Cd     = 0.07
Re     4,000 - 12,000



                               35

                               30

                               25

                                                       A = -0.01H + 28.26
                  Area (mm²)




                               20

                               15

                               10

                                5

                                0
                                    0       10   20     30      40     50        60   70
                                                        Pressure (m)


                                Figure 70 Change in area of Steel 6 mm round hole


                                                        63
                                                                                                Results


4.28. Steel 8 mm Round Hole


                                0.0012


                                0.0010


                                0.0008
                  Flow (m³/s)




                                0.0006

                                                                      Q = 0.0002H0.4390
                                0.0004
                                                                        R2 = 0.9987
                                0.0002


                                0.0000
                                         0        10        20         30       40   50    60
                                                             Pressure (m)


                                Figure 71 H-Q Relationship for Steel 8 mm round hole


The following values were found:
N1     = 0.4390
Cd     = 0.69
Re     60,000 – 140,000



                                60


                                50


                                40
                  Area (mm²)




                                30                                    A = -0.11H + 50.27
                                20


                                10


                                 0
                                     0       10        20             30        40   50    60
                                                                 Pressure (m)


                                  Figure 72 Change in area of Steel 8 mm round hole




                                                                 64
                                                                                             Results


4.29. Steel 10 mm Round Hole


                                0.0014


                                0.0012


                                0.0010
                  Flow (m³/s)


                                0.0008


                                0.0006                     Q = 0.0003H0.4215
                                                             R2 = 0.9990
                                0.0004


                                0.0002


                                0.0000
                                          0       10           20        30             40
                                                       Pressure (m)


                                Figure 73 H-Q Relationship for Steel 10 mm round hole


The following values were found:
N1     = 0.4215
Cd     = 0.69
Re     40,000 – 160,000



                                100


                                 80


                                 60
                  Area (mm²)




                                 40                    A = -0.42H + 78.54

                                 20


                                  0
                                      0         10            20         30             40
                                                         Pressure (m)


                                 Figure 74 Change in area of Steel 10 mm round hole




                                                         65
                                                                                            Results


4.30. Steel 12 mm Round Hole


                               0.0020



                               0.0015
                Flow (m³/s)




                               0.0010


                                                          Q = 0.0004H0.4359
                               0.0005
                                                            R2 = 0.9971

                               0.0000
                                         0       10           20        30             40
                                                      Pressure (m)


                               Figure 75 H-Q Relationship for Steel 12 mm round hole


The following values were found:
N1     = 0.4359
Cd     = 0.64
Re     55,000 – 160,000



                               140

                               120

                               100
                  Area (mm²)




                                80

                                60                     A = -0.40H + 113.10
                                40

                                20

                                 0
                                     0         10            20         30             40
                                                        Pressure (m)


                                Figure 76 Change in area of Steel 12 mm round hole




                                                        66
                                                                                       Results


4.31. Steel 50 mm Longitudinal Split

                                0.0010


                                0.0008


                                0.0006
                  Flow (m³/s)



                                0.0004                        Q = 0.0001H0.4022
                                                                R2 = 0.9915
                                0.0002


                                0.0000
                                         0        20              40     60       80
                                                         Pressure (m)

                Figure 77 H-Q Relationship for Steel 50 mm longitudinal split


The following values were found:
N1     = 0.4022
Cd     = 0.94
Re     18,000 – 27,000


                                25



                                20



                                15                     A = -0.05H + 25.00
                Area (mm²)




                                10



                                 5



                                 0
                                     0       20              40         60        80
                                                       Pressure (m)


                      Figure 78 Change in area of Steel 50 mm longitudinal split




                                                        67
                                                                                 Results


4.32. Steel 100 mm Longitudinal Split

                                0.0020



                                0.0015
                  Flow (m³/s)

                                0.0010                  Q = 0.0003H0.4096
                                                          R2 = 0.9956
                                0.0005



                                0.0000
                                         0        20         40        60   80
                                                        Pressure (m)

                Figure 79 H-Q Relationship for Steel 100 mm longitudinal split


The following values were found:
N1     = 0.4096
Cd     = 1.32
Re     10,000 – 34,000



                                60


                                50


                                40
                  Area (mm²)




                                30


                                20                     A = -0.18H + 50.00

                                10


                                 0
                                     0       20             40         60   80
                                                       Pressure (m)


                   Figure 80 Change in area of Steel 100 mm longitudinal split




                                                       68
                                                                                          Results


4.33. Steel 150 mm Longitudinal Split

                                0.0025


                                0.0020


                                0.0015
                  Flow (m³/s)



                                0.0010
                                                                 Q = 0.0005H0.3924
                                                                   R2 = 0.9945
                                0.0005


                                0.0000
                                          0        10    20           30    40       50
                                                             Pressure (m)

                Figure 81 H-Q Relationship for Steel 150 mm longitudinal split


The following values were found:
N1     = 0.3924
Cd     = 1.30
Re     8,000 – 25,000


                                100



                                 80



                                 60
                  Area (mm²)




                                 40                            A = -0.51H + 75.00

                                 20



                                  0
                                      0       10        20           30     40       50
                                                         Pressure (m)


                   Figure 82 Change in area of Steel 150 mm longitudinal split




                                                         69
                                                                                      Results


4.34. Steel 200 mm Longitudinal Split

                                0.005


                                0.004


                                0.003
                  Flow (m³/s)



                                0.002                        Q = 0.0008H0.4538
                                                               R2 = 0.9928
                                0.001


                                0.000
                                          0    10    20           30    40       50
                                                         Pressure (m)

                Figure 83 H-Q Relationship for Steel 200 mm longitudinal split


The following values were found:
N1     = 0.4538
Cd     = 1.81
Re     10,000 – 40,000



                                120


                                100


                                 80
                  Area (mm²)




                                 60                 A = -0.38H + 100.00

                                 40


                                 20


                                  0
                                      0       10    20            30    40       50
                                                     Pressure (m)


                   Figure 84 Change in area of Steel 200 mm longitudinal split




                                                     70
                                                                                              Results


4.35. Steel 40 mm Circular Crack

                                0.0010



                                0.0008



                                0.0006
                  Flow (m³/s)


                                                                Q = 0.0001H0.4771
                                0.0004
                                                                  R2 = 0.9704

                                0.0002



                                0.0000
                                          0          20         40        60             80
                                                           Pressure (m)


                     Figure 85 H-Q Relationship for Steel 40 mm circular crack


The following values were found:
N1     = 0.4771
Cd     = 1.33
Re     20,000 - 40,000



                                25


                                20


                                15
                   Area (mm²)




                                10                        A = -0.01H + 20.00

                                  5


                                  0
                                      0         20             40         60             80
                                                          Pressure (m)


                                Figure 86 Change in area of Steel 40 mm circular crack




                                                          71
                                                                                              Results


4.36. Steel 80 mm Circular Crack

                                0.0020




                                0.0015

                  Flow (m³/s)

                                0.0010




                                0.0005
                                                            Q = 0.0003H0.3811
                                                              R2 = 0.9918

                                0.0000
                                          0          20         40        60             80
                                                           Pressure (m)


                     Figure 87 H-Q Relationship for Steel 80 mm circular crack


The following values were found:
N1     = 0.3811
Cd     = 1.10
Re     12,000 - 28,000



                                50


                                40


                                30
                   Area (mm²)




                                20                        A = -0.14H + 40.00

                                10


                                  0
                                      0         20             40         60             80
                                                          Pressure (m)


                                Figure 88 Change in area of Steel 80 mm circular crack




                                                          72
                                                                                       Results


4.37. Steel 120 mm Circular Crack

                              0.0020




                              0.0015

                Flow (m³/s)

                              0.0010                       Q = 0.0004H0.3960
                                                             R2 = 0.9969

                              0.0005




                              0.0000
                                        0        10         20        30          40
                                                       Pressure (m)


                Figure 89 H-Q Relationship for Steel 120 mm circular crack


N1   = 0.3960
Cd   = 1.37
Re   12,000 - 24,000


                              70

                              60

                              50
                 Area (mm²)




                              40

                              30                      A = -0.38H + 60.00
                              20

                              10

                                0
                                    0       10             20         30       40
                                                      Pressure (m)


                        Figure 90 Change in area of Steel 120 mm circular crack




                                                      73
                                                                                         Results


4.38. Steel 160 mm Circular Crack

                                0.0025



                                0.0020



                                0.0015
                  Flow (m³/s)



                                0.0010
                                                     Q = 0.0006H0.3770
                                                       R2 = 0.9973

                                0.0005



                                0.0000
                                          0    10         20         30             40
                                                     Pressure (m)


                  Figure 91 H-Q Relationship for Steel 160 mm circular crack


The values were as follows:
N1     = 0.3770
Cd     = 1.35
Re     9,000 - 23,000



                                100


                                 80


                                 60
                   Area (mm²)




                                 40                 A = -0.66H + 80.00

                                 20


                                  0
                                      0       10         20         30          40
                                                    Pressure (m)


                          Figure 92 Change in area of Steel 160 mm circular crack




                                                    74
                                                                                                       Discussion



                                          5. DISCUSSION

5.1.    uPVC Round Holes




                     0.0030

                     0.0025                                         N1 = 0.4941
                                                                                        N1 = 0.4864
                     0.0020
         Flow (m³/




                     0.0015

                     0.0010                         N1 = 0.4511


                     0.0005
                                             N1 = 0.4737
                     0.0000
                              0      20      40            60       80            100   120           140
                                                           Pressure (m)
                                              6mm 8mm 10 mm 12 mm


                                  Figure 93 Comparison of uPVC round holes


As the fracture increases in size, the water loss increases. For Instance, at 2 bar, the
flow becomes three times more if the fracture size is doubled from 6 mm to 12 mm.


As fractures and pressure increase, the flow (or loss) would increase. With excessive
fracture sizes, high pressures cannot be attained which would retard losses but the
flow would still depend on the area of the fracture. Therefore it is important to
control the supply pressure in a municipal system but this will not solve water loss
problems. The best method would be to repair fractures.


The table below serves as a quick reference for the differences in the uPVC pipes in
terms of some characteristic values. The long samples were not included here.




                                                       75
                                                                                                         Discussion

Table 9 Results of all uPVC round holes
  Size                                    N1
                                                                        Cd                  Re
 (mm)       1st                 2nd            3rd         All
   6      0.4815              0.4744       0.4781       0.4768         0.63          40,000 – 100,000
   8      0.5105              0.4680       0.4777       0.4878         0.62          50,000 – 160,000
   10     0.4911              0.4910        0.494       0.4920         0.73          120,000 – 240,000
   12     0.4788              0.4820       0.4877       0.4820         0.47          80,000 – 240,000




                              0.56


                              0.54


                              0.52
                   N1 value




                              0.50


                              0.48


                              0.46
                                      0         2         4          6           8         10       12
                                                                  Hole size (mm)

                                           This Study   Greyvenstein   Cassa    Coetzer   Buckley




                                     Figure 94 All studies results of uPVC round holes


The figure above shows that all results for round holes in uPVC pipes were in the
same order. In this study, the wall thickness was 4 mm whereas all the other results
were from pipes with 3 mm walls. A thinner wall could result in more elasticity and
thus higher N1 values. If the N1 value was larger than 0.5, the fracture size increased
slightly under pressure.                   If the N1 value was lower than 0.5, the fracture size
decreased under pressure.


It is possible that the N1 value does not depend on the fracture size but upon the
material and fracture type. Consider a large hole that would leak a large volume of
water. The pressure in such a system would be low. This implies that a small hole
with high pressure could amount to the same water losses as that of the large hole.




                                                                 76
                                                                                                                                 Discussion


5.2.       uPVC Longitudinal Splits

                             0.008
                                          N1 = 0.9475
                                                                   N1 = 1.2626

                             0.006
             Flo w (m ³/s)




                             0.004

                                                                            N1 = 0.8935

                             0.002

                                                                                                                  N1 = 1.0070

                             0.000
                                     0          10        20       30       40        50          60   70    80      90         100
                                                                                 Pressure (m)


                                                                        50 mm 100 mm 150 mm 200 mm




                                           Figure 95 Comparison of uPVC longitudinal splits


As the pressure increases, the flow increases as the size of the fracture increases. As
the size of a fracture increases though, less pressure could be maintained.


Concerning the area changes, one must consider that not only the width can change
but also the length of the fracture. Physical inspection of the pipes after the test
showed that the length of the fracture was still the same.


Table 10 Results of all uPVC longitudinal splits
  Size                                               N1
                        st                     nd
                                                                                           Cd                Re
 (split)         1                         2               3rd             All
   50       1.1737                       1.2463         1.0157           1.0070            1.72        40,000 – 60,000
  100       0.8839                       0.8610         0.9803           0.8935            1.05        20,000 – 70,000
  150       1.2649                       1.2833         1.2869           1.2626            0.66        20,000 – 80,000
  200       0.9495                       0.9572                -         0.9475            1.32        10,000 – 60,000




                                                                                 77
                                                                                                  Discussion


All the results were well above 0.5 showing that the fracture increased in size as
pressure was applied. Note that the Cd value was also high except that of the 150 mm
sample. This sample showed a large change in area (see Figure 33).




                            2.00

                            1.80

                            1.60
                 N1 value




                            1.40

                            1.20

                            1.00

                            0.80

                            0.60
                                   0           50            100               150          200
                                                           Split length (mm)

                                        This Study   Greyvenstein      Cassa     Buckley




                            Figure 96 All studies results of uPVC longitudinal splits

First note that the areas of the splits of the various studies were not the same making it
difficult to compare the results (refer to section 2.5).                             The Greyvenstein results
showed a tear in the fracture hence permanently deforming the fracture and the
Buckley results were not for the same length of fracture as other studies.


We do see that the same trend was noticeable with other studies in that the N1 value
was also well above 0.5. This would lead to physical deformation of the fracture at
high pressures. The fracture would return to its original state in the absence of
pressure.


Considering the stresses generated around a fracture, this is quite probable. The stress
around the circumference is up to three times that of the stress parallel to the pipe.
This means that with a longitudinal split, the fracture can be opened more easily than
a round hole.




                                                        78
                                                                                                        Discussion


5.3.    uPVC Circular Cracks

In the next graph, the 40 mm sample was excluded as the flow rate values were well
below 0.00015 m/s³. All values below this point were deemed to be inaccurate.



                         0.0018

                         0.0016                                    N1 = 0.3073
                                                                                         N1 = 0.7667
                         0.0014

                         0.0012
                                                                                         N1 = 0.4771
           Flow (m³/s)




                         0.0010

                         0.0008

                         0.0006

                         0.0004

                         0.0002

                         0.0000
                                  0       20        40              60              80   100           1 20
                                                         Pressure (m)


                                                    80 mm      120 mm      160 mm




                                      Figure 97 Comparison of uPVC circular splits


The 80 mm and 120 mm sample showed a decrease in area as pressure increased.
Notice that the N1 values are below 0.5. The 160 mm sample show an increase in
area as pressure was applied and its N1 value was higher than 0.5. Thus far it can be
said that a leakage exponent of 0.5 is the threshold between increasing and decreasing
fracture sizes as pressure is applied.


It can be seen that the larger fractures will lead to more water loss from the flow –
pressure graphs. Notice though that the discharge coefficient for samples with a
decrease in area is large while the same coefficient for samples with an increase in
area is low.




                                                              79
                                                                                                                 Discussion

Table 11 Results of all uPVC circular cracks
  Size                                    N1
                                                                               Cd                     Re
 (split)     1                        2        3                 All
   40        -                        -        -                  -              -                    -
   80      0.4803              0.4660      0.4690               0.4771        0.73           10,000 – 25,000
  120      0.3081              0.3235      0.3307               0.3073        0.87           10,000 – 20,000
  160      0.7553              0.7676      0.8528               0.7667        0.29           5,000 – 20,000


From the previous discussion regarding stresses in the pipe, it would follow that
circular cracks would have the lowest N1 values. In this study, that result can be seen
for shorter cracks. However from the results report in the Cassa study, (as well as the
160 mm sample in this study) the circular cracks resulted in the highest N1 vales.




                               1.00



                               0.75
                    N1 value




                               0.50



                               0.25



                               0.00
                                      0        40                  80               120        160         200
                                                                        Cra ck length (mm)

                                                   This Study            Greyvenstein         Cassa




                                Figure 98 All studies results of uPVC circular cracks

It is important to note that the properties of the pipes in these different studies were
also different such as wall thickness. It could be possible that some flaw existed with
the 160 mm sample but each individual run of the test showed similar results.




                                                                      80
                                                                                                                             Discussion


5.4.       Cast Iron Round Holes

                           0.0020

                                                                                    N1 = 0.4400


                           0.0015                                                                             N1 = 0.4425
             Flow (m³/s)




                           0.0010                                                                            N1 = 0.4343




                           0.0005




                           0.0000
                                    0        10         20         30               40             50        60             70
                                                                     Pressure (m)

                                                              8 mm      10 mm            12 mm


                                        Figure 99 Comparison of Cast iron round holes


The 6 mm sample was not included in the results as the flow rate values were below
0.00015 m/s³. What seems to be apparent so far is that the N1 value seemed to be
relatively constant for each type of fracture. That is to say, the flow and pressure does
not affect the N1 value, but if the N1 value is known then we can relate a known
pressure to a volume of water loss.


Table 12 Results of all Cast iron round holes
  Size                                       N1
                                                                            Cd                          Re
 (split)            1                   2           3         All
    6                -                  -           -          -                -                       -
    8       0.4420                  0.4287        0.4388     0.4343        0.74                  80,000 – 170,000
   10       0.4637                  0.4390        0.4428     0.4425        0.64                  70,000 – 170,000
   12       0.4348                  0.4396        0.4452     0.4400        0.64                  50,000 – 170,000




                                                                   81
                                                                                            Discussion




                           0.52


                           0.50


                           0.48
                N1 value

                           0.46


                           0.44


                           0.42
                                  0     2         4            6           8      10   12
                                                            Hole size (mm)

                                               This Study                 Cassa




                            Figure 100 All studies results of cast iron round holes

The N1 values relate well to that of theory. The Cassa results were obtained from
samples with much thinner wall thicknesses which could account for the higher N1
values.


We now want to see if longitudinal splits result in higher N1 values shown here and
also if circular cracks result in lower N1 values shown here.




                                                        82
                                                                                                                              Discussion


5.5.       Cast Iron Longitudinal Splits

                             0.0040

                             0.0035                                                         N1 = 0.4438

                             0.0030

                             0.0025
             Flo w (m ³/s)




                             0.0020                                      N1 = 0.4219

                             0.0015                                                                  N1 = 0.4596

                             0.0010

                             0.0005                                                                             N1 = 0.4410

                             0.0000
                                      0          10         20           30            40            50            60         70
                                                                          Pressure (m)

                                                               50 mm 100 mm 150 mm 200 mm


                                          Figure 101 Comparison of Cast iron longitudinal splits


Seen here is similar to what has been observed in the previous comparison amongst
uPVC samples. The N1 values are slightly higher than that of the round holes.


Table 13 Results of all Cast iron longitudinal splits
  Size                                           N1
                                                                                  Cd                       Re
 (split)           1                        2           3          All
   50       0.4538                    0.4406          0.4127     0.4410         1.16              15,000 – 30,000
  100       0.5350                    0.4847          0.4097     0.4596         1.17               7,000 – 30,000
  150       0.4271                    0.4293          0.3998     0.4219         1.30               5,000 – 20,000
  200       0.4951                    0.4265          0.4317     0.4438         1.32               7,000 – 30,000




                                                                     83
                                                                                           Discussion




                           0.80



                           0.70



                N1 value   0.60



                           0.50



                           0.40
                                  0   50                  100                  150   200
                                                        Split length (mm)

                                           This Study                  Cassa




                 Figure 102 All studies results of cast iron longitudinal splits

Note here that the Cassa result was obtained from a sample with a very thin wall
thickness. This could account for the N1 value being higher than the results found in
this study. Interesting though is that the Cassa result seen here is higher than the
Cassa results for the round holes.




                                                    84
                                                                                                                                     Discussion


5.6.       Cast Iron Circular Cracks


                            0.0025

                                                                                N1 = 0.4119
                            0.0020



                            0.0015                                                            N1 = 0.4228
             Flo w (m³/s)




                            0.0010
                                                             N1 = 0.4107
                                                                                                                       N1 = 0.4299
                            0.0005



                            0.0000
                                     0        10        20     30          40        50          60         70    80     90      100
                                                                                Pressure (m)


                                                              40 mm        80 mm          120 mm        160 mm


                                         Figure 103 Comparison of Cast iron circular cracks


It has thus far become a given that as the fracture size increases the flow increases.
Note here that it was difficult to relate the result of the 40 mm sample to the others as
the pressure zone was completely different.

Table 14 Results of all Cast iron circular cracks
  Size                                             N1
                                                                                          Cd                      Re
 (split)            1                     2              3            All
   40       0.4269                   0.4573         0.4141          0.4299             1.22                 30,000 – 40,000
   80       0.4161                   0.4070         0.4048          0.4107             1.30                 7,000 – 20,000
  120       0.3995                   0.4247         0.4327          0.4228             0.98                 9,000 – 25,000
  160       0.3825                   0.4365         0.4221          0.4119             1.17                 8,000 – 24,000




                                                                            85
                                                                                               Discussion




                           1.00



                           0.75

                N1 value
                           0.50



                           0.25



                           0.00
                                  0       40           80              120         160   200
                                                             Crack length (mm)

                                                This Study                 Cassa




                           Figure 104 All studies results of cast iron circular cracks

The results show that the circular cracks do lead to the lowest N1 values. The Cassa
results again show that circular cracks have the highest N1 values.


The wall thickness used in the Cassa tests was very thin which would account for the
N1 values being higher than those found in this study. However when comparing all
the Cassa results to one another, the result for cast iron pipes is that circular cracks
have the highest exponents followed by the longitudinal splits and then the round
holes.


This study shows that longitudinal splits lead to the highest exponents, followed by
round holes and then circular cracks.




                                                         86
                                                                                                                        Discussion


5.7.       Steel Round Holes

                           0.0020

                           0.0018                                                       N1 = 0.4359

                           0.0016

                           0.0014                                                      N1 = 0.4215

                           0.0012
             Flow (m³/s)




                           0.0010

                           0.0008                                                                         N1 = 0.4397

                           0.0006

                           0.0004

                           0.0002

                           0.0000
                                    0          10         20              30             40               50            60
                                                                      Pressure (m)

                                                               8 mm      10 mm       12 mm



                                            Figure 105 Comparison of Steel round holes


The 6 mm sample was not included as it was regarded as inaccurate. Thus far, all
samples showed that a larger fracture produced a larger flow. Also the N1 value
seems to have no direct relation to the size of the fracture.


Table 15 Results of all Steel round holes
  Size                                        N1
                                                                               Cd                    Re
 (split)            1                   2           3          All
    6                 -                 -           -           -              -                      -
    8       0.4391                  0.4367      0.4390    0.4390           0.69          60,000 – 140,000
   10                 -             0.4203      0.4236    0.4215           0.69          40,000 – 160,000
   12       0.4241                  0.4331      0.4447    0.4359           0.64          55,000 – 160,000




                                                                    87
                                                                                                    Discussion




                          0.52


                          0.50


                          0.48
               N1 value

                          0.46


                          0.44


                          0.42
                                 0        2         4             6           8           10   12
                                                               Hole size (mm)

                                                  This Study      Greyvenstein    Cassa



                                 Figure 106 All studies results of steel round holes

Here we see that the Cassa results were very much like that of theory. This study
showed lower values for N1, perhaps as a result of a thicker wall with each sample.
Still, an exponent value higher than 0.5 would imply that the area of the fracture
would increase as pressure was applied.




                                                         88
                                                                                                                                 Discussion


5.8.       Steel Longitudinal Splits

                            0.005

                                                                                     N1 = 0.4476

                            0.004



                            0.003
             Flo w (m³/s)




                                                                            N1 = 0.3924

                            0.002
                                                                                                             N1 = 0.4096


                            0.001

                                                                                                                   N1 = 0.4022

                            0.000
                                    0         10          20      30            40            50        60           70          80
                                                                         Pressure (m)

                                                               50 mm   100 mm        150 mm    200 mm

                                          Figure 107 Comparison of Steel longitudinal splits


The exponents found here were very similar to that of the round holes. Normal there
is a clear difference between longitudinal splits and round holes as seen so far.


Table 16 Results of all Steel longitudinal splits
  Size                                           N1
                                                                                     Cd                      Re
 (split)           1                      2           3            All
   50       0.4102                      0.3646        -         0.4022           0.94              18,000 – 27,000
  100       0.4090                      0.4043     0.4160       0.4096           1.32              10,000 – 34,000
  150       0.3707                      0.3934     0.3989       0.3924           1.30              8,000 – 25,000
  200       0.4428                      0.4521     0.4538       0.4538           1.81              10,000 – 40,000




                                                                       89
                                                                                                                           Discussion




                                        0.80



                                        0.70



                             N1 value   0.60



                                        0.50



                                        0.40
                                               0          50                   100                    150        200
                                                                             Split length (mm)

                                                               This Study                     Cassa


                                        Figure 108 All studies results of steel longitudinal splits

The figure above shows that the N1 values found here are quite low but they are still
consistent with one another. The Cassa sample had a very thin wall which could lead
to a higher exponent value.




5.9.    Steel Circular Cracks

                         0.0025
                                                                                N1 = 0.3770

                         0.0020

                                                                                 N1= 0.3960
                         0.0015                                                                             N1 = 0.3811
          Flo w (m³/s)




                         0.0010

                                                                                                            N1 = 0.4771
                         0.0005



                         0.0000
                                    0              10     20            30             40              50   60            70
                                                                            Pressure (m)


                                                               40 mm        80 mm   120 mm       160 mm




                                                                        90
                                                                                                           Discussion

                                     Figure 109 Comparison of Steel circular cracks


Here the N1 values found were the lowest of all fracture types hence agreeing with
previous findings.


Table 17 Results of all Steel circular cracks
   Size                                  N1
                                                                       Cd                    Re
 (crack)       1                     2        3          All
    40      0.5020                   -    0.4354 0.4771               1.33          20,000 – 40,000
    80      0.3856 0.3620 0.3885 0.3811                               1.10          12,000 – 28,000
   120      0.3638 0.4020 0.4056 0.3960                               1.37          12,000 – 24,000
   160      0.3727 0.3807 0.3767 0.3770                               1.35              9,000 – 23,000




                              1.00



                              0.75
                   N1 value




                              0.50



                              0.25



                              0.00
                                     0            40           80             120           160      200
                                                                    Crack length (mm)

                                                       This Study                 Cassa




                                Figure 110 All studies results of steel circular cracks

Seen in the figure above is the consistency of the N1 values found for steel circular
crack samples. The Cassa results are similar to that of the cast iron samples with a



                                                                91
                                                                       Discussion


large variance in N1. This could be attributed to the pipe properties such as wall
thickness.




                                       92
                                                                                                              Discussion


5.10. All Round Holes


                 0.0030




                 0.0025        Steel 12     Cast Iron 12                                                     uPVC 12
                              N1 = 0.4359   N1 = 0.4400                                                     N1 = 0.4820




                 0.0020
                                                                                                             uPVC 10
                                                                                                            N1 = 0.4920


                                                                                                            Cast Iron 10
                                                                                                            N1 = 0.4425
   Flow (m³/s)




                 0.0015

                                                                                                            Cast Iron 8
                                                                                                            N1 = 0.4343


                                                                                                              Steel 8
                                                                                                            N1 = 0.4397
                 0.0010

   Steel 10                                                                                                  uPVC 8
  N1 = 0.4215                                                                                               N1 = 0.4878



                                                                                                             uPVC 6
                 0.0005
                                                                                                            N1 = 0.4768




                 0.0000
                          0          20          40          60              80           100   120   140
                                                                  Pressure (m)

                                                           uPVC      Cast Iron    Steel




                                            Figure 111 Comparison of All round holes




                                                                        93
                                                                                      Discussion


The figure below shows that the N1 value of uPVC is higher than that of cast iron and
steel which is very similar.




                      0.50


                      0.48


                      0.46
           N1 value




                      0.44


                      0.42


                      0.40
                                  6              8                 10            12
                                                       Hole size (mm)

                                                     uPVC   Cast Iron   Steel



                             Figure 112 Comparison of N1 values of round holes




                                                     94
                                                                                    Discussion


5.11. All Longitudinal Splits

                   0.008




                   0.007
                                                       uPVC 200
                                                      N1 = 0.9475

                                                       Steel 200
                                                      N1 = 0.4476
                   0.006

                                                      Cast Iron 200
                                                      N1 = 0.4438

                   0.005
                                                       uPVC 150
                                                      N1 = 1.2626
     Flow (m³/s)




                   0.004                              Cast Iron 150
                                                      N1 = 0.4219
                                                                                          uPVC 100
                                                        Steel 150                        N1 = 0.8935
                                                       N1 = 0.3924
                   0.003                                                                 Cast Iron 100
                                                                                         N1 = 0.4596

                                                                                          Steel 100
                                                                                         N1 = 0.4096
                   0.002
                                                                                          uPVC 50
                                                                                         N1 = 1.007

                                                                                         Cast Iron 50
                   0.001                                                                 N1 = 0.4410

                                                                                          Steel 50
                                                                                         N1 = 0.4022
                   0.000
                           0     20            40                     60      80   100
                                                    Pressure (m)


                                               uPVC     Cast Iron     Steel




                               Figure 113 Comparison of All longitudinal splits




Again the uPVC samples show much higher N1 values than the other two which are
similar.

                                                        95
                                                                                  Discussion




           1.25


           1.00
N1 value




           0.75


           0.50


           0.25


           0.00
                         50              100                150             200
                                                Split length (mm)

                                           uPVC      Cast Iron      Steel


                  Figure 114 Comparison of N1 values of longitudinal splits




                                               96
                                                                                                                     Discussion


5.12. All Circular Cracks

                                       Steel 160     Cast Iron 160           Steel 120              Cast Iron 120
                                      N1 = 0.3770    N1 = 0.4119            N1 = 0.3960             N1 = 0.4228

                  0.0022


                  0.0020


                  0.0018
                                                                                                                           uPVC 160
                                                                                                                          N1 = 0.7667
                  0.0016

                                                                                                                           uPVC 120
                  0.0014                                                                                                  N1 = 0.3026



                  0.0012
    Flow (m³/s)




                               Cast Iron 80                                Steel 80                                        uPVC 80
                               N1 = 0.4107                                N1 = 0.3811                                     N1 = 0.4771
                  0.0010


                  0.0008


                  0.0006


                  0.0004                              Steel 40        Cast Iron 40
                                                     N1 = 0.4771      N1 = 0.4299

                  0.0002


                  0.0000
                           0                  20          40                60                 80             100   120
                                                                      Pressure (m)


                                                                   uPVC    Steel   Cast Iron




                                              Figure 115 Comparison of All circular cracks




                                                                          97
                                                                                         Discussion


The table shows a definite similarity between cast iron and steel samples as with the
previous types of fractures but the uPVC samples do not.




                      1.00



                      0.75
           N1 value




                      0.50



                      0.25



                      0.00
                                   40             80                 120           160
                                                       Crack length (mm)

                                                       uPVC   Cast Iron    Steel



                             Figure 116 Comparison of N1 values of circular cracks




                                                       98
                                                                                      Conclusions



6. CONCLUSIONS


6.1.    Results Obtained

The following figure shows the leakage exponents for the samples tested in this
investigation and are reflected in the summary.




                           1.00



                           0.75
                N1 value




                           0.50



                           0.25



                           0.00
                                      uPVC              Ca st Iron            Steel

                                                Holes     Splits     Cracks




                                  Figure 117 Summary of leakage exponents

The following conclusions were made:

   •   Leakage exponents for round holes always occur in the same range and are
       similar to that of theory.
   •   Longitudinal splits result in slightly lower N1 values and circumferential
       cracks still lower.
   •   The size of a fracture does not seem to influence the N1 value.
   •   Type of material does have an influence on the N1 value but only as far as the
       hardness of the material, where harder materials have lower exponents.
   •   The shape of the fracture has some influence on the leakage exponents where
       the softness of the material can be influence by the circumferential stresses
       along a longitudinal split.



                                                    99
                                                                           Conclusions


6.2.    Conclusions

The best way to combat water loss is to have leaks repaired quickly and efficiently.
Even better would be to predict failures and replace sections of pipeline in advance.


The next best weapon would be to employ pressure management. There is no doubt
that reducing pressure would lead to water savings. Noted in this study was that very
small leaks resulted in zero flow at low pressures. Therefore this management would
have to be applied with discretion..


Pressure variation between peak and night flow must be kept minimal so as to reduce
additional stresses on the pipe material. Hence, minimum and maximum flow rates
can be found during minimum night flow and peak times respectively. The pressure
at these times can be chosen to meet the level of service needed and to have the
minimum amount of variation.

In doing so, the pipe would undergo fewer changes due to stress and thus so would
any fractures on the pipe. If the stresses around a fracture can be controlled then the
amount of leakage can be controlled.




                                          100
                                                                              Conclusions


6.3.    Recommendations

This investigation:

The amount of samples tested in this investigation seems ample for the results and
conclusions that were drawn.


Within each sample type, perhaps more fracture sizes could be tested so as to make
better comparisons between factors such as the coefficient of discharge and the
Reynolds numbers. Area change of water expelled is related to both these factors.
Strain gauges could be used to accurately measure any change in area.


To improve results, the setup could be changed. If water at a certain pressure is
allowed to flow in a circuit, which has a fracture, with a known volume for a known
time, then one could calculate the flow from the fracture. This would better simulate
a real distribution network.

Further investigations:

Increase N1 database:           The most obvious topic would be to further add to this
                                data base of leakage exponents by investigating other
                                fracture sizes, different materials and different shapes of
                                the fracture. By shape, it is meant that one could look
                                more closely at actual failed pipes due to the
                                manufacturing process or even by being struck
                                accidentally in the field.


Study of restricting factors:   Seen in this investigation was that fact that the setup
                                could have an effect on the results. An investigation
                                could show if this is indeed the case. It must also be
                                considered that in practice there are already a number of
                                restricting factors such as the soil itself (bedding and
                                backfill as per SABS), thrust blocks on bends and
                                diameter    changes,    pipes   joined   to   each   other,



                                            101
                                                                       Conclusions


                           installation of valves and such, etc. Can any of these
                           factors be changed or enhanced to reduce water loss.


Leak repairs:              Many studies have already covered the quality and
                           speed of repairs stating was is acceptable and what is
                           not. However in a developing country such as South
                           Africa, the is a large gap between ‘how to’ and ‘how it’s
                           done’.   Most agencies relate incentive programs to
                           number of complaints.         This method treats the
                           symptoms of water loss but not the causes. This would
                           mean developing a method where leaks are repaired but
                           also further problems are identified and handled
                           timeously.


Relationship of factors:   Where one factor is known then all others can be
                           calculated or assumed fairly accurately. For example if
                           Re is known, this would lead to flow and pressure and
                           Cd. This would lead to change in area and coefficients
                           of friction and contraction. This then could verify Cd as
                           well as flow and pressure. Hence an iterative procedure
                           could be developed. A field study would best address
                           this study where a known leak is unearthed and
                           measured in terms of pressure, flow and area. The pipe
                           is then left as it was and is then re-measured at regular
                           intervals to assess any changes.




                                        102

								
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