computer aided water distribution network model

8/9/2019 Computer Aided Water Distribution Network Model

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CHAPTER ONE

INTRODUCTION

Water distribution is an important component of public utilities. A good

water distribution system should be able to deliver potable water over spatially

extensive areas in required quantities and under satisfactory pressures. Water

pressure at industries should be different from those required at home. An

important tool that is used to analyse water distribution network are models

based on conventional approaches of Darcy- Weisbachs headloss computation

and von-Karmans friction factor for turbulent flow and computer method.

SCOPE OF WORK

The water supply piping network model used is that of Hardy-

Cross(1936). The method permits the accurate computation of the flow through

the system and the resulting headloss. It is a trial and error method by which

corrections are applied to assumed piezometric heads or assumed flow rates

until an acceptable hydraulic balance of the system is achieved. Nwaogazie, I.

and Okoye, D. (1994).

CHAPTER TWO

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LITERATURE REVIEW

INTRODUCTION

Water supply distribution network model (WASDIM) is based on the

conventional approaches of Darcy-Wiesbachs headloss computation and Von-

Karmans friction factor for turbulent flows. Mathematical modelling of piping

systems involves two main approaches; the empirical method and the scientific

method. Simon, (1981). An example of the empirical method is the Hazen-

William equation, while for the scientific method is the Darcy-Weisbachs

formula and Von Karmas friction factor formula.

2.1 EMPIRICAL METHOD

The Hazen-William Equation is one of the early empirical equations that

is still widely in use today. It has an inherrent uncertainty in the determination

of its coefficient of friction which is assumed to be a constant but indeed is not.

2.2 SCIENTIFIC APPROACH

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The Darcy-weisbach formula is a scientific approach for headloss

computation and Von Karmas friction factor formula for turbulent flow

conditions. Their equations are:

hl= flv2/2Dg_ _ _ _ _ _ _ _ _ _2.1

and 1/f1/2 = 2log D/e + 1.14_ _ _ _ _ _ _ _2.2

equations 2.1 and 2.2 are combined for maximum flow to give:

Q = [2g (log D/e + 1.14) D^2.5] (h/L) 1/2_ _ _ _2.3

and Q = K (h/L) ^1/2 = KS_ _ _ _ _ _ _ _2.4

2.3 HARDY-CROSS METHOD

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The network analysis through Hardy-Cross method for initial

piezometric heads involves the principle of continuity, which involves

all continuity equation being satisfied. This is given by:

Q = Q_ _ _ _ _ _ _ _ _ _2.5

On account of the error, Q assumed piezometric heads must be

adjusted by an amount H. The aggregate effect ofH on the excess

Q at a junction may be evaluated by the weighted formula (Simon,

1981)

H = 2Q/ (Q/h)_ _ _ _ _ _ _ _ _2.6

CHAPTER THREE

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METHODOLOGY

The method involved in carrying out this work is by use of the

computer program (WASDIM). Pressure heads were assumed for the

internal nodes. Both the nodes and flow designations were numbered

and direction of flow were indicated by arrows. This was done in such

a way that water flows from a high pressure to a low pressure. As the

water flows down to the exit point, the pressure reduces until it

reaches the given pressure for the dead end.

Input data files was created for both networks and the input data

was entered using WATFOR 77. The files were taken to the

Department of Civil and Environmental Engineering Computer-Aided

Desing lab and the program was executed using the WASDIM

software by entering both input file name and output file name. The

output file name was saved in dot res, while the input file name was

saved in dot dat. The result which shows the computed error on

delta H was extracted and printed and attached in the appendix of the

report. Network diagrams were also drawn using autocard.

CHAPTER FOUR

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RESULTS

The results obtained for the network model is presented in tables

and graphs as shown below. The pipe was steel. The length and width

of the water distribution network was given. The length and diameter

of the diagonal was assumed,. The unit used was the metric system of

units. The computer generated results for both networks were attached

in the appendix.

BASIC PARAMETERS AND ASSUMPTIONS

Pipe length = 500m

Pipe width = 450m

Length of diagonal = 600m (assumed)

Pipe diameter (l) = 0.2500m

Pipe diameter (w) = 0.2000m

Pipe diameter (Diagonal) = 0.3000m (assumed)

Results for network B1.

Table 4.1 Pipe length and diameter.

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Pipe no. Pipe length(m) Pipe diameter(m)

1 450 0.2000

2 500 0.2500

3 450 0.2000

4 600 0.3000

5 450 0.2000

6 500 0.2500

7 600 0.3000

8 450 0.2000

9 500 0.2500

10 500 0.2500

11 450 0.200012 600 0.3000

13 500 0.2500

14 450 0.2000

Table 4.2 Assumed Heads and final Heads after 7 iterations.

Junctions Guessed Head Current Head

1 0.12000E+02 0.12000E+02

2 0.10500E+02 0.95880E+01

3 0.95000E+01 0.88117E+01

4 0.85000E+01 0.81725E+01

5 0.75000E+01 0.78312E+01

6 0.65000E+01 0.72555E+01

7 0.60000E+01 0.68542E+018 0.75000E+01 0.66972E+01

9 0.50000E+01 0.50000E+01

Table. 4.3 Number of iterations and Computed error on delta-H.

No. of iterations Computed error on delta-H

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1 0.88203E+00

2 0.80327E+00

3 0.72725E+00

4 0.65587E+00

5 0.59019E+00

6 0.55102E+00

7 0.53360E+00

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Fig. 4.1 computed piezometric head error sum of junctions

against iteration number.

Results for network B29


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Table 4.4 Pipe length and diameter.

Pipe no. Pipe length(m) Pipe diameter

1 450 0.2000

2 500 0.25003 500 0.2500

4 450 0.2000

5 500 0.2500

6 450 0.2000

7 450 0.2000

8 450 0.2000

9 500 0.2500

10 450 0.200011 450 0.2000

12 500 0.2500

13 500 0.2500

14 450 0.2000

15 500 0.2500

16 450 0.2000

17 500 0.2500

18 450 0.2000

19 450 0.2000

20 450 0.2000

21 500 0.2500

22 500 0.2500

23 450 0.2000

24 500 0.2500

25 450 0.200026 500 0.2500

27 450 0.2000

28 450 0.2000

29 500 0.2500

30 500 0.2500

31 500 0.2500

32 500 0.2500

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Table 4.5 Assumed Heads and final Heads after 10 iterations.

Junctions Guessed Head Current Head

1 0.25000E+02 0.25000E+022 0.22000E+02 0.21131E+02

3 0.20000E+02 0.20133E+02

4 0.19500E+02 0.20395E+02

5 0.20000E+02 0.18645E+02

6 0.21000E+02 0.21441E+02

7 0.19500E+02 0.18784E+02

8 0.19000E+02 0.18732E+02

9 0.18500E+02 0.18093E+02

10 0.17000E+02 0.17037E+02

11 0.15000E+02 0.16661E+02

12 0.16000E+02 0.15728E+02

13 0.15500E+02 0.15591E+02

14 0.15000E+02 0.14610E+02

15 0.13000E+02 0.13354E+02

16 0.12000E+02 0.12880E+02

17 0.14000E+02 0.13736E+02

18 0.13000E+02 0.13318E+02

19 0.10000E+02 0.11803E+02

20 0.80000E+01 0.99050E+01

21 0.75000E+01 0.75000E+01

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Table. 4.6 Number of iterations and Computed error on delta-H.

No. of iterations Computed error on delta-H

1 0.22972E+01

2 0.19632E+01

3 0.16372E+01

4 0.13685E+01

5 0.11123E+016 0.98167E+00

7 0.96192E+00

8 0.94751E+00

9 0.93775E+00

10 0.92885E+00

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Fig. 4.2 computed piezometric head error sum of junctions

against iteration number.

CHAPTER FIVE

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CONCLUSION

In conclusion, the computer program (WASDIM) can be used

effectively to design water distribution network for any community or

location. This has been achieved for the two network problems

presented in this report by verifying that the error diminishes as the

number of iterations increases.

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computer aided water distribution network model

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