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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