This research work intends to develop a thumb rule to find a suitable location for the split pipe to get the optimal solution with less effort. Furthermore, the equivalent pipe concept was applied to find the exact lengths of the split diameters. To achieve this objective, two schemes were selected: Anytown network (a literature network), and a planned and flat Central Park housing scheme in Lahore, Pakistan. Two alternatives were developed by splitting the primary and secondary pipes at different locations in both networks. The hydraulic design of all the alternatives was defined using EPANET2, United States Environmental Protection Agency public domain software. Splitting primary and secondary pipes, away from the overhead tank, gave the optimized solution. It effectively reduced by 2% and 3–4% the cost of the Anytown and Central Park networks, respectively. This alternative was also hydraulically efficient, with 58% of the nodes meeting the desirable pressure head range of 12 to 14 m for the Central Park housing scheme. The study results revealed that the split pipe method can be successfully implemented for optimization of the water distribution network (WDN). Findings of the study can be used as a thumb rule for efficient and cost effective hydraulic design with less effort and resources for medium- and large-scale WDNs.

## INTRODUCTION

Water distribution networks (WDNs) are constructed to transport water from the water source to the consumers. The WDN is the most important part of the water supply system, which involves electromechanical elements such as pipes, valves, overhead tank (OHT) and pumps. The cost of WDN linear assets (pipes) can approach up to 80% of the total WDN cost (Stone & Webster Consultants 2004). This can be reduced by efficient (optimal) design of the WDN. The optimal design of the WDN is a complex problem. This is due to the nonlinear relationship between flow and head loss in pipes. The availability of discrete sizes of pipes in the market is another constraint in optimization. The cost function of the network is also a complex and nonlinear problem and induces great difficulty in design optimization of the WDN (Cunha & Sousa 2001; Eusuff & Lansey 2003).

Over the last decade, researchers were keen on working to find new optimization methods rather than using traditional optimization techniques such as the genetic algorithm (GA) in pipe network optimization (Simpson *et al.* 1994). In the GA, a set of commercially-available pipe diameters is chosen. The diameters of pipes are assigned binary coding. GA consists of three simple operators, i.e. reproduction, crossover, and mutation, and uses them for the production of coded strings. Coded strings, which can best describe sets of solutions, are investigated by the GA. The GA randomly starts generating the population of coded strings of WDN designs, and evaluates string appropriateness, called fitness. The fitness of the coded string is calculated by the cost of the distribution network, which includes the penalty cost (due to the lower pressure as compared to defined residual pressure) and the total network cost (capital cost). The strings which have a higher fitness value (lower cost) have a higher probability of being selected. In Dandy *et al.* (1996), the GA was compared to other techniques for pipe optimization.

Unlike the GA, the enumeration technique evaluates each possible option. A set of pipes of discrete sizes is selected and each pipe size is tested at each location, at each possible solution. For each solution, the hydraulic analysis is run to calculate the nodal pressures for given flows. Fitness cost, proportional to the magnitude of violations, is calculated. The total cost is calculated by adding the fitness cost and network cost. The solution with the lowest cost is selected (Gessler 1985).

Tabu search is another optimization technique, which effectively uses the adaptive memory, which may be short or long term. In the short term memory, the recent moves history is stored. On the other hand, in the long term memory, the history of all moves is kept on record. The method is based on the search for the best solutions in the near vicinity (Tospornsampan *et al.* 2007b).

Other optimization methods include linear programming (Alperovits & Shamir 1977; Sonak & Bhave 1993), two-phase composition methods (Fujiwara & Khang 1990; Eiger *et al.* 1994), nonlinear programming (Djebedjian *et al.* 2000), GA and pipe index vector (Vairavamoorthy & Ali 2005), modified GA (Montesinos *et al.* 1999), hybrid GA (Čistý & Bajtek 2009), multi-objective evolutionary algorithms (Wang *et al.* 2015), GA linked with integer linear programming (Haghighi *et al.* 2011), shuffled leapfrog algorithm (Eusuff & Lansey 2003), particle swarm optimization (Suribabu & Neelakantan 2006), differential evaluation (Vasan & Simonovic 2010) and more recently ant colony optimization (Maier *et al.* 2003; Zecchin *et al.* 2007).

In the split pipe method, the optimal design of the WDN is determined by finding the combination of commercially-available pipes with discrete diameters in place of a single pipe of continuous diameter in a street.

The split pipe method is also used in combination with simulated annealing for the optimization of WDNs (Tospornsampan *et al.* 2007a). Similarly, the split pipe method was successfully applied to optimize a WDN with a combination of GA and Tabu search (Tospornsampan *et al.* 2007b).

Although the split pipe method gives optimal and least cost design with the required pressure head at each node, it has certain demerits, which are: (1) the optimal solution may give discrete pipe sizes which are not commercially available, (2) the discrete size of diameter commercially available may not give an accurate optimal solution, (3) it may result in the minimization of the required pressure head at the nodes, (4) use of the split pipe method is very uncommon in practice, and (5) it requires a large number of iterations to find a best optimal alternative design of pipe network. These demerits cannot be ignored, but they can be overcome by taking special care while designing the WDN and by developing a thumb rule. The design engineers in the past had serious reservations regarding this method due to the above mentioned demerits.

This study was conducted to overcome the split pipe methodology demerits and prove it to be a worthy optimized method for a planned housing scheme WDN with the following additional objectives: (1) to find an optimized design for the medium scale pipe network by using the split pipe method, (2) to develop an appropriate criterion (thumb rule) for the split pipe method to avoid frequent iterations and to overcome demerits nos 3, 4 and 5 discussed above, and (3) to introduce the equivalent pipe concept to determine the split lengths exactly. The proposed approach will provide guidelines to design engineers to obtain optimal or near optimal WDNs with reduced time and effort. This research was carried out considering a flat area scheme and a WDN containing three OHTs, to fulfill the pressure head requirements.

## SPLIT PIPE METHODOLOGY

The design on the EPANET was run successfully using commercially-available pipe diameters (discrete sizes). Each time, the discrete size diameter was reduced by the integer 1 mm from the selected location in the WDN. After each trial, the software was run to check the pressure heads on nodes. It was easy to read pressure heads at nodes by assigning colors. The size reductions continued until the pressure head dropped to less than the required pressure head anywhere in the WDN. The minimum diameter which fulfilled the requirements (pressure head and flow) was obtained, but this diameter of pipe was not available commercially (continuous size). To overcome this problem, the equivalent pipe concept was applied. A pipe or set of pipes is said to be equivalent if they have the same head loss for the same amount of flow (Swamee & Sharma 2008).

*H*is the pressure head loss in metres,

*Q*is the flow in pipe in m

^{3}/s,

*L*is the length of pipe in metres,

*D*is the diameter of pipe in metres, and

*C*is the roughness coefficient. For the equivalent pipes system, the flow remains constant, so Equation (1) can be written as:

Suppose the initial diameter, which fulfilled the requirements and is available commercially is *D _{i}*. The minimum diameter which does not reduce pressure below the minimum required pressure is the minimum optimum diameter (continuous size)

*D*. Split the pipe into two diameters, one length

_{o}*L*of original diameter

_{i}*D*and another length

_{i}*L*of smaller diameter

_{s}*D*as compared to

_{s}*D*and

_{o}*D*. The lengths

_{i}*L*and

_{i}*L*after splits should be such that the head loss in the split pipe system and the optimum diameter pipe length are equal.

_{s}*D _{i}*,

*D*,

_{s}*D*and

_{o}*L*are known. By solving Equations (6) and (7), the exact lengths of

*L*and

_{s}*L*can be determined without disturbing the pressure heads at any node in the network.

_{i}It is suggested that the following methodology be followed for the split pipe design:

Design the WDN with discrete pipe diameter (commercially available diameters).

Start to reduce the pipe diameter to the continuous pipe sizes (commercially not available) away from the OHTs.

Select the diameters which allow a reduction in sizes without reducing pressure head to less than the minimum residual pressure head at any node.

Reduce the diameter until it reduces the pressure head at any node. The minimum diameter, which does not reduce pressure head to less than the minimum residual pressure head, would be known as the continuous diameter (

*D*), which is smaller than the initial diameter (_{o}*D*)._{i}Select two commercially available diameters; one less than the continuous diameter (

*D*) which would be known as (_{o}*D*), and another the same as the initial diameter (_{s}*D*)._{i}Apply the equivalent pipe concept to calculate the exact lengths to be split for both diameters

*D*and_{s}*D*._{i}

## RESULTS AND DISCUSSION

Two network examples were taken to apply the aforementioned methodology. One network was selected from the literature: Anytown network, and a second real network, the Central Park housing scheme in Lahore. The Anytown network has fewer loops and uneven terrain, while the Central Park scheme has even terrain and numerous loops.

### Illustrative example 1: Anytown network

An example from the literature was taken and the thumb rule was applied to it. The Anytown network is a hypothetical WDN introduced by Walski *et al.* (1987). It is a small network which contains all types of constraints and design problems that an actual WDN may contain.

#### Network description and design criteria

The network had 41 pipes, 22 nodes, four OHTs, and one pump. The lower and higher operating levels of water were kept at 68.576 m and 76.2 m, respectively. The topography of the town was uneven. The elevation, average demand and peak hourly demand of the nodes are given in Table 1. The fire flows required at the nodes J5, J6, J7, J11, J15, and J19 were 94.5, 94.5, 94.5, 63, 63, and 157.3 litres per second (LPS), respectively. The peak flow required was 1.8 times the average flow. The minimum residual pressure head required, in simultaneous fire and peak flow conditions, was 14 m (20 psi), while in only the peak flow condition the residual pressure head was kept at 28 m (40 psi).

Node ID | Elevation (m) | Base demand (LPS) | Demand (LPS) |
---|---|---|---|

Junc J1 | 6.1 | 31.5083 | 56.71 |

Junc J2 | 15.24 | 12.603 | 22.69 |

Junc J3 | 15.24 | 12.603 | 22.69 |

Junc J4 | 15.24 | 37.81 | 68.06 |

Junc J5 | 24.38 | 90.31 | 162.56 |

Junc J6 | 24.38 | 90.31 | 162.56 |

Junc J7 | 24.39 | 90.31 | 162.56 |

Junc J8 | 24.38 | 25.206 | 45.37 |

Junc J9 | 36.57 | 25.06 | 45.11 |

Junc J10 | 36.57 | 25.206 | 45.37 |

Junc J11 | 36.57 | 60.206 | 108.37 |

Junc J12 | 15.24 | 31.5083 | 56.71 |

Junc J13 | 15.24 | 31.5083 | 56.71 |

Junc J14 | 15.24 | 31.5083 | 56.71 |

Junc J15 | 36.57 | 98.0166 | 176.43 |

Junc J16 | 15.24 | 31.5083 | 56.71 |

Junc J17 | 15.24 | 31.5083 | 56.71 |

Junc J18 | 36.57 | 25.206 | 45.37 |

Junc J19 | 15.24 | 150.51 | 270.92 |

Node ID | Elevation (m) | Base demand (LPS) | Demand (LPS) |
---|---|---|---|

Junc J1 | 6.1 | 31.5083 | 56.71 |

Junc J2 | 15.24 | 12.603 | 22.69 |

Junc J3 | 15.24 | 12.603 | 22.69 |

Junc J4 | 15.24 | 37.81 | 68.06 |

Junc J5 | 24.38 | 90.31 | 162.56 |

Junc J6 | 24.38 | 90.31 | 162.56 |

Junc J7 | 24.39 | 90.31 | 162.56 |

Junc J8 | 24.38 | 25.206 | 45.37 |

Junc J9 | 36.57 | 25.06 | 45.11 |

Junc J10 | 36.57 | 25.206 | 45.37 |

Junc J11 | 36.57 | 60.206 | 108.37 |

Junc J12 | 15.24 | 31.5083 | 56.71 |

Junc J13 | 15.24 | 31.5083 | 56.71 |

Junc J14 | 15.24 | 31.5083 | 56.71 |

Junc J15 | 36.57 | 98.0166 | 176.43 |

Junc J16 | 15.24 | 31.5083 | 56.71 |

Junc J17 | 15.24 | 31.5083 | 56.71 |

Junc J18 | 36.57 | 25.206 | 45.37 |

Junc J19 | 15.24 | 150.51 | 270.92 |

#### Alternatives

The Anytown network was designed with discrete pipe sizes (single pipe design) and then the split pipe method was applied to it. The pipes were split away from the OHT and the methodology suggested in the ‘Split pipe methodology’ section above was applied. The split pipes' details are given in Table 2. The hydraulic design of all the alternatives was performed using EPANET2 (EPANET 2002). The splitting of pipes near the OHTs was also tried. The small network (few loops) did not allow pipes to be split near to the OHT without excessive disturbance of the nodal pressures.

Sr. no. | Pipe split | Di (mm) | L (m) | Do (mm) | Ds (mm) | Ls (m) | Li (m) | New pipes |
---|---|---|---|---|---|---|---|---|

1 | L22 | 200 | 1,828.7 | 170 | 150 | 721.3 | 1,107.4 | Ls = L44, Li = L22 |

2 | L39 | 200 | 1,828.7 | 170 | 150 | 721.3 | 1,107.4 | Ls = L45, Li = L46 |

3 | L32 | 150 | 1,828.7 | 75 | Nearby pipe split allowed reduction of diameter to 75 mm throughout the whole length | |||

4 | L35 | 150 | 1,828.7 | 120 | 100 | 579 | 1,249.7 | Ls = L47, Li = L48 |

5 | L17 | 200 | 1,828.7 | 170 | 150 | 721 | 1,107.4 | Ls = L49, Li = L50 |

6 | L16 | 200 | 1,828.7 | 180 | 150 | 401 | 1,427.7 | Ls = L51, Li = L52 |

Sr. no. | Pipe split | Di (mm) | L (m) | Do (mm) | Ds (mm) | Ls (m) | Li (m) | New pipes |
---|---|---|---|---|---|---|---|---|

1 | L22 | 200 | 1,828.7 | 170 | 150 | 721.3 | 1,107.4 | Ls = L44, Li = L22 |

2 | L39 | 200 | 1,828.7 | 170 | 150 | 721.3 | 1,107.4 | Ls = L45, Li = L46 |

3 | L32 | 150 | 1,828.7 | 75 | Nearby pipe split allowed reduction of diameter to 75 mm throughout the whole length | |||

4 | L35 | 150 | 1,828.7 | 120 | 100 | 579 | 1,249.7 | Ls = L47, Li = L48 |

5 | L17 | 200 | 1,828.7 | 170 | 150 | 721 | 1,107.4 | Ls = L49, Li = L50 |

6 | L16 | 200 | 1,828.7 | 180 | 150 | 401 | 1,427.7 | Ls = L51, Li = L52 |

#### Cost estimation

The WDN is always designed for optimal cost giving maximum efficiency while fulfilling requirements. Both the capital cost and the operational cost of water distribution system are important. Calculation of the operational cost is beyond the scope of this study. Hence, cost analysis and comparison are based on the capital cost of the WDN only. The commercially available pipe diameters and their respective composite cost are given in Table 3. Composite cost includes the transportation of pipes, excavation, laying down and labor cost. It also includes the removal of surplus debris, unused materials and byproducts. The cost was estimated by measuring the total lengths of pipes of different diameters. Lengths of different diameters were multiplied by respective per metre cost.

Pipe diameter (mm) | Per foot cost (Rs.) | Per metre cost (Rs.) |
---|---|---|

75 | 103.5 | 339.4 |

100 | 156.9 | 514.7 |

125 | 215.35 | 706.3 |

150 | 302.55 | 992.4 |

200 | 465.05 | 1,525.3 |

250 | 738.95 | 2,433.85 |

300 | 1,030.05 | 3,378.6 |

350 | 1,238.95 | 4,083.80 |

400 | 1,483.23 | 4,865.70 |

Pipe diameter (mm) | Per foot cost (Rs.) | Per metre cost (Rs.) |
---|---|---|

75 | 103.5 | 339.4 |

100 | 156.9 | 514.7 |

125 | 215.35 | 706.3 |

150 | 302.55 | 992.4 |

200 | 465.05 | 1,525.3 |

250 | 738.95 | 2,433.85 |

300 | 1,030.05 | 3,378.6 |

350 | 1,238.95 | 4,083.80 |

400 | 1,483.23 | 4,865.70 |

#### Results of Anytown network

### Illustrative example 2: Central Park housing scheme

The study area selected was a Central Park housing scheme located on Ferozepur Road, Lahore, Pakistan. The total area of the scheme was 9,716 Kanals (491 hectares). The housing scheme was well planned and consisted of commercial areas, mosques, schools and parks. The area of the selected scheme was flat. The elevation from mean sea level was 207 to 208 m. Water demand for different uses is given in Table 4. The population of the area was 50,000 persons. Three OHTs were used to maintain the required pressure head and water demand at nodes. A height of 19 m was selected for a cost effective overhead reservoir. The total demand of the community is 15,680 m^{3}/d. The WDN consisted of 560 nodes and 860 pipes. A grid iron (loop system) WDN was laid down.

Sr. no. | Water uses source | Water demand |
---|---|---|

1 | Per capita demand | 300 lit/day |

2 | School | 60 lit/student-day (250 student) |

3 | Commercial area | 3 lit/m^{2}-day |

4 | Parks | 7 lit/m^{2}-day |

5 | Hospital | 50 lit/bed (200 beds) |

6 | Mosque | 60 lit/follower-day (250 followers) |

7 | Petrol pump/shop | 20 lit/worker-day |

Sr. no. | Water uses source | Water demand |
---|---|---|

1 | Per capita demand | 300 lit/day |

2 | School | 60 lit/student-day (250 student) |

3 | Commercial area | 3 lit/m^{2}-day |

4 | Parks | 7 lit/m^{2}-day |

5 | Hospital | 50 lit/bed (200 beds) |

6 | Mosque | 60 lit/follower-day (250 followers) |

7 | Petrol pump/shop | 20 lit/worker-day |

#### Design of WDN (single pipe)

#### Alternatives description

Two different methodologies were adopted to split the pipe. The description of the alternatives is given below.

*(a) Alternative 1 (A1): Splitting primary and secondary pipes near the OHT.*When pipes of larger diameters were split near the OHT (encircled pipes in Figure 6) into a combination (one with smaller diameter), it reduced the required pressure head at many nodes. To cater for this problem, pipes of larger diameters were used away from the OHT. Only a few pipes could be split. The percentage of the nodes that contain a pressure head between 12–14 m increased in A1, i.e. 56% as compared to the single pipe design. Approximately 32% of the nodes had a pressure head between 14–16 m. Only 12% of the nodes had a pressure head greater than 16 m. The green zone area is greater in the A1 pressure head contour map as compared to the single pipe design. The yellow contour area also increased in A1 as compared to the single pipe design. The red area decreased in A1 as compared to the single pipe design option (Figure 7). Overall, in A1 the average pressure head was less compared to the single pipe design.

*(b) Alternative 2 (A2): Splitting primary and secondary pipes away from the OHT.*In this alternative, splitting primary and secondary pipes away from the OHT (encircled pipes in Figure 8) did not disturb the pressure at many nodes. The small disturbance of the nodal pressure which did occur was catered for by changing the tertiary pipe diameter.

A2 had the highest percentage of nodes with a pressure head ranging between 12–14 m, i.e. 58%. Approximately 31% of the nodes had a pressure head between 14–16 m. Only 11% of the nodes had a pressure head greater than 16 m.

### Summary of the results

The summary of the pressure head distribution at nodes of all the alternatives is given in Table 5.

Sr. No. | Alternative | Residual pressure head 10–12 m | Residual pressure head 12–14 m | Residual pressure head 14–16 m | Residual pressure head >16 m |
---|---|---|---|---|---|

1 | Single pipe design | 0% | 50% | 36% | 14% |

2 | A1 | 0% | 55% | 38% | 7% |

3 | A2 | 0% | 58% | 31% | 11% |

Sr. No. | Alternative | Residual pressure head 10–12 m | Residual pressure head 12–14 m | Residual pressure head 14–16 m | Residual pressure head >16 m |
---|---|---|---|---|---|

1 | Single pipe design | 0% | 50% | 36% | 14% |

2 | A1 | 0% | 55% | 38% | 7% |

3 | A2 | 0% | 58% | 31% | 11% |

Descriptive statistics | Single pipe | A1 | A2 |
---|---|---|---|

Mean | 14.39 | 14.17 | 14.04 |

Standard error | 0.07 | 0.06 | 0.06 |

Median | 14.15 | 13.88 | 13.74 |

Mode | 13.44 | 13.22 | 12.68 |

Standard deviation | 1.54 | 1.49 | 1.59 |

Sample variance | 2.38 | 2.21 | 2.53 |

Kurtosis | −0.09 | 1.27 | 0.55 |

Skewness | 0.67 | 1.23 | 0.98 |

Range | 6.84 | 6.92 | 6.86 |

Minimum | 12.02 | 12.01 | 12.01 |

Maximum | 18.86 | 18.93 | 18.87 |

Descriptive statistics | Single pipe | A1 | A2 |
---|---|---|---|

Mean | 14.39 | 14.17 | 14.04 |

Standard error | 0.07 | 0.06 | 0.06 |

Median | 14.15 | 13.88 | 13.74 |

Mode | 13.44 | 13.22 | 12.68 |

Standard deviation | 1.54 | 1.49 | 1.59 |

Sample variance | 2.38 | 2.21 | 2.53 |

Kurtosis | −0.09 | 1.27 | 0.55 |

Skewness | 0.67 | 1.23 | 0.98 |

Range | 6.84 | 6.92 | 6.86 |

Minimum | 12.02 | 12.01 | 12.01 |

Maximum | 18.86 | 18.93 | 18.87 |

#### Cost comparison

## CONCLUSIONS

The study was conducted to find the appropriate methodology to split pipes for the optimization of a WDN. The equivalent pipe concept was applied to find the exact lengths of the split pipes. Furthermore, the study investigated the location where the split of pipes is more beneficial. A small network (Anytown network), and a large network (Central Park network) were selected to evaluate the suggested methodology. Application of the split pipe method saved 2% of the cost for the Anytown network. In the case of the large network, Central Park, the alternative A2 cost was less compared to the single pipe design and A1, i.e. 3.12% and 6.57% lower, respectively. It is concluded that the split pipe method gives reliable, robust, practicable and optimized solutions for medium- and large-scale water supply schemes. Sometimes it gives unreliable and unrealistic solutions, but this problem is eradicated by developing a thumb rule to split primary and secondary pipes away from the OHT.

In the small network, splitting pipes away from the OHT did not affect the pressure distribution substantially. On the other hand, in the large network, the split of pipes away from the OHT improved the pressure distribution and avoided excessive pressure. In A2, the maximum percentage of the nodes had pressure head in the desired residual pressure head range, i.e. 12–14 m. The single pipe and A2 had higher average pressure than A1. Higher pressure heads are avoided in WDNs as they cause more leakage losses and reduce the pipe life. Therefore, splitting pipes away from the OHT would help with increasing pipe life and reduction in leakages. So, as the size of the network increased the split pipe method application advantages improved. The split pipe method is uncommon in practice because it requires a large number of iterations. Now, the thumb rule, developed in this study, would reduce the iterations and less computation time would be required to design the optimal solution of any medium- or large-scale WDN. Furthermore, the exact lengths of the split parts of pipes can be determined using the equivalent pipe concept, to optimize pairs of pipes without disturbing the nodal pressure.