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Pipe Network Proposal
Pollux City Industrial Park
Henry L. Jones, II
Summary
Introduction
Whenever industries search for a site for the location of a new plant, one of their first concerns is the availability of water. The city of Pollux has taken a very important step in initiating the process for the construction of a water pipe network for its new industrial park. H. L. Jones Consulting has been very pleased with the attitude of the city of Pollux and the Pollux City Council, and we hope that the Council will be pleased with the work of Jones Consulting. We have designed three feasible variations of the same network, each having its own positives and negatives. The following report describes the basics of each system, sketches of the systems, a breakdown of system costs, and a description of the methods used to produce these designs.
System Basics: System One
No Pumps -- Reliability and Economy
A basic description of this system would be a large loop that is the main water carrier to all ten outlets with the addition of a cut-off pipe that divides the loop in half. After a great deal of trial and error, this was determined to be the best layout for a system which did not include any pumps. For simplicity's sake, the system was optimized exclusively using each of the two locally available pipe types. Once the validity of this layout had been established, different pipe types were substituted and combined in one system. This combination system was the least expensive system found over a fifteen-year period. A more detailed description of the optimization system used and the actual lengths, types, and flow rates of the pipes are given later in this report.
System Basics: System Two
Small Pipes -- Least Expensive Installation
Using the pipe layout of System One, this System incorporates two pumps located next to the reservoir. The pumps raise the initial head of the network and as a result smaller diameter pipes may be used. As in System One, different types of pipe were substituted into the system until the most economical combination was found. This system uses much smaller pipe than either of the other systems.
System Basics: System Three
Large Pipes -- Planning for the Future
Basically the same as System One, this system is the most expensive system of the three designs but far and away the most expandable. The use of large pipes makes this network able to handle almost anything required of it. This system should have no difficulty handling increases in flow rate, number of outlets, or decrease in reservoir head. The smoother pipe was chosen for this system, and although larger pipe was available, the decrease in head loss was not worth the extra one hundred thousand dollars the larger pipe would cost.
System Sketches
System One
Figure 1 shows the pipe diameter, roughness, and length of pipe used in each segment. The combination of materials, as stated earlier, was used to minimize the cost. Although the different pipe types may seem confusing, Jones Consulting feels that any company employed to install the system would not have any difficulty installing this system without confusion about the type of pipe to use. As one may notice from this figure, the diameters of the pipes are smaller in the segments further away from the reservoir. This reduction is necessary to reduce costs, and is possible due to the much smaller flow rates (shown in Figure 2) in these pipes.
Figure 2 shows the element number, computed flow rate, and direction of the flow in each segment. As just mentioned, the flow in the pipes far away from the reservoir is much smaller than those close to the reservoir. The cut-off pipe noted in the figure will normally carry a small flow, but it has mainly been installed so that the system can recover more easily if there is a problem with another pipe.
Figure 3 shows a 3-D graphical representation of the pressure heads at each pipe junction and hydraulic grade lines which connect these heads. Figure 4 gives the exact value for these heads at each junction. These figures show that the pressure heads decrease as the distance from the reservoir increases. This head loss is due only to the friction of the pipes because all of the junctions are at the same altitude and all junctions are at atmospheric pressure.
As stated above, there were no pumps used in this system, so a sketch of the locations and characteristics of pumps is not necessary.
System Two
Figure 5 shows the pipe diameter, roughness, and length of pipe used in each segment. The combination of materials, as in System One, minimizes the cost of the network. These pipe diameters are the smallest of the three systems in this report.
Figure 6 shows the element number, computed flow rate, and direction of the flow in each segment. As in System One, the flow in the pipes far away from the reservoir is much smaller than those close to the reservoir. Again, the cut-off pipe noted in the figure will normally carry a flow, but it has mainly been installed so that the system can recover more easily if there is a problem with another pipe.
Figure 7 shows a 3-D graphical representation of the pressure heads at each pipe junction and hydraulic grade lines which connect these heads. Figure 8 gives the exact value for these heads at each junction. These figures show that the pressure heads decrease as the distance from the reservoir increases. This head loss is due only to the friction of the pipes because all of the junctions are at the same altitude and all junctions are at atmospheric pressure.
Figure 8 also shows the locations of the pumps used in this system, and the characteristics of the pumps are given in Table 1 below. Each of the three pumps available were tried in each position, and the final combination produced the highest head throughout the entire system.
Table 1. Pump Characteristics
Element #
Q (m3/s)
H (m)
Power (W/s)
Installation Cost ($)
13
.1005
18.964
18696.7
5000
14
.1245
17.610
21507.9
6000
System Three
Figure 9 shows the pipe diameter used in each segment. This system only uses .3 m pipe of the .002 mm roughness type. This system would be very easy to install.
Figure 10 shows the element number, computed flow rate, and direction of the flow in each segment. Although the flow in the pipes far away from the reservoir is much smaller than those close to the reservoir, this system is designed to handle much larger flow rates at any section of the network. The cut-off pipe noted in the figure will normally carry a flow, but it has mainly been installed so that the system can recover more easily if there is a problem with another pipe. Also, this pipe is large enough to handle the flow that would be required if another reservoir was installed there at a later date.
Figure 11 shows a 3-D graphical representation of the pressure heads at each pipe junction and hydraulic grade lines which connect these heads. Figure 12 gives the exact value for these heads at each junction. These figures show that the pressure heads decrease as the distance from the reservoir increases. This head loss is due only to the friction of the pipes because all of the junctions are at the same altitude and all junctions are at atmospheric pressure.
As with System One, there were no pumps used in this system, so a sketch of the locations and characteristics of pumps is not necessary.
Project Cost
System One
Because System One does not contain any pumps, the cost of installation will be the total cost of the system for the fifteen year period. The total cost for the fifteen year life of this system is $202,812.47. All costs are included in this amount, including valves, joints, and meters. So that incidental costs may be included, $205,000 should probably be budgeted for this project. The breakdown of this cost is given below in Table 2 below. The cost analyses of the preliminary systems as well as the final combination system as they were initially performed is shown in Appendix A.
Table 2. System One Cost Composition
Pipe #
Unit Cost ($)
Length (m)
Total Cost ($)
1
210
120.83
25374.40
2
200
100
20000.00
3
50
100
18000.00
4
50
148.66
22299.11
5
90
130
11700.00
6
70
70
4900.00
7
90
100
9000.00
8
150
78.1
11715.38
9
150
100
15000.00
10
200
172.63
34525.36
11
250
126.49
25298.22
12
25
200
5000.00
Total Cost:
202812.47
System Two
Because System Two does contain pumps, the cost composition is made up of installation and operating costs. The installation costs broken down by pipe are shown in Table 3. The total cost for the installation of this system, as found in Appendix A, is $163,867.89. Appendix B shows the cost of running the pump required for this system for fifteen years. This cost would be at least $187,213, given that the cost of power does not increase within that period of time. As one can see, this amount is even greater than the cost of installation. Because further details about the pump are not available, an estimation of the maintenance required for a fifteen-year life span was not possible. Therefore, no maintenance costs are included in this cost. The total fifteen-year cost of this system is $351,081.
System Three
Although there are no pumps, System Three is by far the most expensive of the three systems. All 1450 feet of pipe are .3 m in diameter and cost $250 per meter, so the total cost of this system is $362,500. There are no maintenance or operation costs because there are no pumps. Over a very long period of time, this System may turn out to be the best of the three designs, because there is no maintenance and the system is very versatile.
Discussion of Methods
Computation Method
For the complicated process of determining flow through a system of pipes, hand calculation would have been extremely time-consuming. A BASIC program was available which applied the Hardy-Cross loop balancing scheme to this problem. The program was run multiple times with many different pipe system setups. The three systems presented to the Council are the three best found using extensive trial and error. Copies of the output of this program concerning the three chosen systems are given in Appendix C.
Optimization Method
The task of finding the optimum pipe diameter for extensive systems such as the ones designed for the Pollux Industrial Park is the most time consuming aspect of the design process. In an attempt to optimize these diameters using theoretical means, H. L. Jones Consulting devised a preliminary system for determining pipe diameters, shown in Appendix D. Using Mathcad, this system attempts to find the diameters which generate a constant drop in head loss per unit of length.
The theory behind this optimization idea is not confusing. Because increases in pipe diameter caused increases in cost, H. L. Jones Consulting wanted to find the smallest diameters possible. The main question was how to determine whether the diameter of a certain pipe or neighboring pipes should be changed. The changes in diameter greatly affected the amount of head loss in the pipes. From experience in managerial economics, Jones Consulting knew that the optimum amount of head loss for a pipe would be related to how its length compared to the total length of the system. In other words, short pipes should have less total head loss than long pipes. If the amount of head loss per meter was the same for the entire system, then the rate of head loss would be optimized. Head loss was controlled by the diameter of the pipes, and as a result the diameters of the pipes would be optimized as well. This process is shown and explained further in Appendix D. The diameters found using this method were used as initial values, and the final diameters were determined using trial and error. Nonetheless, the overall idea of constant head loss per meter was used in all optimizing methods.
Major Decisions
Figure 13 shows the relationship between the price of the pipes available versus the diameter. The head loss for a given flow rate is a function of velocity, which is a function of the area, which is a function of the diameter. This graph therefore shows that the smaller diameter pipes are a much better value for incremental reduction of the head loss, even if the total head loss might be greater. From .05 m to .1 m, the slope is not very great. The .15 m and .2 m pipes seem to be about the same. The most dramatic aspect of the graph is the large increase from the .25 m pipe to each subsequent pipe. From this graph, it was determined that every attempt should be made to reduce the diameters of the pipes to .2 meter or below as often as possible.
Rather than install a simple loop which connected all outlets, a cut-off pipe was also designed as part of the pipe network. There were two reasons for this pipe: first, the pipe helped equalize the head on the upper and lower sides about halfway between the reservoir and what were effectively the ends of each side, outlets five and six. Second, in case of a ruptured pipe anywhere in the system, this pipe will provide much faster and more efficient equalization of the heads due to its halving position in the network as explained above. The system would function without this cut-off pipe, but the safety that it adds to the system is invaluable for the requirements of an industrial park.
With pipe length the most influential element in the cost of the network, it may seem that a tree structure might have used less pipe and consequently would cost less. Although such a setup would require less pipe, the size of the pipe necessary to act as the trunk of this tree made this configuration uneconomical. The loop structure was able to divide the flow between two main pipes, which could be much smaller.
H. L. Jones Consulting would like to suggest that the Pollux City Council reevaluate the location of the industrial park in respect to the location of the reservoir. If the reservoir was located in the middle of the park, perhaps around coordinate (340, 200), then a great deal of money could be saved and the network would be much safer. A change in location would allow pipes to be constructed that would serve no more than three outlets. This reduction in flow and distance would allow much smaller pipes to be used for shorter distances, drastically reducing the price. If the Council has not yet established either the reservoir or the relative locations of the outlets, it should very seriously consider doing so. H. L. Jones Consulting would be more than happy to assist the Council in the planning of a water supply network based on this layout.
Conclusion
Soon after H. L. Jones began its analysis of the Pollux City Industrial Park and the limitations of the reservoir location, pipe costs, and lifetime pump costs, we realized that we faced quite a dilemma. The required flows called for the use of expensively large pipe diameters. The long distances also required large diameters, but the long distance multiplied by the expensive pipes resulted in very expensive networks. The only remedy available was the addition of pumps to add pump head so that the flow could be "pushed through" the smaller diameter pipes. Although the initial installation and purchase costs of the pumps were not very high, the fifteen-year lifetime costs nullified the cost savings of the smaller pipes used.
Given the present layout of the Pollux City Industrial Park, H. L. Jones Consulting recommends that System One be installed. This system is the least expensive network for a fifteen-year lifetime, requires no extra energy, will not have any maintenance costs, and will be the least likely to fail. If the City Council decides that immediate costs are the most important, then System Two would be their best choice. For political reasons, the Council could possibly install this less expensive system immediately and transfer the cost onto the future Councils. Although this system is the least expensive to install, it will require more money in the future for energy and maintenance. Also, this system is the most likely to fail due to possible mechanical or power failures. The Council should realize that both of these Systems are designed specifically for the flow rates and junctions specified. If the flow rate increases or more outlets are added, the flow will most likely be disrupted. The most likely location for such a problem is at outlets five and six. Unplanned increases in flow in any of the other outlets will cause an unacceptable drop in head and flow rate at these outlets.
If the City Council decides that safety, dependability, and expansion are the most important factors, then System Three should be used. The loss of any pipe or a reasonable increase in flow rates above planned values, two possibilities which would cause problems in the other systems, would have almost no effect on System Three. No pumps would be used, so the initial cost would be all that is ever required for this system. The addition of outlets would be accepted by the network without modification, and additional reservoirs would be handled easily. If the Council can accept the larger cost of this system, which is actually not much more than System Two, they would not have to be concerned with the water supply network for the industrial park for many years to come.
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