Original On the Optimum Pipe Diameter of Water Pumping System by Using Engineering Economic Approach in Case of Being the Installer for Consuming Water M. Pang-Ngam 1, N. Soponpongpipat 1 Abstract The purpose of this research is to determine the pipe diameter of the water pumping system by using engineering economic approach to achieve the lowest total cost. The study was carried out by using the flow equation of fluid in pipe. Subsequently, the data gained from the flow equation was used to calculate the engineering total cost. The cost in this study was classified into 5 groups: pipe cost, water pump cost, electricity cost, labor cost for installation, and maintenance cost. All simulations were done based on case studies. The diameters of Polyvinyl Chloride (PVC) pipes were specified in the range from 0.25 m. to 0.60 m., and the flow rate was 50 to 500 L/min. These conditions were applied to the building height of 20 m to 48 m. It was found from the above values of the flow rate that the optimum diameter of pipe should be in the range from 0.035 m. to 0.125 m. which exhibited the lowest cost as 29,208.6 baht to 233,308.87 baht. In addition, the height of building had no effect on the optimum diameter of pipe. From the case studies, at the flow the rate of 200 L/min, the optimum diameter of the height of 20 m to 48 m should be at 0.065 m. Finally, the simulation model showed that the optimum diameter would increased if the flow rate increased. Keywords: Optimum pipe diameter, Total cost, Engineering economic Introduction The supplying system of water is mainly classified in 2 types that are the up-feed system and the downfeed system. The up-feed system is performed by pumping water from the bottom storage tank. The pressure of pumping will supply water to the units at any floors of the building. This system has no storage tank on the top of the building which is suitable for a building that is not too high. On the other hand, the down-feed system has the storage tank on the top of the building. It is performed by pumping the water from the bottom storage tank to be kept in the top storage tank, and then water will be discharged to the units on various floors of the building. The water flow is enhanced by the gravity force. The advantage of down-feed system is a lack of energy loss for supplying water at any floors. For designing the pipes in the engineering field, there are many ways to achieve the effective design. For instance, if the system delivers water with the flow rate of 100 L/min, the pipe can be chosen from the diameter of 1 1/2 inch, 2 inch, 2 1/2 inch and 3 inch. 1 Department of Industrial Engineering and Management, Faculty of Engineering and Industrial Technology, Silapakorn University, Nakornprathom 73000, Thailand E-mail: mek_new@hotmail.com * Department of Mechanical Engineering, Faculty of Engineering and Industrial Technology, Silapakorn University, Nakornprathom 73000, Thailand Tel. +66 34 259025, Fax +66 34 219367
Vol 31, No 5, September-October 2012 On the Optimum Pipe Diameter of Water Pumping System by Using Engineering Economic Approach in Case of Being the Installer for Consuming Water 619 However, it was found that using these diameters resulting in the total cost of 65,042.54 baht, 63,756.07 baht, 64,804.64 baht and 66,752.26 baht respectively. It can be seen that there are various sizes of the water pipes used in engineering, that leads to the different total cost. Therefore, the optimum diameter should keep the total cost of the system as low as possible. This is the basic concept of economics-engineering analysis. There are many studies using economicengineering to analyze the optimum point (Soylemez, 1999; Umberto et al., 2009; Soylemez, 2001; David et al., 2009; Yang Zhao et al., 2003, Soylemez, 2008). Soylemez (2000) studied the suitable space of Heating and Ventilation Air Conditioning (HAVC) by calculating pressure drop in round pipe and square pipe and studied the results of economic factors to find the optimum size and the lowest total cost. He discovered that the smaller the size was, the higher the total cost was. That was because of the loss of pressure and friction. Moreover, he found that round pipe was useful to decrease the total cost. Soponpongpipat et al., (2010) analyzed the optimal thickness of pipe insulation in the air conditioner which contained the layers of rubber and fiber-glass. They used thermo-economics method to consider the thermal conductivity coefficient at inner and outer duct size of 0.5 m. With the consideration on material cost by using thermo-economics, they found that the 2 layers of insulation were recommended to use in case of main insulation cost was higher than minor insulation. From the above mention, there is no research dealing with the optimum point of pumping system for building. As a result, this research carries out the total cost in pumping system, appropriate diameter of pipe, effects of flow rate on the optimum pipe diameter, effects of the building height on the optimum pipe diameter, and effects of the building height on the optimum cost. Setup and Procedure Flow Simulation of Fluid The objective of flow simulation of fluid is to determine the capacity of water pump shown in Figure (1). The water is delivered from the bottom storage, through the suction pipe to the discharge pipe, along the pipe system. The pipe length is 4 m. There is a joint for every 4 m long in each pipe. The model of flow was established by energy equation as shown in equation 1 to determine the power of pump (H p ) and pumping capacity. Figure 1 Up-feed pumping system (1) The model of flow was based on the assumption of the open reservoir. Thus, Pressure (P 1 ) and Pressure (P 2 ) were equal, and the change of velocity from V 1 to V 2 was very small and could be neglected. Thus, the equation could be written as follows: = Specific gravity of water (N/m 3 ) = Dynamic viscosity (m 3 /s) = Flow rate of water (m 3 /s) (2) (3)
620 M. Pang-Ngam and N. Soponpongpipat J Sci Technol MSU = Power of pump (Watt) = Pumping head (m) = Pumping efficiency = Total head loss (m) = Length of pipe (m) = Diameter of pipe (m) = Different pressure between location 1 and 2 = Different pressure between the suction pipe and the discharge pipe (m) = Gravity acceleration (m/s 2 ) whose unit is meter is the total loss of flow in pipe categorized into 2 groups. The first type is called major loss, and the second one is known as minor loss. They can be calculated by equation 4 and 5 (4) (5) According to the above equations, the equation of pumping capacity is as follows: (6) Establishing of Total Cost Equation There are 5 groups of cost: pipe cost, water pump cost, electricity cost, labor cost for installation, and maintenance cost. The equation in each cost is detailed as follows: Equation of Pipe Cost Water pipe is considered as a main cost of system. The cost depends on diameter and length of pipe. Figure 2 Equation of pipe cost From the figure 2, the y-axis presents the price of water pipe expressed in baht, and the x-axis is volume of pipe matter in m 3. The cost equation could be formed by plotting the market prices of various pipe sizes, compared with the volume of each size. The slope of graph (C 1 ) is obtained to substitute the equation of pipe cost in equation (7) (7) C 1 = Constant value obtained from slope in Figure 2 t = Thickness of pipe (m) D = Diameter of pipe (m) L = Length of pipe (m) Equation of Water Pump Cost In order to establish the cost equation of water pump, the market prices of various capacities of water pump were plotted to find out the relationship as seen in Figure 3. The vertical axis shows the price of water pump (baht), and the horizontal axis presents the value of pump power multiply by the suction to discharge diameter ratio. From figure 3, the equation of water pump cost is: (8) D suc /D dic = The ratio of suction to discharge diameter
Vol 31, No 5, September-October 2012 On the Optimum Pipe Diameter of Water Pumping System by Using Engineering Economic Approach in Case of Being the Installer for Consuming Water 621 Figure 3 Equation of water pump cost Figure 4 Equation of labor cost After that, equation 6 was replaced in equation 8 to obtain equation 9 Thus, the equation of pipe installation cost is: Equation (11) (11) (9) Equation of Electricity Cost Electricity cost is considered as a direct cost depending on pumping capacity and the pumping duration as expressed in equation (10) Equation of Maintenance Cost It is necessary to maintain the system in a good condition for long working life. In order to estimate the maintenance cost of the pump used for 10 years, 5 percents of summation of pipe cost, pump cost, electricity cost and installation cost are calculated as seen in Equation (12). (12) (10) H = Pumping Hour (Hour) E p = Price of Electricity (Baht/Kilowatt- Hour) F = Duty Factor (in this study, f = 0.70 is used) Equation of Labor Cost Labor cost is also a part of the total cost, establishing the equation is for the convenience to calculate the cost. The equation of installation cost was obtained from plotting graph between labor cost in construction estimated books and diameter of pipe. The x-axis is diameter of pipe, and the y-axis is labor cost of pipe installation (baht/ 1 m length). As this, the total cost equation is: (13) Case Study The research was carried out from the case of pumping system as illustrated in Figure 1. The conditions are as follows: - Flow rate is 50 to 200 L/min. - Height of building is from 20 m. to 48 m. Results and Discussions Total Cost of Pumping System Figure 5 shows the relationship between the total cost and the diameter of pipe. The vertical axis displays the total cost in baht, and the horizontal axis demonstrates the diameter of pipe in meter. An
622 M. Pang-Ngam and N. Soponpongpipat J Sci Technol MSU increase of diameter of pipe from 0.035 m to 0.08 m. leads to a decrease of total cost of pumping system from 236,744.71 baht to 120,252.42 baht. Furthermore, an increase of pipe diameter from 0.08 m to 0.60 m results in a rise of total cost of pumping system from 120,252.42 baht to 387,220.12 baht. By considering the overview of the total cost of pumping system, it was found that there was a specific diameter, possibly resulting in the lowest cost. This was due to the high pressure loss in the small duct of 0.035 m to 0.08 m. That required a large water pump and a lot of electricity to effectively supply water. Therefore, the cost of water pump and energy was significantly higher than the cost of pipe. It could be said that the cost of water pump and electricity had an influence on the whole cost of pumping system in range of pipe diameters from 0.035 m to 0.08 m. Accordingly, in the range of pipe diameters from 0.035 m to 0.08 m, it was found that when the pipe was larger, pressure drop would decrease rapidly. The pump capacity and energy was less required, which caused a decreasing of whole cost of pumping system. Nevertheless, in the range of pipe diameters from 0.08 m to 0.60 m, there was a small change of pressure drop in pipe when the pipe size was larger. As a result, in this range, the change of the cost of pump and energy was less than the change of pipe cost. It also showed that the pipe cost had the effect on the total cost of pumping system. The use of bigger pipe tended to increase the pipe cost and the total cost. It may be concluded that the total cost of pumping system tends to decrease when the diameter of pump is between 0.035 m to 0.08 m. The reason is the effect of water pump cost and energy. On the other hand, the total cost of pumping system tends to rise when the diameter of pipe is between 0.08 m to 0.60 m. That is because of a significant influence of the pipe cost. Moreover, there is an existence of optimum pipe diameter that leads to the lowest cost of pumping system. The Optimum Pipe Diameter Figure 6 exhibits the relationship between the total cost and the pipe diameter in variety of flow rates. The y-axis demonstrates the total cost (baht), and the x-axis presents pipe diameter (m). It was discovered that the optimum pipe diameter was in range from 0.035 m to 0.0125 m. The optimum diameter was approximately 0.055 m at the flow rate of 150 L/ min showing the lowest cost of 51,043.97 baht. The optimum diameter had an increase tendency with an increase of flow rate. For the flow rate of 300 L/min, the optimum diameter was around 0.08 m and the lowest cost was 82,589.27 baht. Figure 6 Calculation of total installation cost for 20 m building. Figure 5 The relationship between the total cost and the diameter of pipe. It might be said that the optimum pipe diameter is from 0.035 m to 0.125 m for the flow rate of 150 L/ min to 300 L/min generating the total cost of 51,043.97 to 82,589.27 baht respectively.
Vol 31, No 5, September-October 2012 On the Optimum Pipe Diameter of Water Pumping System by Using Engineering Economic Approach in Case of Being the Installer for Consuming Water 623 Effect of The Flow Rate on The Optimum Pipe Diameter Figure 7 illustrates the relationship between the optimum pipe diameter and the flow rate. The y-axis indicates the optimum pipe diameter (m), and the x-axis exhibits the flow rate value (L/min). It was found that an increment of flow rate from 150 L/min to 200 L/ min resulted in changing the optimum diameter from 0.055 m to 0.065 m. Thus, the flow rate of water has a significant effect on the optimum pipe diameter. An estimation of water flow rate in pipe is necessary and required for the accuracy of a new project planning. the height of building increases from 20 m to 40 m. This increase tendency can be found for every flow rate. As a result, there is no effect of height on the optimum pipe diameter. Nonetheless, it can increase the total cost at the lowest point if the vertical height of the system increases. That is because a rise of building height leads to a linear increment of 5 costs at the same rate. Consequently, the optimum diameter does not change. However, a rise of cost for every type results in higher cost at the lowest point when the vertical height increases. It can be stated that the vertical height of pumping system has no effect on the optimum pipe diameter. Nevertheless, it increases the total cost at the lowest point of pumping system with a rise of building height. Figure 7 The relationship between the optimum pipe diameter and flow rate It can be concluded that when the flow rate increases, the optimum pipe diameter increases. The optimum pipe diameter is 0.055 m for the flow rate of 150 L/min. and 0.08 m for 300 L/min Effect of Height on The Optimum Pipe Diameter Figure 8 exhibits the relationship between the optimum pipe diameter and the height at different flow rates. The vertical axis is the optimum pipe diameter (m), and the horizontal axis is the height (m). Figure 9 shows the relationship of the total cost (baht) at the y-axis and the height of building (m) at the x-axis. According to the graphs, the optimum pipe diameter is 0.035 m for the flow rate of 150 L/min, and it is constant for all studied heights. Additionally, by considering on the total cost, it has an increase tendency with an increase of building height. The total cost is up from 51,044.00 baht to 74,916.00 baht when Figure 8 The relationship between the optimum pipe diameter and the height of building at different flow rates. Figure 9 The relationship between the total cost at the lowest point and the height of building at different flow rates.
624 M. Pang-Ngam and N. Soponpongpipat J Sci Technol MSU Conclusion The study of optimum pipe diameter in pumping system was carried out, and the findings are as follows: 4.1 The total cost of pumping system tends to reduce when the pipe diameter is in the range from 0.035 m to 0.08 m due to the influence of water pump cost and energy cost. In addition, the total cost has a rise tendency when the pipe diameter is 0.08 m to 0.60 m because of the pipe cost. There is also a real presence of optimum diameter of pipe that is a factor to reduce the total cost to the lowest point. 4.2 The optimum pipe diameter is 0.035 m to 0.125 m for the flow rate of 150 L/min to 300 L/min which generates the cost from 51,043.97 baht to 82,589.27 baht respectively. 4.3 The optimum pipe diameter increases with an increment of flow rate. The optimum pipe diameter is equal to 0.055 m for the flow rate of 150 L/min and 0.08 m for the flow rate of 300 L/min. 4.4 The vertical height of pipe system has no effect on the optimum pipe diameter. However, it can lead to a rise of total cost at the lowest point with a rise of building height. [4] David, B., M. Gassner, T. Fuchino and F. Marechal, Thermo-economic analysis for the optimal conceptual design of biomass gasification energy conservation system. Applied Thermal Engineering, Vol. 29, pp. 2137-2153, 2009 [5] Yang Zhao, Zhang Shigang, Li Xun, Cost-effective optimal design of groundwater source heat pump, Applied Thermal Engineering, Vol. 23, pp. 1595 1603, 2003. [7] Soylemez, M.S., Optimum length of finned pipe for waste heat recovery, Energy Conversion and Management, Vol. 49, pp. 96-100, 2008. [8] Soponpongpipat, N., P. Jaruyanon and S. Nantoe, The Thermo-Economics Analysis of the Optimum Thickness of Double-La Acknowledgement The authors would like to thank the Department of Mechanical Engineering, Silpakorn University for the funding support. References [1] Soylemez, M.S., M. Unsal, Optimum insulation thickness for refrigeration applications, Energy Conversion and Management, Vol. 40, pp. 13-21, 1999. [2] Umberto, D., S. Proietti and P. Sdringola, Solar-powered cooling systems, Technical and economic analysis on industrial refrigeration and air-conditioning applications, Applied Energy, Vol. 86, pp. 1376 1386, 2009. [3] Soylemez, M.S., On the optimum channel sizing for HVAC systems, Energy Conversion and Management, Vol. 42, pp. 791-798, 2001.