Pipe Loss Experimental Apparatus

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1 Pipe Loss Experimental Apparatus Kathleen Lifer, Ryan Oberst, Benjamin Wibberley Ohio Northern University Ada, OH Abstract The objective of this project was to develop an educational tool for use in an undergraduate thermal sciences laboratory. The apparatus was designed such that major and minor losses through a piping system could be determined for turbulent flow. The device cycles water through a closed-circuit, pressurized network. Water is drawn out of a reservoir and pumped through a filter. It then enters the experimental section and passes through a flow meter. Finally, the water flows through a pressure-control valve and then returns to the reservoir. In the experimental section, valves direct the flow of water through one of three equal length, equal diameter pipes. The control section, a segment made from smooth copper piping, is used to calculate the friction factor. The segment made from roughened copper piping is used to experimentally determine the pipe-wall roughness. The segment constructed of smooth copper piping and a gate valve is used to demonstrate minor losses in a pipe network. The pipe loss experimental apparatus provides undergraduate students with practical fluidmechanics experience to supplement lecture material. Introduction Fluid mechanics is a commonly studied subject by undergraduate students in a mechanical engineering curriculum. One area of fluid mechanics is the study of internal flow, which incorporates the concepts of major and minor losses. To help students at Ohio Northern University develop a fundamental understanding of these ideas, a laboratory experimental apparatus was commissioned as a senior design project. The apparatus was to be designed in such a way that major and minor losses through a piping system could be determined for turbulent flow. Specifically, the objectives of the experiment would have students calculate the friction factor, pipe wall roughness, and minor loss coefficients. For practical purposes, the apparatus was to be designed such that it is convenient to transport, easy to set up and safe to use. Also, budget restrictions limited the cost of the apparatus to $1000. System Analysis Major losses result from the dissipation of energy due to friction as fluid flows through a pipe. A minor loss, also the result of energy dissipation due to friction, occurs when fluid flows through or encounters a fitting in the pipeline (e.g. expansions, contractions, bends, or valves). Copyright 2011, American Society for `Engineering Education 1

2 Major and minor losses are commonly quantified as head loss, and have dimensions of length. Head loss is represented by the equation 1 below 2, 2 (1) where f is the dimensionless friction factor, K L is the minor loss coefficient, V is the flow velocity, L is the pipe length and D is the pipe diameter. The friction factor for turbulent flow can be calculated using the Haaland equation. 1 Turbulent flow is characterized by highly disordered motion and is expected when Reynolds numbers (Re) are greater than The Haaland equation takes the form of ε (2) 3.7 where ε is the measure of pipe-wall roughness and has the same units as the diameter. The head loss equation, seen below, relates multiple parameters at two points of flow, including: pressure (P), velocity (V), head loss (h L ), elevation (z), and pump and turbine losses (h pump, h turbine ). The equation also includes the constants: density (ρ) and gravity (g). 2 2 (3) If the fluid does not undergo an elevation change or pass through a pump and/or turbine and flows at a constant velocity, then the head loss equation can be modified to solve for the head loss as seen in equation 4. (4) The friction factor for major losses can be calculated with a known pressure drop and volumetric flowrate as seen in equation 5. 2 The minor loss coefficient can then be calculated given a known friction factor and head loss. (5) 2 (6) The Colebrook equation 1 can be used iteratively to solve for pipe roughness given a known friction factor, Reynolds number, and diameter. Copyright 2011, American Society for `Engineering Education 2

3 ε/d 3.7 (7) Flow Generation System Options The flow generation system is the portion of the apparatus which will provide the means for water to circulate through an experimental section. Three alternatives corresponding to the design of this system were developed for this project. The first design alternative connected the experimental section directly to a building water supply. This would have provided a simple, low-cost solution for providing flow. However, this option was not favorable because building water supplies do not always produce consistent flow, thus jeopardizing the credibility of the experiment. Furthermore, the design would have limited the mobility of the apparatus in regards to where it could be used. The second design alternative utilized a gravity-feed tank and a return pump. Water stored in an elevated tank would drain down through the experimental section and then return to the tank, at the same rate, by way of a pump. This option would have produced a steady and predictable flow through the pipe network. However, a model of the system, developed using Engineering Equation Solver (EES), indicated that reasonable pressure drops along the experimental section could not be obtained without constructing a system that would have limited the mobility and ease of set up of the apparatus. The third design alternative was a pressurized, closed-circuit system. This design included using a pump, water storage tank, and valve. Water would first be pumped from the tank to the experimental section, then through a pressure control valve and back to the tank. The valve would allow the system behind it to be pressurized. Favorable pressure drops were obtained from system modeling completed with EES. Furthermore, it was determined that this alternative would be able to meet the constraints and criteria of mobility, ease of use and safety. Thus, this design was chosen as the flow system for the Pipe Loss Experimental Apparatus. Design The Pipe Loss Experimental Apparatus consists of two subsystems: the flow system and the experimental section. The flow system- in addition to the tank, pump and pressure valve- consists of a filter and flow meter. The filter removes excess particles in the water so that they do not pass through the pump, flow meter, and experimental section. This helps to reduce damage to the components, and increases the reliability of the apparatus as a whole. The flow meter provides the volumetric flow rate of water through the apparatus. Copyright 2011, American Society for `Engineering Education 3

4 The experimental section consists of three parallel runs of copper piping. Valves control the flow of water to the desired pipe. Each pipe is three feet in length and half an inch in diameter. The first pipe section has a smooth interior. The second pipe section has a roughened interior. The third pipe section has a smooth interior, but also consists of a gate valve at the middle. Pressure taps are located at the entrance and exit of each pipe section. The pressure drop across each pipe is measured by a differential pressure transducer in conjunction with a strain meter. There is only one pressure transducer to measure the drop across all three pipes, and thus a gang-valve is used to control which pressure line leads into the pressure transducer, as depicted in Figure 1. A schematic diagram of the apparatus can be seen in the Figure 2. Figure 1: Gang-Valve with Line 1 Open for Measuring Pressure Figure 2: Schematic of Proposed Design The water circulates through the system beginning from the water reservoir. It then continues through the filter, pump, experimental section, flowmeter and flow control valve. The cycle concludes by the water returning to the reservoir. Copyright 2011, American Society for `Engineering Education 4

5 The apparatus includes many features that increase its mobility, versatility, functionality and safety. The final design houses the instrumentation, flow system and experimental section on a cart, thereby improving the mobility of the apparatus. The cart dimensions are such that it can fit through any standard doorway. A two shelf design allows the experimental section, contained on the top shelf, to be removed from the rest of the apparatus thereby permitting use of the apparatus for future experiments. Flexible tubing implemented from the flow system to the experimental section reduces the constraint of attachment point locations on future experimental section designs. The flow system is designed in such a manner that the pump is primed due to gravitational effects on the water in the reservoir. A drain valve located at the lowest point of the system allows easy drainage of all components. The filter can be by-passed in order to reduce flow constriction. A water catch basin beneath the filter prevents water spillage during filter-cartridge replacement. A ball valve located after the flow meter allows pressurization of the system. A computer rendition of the apparatus can be seen in the Figure 3 and a photograph of the constructed apparatus with labeled components can be seen in Figure 4. Figure 3: Computer Rendition of Apparatus Copyright 2011, American Society for `Engineering Education 5

6 Figure 4: Experimental Pipe Loss Apparatus Figure 5 is a photo of the experimental section that includes the three test runs, pressure taps, and valves. Figure 5: Removable Experimental Section Copyright 2011, American Society for `Engineering Education 6

7 The selection of components for the apparatus was based on the results of system modeling. The specifications of the components can be found in Table 1. The total cost for the construction of the apparatus was $ Table 1: Components Specifications Component Capacity Accuracy Flowmeter gpm ± 5% Pressure Transducer psi ± 1% Pump 4 12 gpm - Filter 5 7 gpm - Tank 6 26 gal - Predicted Performance The software package, EES, was used to calculate the system performance using the fluid mechanics equations previously mentioned. The system parameters were varied in EES until optimal parameters and ideal results were obtained. The chosen parameters and corresponding values are listed in Table 2. Table 2: System Parameters Parameter Value Reynolds Number Pipe Length 3 feet Pipe Diameter 0.5 inches Flow Rate 6 gpm Friction factor, smooth The pressure drops and friction factors from modeling are summarized in Table 3. Modeling projected a pressure drop ( P) of 1.03 psi for the smooth copper pipe. The pressure drop for the roughened pipe was expected to be greater than 1.03 psi, however no specific value is available due to an unknown pipe roughness. Pressure drops along the pipe with the gate valve were projected to be 1.15 psi (fully-open) and 2.38 psi (half-open). Table 3: Expected Results per System Modeling Gate Valve Smooth Roughened Fully Open Half Open P, psi 1.03 > f > Copyright 2011, American Society for `Engineering Education 7

8 Validation Plan Prior to collecting results from the apparatus, the accuracy of the flowmeter and pressure transducer were validated. Flow Meter The accuracy of the flowmeter was validated by the following procedure: 1) Water flowed through the flowmeter and discharged into a 5 gallon tank. 2) Beginning at an indicated flowrate of 1 gpm, the time required to fill the tank was recorded. 3) This procedure was repeated in increments of 1 gpm up to an indicated flowrate of 6 gpm. 4) A total of three trials were performed, and the averaged times were calculated for each flowrate. 5) The theoretical times required to fill the tank for flowrates ranging from 1-6 gpm were calculated and compared to the averaged experimental times. The results of the experiment can be seen in Table 4. The data suggests that the flowmeter should be used in the 3-6 gpm range in order to minimize error due to flow rate. Indicated Flowrate (gpm) Table 4: Flowmeter Validation Data Experimental Theoretical Average Time Time (s) (s) Percent Error (%) Pressure Transducer The accuracy of the pressure transducer was validated through a hydrostatic experiment: 1) A water column of a known height was attached to the pressure transducer. 2) The water level was varied between ½ and 25 feet. 3) The resulting hydrostatic pressure was displayed by a digital meter attached to the pressure transducer. 4) The theoretical hydrostatic pressure was compared to the experimental data, and the errors were calculated. Copyright 2011, American Society for `Engineering Education 8

9 The results of the experiment can be seen in Table 5. Column Height (ft) Table 5: Pressure Transducer Validation Data Experimental Theoretical Pressure Pressure (psi) (psi) Percent Error (%) The results of the experiment indicate errors in the accuracy of the pressure transducer up to 15%. Some error can be attributed to the measuring tools used to determine the height of the water column. Final Results The testing of the apparatus yielded the following results, also summarized in Table 6. The smooth copper pipe was found to produce a pressure drop of 0.49 psi at a Reynolds number of 36952, which resulted in a friction factor of The roughened copper pipe was found to produce a pressure drop of 0.63 psi which resulted in a friction factor of and thus a pipe roughness of mm. The pipe with a gate valve was found to produce a pressure drop of 0.9 psi (fully open) and a pressure drop of 1.18 psi (half open) and ultimately a minor loss coefficient of (fully open) and (half open). Table 6: Final Results Gate Valve Smooth Roughened Fully Open Half Open P, psi f The friction factor of the smooth run was compared between the theoretical and the experimental values. These values and the resulting percent error are listed in Table 7. The theoretical and experimental minor loss coefficients were also compared and can be seen in Table 8. Copyright 2011, American Society for `Engineering Education 9

10 Table 7: Comparison of Predicted and Actual Results Theoretical Friction Factor Experimental Friction Factor Percent Error (%) Smooth Table 8: Comparison of Minor Loss Coefficients Theoretical 1 Experimental Percent Error Minor Loss Coefficient (Fully Open) Minor Loss Coefficient (Half Open) Discussion The data gathered from testing the apparatus revealed mixed results. The smooth pipe section yielded an error of 28% for the friction factor. The roughened pipe section resulted in a pressure drop and friction factor greater than that of the smooth pipe section, as expected. Furthermore, the roughness of the pipe is mm as calculated by using the Colebrook equation (eq. 7). This roughness is comparable to that of smooth rubber, as indicated in Fluid Mechanics: Fundamentals and Applications by Yunus Çengel (2 nd edition). The minor loss coefficients calculated for the gate valve in fully and half open positions resulted in errors of 63%. These errors are due in part by assuming coefficient values published by Çengel (coefficient values were unavailable from the gate valve manufacturer). Provided that this apparatus is intended to demonstrate major losses as a means of reinforcing concepts learned in lecture, all of the above errors are acceptable. There are multiple common sources which can lead to errors in the experiment. Such sources include inaccuracies in the pressure transducer and flow meter. Furthermore, before the water reaches the pressure taps in the pipe sections, it incurs a minor loss due to passing through a fitting. Additionally, manufacturing imperfections, such as the pipe diameter and length between pressure taps, can further attribute to error. Conclusion The purpose of this project was to develop an educational tool for use in the thermal sciences laboratory at Ohio Northern University. The apparatus was developed so that students can gain hands on experience with the concepts of major and minor losses, thus extending their education beyond the classroom. The device is a mobile and pressurized system that has the capability of measuring flowrate though-, and pressure drop across, a removable experimental section. Testing of the apparatus produced acceptable results for both major and minor losses. The project was completed within the constraints and criteria set forth at the beginning including: cost, mobility, ease of set up, and safety. The apparatus will be a valuable addition to the mechanical engineering department at Ohio Northern University. Copyright 2011, American Society for `Engineering Education 10

11 References 1. Cengel, Yunus A., and John M. Cimbala. Fluid Mechanics: Fundamentals and Applications. Boston: McGraw-Hill Higher Education, Print. 2. Hedland. Installation Instructions For EZ-View Flow Meter and EZ-View Flow-Alert Flow Meter. Hedland, Print. 3. Omega Engineering Inc. PX26 Series Pressure Transducer. Omega Engineering, Print. 4. Northern Tool & Equipment Co., Inc. 1" Clear Water Pump Owner s Manual. Northern Tool & Equipment. Print. 5. "Water Filters." McMaster-Carr. Web. 17 Mar <http://www.mcmaster.com/#waterfilters/=bh92vz>. 6. "26 Gallon Rectangle Utility Tank, 18" W X 25" L X 19" H - Go-To-Tanks." Water Storage Tanks Plastic Water Tanks - Go-To-Tanks. Web. 17 Mar <http://gototanks.com/26-gallon-rectangle-utility- Tank.aspx>. Copyright 2011, American Society for `Engineering Education 11

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