Flow Measurement Techniques: Lab 1 Insights in Thermofluids

Flow Measurement Experimental Lab 1 ENGN 2620: Winter 2024 Thermofluids II University of Prince Edward Island Professor Sundeep Singh Team Members: R. Shokunbi – # 0346275 T. Adebowale – #347968 M. Macdonald – #0355870 N. Manholland - #357199 M. Saleh Mohammad Albarari Feb 12 th , 2024

Lab #1 Flow Measurements Group C1 University of Prince Edward Island Page | 2 Abstract The following experiment's goal was to determine the water's flow rate through a variety of orifices found in a Flow Measurement apparatus. Using the Bernoulli, Steady-Flow Energy Equation and their derivatives, the flow rates for a discharge through a Venturi flow meter, standard flow meter, orifice plate flow meter, and rotameter were determined and compared with a known standard flow. In addition, the head losses with each meter were determined and compared with those of a ninety-degree elbow pipe. The flow rates in the experiment were found to vary only slightly from the known values, and the data for the individual orifices can be found in appendix A-H.

Lab #1 Flow Measurements Group C1 University of Prince Edward Island Page | 3 Table of Contents 1.0 Introduction ............................................................................................................ 4 2.0 Methodology ........................................................................................................... 5 2.2 Procedure ............................................................................................................ 6 3.1 Calculations ......................................................................................................... 7 4.0 Discussion ............................................................................................................... 9 5.0 Conclusion ............................................................................................................ 10 References .................................................................................................................. 12 Appendix A: Data Readings ......................................................................................... 13 Appendix B: Venturi Meter Mass Flow Rate Calculation ............................................... 14 Appendix C: Orifice Meter Mass flow rate Calculation ................................................. 15 Appendix D: Rotameter Mass Flow Rate Calculation .................................................... 16 Appendix E: Venturi Meter Head Loss and Kinetic Head Calculations ........................... 17 Appendix F: Orifice Meter Head Loss and Kinetic Head Calculations ............................ 18 Appendix G: Rotameter and Wide- Angled Diffuser ΔH/Inlet Kinetic Head ..................... 19 Appendix H – Right-Angle Bend Head Loss and Kinetic Head Calculations .................... 20

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Lab #1 Flow Measurements Group C1 University of Prince Edward Island Page | 4 1.0 Introduction Flow measurement is a crucial aspect of fluid mechanics, playing a significant role in various engineering applications such as water supply systems, HVAC systems, chemical processing industries and many others. Understanding the different methods of measuring fluid flow and analyzing associated head losses are essential for engineers and scientists. There are many different devices for measuring the flow rate of fluids, including rotameters, differential pressure flow measurement devices, turbine flow meters and many others. No matter the type of device used, they need to be calibrated or tested to ensure accuracy and account for any discrepancies in the machinery. This experiment's objectives were to measure the volumetric rate using a venturi meter, an orifice meter and a rotameter, and compare the experimental values to a known standard volumetric flow rate based on a measured flow volume and time. The experiment also aimed to compare the head losses associated with these three meters with those associated with a rapidly diverging section or wide-angled diffuser, and with the right-angles bend or elbow. Assuming steady-state, adiabatic conditions, the energy equation for an incompressible fluid can be written as follows: 𝑝 1 𝑝𝑔 + 𝑉 1 2 2𝑔 + 𝑧 1 = 𝑝 2 𝑝𝑔 + 𝑉 2 2 2𝑔 + ℎ 𝐿 Where 𝑝 1 𝑝𝑔 = Hydrostatic head 𝑉 1 2 2𝑔 = Kinetic head (v is the mean velocity) Z = Potential head 𝑝 1 𝑝𝑔 + 𝑉 1 2 2𝑔 = Total head When the liquid moves into a venturi meter, this equation must be altered somewhat; the venturi flowmeter opens with a contracting duct, meaning the head loss ( ℎ 𝐿 ) becomes negligible due to the reduction in flow diameter. As such, the ℎ 𝐿 term goes to almost zero, and the change in height is so small it can be ignored. This leads into the venturi meter derivation of the energy equation: Equation 1

Lab #1 Flow Measurements Group C1 University of Prince Edward Island Page | 5 𝑄 = 𝐴 𝐵 𝑉 𝐵 = 𝐴 𝐵 [( 2𝑔 1−( ? ? ? ? ) 2 ) ( 𝑃 ? 𝑝𝑔 − 𝑃 ? 𝑝𝑔 )] 1 2 The base equation can also be altered to fit an orifice plate meter. The head loss is not negligible because it goes through a wide-angle diffuser, which creates a head loss big enough to minimize the manometric height difference, resulting in the following equation. 𝑄 = 𝐴 𝐹 𝑉 𝐹 = 𝐶𝐴 𝐹 [( 2𝑔 1−( ? ? ? ? ) 2 ) ( 𝑃 ? 𝑝𝑔 − 𝑃 ? 𝑝𝑔 )] 1 2 𝑄 = 𝑉 𝑡 ṁ = 𝜌 ∗ 𝑄 2.0 Methodology This section presents a detailed description of the setup for the experiment, along with the steps taken to complete the experiment successfully. 2.1 Setup The setup for this experiment was completed primarily when the student arrived at class. Figure 1 shows the experimental setup of the lab. Figure 1: Experimental Setup of Lab Equation 2 Equation 3 Equation 4 Equation 5

Lab #1 Flow Measurements Group C1 University of Prince Edward Island Page | 6 2.2 Procedure The following steps were followed to conduct the flow measurement experiment. Step 1: The apparatus valve was opened until the rotameter showed a reading of approximately 20mm. Step 2: The volumetric flow rate (L/s) using the Hydraulic Beach was measured by measuring the time taken to fill the Hydraulic Beach reservoir to a known volume of water as outlined in its manual. This was taken as the standard volumetric flow rate. Step 3: Readings of the various manometers, A-I were recorded during step 2. Step 4: This procedure was repeated for a number of equidistant values of rotameter readings up to the point at which the maximum pressure values can be recorded from the manometer. 3.0 Results The initial values determined from the experiment are shown in Table 1. Table 1: Initial Values from Experiment Test Number Rotameter (mm) Water (L) Time (s) Test 1 150 5 28 Test 2 100 5 32:92 Test 3 50 5 1:47 Data readings taken during the experiment can be found in Table 2 in Appendix A. Using Table 2, the Rotameter Height vs Mass Flow Rate was created. Figure 2: Rotameter Mass Flow Rate

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Lab #1 Flow Measurements Group C1 University of Prince Edward Island Page | 7 A linear trendline can be seen in figure 2 which indicates that the mass flow rate is constant. 3.1 Calculations Based on the information presented in Table 1, the mass flow rate for the weight tank based on the known standard volumetric flow rate was found. 150 cm Rotameter: Volumetric Flow Rate: Using equation 4, for a 150 cm rotameter the volumetric flow rate was found. This calculation was made by dividing the volume of the liquid by the time it took. 𝑄 = 𝑉 ? = 0.005 28? = 0.00018𝑚 3 /? Mass Flow Rate: Substituting equation 4 into 5, the mass flow rate of a 150 cm rotameter was found. This calculation was made by multiplying the density of water by the calculated volumetric flow rate of the rotameter. ṁ = 𝜌𝑄 = ( 1000𝑘𝑔 𝑚 3 ) ( 0.00018𝑘𝑔 ? ) = 0.18𝑘𝑔 ? 100 cm Rotameter: Volumetric Flow Rate: Using equation 4, for a 100 cm rotameter the volumetric flow rate was found. This calculation was made by dividing the volume of the liquid by the time it took. 𝑄 = 𝑉 ? = 0.005 32.92? = 0.00015𝑚 3 ? Mass Flow Rate: Substituting equation 4 into 5, the mass flow rate of a 100 cm rotameter was found. This calculation was made by multiplying the density of water by the calculated volumetric flow rate of the rotameter. ṁ = 𝜌𝑄 = ( 1000𝑘𝑔 𝑚 3 ) ( 0.00015𝑘𝑔 ? ) = 0.15𝑘𝑔 ?

Lab #1 Flow Measurements Group C1 University of Prince Edward Island Page | 8 50 cm Rotameter: Volumetric Flow Rate: Using equation 4, for a 50 cm rotameter the volumetric flow rate was found. This calculation was made by dividing the volume of the liquid by the time it took. 𝑄 = 𝑉 ? = 0.005 107? = 0.000047𝑚 3 ? Mass Flow Rate: Substituting equation 4 into 5, the mass flow rate of a 50 cm rotameter was found. This calculation was made by multiplying the density of water by the calculated volumetric flow rate of the rotameter. ṁ = 𝜌𝑄 = ( 1000𝑘𝑔 𝑚 3 ) ( 0.000047𝑘𝑔 ? ) = 0.047𝑘𝑔 ? Using the information from Appendix A, the volumetric flow rate of the Venturi meter, Orifice meter, and Rotameter were calculated using their corresponding manometer levels and areas to determine their mass flow rate. Equations 2 and 3 were used to calculate the volumetric flow rate of the Venturi meter and the Orifice meter. Equation 5 and the known density of water as 1000𝑘𝑔 𝑚 3 was used to calculate the mass flow rate for the rotameter using the water height of each rotameter as depicted in Figure 3. These calculations can be found in Appendix E-H.

Lab #1 Flow Measurements Group C1 University of Prince Edward Island Page | 9 Figure 3: Graph Used to Determine Rotameter Volumetric Flow Rate [2] Using the manometer levels obtained from the experiment in Table 2, which can be found in Appendix A, the Head loss ΔH and Inlet Kinetic heads of the Flow meters were calculated using the Equations in the H10 flow measurement apparatus manual [2]. The rotameter's head loss is known to be essentially independent of the water discharge, with a constant value of roughly 100 mm. Calculations that confirm this can be found in Appendix E and G. The resulting values can be used to calculate the head loss ratio to inlet kinetic head for various rotameter heights. 4.0 Discussion Comparing the resulting mass flow rates of the different apparatus’, it was noticed that the differences between the venturi meter and the orifice meter were very little compared to the mass flow rates of the standard mass flow rate as well as the mass flow rate of the rotameter. Comparing the values of the orifice meter and the venturi meter to the values given in the Lab #1 Flow Measurement Apparatus Operations Manual [1], the values were very similar during comparison, meaning there were very minimal discrepancies during the calculations as well as the experiment itself. This lab's theory was to show how the mass flow rate is affected by the different dimensions of the apparatus, meaning the larger the diameter of the tube, the slower the water would flow. Considering the calculations, this theory proved to be correct as our calculations showed that our resulting mass flow rate would vary depending on the meter used. However, the flow rate was proportional to the diameter of the tube.

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Lab #1 Flow Measurements Group C1 University of Prince Edward Island Page | 10 Comparing the calculated results with the given results from the example results, it's clear that there are some improper measurements taken, whether they be the fault of human error, or a faulty reading given by the instrument used in the experiment. Moreover, in the analysis of head losses within various flow meter components, it is evident that broader flow channels correspond to increased head losses. The Venturi meter exhibits the least head loss, attributed to its gradual expansion design, minimizing energy dissipation. Conversely, the Orifice meter, while also displaying low head losses, shows a higher sensitivity to fluctuations in flow rate. The Rotameter, however, incurs the highest head loss at low flow rates (Q), owing to the immediate expansion, which impacts accuracy for head loss measurements. Despite this, its user-friendliness and suitability for mass flow rate estimations compensate for its shortcomings. Head losses in both the diffuser and elbow are consistent with predictions but may be further minimized by optimizing the elbow’s geometry. These losses are primarily du e to the increased cross-sectional area reducing flow velocity, while in the diffuser and elbow, they arise from momentum changes due to immediate directional shifts, potentially exacerbated by flow separation and turbulence at the expansion zones. Furthermore, Equation 1 can become Equation 2 because of the nature of the head loss being caused by vorticity. Because the diameter of the flow is being reduced (flowing through a contracting duct) as it moves into the venturi meter, the fluid becomes more uniform and thus head loss becomes so small it can be effectively thought of as negligible. Because there is assumed to be negligible loss, the potential head can also be thought of as negligible and canceled out, as there is no significant change in height. This assumes a steady-state flow, which is important to eliminate changes in velocity, pressure and individual fluid density that could affect the equation. However, the head loss is not negligible when flowing through the orifice meter, as it is not a contracting duct (and in fact diverges). This significant head loss ends up reducing the difference in manometric height (the h E - h F term) to very small levels, meaning the change in potential energy can be assumed negligible with the heights so close together. It is also vital for the derivation of both equations that the process is adiabatic, the fluid experiences no loss of velocity or energy due to friction, and there is no external work being done on the fluid. Worth noting as well is the above is only true for an incompressible fluid, as the equation cannot be simplified with a compressible fluid due to expected changes in velocity, pressure, and other basic properties. 5.0 Conclusion This comprehensive investigation into flow measurement across various metering devices has yielded insightful findings that enhance our understanding of fluid dynamics in practical applications. Our study meticulously compared the performance of Venturi meters, Orifice meters, and Rotameters, revealing the nuanced interplay between design characteristics and their

Lab #1 Flow Measurements Group C1 University of Prince Edward Island Page | 11 operational efficiencies. Moreover, the Venturi meter, with its optimized design facilitating a gradual increase in the flow area, demonstrated the lowest head losses, thereby affirming its superiority in energy conservation. This efficiency is critical in applications where minimal energy dissipation is paramount. On the other hand, the Orifice meter, although presenting low head losses, displayed a pronounced vulnerability to variations in flow rate, suggesting a need for careful application where flow rates are expected to remain relatively stable. Furthermore, the Rotameter, while experiencing the highest head losses at low flow rates due to its immediate expansion design, stood out for its operational simplicity and reliable mass flow rate measurements. This balance between ease of use and measurement accuracy makes it a valuable tool in less critical applications or where rapid user feedback is required. Moreover, Our analysis also extended to the components such as the diffuser and the elbow, where we observed head losses that align with theoretical predictions. These losses, however, present opportunities for optimization, particularly through the redesign of the elbow to reduce resistance and improve flow dynamics. Further, our findings highlight the critical importance of meter calibration and the selection of appropriate metering devices based on the specific requirements of each engineering scenario. As fluid mechanics continues to be an essential aspect of various engineering fields, the insights garnered from this study will undoubtedly contribute to more efficient designs and operations. Given these insights, we recommend further studies to explore the long-term reliability of these meters under varying operational conditions and to potentially develop new designs that minimize energy losses further. The pursuit of excellence in flow measurement technology is a continual process.

Lab #1 Flow Measurements Group C1 University of Prince Edward Island Page | 12 References [1] S. Singh , “ENGN 26 20: Thermo fluids II lab #1- “ Flow measurement ” lab handout, Faculty of Sustainable Design Engineering, Univ. of Prince Edward Island, Charlottetown, PE, Canada, 2023. [2] S. Singh , “ENGN 26 20: Thermo fluids II lab #1- H10 flow measurement apparatus manual, lab handout, Faculty of Sustainable Design Engineering, Univ. of Prince Edward Island, Charlottetown, PE, Canada, 2023.

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Lab #1 Flow Measurements Group C1 University of Prince Edward Island Page | 13 Appendix A: Data Readings Table 2: Data readings Manometer levels Test 1 (mm) Test 2 (mm) Test 3 (mm) A 375 365 355 B 225 290 335 C 355 355 354 D 360 358 355 E 365 360 356 F 195 276 330 G 223 290 335 H 219 289 333 I 112 190 50 Rotameter (cm) 150 100 50 Water (L) 5 5 5 Time (seconds) 28 32:92 1:47 Mass Flow Rate (kg/s) Venturi 0.37 0.26 0.14 Orifice 0.33 0.23 0.13 Rotameter 0.35 0.23 0.12 Weight Tank 0.18 0.15 0.047 ∆ H/Inlet Kinetic Head Venturi 0.8 0.8 0.3 Orifice 89.9 89.4 102.8 Rotameter 107 99 98 Diffuser 0.79 0.74 0.68 Elbow 1 -0.05 12.05

Lab #1 Flow Measurements Group C1 University of Prince Edward Island Page | 14 Appendix B: Venturi Meter Mass Flow Rate Calculation

Lab #1 Flow Measurements Group C1 University of Prince Edward Island Page | 15 Appendix C: Orifice Meter Mass flow rate Calculation

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Lab #1 Flow Measurements Group C1 University of Prince Edward Island Page | 16 Appendix D: Rotameter Mass Flow Rate Calculation

Lab #1 Flow Measurements Group C1 University of Prince Edward Island Page | 17 Appendix E: Venturi Meter Head Loss and Kinetic Head Calculations

Lab #1 Flow Measurements Group C1 University of Prince Edward Island Page | 18 Appendix F: Orifice Meter Head Loss and Kinetic Head Calculations

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Lab #1 Flow Measurements Group C1 University of Prince Edward Island Page | 19 Appendix G: Rotameter and Wide-Angled Diffuser ΔH/ Inlet Kinetic Head

Lab #1 Flow Measurements Group C1 University of Prince Edward Island Page | 20 Appendix H – Right-Angle Bend Head Loss and Kinetic Head Calculations

Lab 1 Flow Measurement Group C1 (1)

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