Lab_4

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Department Of Mechanical And Industrial Engineering Measurement And Visualization Of Flow By Kisei Mano Team 1 1. Kisei Mano 2. Clair Wagner 3. Courage Lahban 4. Elijah Smith Date of Experiment: 6-7-2023 & 6-8-2023 Instructor: B. S. Mani ME343-011, MECHANICAL LAB-1 Summer 2023 1

Table of Contents  Cover Page………………………………………………………………………………………………………………………… Page 1  Table of Contents………………………………………………………………………………………………………………. Page 2  Grading Citaria………………………………………………………………………………………………………………….. Page 3  Table of Tables…………………………………………………………………………………………………………………… Page 5  Table of Figures…………………………………………………………………………………………………………………. Page 5  Abstract…………………………………………………………………………………………………………………………….. Page 6  Introduction………………………………………………………………………………………………………………………. Page 7  Experimental systems……………………………………………………………………………………………………….. Page 8 o Equipment……………………………………………………………………………………………………………. Page 8 o Experimental description…………………………………………………………………………………... Page 12  Data and Result………………………………………………………………………………………………………………. Page 15  Discussion……..………………………………………………………………………………………………………………… Page 23  Conclusion………………………………………………………………………………………………………………………. Page 25  Bibliography……………………………………………………………………………………………………………………. Page 26  Appendix………………………………………………………………………………………………………………………… Page 27  Bonus Points…………………………………………………………………………………………………………………… Page 35 2

MEASUREMENT OF Flow Through Pipes Grading Criteria for Lab Report 3 (Maximum Possible 50 points ) 1. General Format ( 12.5 points )  Cover page  Grading Criteria  Table of Contents  Abstract  Introduction  Theory (See details given at 2 below) ( 12.5 points )  Methodology  Experimental system (See details below given separately) ( 12.5 points )  Sample Analysis (See details given at 4 below AND include this section in appendix) ( 12.5 points )  Results and discussions (See details below given separately)  Conclusion  Nomenlecture  Appendices  Original data  Data conversion with sample analysis 2. Theory ( 12.5 points )  Methods based on Bernoulli equations  Flow rate equation for venturi and orifice (with discharge coefficient)  Local velocity equation for Pitot’s tube (with inclined manometer) 3. Experimental Systems ( 12.5 points )  Flow rate measurement system – Flow Stand  Schematic diagram of experimental system  Photograph of the system and its key components  Photograph of the system and its key components 3

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 Schematic diagram of experimental system  Photograph of the system and its key components 4. Sample Analysis (include this section in the appendix) (12.5 points)  Theoretical flow rate calculation (venturi & orifice)  Jet velocity calculation (Pitot tube) 5. Results and Discussions : Calibration of flow rate  Calibration of rotameter (Plot flow rate vs float height)  Calibration of venturi, comparison against theory and determination of discharge coefficient  Calibration of orifice, comparison against theory and determination of discharge coefficient  Determination of jet boundary - Plot the three velocity profiles on the same graph Normalize, and determine the jet entrapment in pitot’s tube experiment. 4

Table of Figures Figure # Description Page # 1 Flow measurement Workbench 9 2 Digital Flow rate Annunciator 10 3 Venturi and Orifice Devices 10 4 Flow measurements – apparatus and components 10 5 Monometer 11 6 Rotameter 11 7 Control Valves 12 8 Compressed air inlet 12 9 Pitot Tube Jet Flow 12 10 Air Jet nozzle 13 11 Manometers 13 12 Pitot Tube Adjustment Apparatus 14 13 Work bench schematic 14 14 Pitot Tube Schematic 15 15 Graph of rotameter 17 16 Graph of Orifice 19 17 Graph for Venturi 19 18 Jet Flow Measurement (Pitot Tube) 21 19 Normalized Jet Flow measurements 22 Table of Tables Table # Page # 1 16 2 15 3 15 4 16 5 17 6 17 5

Abstract The abstract of this lab was based on how the fluid streams. To understand how the flow behaves we used many kinds of devices like Venturi tube, orifice tube and a turbine. We obtained the measurements by reading the pressure difference when the fluid would come in and out of a specific device. Another method was the use of pitot tube to determine the pressure differences. Even though both methods were very similar, measuring the flow of two different materials; air and water, this experiment showed that both were behaving in similar ways. After we acquired the important data, we had a better understanding of how pressure reacts during a steady flow process and how they are measured. 6

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Introduction The importance of experiments in the engineering society is to understand how the pressure and velocities of the liquid through pipelines are measured. One of the ways is the use of Bernoulli’s equation a fundamental principle in fluid dynamics that relates the pressure, velocity, and height of a fluid in a streamline. This equation is mainly used in aerodynamics, hydrodynamics, plumbing, and the design of fluid flow systems. For this experiment we used water for the liquid flowing through the two measuring devices. The first one is called the Flow Measurement Workbench, this is used for the calibration, testing, and evaluation of flow meters and flow measurement devices. Another is called the Pitot’s Tube Jet Nozzle; this uses a jet stream of air to measure fluid flow velocity. Eventually after this experiment we were able to acquire the experimental measurement of the flow and velocity as well as the calculation of the theoretical values. 7

Theory and Methology 1. Flow Rate Equation a) Venturi With the equation: ρ ∗ A A v A = ρ ∗ A B v B We were able to get: Q = A B v B = A B ( ( 2 g 1 − ( A B A A ) 2 ) ∗ ( P A − P B pg ) ) 1 2 b) Orifice Basically it’s similar to the venturi equation. Q = A F v F = C A F ( ( 2 g 1 − ( A F A E ) ) ∗ ( P E − P F pg ) ) 1 2 The discharge coefficient (C) is a dimensionless factor that accounts for the efficiency of the flow through a particular device or constriction. It takes into consideration various factors such as the shape, design, and condition of the flow element, as well as any flow disturbances or losses. The Discharge Coefficient, C, is determined by the two-flow rate theoretical discharge rate: C = Q actual Q ideal . Local velocity Equation for Pitot’s Tube: V = √ 2 ( P 1 − P 2 ) ρ air 8

This is true when taking the pressure difference in the pipeline. Experimental systems Equipment and Description: Figure 1: Flow Measurement Workbench Flow Measurement Workbench: This workbench produces a specific flow rate that’s being passed through the tubes. We could control the flow of the water in the tubes using the control valve that is connected to layout pipes. By using the flow rate annunciator, we were able to digitally read how much flow rate could be passed through the pipes. The volume flow rate changes depending on the size of the piping. It is an essential tool in industries where accurate flow measurement is crucial, such as oil and gas, chemical processing, water management, and manufacturing. 9

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Figure 2: Digital flow rate annunciator Digital flow rate annunciator: This device can display the amount of volume flow rate in L/sec and L/min. Figure 3: Venturi & orifice devices Figure 4: Flow measurements – apparatus and components 10

Monometer: This is a device used to measure pressure, typically in a fluid system of the workbench. This is connected to the Venturi and Orifice tube. The pressure at various points in the workbench can be read on the monometers. The manometer operates based on the principle of hydrostatic pressure, which reads on the manometer changes depending on volume flow rate at the given point. Figure 5: Monometer Figure 6: Rotamter Rotameter: This device is used to measure the height of how high the float rises from the initial height to the final height. 11

Figure 7: Control valves Figure 8: Compressed air inlet (used for purging) Figure 10: Pitot Tube Jet Flow 12

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Pitot Tube Jet Flow : This is a device that is used to measure fluid flow velocity, particularly in applications involving gases or liquids. It works based on the principle of Bernoulli's equation, which relates fluid velocity to pressure changes. A fluid jet refers to a stream of fluid (liquid or gas) being discharged from a nozzle or an orifice at a high velocity. It is often used in applications such as water jets, hydraulic systems, propulsion systems, and aerodynamics. Figure 9: Air jet nozzel Figure 10: Manometers 13

Figure 12: Pitot Tube Adjustment Appartus Equipment and Description: Figure 13: Schematic of Workbench As you can see in the diagram above, as the control valve ejects water it goes through the venturi and Orifice tube eventually leading through the rotameter. The tube is connected to the manometer. 14

Figure 14: schematic diagram of using thermistor. As you can see in the diagram above as the Jet flow Nozzle releases air, some of them go into the apparatus though the pipe eventually leading to the manometer. 15

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Sample Analysis Theoretical Flow Rate Calculation for Venturi: Q = A B v B = A B ( ( 2 g 1 − ( A B A A ) 2 ) ∗ ( P A − P B pg ) ) 1 2 ¿ ( 530.9291585 ) ∗ ( ( 2 1 − ( 530.9291585 201.0619298 ) 2 ) ∗ ( 242 − 250 0.000000997 ) ) 1 2 ¿ 870274.6904 L ( mm ) 3 Theoretical Flow Rate Calculation for Orifice: Q = A E v E = A E ( ( 2 g 1 − ( A E A F ) 2 ) ∗ ( P E − P F pg ) ) 1 2 ¿ ( 530.9291585 ) ∗ ( ( 2 1 − ( 314.2 2115.6 ) 2 ) ∗ ( 250 − 238 0.000000997 ) ) 1 2 ¿ 1343027.9 L ( mm ) 3 Results And Discussion 16

1. Rotameter Table 1: Rotameter Data # Flow Rate (L/m) Flow Rate (L/S) Height (mm) B (mm) C (mm ) D (mm) E (mm ) F (mm) H (mm) 1 6.06 0.101 29 242 250 250 238 243 142 2 7.2 0.12 39 244 256 256 240 246 146 3 8.58 0.143 49 248 268 268 244 250 150 4 9.96 0.166 59 252 276 278 246 252 152 5 11.28 0.188 69 254 286 294 248 254 154 6 12.78 0.213 79 256 298 332 248 256 156 7 14.52 0.242 89 258 314 356 248 260 160 8 15.72 0.262 99 264 326 368 264 264 164 9 17.1 0.285 109 272 348 382 270 272 172 10 18.6 0.31 119 280 372 400 288 282 182 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0 20 40 60 80 100 120 140 f(x) = 424.37 x − 12.15 R² = 1 Rotameter (experimental) Flow Rate (L/s) Height (mm) Figure 13: Graph of Rotermeter Flow rate (L/s) vs Height (mm) 2. Venturi and Orifice 17

d 1 = 16 mm A 1 = 201.0619298 m m 2 d 2 = 26 mm A 2 = 530.9291585 m m 2 Table 2: Thermocouple Data for Close Device Rotameter Venturi Orifice Flow Rate (L/S) Height (mm) B: P1 (mm) C: P2 (mm) Flow rate Q thoretical Flow rate *10^-6 Coefficient of discharge © E: P1 (mm) F: P2 (mm) Flow rate (theoretical) 0.101 29 242 250 870274.6 904 0.0870 0.862 250 238 1343027.9 0.12 39 244 256 1065864. 464 0.1066 0.888 256 240 1598601.3 0.143 49 248 268 1376025. 106 0.1376 0.962 268 244 2121071.8 0.166 59 252 276 1507359. 98 0.1507 0.908 278 246 2311230.8 0.188 69 254 286 1740549. 381 0.1741 0.926 294 248 2825314.9 0.213 79 256 298 1994049. 822 0.1994 0.936 332 248 3860606.0 0.242 89 258 314 2302530. 403 0.2303 0.952 356 248 4448988.9 0.262 99 264 326 2422742. 204 0.2423 0.925 368 264 4243087.8 0.285 109 272 348 2682366. 744 0.2682 0.941 382 270 4481689.3 0.31 119 280 372 2951245. 063 0.2951 0.952 400 288 4533274.6 18

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0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.0 500000.0 1000000.0 1500000.0 2000000.0 2500000.0 3000000.0 3500000.0 4000000.0 4500000.0 5000000.0 f(x) = 16786665.83 x − 209441.08 R² = 0.93 Orifice Orifice Linear (Orifice) Experimental Flow rate (L/m) Theoretical Flow rate (L/m) Figure 14: Graph of Orifice 4 6 8 10 12 14 16 18 20 0 500000 1000000 1500000 2000000 2500000 3000000 3500000 f(x) = 162704.66 x − 90441.95 R² = 1 Venturi Flow Rate (L/m) Linear (Flow Rate (L/m)) Experimental Flowvrate (L/m) Theoretical Flow rate (L/m) Figure 15: Graph for Venturi 19

3. Jet Flow Table 3 Jet Flow Measurement Data Y = 50 X(mm) P1(mm ) P2 (mm) Delta P V:Y50 V_Norm: Y50 0.0 135.0 275.0 140.0 15.5 1 5.0 136.0 276.0 140.0 15.5 1 10.0 137.0 277.0 140.0 15.5 1 15.0 138.0 278.0 140.0 15.5 1 20.0 141.0 276.0 135.0 15.2 0.977781629 25.0 182.0 274.0 92.0 12.6 0.76651989 30.0 264.0 269.0 5.0 2.9 0 Y = 200 X P1(mm ) P2 (mm) Delta P V:Y200 V_NORM: Y200 0.0 140.0 275.0 135.0 15.0 1.0 5.0 140.0 276.0 136.0 15.1 1.0 10.0 145.0 275.0 130.0 14.7 1.0 15.0 155.0 275.0 120.0 14.1 0.9 20.0 180.0 273.0 93.0 12.4 0.8 25.0 205.0 271.0 66.0 10.5 0.7 30.0 233.0 270.0 37.0 7.9 0.5 35.0 250.0 269.0 19.0 5.6 0.3 40.0 259.0 268.0 9.0 3.9 0.2 45.0 265.0 267.0 2.0 1.8 0.0 20 Y = 350 X P1(mm) P2 (mm) Delta P V:Y350 0.0 160.0 275.0 115.0 13.8 5.0 170.0 275.0 105.0 13.2 10.0 180.0 275.0 95.0 12.6 15.0 195.0 273.0 78.0 11.4 20.0 210.0 270.0 60.0 10.0 25.0 220.0 270.0 50.0 9.1 30.0 235.0 269.0 34.0 7.5 35.0 240.0 269.0 29.0 7.0 40.0 250.0 268.0 18.0 5.5 45.0 255.0 268.0 13.0 4.7 50.0 260.0 266.0 6.0 3.2 55.0 265.0 267.0 2.0 1.8

-80.0 -60.0 -40.0 -20.0 0.0 20.0 40.0 60.0 80.0 0.0 2.0 4.0 6.0 8.0 10.0 12.0 14.0 16.0 Jet flow Measurment (Pitot tube) V_Norm: Y50 Polynomial (V_Norm: Y50) V_NORM: Y200 Polynomial (V_NORM: Y200) V_NORM:Y350 Polynomial (V_NORM:Y350) Distanbce from Center of Jet Flow (mm) Velocity of Air(mm/s) Figure 16: Thermistor Temperature vs Resistance Table 4 – Normalized Jet Flow Measurement Data Normalized Distance Normalized 50 mm jet flow Normalized Distance Normalized 200 mm jet flow Normalized Distance Normalized 350 mm jet flow -0.54545 0 -0.81818 0 -1 0 -0.45455 0.76651989 -0.72727 0.154745743 -0.90909 0.117208987 -0.36364 0.977781629 -0.63636 0.287351131 -0.81818 0.235384942 -0.27273 1 -0.54545 0.455570852 -0.72727 0.3038186 -0.18182 1 -0.45455 0.654764605 -0.63636 0.42654408 -0.09091 1.0 -0.36364 0.803052885 -0.54545 0.474428789 21

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0 1 -0.27273 0.930964674 -0.45455 0.6076372 0.090909 1 -0.18182 0.974613837 -0.36364 0.680132203 0.181818 1 -0.09091 1 -0.27273 0.796763974 0.272727 1 0 0.995808446 -0.18182 0.895053298 0.363636 0.977781629 0.090909 1 -0.09091 0.948778148 0.454545 0.76651989 0.181818 0.974613837 0 1 0.545455 0 0.272727 0.930964674 0.09091 0.948778148 0.363636 0.803052885 0.18182 0.895053298 0.454545 0.654764605 0.27273 0.796763974 0.545455 0.455570852 0.36364 0.680132203 0.636364 0.287351131 0.45455 0.6076372 0.727273 0.154745743 0.54545 0.474428789 0.818182 0 0.63636 0.42654408 0.72727 0.3038186 0.81818 0.235384942 -1.5 -1 -0.5 0 0.5 1 1.5 0 0.2 0.4 0.6 0.8 1 1.2 Normalized Jet Flow Measurments Y = 50 Polynomial (Y = 50) Y = 200 Polynomial (Y = 200) Y = 350 Polynomial (Y = 350) Normalized Distance from Center of Jet Flow (x/x_max) Normalized velocity of Air (U/U_max) Figure 19: normalized Jet Flow Measurement Conclusion In conclusion, we were able to understand how to measure the flow in different types of pipelines. Also, this experiment taught us how to use the pitot tube, jet nozzle, manometers, rotameters, 22

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various tubing, and other tools. By using Bernoulli’s equation, we were able to calculate the velocity of the flow rate from the Pitot tube and workbench. Eventually with that data we were able to obtain a graph with the use of Excel. In the end we understand that frequencies change and there is a low chance of obtaining the perfect frequency. Bibliography  Holman, J. Experimental Methods for Engineers 8 th edition . Mc Graw Hill. Zhu, C. (2009). Me 343 Laboratory Introduction . 23

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Appendix Detailed Sample Calculation : 24

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Theoretical Flow Rate Calculation for Venturi: Q = A B v B = A B ( ( 2 g 1 − ( A B A A ) 2 ) ∗ ( P A − P B pg ) ) 1 2 ¿ ( 530.9291585 ) ∗ ( ( 2 1 − ( 530.9291585 201.0619298 ) 2 ) ∗ ( 242 − 250 0.000000997 ) ) 1 2 ¿ 870274.6904 L ( mm ) 3 Theoretical Flow Rate Calculation Venturi: C = 0.087027469 0.101 = 0.861658109 Theoretical Flow Rate Calculation for Orifice: Q = A E v E = A E ( ( 2 g 1 − ( A E A F ) 2 ) ∗ ( P E − P F pg ) ) 1 2 ¿ ( 530.9291585 ) ∗ ( ( 2 1 − ( 314.2 2115.6 ) 2 ) ∗ ( 250 − 238 0.000000997 ) ) 1 2 ¿ 1343027.9 L ( mm ) 3 Theoretical Flow Rate Calculation Orifice: C = 0.087027469 0.101 = 0.861658109 Jet Velocity Calculation: √ 2 ( P 1 − P 2 ) ρ air = √ 2 ( 135 − 275 ) 1.165 = ¿ Nomenclature: Symbol Description y Height for Jet Flow 25

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P 1 Pressure 1 P 2 Pressure 2 C Discharge Coefficient Q Flow Rate A Area V Velocity ρ Density ME 343 Laboratory Instructions 26

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Safety Hazards Instrumentation Laboratory Room 214 HAZARD: Rotating Equipment / Machine Tools Personal Protective Equipment : Safety Goggles; Standing Shields, Sturdy Shoes. Personal Care 1. Do not wear loose clothing, Neck Ties/Scarves; Jewelry (remove). 2. Tie back long hair. HAZARD: Heating – Burns Personal Protective Equipment : High temperature gloves; High temperature apron. HAZARD: Electrical - Burns / Shock Personal Care: Take Care while doing electrical connections, particularly with grounding; do not use frayed electrical cords. HAZARD: Water / Slip Hazard Personal Care: Clean any spills immediately. HAZARD: Noise Personal Protective Equipment: Ear Plugs Measurement of Flow & System Uncertainty Analysis Objectives: 27

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1. Flow pattern analysis. 2. Flowrate measurement with Venturi meter and Orifice plate. 3. Flow velocity profile measurement with Pitot tube. 4. System Uncertainty Analysis a. Flowrate (Orifice Plate) OR Pitot tube 1) Calibration of Flow-meters 1. Set the flow rate on the rotameter with the inlet hand valve to a value of 5. 2. Record the weight of the tank and close the bypass to the pump so the water goes to the tank for a period of 1 minute for higher flow rate and 2 3. minutes for lower flow rate. 4. 3. Record the pressure drop ΔPL through the rotameter on the differential 5. pressure gage by opening valves Q and R. 6. 4. Record the pressure drop ΔPL through the Turbine flow meter on the 7. differential pressure gage by opening valves A and B. 8. 5. Record the pressure drop ΔPM through the Venturi on the differential 9. pressure gage by opening valves E and D. Then record the pressure drop 10. ΔPL through the Venturi on the differential pressure gage by opening 11. valves C and F. 12. 6. Record the pressure drop ΔPM through the nozzle on the differential 13. pressure gage by opening valves I and H. Then record the pressure drop 14. ΔPL through the nozzle on the differential pressure gage by opening 15. valves J and G. 16. 7. Record the pressure drop ΔPM through the orifice on the differential 17. pressure gage by opening valves M and L. Then record the pressure drop 18. ΔPL through the orifice on the differential pressure gage by opening valves 19. N and K. 28

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20. 8. Record the digital output from the counter of Turbine flow meter. 21. 9. Repeat steps 1 through 8 for rotameter settings of 4.5, 4, 3, 2, and 1.5. 22. C. Zhu, September, 2009 2 23. ME343 Laboratory Instruction 2) Measurement of Air Jet Velocity a. Adjust the horizontal balance of a fan. Set the Pitot tube in an alignment with the centerline of the jet exit from the fan and record the axial distance from the jet exit. b. Remove the cap from the vertical manometer which is connected to the Pitot tube. Record the initial reading of manometer. c. Turn on the power of fan and set the power to maximum. Record the manometer reading. If the variation of manometer readings is within the range of inclined manometer measurement, repeat steps 2 and 3 to use the inclined manometer instead of the vertical manometer. d. Recording the manometer reading in both traverse directions for at least 6 points on each side or until the change in manometer reading becomes insignificant. e. Repeat steps 1 to 4 for different axial distances (each group measures at least two velocity profiles at different axial distances). 3) Measurement using Laser Doppler Velocimetry (LDV) (Optional) Caution: Wear the Laser Safety Goggle!!! a. Take off the cap from head of Laser beam tube. b. Turn on the Computer, Laser Generator and Processor. Wait until the “Ready” light on Processor turn to Green. Double click “BSA flow” Button to open software on the desktop. c. Click on “New Project”, make sure “black Project” in “Project” Tab is highlighted. Click on “ok”. d. Click from main menu “File” → “New” to start a new measurement. Highlight “BSA Application” in “Object” Tab. Click on “OK”, then “Connect”, wait until the light “On line” of Processor turns to green. e. In BSA Application window, select the Group 1 to edit properties in property window which is located at left side of the window. Set the termination criteria of a data acquisition (max. Samples: 3000 max. Acquisition time100 second). f. In BSA Application window, select the LDA 1 to edit properties in property window. Set the Center frequency (0.0 m/s), Bandwidth 29

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(0.23412 m/s), High voltage level (1800V), and Signal gain (28 dB). It is noted that these variables may be reset for different flow measurements. g. To monitor the Doppler signals, right click on Processor, Group 1 or LDA 1 in the BSA Application window, and select System Monitor from the list, click on “File” → “New”→ “Histogram” and . “File” → “New”→ “list” to show the data diagram and list on screen. h. Turn the laser block shutte r from Closed to Open . i. Precisely adjust the laser focus point to the measurement location, using the traversing stage. Move stage up/down and left/right to let laser beam focus at center of cylinder. Move left/right to let focus at right edge of cylinder. Move 5 cycles of stage further to let the focus reach to first measuring location. In this part, a velocity profile in the wake of a cylinder needs to be obtained with at least 6 points at different locations (see below for locations). 30

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