Measurement of Flow Rate, Velocity Profile and Friction Factor in Pipe Flows S. Ghosh, M. Muste, M. Wilson, S. Breczinski, and F.

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1 57:00 Mechanics o Fluids and Transer Processes Exercise Notes or the Pipe Flo TM Measurement o Flo Rate, Velocity Proile and Friction Factor in Pipe Flos S. Ghosh, M. Muste, M. Wilson, S. recinski, and F. Stern 1. Purpose The purpose o this investigation is to provide students ith hands-on experience using a pipe stand test acility and modern measurement systems including pressure transducers, pitot probes, and computeried data acquisition ith Labvie sotare, to measure lo rate, velocity proiles, and riction actors in smooth and rough pipes, determining measurement uncertainties, and comparing results ith benchmark data. Additionally, this laboratory ill provide an introduction to PIV analysis, using an epiv system ith a step-up model.. Experimental Design.1 Part 1: Pipe Flo The experiments are conducted in an instructional airlo pipe acility (Figure 1). The air is blon into a large reservoir located at the upstream end o the system. builds up in the reservoir, orcing the air to lo through any o the three horiontal pipes. taps are located on each pipe, at intervals o 1.54m, or static pressure measurements. Characteristics or each o the pipes are provided in Appendix A. At the donstream end o the system, the air is directed donard and back, through any o three pipes o varying diameters itted ith Venturi meters (Figure ). The top three valves control lo through the experimental pipes, hile the bottom three valves control the Venturi meter to be used. The Venturi meter ith 5.08cm diameter is used to measure the total lo rate, hile the other to are kept closed. Six gate valves are used or directing the lo. The top and bottom 5.08cm pipes are used or measurements, hile the middle one is kept closed during the experiment. Velocity measurements in the top and bottom pipes are obtained using pitot probe (Figure 3). Figure1. Airlo pipe system Figure. Venturimeter Figure 3. Pitot-probe s are acquired either manually, using simple and dierential manometers or data acquisition, or automatically, ith the manometers connected to an automated Data Acquisition (DA) system that converts pressure to voltages using pressure transducers. Data acquisition is controlled and interaced by Labvie sotare, described in Appendix. The schematic o the to alternative measurement systems is provided in Figure 4. Data Acquisition Instrumentation Dierential manometer Venturimeter Pitot tube tap transducer Static Simple manometer Stagnation transducer Simple manometer transducer Labvie Labvie Labvie Figure4. Manual and automated measurement systems used in the experiment 1

2 All pressure taps on the pipes, Venturi meters, and pitot probes have 0.635cm diameter quick coupler connections that can be hooked up to the pressure transducers..1.1 Data reduction (DR) equations In ully developed, axisymmetric pipe lo, the axial velocity u = u(r), at a radial distance r rom the pipe centerline, is independent o the direction in hich r is measured (Figure 5). Hoever, the shape o the velocity proile is dierent or laminar and turbulent los. Laminar and turbulent lo regimes are distinguished by the lo Reynolds number, deined as Re VD 4Q (1) D Where, V is the average pipe velocity, D is the pipe diameter, Q is the pipe lo rate, and ν is the kinematic viscosity o the luid. For ully developed laminar lo (Re < 000), an analytical solution or the dierential equations o the luid lo (Navier-Stokes and continuity) can be obtained. For turbulent pipe los (Re > 000), there is no exact solution, hence semi-empirical las or velocity distribution are used instead. The pipe head loss due to riction is obtained rom the Darcy-Weisbach equation: L V h D g Figure 5. Velocity distributions or ully developed pipe lo: a) laminar lo; b) turbulent lo () here, is the (Darcy) riction actor, L is the length o the pipe over hich the loss occurs, h is the head loss due to viscous eects, and g is the gravitational acceleration. The Moody diagram provides the riction actor or pipe los ith smooth and rough alls in laminar and turbulent regimes. The riction actor depends on the Reynolds number and the relative roughness k/d o the pipe (or large enough Re, the riction actor is solely dependent on the relative roughness). Velocity distributions in the pipes are measured ith Pitot tubes housed in glass-alled boxes (Figure 3). The data reduction equation (DRE) or the measurement o the velocity proiles is obtained by applying ernoulli s equation or the Pitot tube: g u( r) SM Stag r SMStat (3) a here u(r) is the velocity at the radial position r, g is the gravitational acceleration, SM (r) is the stagnation pressure head determined by the Pitot probe located at radial position r, and SM Stat 1/ Stag is the static pressure head in the pipe, equal to that o the ambient pressure inside the glass-alled box. These pressure head readings are given in height o a liquid column (t o ater). The DRE or the riction actor is one o the Darcy Weisbach equation orms (Roberson & Croe, 1997), given as ollos: g D 8LQ 5 a here ρ, is the density o ater, ρ a is the density o air, L is the pipe length beteen pressure taps i and j, and is the dierence in pressure beteen pressure taps i and j. The lo rate Q is directly measured using the SMi SM j calibration equations or the Venturi meters (Rouse, 1978): here C d is the discharge coeicient, Q SM i SM j Cd At g DM (5) a A is the contraction area, and t DM (4) is the head drop across the Venturi, measured in height o a liquid column (t o ater) by the dierential manometer or the pressure transducer. Appendix A lists Venturi meter characteristics. Alternatively, the lo rate can be determined by integrating the measured velocity distribution over the pipe cross-section, as ollos:

3 Q i r u( r) rdr (6) 0. Part : epiv EFD Lab 1 investigated the use o epiv as a method or visualiing streamlines around a circular cylinder. This laboratory ill urther explore the uses o Particle Image Velocimetry (PIV) to track luid motion and calculate velocity vectors to describe the lo around a step-up model. In epiv analysis, a seeded luid is illuminated by a laser sheet, and a camera takes rapid photographs o the luid lo, at a rate o 30 H. Four parameters are used to control the camera settings; rightness This controls the overall brightness o the image. For the best PIV results, brightness should be set to a medium-lo value. Exposure This controls ho long the camera sensors are exposed per image rame taken. Higher values correspond to shorter exposure times, and loer values correspond to longer exposure times. PIV analysis beneits rom high exposure values (short exposure times), to acilitate sotare tracking o patterns o particles. Gain This controls the sensitivity o the sensors per unit time. Using higher gain ill ampliy the signal obtained by the sensors, so typically higher gain values are needed or images taken ith short exposure times, hich ould otherise be very dark. Hoever, increasing the gain has a side eect: using higher gain increases the noise in the image. Frames This speciies ho many images the camera ill take, or PIV analysis. At least to images are needed to process vectors, and taking more ill allo the sotare to average results and reduce precision error. Ater images are captured, they are processed to determine velocity vectors and magnitudes. The sotare takes a pair o consecutive images and breaks it into many small regions, called interrogation indos. In each interrogation indo, the PIV sotare compares the to images, determines ho ar the pattern o particles has moved in the amount o time beteen the to images, and calculates a single velocity vector or that indo. This is repeated across the entire measurement area, generating a vector ield. With the epiv system, three PIV parameters can be adjusted. Windo Sie This sets the sie (in pixels) o the interrogation indo. Ideally, smaller indos are desired, because they sho more lo detail, averaging over a smaller region o the lo. Hoever, i values are too small, eer particles pass through the interrogation indo, hich can result in unstable vector computation. Shit Sie This determines the distance (in pixels) that the sotare moves to start a ne interrogation indo. For example, i a indo sie o 80 and a shit sie o 40 ere used, the sotare ould compute a vector in the irst 80x80 interrogation indo, and then shit 40 pixels, computing a second vector in a ne 80x80 indo. The to indos ould overlap by 50%. A smaller shit sie results in more vectors being computed, but the increased overlap means that some o the data reported is repeated beteen the vectors. PIV Pairs This speciies ho many pairs o images are used or PIV calculations. PIV analysis compares any to consecutive images, i 10 images are captured, up to 9 PIV pairs can be speciied or computation. Results computed or each individual pair are averaged together, reducing precision error. 3

4 3. Experimental Process 3.1 Part 1: Pipe Flo Test Set-up Data Acquisition Data Reduction Uncertainty Analysis Data Analysis Facility & conditions Airlo pipe system Prepare experimental procedures Set bloer speed Statistical analysis Remove outliers Estimate bias limits Compare results ith benchmark data, CFD, and /or AFD Install model Calibration Prepare measurement systems N/A N/A Initialie data acquisition sotare Set valves in proper positions Open Labvie program Data reduction equations Evaluate Eq. 3 Evaluate Eq. 4 Evaluate Eq. 5 Evaluate Eq. 6 Table 1 Estimate precision limits Evaluate Eq. 9 Evaluate Eq. 13 Use Fig 8 as reerence value or velocity proile Use Fig 9 as reerence value or riction actor Plot experimental velocity proile and riction actor on reerence data Report dierence beteen experimental and reerence data Venturimeter transducer Valve maniold Run tests & acquire data Enter hardare settings Estimate total uncertainty Evaluate Eq. 7 Evaluate luid physics, EFD process and UA Pitot tube Micrometer Measure room and pipe temperature Evaluate Eq. 11 Anser questions in section 4 Measure total discharge Prepare report Measure pressure drop in pipe Measure velocity proile Repeat discharge measurement Store data Write results to output ile Figure6. EFD Process Test-setup The experimental measurement systems or the manual and automated conigurations are shon belo: Manual Data Acquisition 4 Automated Data Acquisition Facility (Figure 1) Facility (Figure 1) Thermometers (room and inside the setup) Thermometers (room and inside the pipe) Venturi meter (Figure ) Venturi meter (Figure ) Pitot-tube assembly (Figure 3) Pitot-tube assembly (Figure 3) Micrometer or Pitot positioning (Figure 3) Micrometer or Pitot positioning (Figure 3) Simple manometer DA (see Appendix ) Dierential manometer DA (see Appendix ) DA maniold DA maniold 3.1. Data Acquisition Each student group ill obtain velocity distributions and ill determine the riction actor or one o the 5.08cm pipes, either the top (smooth) or bottom (rough) pipe. Data acquired ith the DA are recorded electronically and ill subsequently be used or data reduction, using the Data reduction sheet. The experimental procedure ollos the sequence described belo, and is the same or both rough and smooth pipes:

5 1. Starting ith the lo velocity initially set, gradually increase the lo rate until the desired Re (96,000) is attained in the test section. The desired Re can be achieved or both upper and loer pipes, ith a setting o 5% on the bloer motor controller and control valve ully open or only one o the to pipes( i.e. hile smooth pipe valve is ully opened rough control valve must be closed). The other to venture meters should be kept close. Take temperature readings ith the digital thermometer (resolution 0.1 F) o the ambient air and the inside o the pipe, or calculating the corresponding ater and air densities, respectively. Input the temperature readings as requested by DA sotare interace. Use Labvie to record the venture meter reading ater entering the temperature o air inside the pipe. The remainder o the experiment ill be carried out at 5% bloer settings.. Since the temperature ill increase during the experiment, take three temperature readings, at the beginning, in the middle, and at the end o the measurements. 3. The velocity distribution is obtained by using the DA to measure stagnation heads across the ull pipe diameter, along ith the readings o the static heads, using the appropriate Pitot-tube assembly. Measure stagnation heads at radial intervals no greater than 5 mm. The recommended spacing or hal o the diameter o the upper and loer pipes is 0, 5, 10, 15, 0, 3, and 4 mm. Pitot tube position ithin the pipe is measured ith a micrometer (resolution o 0.01 mm). To establish precision limits or velocity proiles, measurements closest to the pipe all (at 4mm) should be taken 10 times. 4. Keeping the bloer setting at 5%, measure the pressure heads at taps 1,, 3, and 4 sequentially as indicated in Figure 1, using the DA, by connecting each tap to the pressure transducer. To establish precision limits or the riction actor, measurements at taps 3 and 4 should be repeated 10 times. The repeated measurements should be made alternatively beteen taps 3 and 4. It is important to note that the pressure in the pipe system luctuates hen opening or closing maniold valves, hence it is necessary to ait a e seconds beteen consecutive measurements or the pressure luctuation to settle don. 5. Record the venture meter reading again using the DA sotare Data Reduction Data reduction or pipe lo includes the olloing steps: 1. Use the average temperatures T and T a to determine, a, and a rom luid property tables. Determine the lo rate Q in the individual pipes using Equation (6), and the corresponding Re using Equation (1). The method or calculating lo rate (Equation 6) in individual pipes is explained in the Data reduction sheet.. Compare the lo rate readings taken ith the manometer and pressure transducer. 3. Calculate velocity distribution proiles or the pipe that you tested, using Equation (3). Plot the measured velocity proile, including the total velocity uncertainties calculated or measurements at the centerline and near the all. Compare the measured velocity distribution ith the benchmark data provided in Figure Calculate the riction actor or the pipe that you tested, using Equation (4). Use pressure readings rom taps 3 and 4, here the lo is ully developed. Compare ith benchmark data, including the uncertainty band or the measured Uncertainty Analysis Uncertainties or the experimentally-measured velocities and riction actor ill be evaluated. The methodology or estimating uncertainties ollos the AIAA S-071 Standard (AIAA, 1995) as summaried in Stern et al. (1999), or multiple tests (M = 10). Figure 7 shos to block diagrams depicting error propagation methodology or velocity and riction actor. Elemental errors or each o the measured independent variables in the data reduction equations should be identiied using the best available inormation or bias errors, and using repeated measurements or precision errors. In this analysis, e ill consider only the largest bias limits, and e ill neglect correlated bias errors. The spreadsheet or evaluating the uncertainties is provided in Data reduction sheet. The spreadsheet includes bias limit estimates or the individual measured variables. UA or Velocity Proile The DRE or the velocity proile, Equation (3), is o the orm: u r) F( g,,,, ). We ill ( a SM stag SM stat only consider bias limits or SM stag and SM stat. The total uncertainty or velocity measurements is: 5

6 The bias limit, u, and the precision limit, P u, or velocities are given by: u j i i1 i U u Z P (7) SMstag u Z Pu KSu / M (9) here S u is the standard deviation o the repeated velocity measurements. K = or (M =) 10 repeated measurements. The sensitivity coeicients (calculated using mean values or the independent variables) are: Z SMstag SM stag UA or Friction Factor SM stat g a s ; u SMstag Z SMstat Z SMstat g s SM stat a (10) ZSMstat The DRE or the riction actor, Equation (4), is o the orm: F g, D, L, Q,,,, ). We SM stag (8) ( a SM i SM j ill only consider bias limits or SM i and SM j. The total uncertainty or the riction actor is: U P (11) The bias limit,, and the precision limit, P, or the result are given by: j i i1 i SMi SMi P KS / M SM j SM j (1) (13) here S is the standard deviation o the repeated riction actor measurements. K = or (M =) 10 repeated measurements. The sensitivity coeicients (calculated using mean values or the independent variables) are: g D 8LQ ( m ) 1 ( m ) Z SMi a Z SM j g D 8LQ 5 (14) a a) b) Figure 7. lock diagrams or uncertainty estimation: a) velocity; b) riction actor Table1. ias limits or the individual variables included in the data reduction equations 6

7 u/umax Friction Factor = (L/D)V /(g) Relative Roughness, k /D Data Analysis Measurements obtained in the experiments ill be compared ith benchmark data. The benchmark data or velocity distribution is provided in numerical and graphical orm in Figure 8. The benchmark data or riction actor is provided by the Moody diagram (Figure 9) and by the Colebrook-White-based ormula (Roberson and Croe, 1997): 0.5 k D 5.74 log Re The olloing questions relate to luid physics, the EFD process, and uncertainty analysis. The solutions to these questions must be included in the Data analysis section o the lab report. Use the Data reduction sheet and attach it to your lab report. 1. Plot the velocity proile u(r) obtained rom the experiment, normalied by the maximum velocity in the pipe (u/u max ), against radial distance r, normalied by maximum radius (r/r). Plot the Schlichting data given in Figure 8 on the same plot. Compare the to proiles. Choose a point near the all here the value o r/r is close to 1. Sho the total percentage o uncertainty at that point using an uncertainty band.. Plot the head (in t o ater) at each pressure tap as a unction o distance along the pipe. Comment on the pressure head drop distribution along the pipe and comment on uncertainties and unaccounted error sources. 3. Calculate the riction actor and compare your results ith the Moody diagram. Sho the experimental value o the riction actor on the Moody diagram, along ith the uncertainty band. 4. What is the advantage o using non-dimensional orms or variables, such as those shon in Figures (8) and (9)? (15) r/r u/u max Schlichting Data (Re = 10 5 ) r/r Figure 8. enchmark data or the velocity proile h Laminar Flo Laminar Flo = 64/Re Critical Zone Transition Zone Hydraulically Smooth Complete Turbulence, Hydraulically Rough k /D = k /D = Reynolds Number, Re = VD Figure 9. enchmark data (Moody chart) or pipe riction actor Part : epiv 3..1 Test Setup Prior to the experiment, your TA ill set up the epiv system ith a Step-up lo insert. 3.. Data Acquisition The epiv experimental procedure ollos the steps listed belo: 1. Turn on the epiv system by lipping the sitch on the back o the device.. Adjust the knob on the ront o the epiv system to maximie the lo rate. 7

8 3. On the computer desktop, open the FLOWEX sotare. Click on the Acquire button, on the let side o the screen. 4. Speciy camera parameters or PIV image acquisition. Recommended values are 35, 100, 100, and 10, or brightness, exposure, gain, and rames, respectively. 5. Click on the Capture button to acquire 10 images. When FLOWEX returns to the Acquire dialogue, press F5 to reresh the screen and vie your images, hich should appear similar to the example in Figure 10, belo. I your images look signiicantly dierent, modiy your camera settings and re-capture the images. 6. Once you have satisactory results, click on the Analye button on the let side o the FLOWEX screen. 7. Speciy parameters or PIV processing. Values o 80, 0, and 9 are recommended or indo sie, shit sie, and PIV pairs, respectively. 8. Click on the Process button to begin PIV processing. This computation ill take a e minutes to complete. When FLOWEX returns to the Analye dialogue, press F5 to reresh the screen to vie your results. You should be able to see images o a velocity vector ield and velocity magnitude contours. Scroll the screen don belo the to images under the Results section. Right-click on Velocity vector ield data and save the ile to a orking directory on the computer. Rename the ile to include your group number Figure 10. Sample ra data or epiv step-up insert 3..3 Data Reduction Data reduction or epiv includes the olloing steps: 1. Open the text ile containing your velocity vector data and copy the entire contents o the ile. Open the ile EFD_ePIV_Data_Reduction, and paste the copied data into the green cells on the irst tab, labeled Ra Velocity Vector Data.. The second tab in the Excel ile, labeled Calculations, lays out the x-components o your velocity vector data into a matrix corresponding to the geometry o the step-up epiv model, and calculates the average velocity and lo rate or every x-value in the recorded data. 3. Plot the calculated average velocities and lo rates versus x-position Data Analysis Your lab report should include your plots o average velocity and lorate versus x-position. You should anser the olloing questions and include them as ell: 1. What happens to the average lo velocity as the cross-sectional area o the channel narros? Why does this happen?. Ho does the lo rate change ith x-position? Is this expected? Why or hy not? 4. Reerences Roberson, J.A. and Croe, C.T. (1997). Engineering Fluid Mechanics, 7th edition, Houghton Schlichting, H. (1968). oundary-layer Theory, McGra-Hill, Ne York, NY. Rouse, H. (1978). Elementary Mechanics o Fluids, Dover Publications, Inc., Ne Yoirk, NY. Milin, oston, MA. 8

9 Stern, F., Muste, M., eninati, L-M, Eichinger,. (1999). Summary o Experimental Uncertainty Assessment Methodology ith Example, IIHR Report No. 406, Ioa Institute o Hydraulic Research, The University o Ioa, Ioa City, IA. APPENDIX A SPECIFICATIONS FOR THE EXPERIMENTAL FACILITY COMPONENTS Table A1. Pipe characteristics Table 1. Pipe characteristics Experimental Pipe Top Middle ottom Diameter (mm) Internal Surace Smooth, k = 0.05 mm Smooth Rough, k =0.04 mm Number o Taps Tap Spacing (t) Table A. Venturi meter characteristics Venturi speciications Small Medium Large Contraction Diameter, D t (mm) Discharge Coeicient, C d Pitot-Tube Housing Tested Pipe To Atmosphere Static rom Taps To Atmosphere DA DA 1 Dierential Manometer Static Transducer Valve Maniold Stagnation Simple Manometer Venturi Meter Return Pipe LEGEND Tygon Tubing Connections a) Photograph o experimental setup b) Schematic o experimental setup Figure A.1. Layout o the data acquisition systems 9

10 APPENDIX THE AUTOMATED DATA ACQUISITION SYSTEM (ADAS) Step 1: Initial Setup 1. Getting Started ith DA Double click on the shortcut ound on the DA computer: Pipe_lov7.vi. A indo as shon in Figure.1 ill open. Hit Run to run the program.. Under Speciications (see Figure.), TAs/students can add comments regarding the experiment i needed. (characteristics o pipe selected or the measurements, targeted Re, etc.). Figure.1. Hit Run to run the program Figure.. Experiment Speciications area 3. Type in the reading o the air temperature ( o C) in the acility in the Temperature indo, as shon in Figure.3. Step : Discharge Measurements 4. Select the DPD menu to measure the lo discharge in the pipe. To select it, click on the DPD tab as shon in Figure.4. Connect the largest venturimeter in the loermost pipe directly to the pressure transducer. Figure.3. Set pipe air temperature 5. Click Acquire button in the Measurement indo on the right side o the interace to obtain a reading o the head drop on the Venturi meter (Figure.5). Note: Discharge measurements are taken at the beginning and at the end o the experiment. The average o the to discharges is considered or the lab report to account or the variation o the temperature during the experiment. Step 3: Velocity Distribution Measurements Figure.4. Open DPD menu Figure.5. Click on Acquire 10

11 Velocity data ill be measured ith the appropriate pitot-tube according to the instructions given by the TA. Select the DPV tab, see Figure.6. Connect the stagnation point on the pitot probe to the high side o the transducer and leave the lo side open. 6. Move the Pitot tube in the housing at the desired location or the velocity measurement (e.g. 0 mm rom the centerline). Click Acquire (Figure.7). The screen shon in Figure.7 ill then prompt the user or the pitot-tube location. Enter Pitot-tube position in the dialog box. Click OK to start the measurement. 7. Folloing step 7, the screen shon in Figure.8 ill appear. Open the stagnation point and connect the static point rom the pitot probe to the high side o the transducer, in this case also the lo side o the transducer remains open. Click OK on the screen shon in Figure.8. Note: To establish precision limits or the simple manometer measurements, measurements should be taken at least 10 times. The repeated measurements should be made using an alternative pattern to avoid successive measurements at the same location. Velocities are displayed graphically in a indo ater each measurement is taken. 8. Record inal ambient and pipe air temperatures as indicated in step 3. Step 4: Friction Factor Measurements 9. Select DPF tab in the main menu (Figure.9). Choose the desired pressure tap that is to be measured and connect it to the high side o the pressure transducer and leave the lo side open to atmosphere. Figure.6. Click on DPV tap to measure Dierential or Velocity Figure.7. Enter position o pitot-tube Figure.8. Click OK hen ready or static pressure measurement 10. Then enter the pressure tap number in the indo shon in Figure.10. Click OK. Click on Acquire as shon at Step 7 to make the measurement. Close the inger valve on the maniold and open the valve leading to the next measurement location. Note: The pressure drop along the pipe is shon on a plot and ideally a linear curve should be observed. Figure.9. Click on DPF tap to measure Dierential or Friction Factor Figure.10. Enter 1 or tap Z sm1, or tap Z sm,...etc. 11

12 11. Write measurements to a ile. Click on Write Results (see Figure.11). Figure.11. Click on Write Results 1. The screen indicated in Figure.1 ill appear. Save the result ile in the directory indicated by the TAs using a.txt extension or the ile name. The data is outputted in Excel compatible ile ormat. Units or the measured variables are speciied in the output ile. Figure.1. Write results to a ile 1