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

Transcription

1 57:00 Mechnics o Flids nd Trnser Processes Exercise Notes or the Pipe Flo TM Mesrement o Flo Rte, Velocity Proile nd Friction Fctor in Pipe Flos S. Ghosh, M. Mste, M. Wilson nd F. Stern. Prpose To provide stdents hnds-on experience ith Pipe stnd test cility nd modern mesrement systems inclding pressre trnsdcers nd pitot probes nd compteried dt cqisition sing Lbvie. To mesre lo rte, velocity proiles nd riction ctors in smooth nd rogh pipes, determine the mesrement ncertinties, nd compre the reslts ith benchmrk dt.. Experimentl Design The experiments re condcted in n instrctionl irlo pipe cility (Figre ). The ir is blon into lrge reservoir locted t the pstrem end o the system. Pressre bilt p in the reservoir, orces the ir to lo throgh ny o the three horiontl pipes. Pressre tps re locted on ech pipe long intervls o.54m, or sttic pressre mesrements. The pipe chrcteristics or ech o the pipes re provided in Appendix A. At the donstrem end o the system, the ir is directed donrd nd bck, throgh ny o the three pipes o vrying dimeters itted ith Ventri meters (Figre ). The top three vlves control lo throgh the experimentl pipes, hile the bottom three vlves control the Ventri meter to be sed. The ventre meter ith 5.08cm dimeter is sed to mesre the totl lo rte, the other to re kept closed. Six gte vlves re sed or directing the lo. The top nd bottom 5.08cm pipes re only sed or mesrements hile the middle one is kept closed dring the experiment. Velocity mesrements in the top nd bottom pipes re obtined sing pitot probe (Figre 3). Figre. Airlo pipe system Figre. Ventrimeter Figre 3. Pitot-probe Pressres re cqired either mnlly, sing simple nd dierentil mnometers or dt cqisition, or tomticlly hereby the mnometers re connected to n tomted Dt Acqisition (DA) system tht converts pressre to voltges sing pressre trnsdcers. Dt cqisition is controlled nd interced by Lbvie sotre described in Appendix. The schemtic o the to lterntive mesrement systems is provided in Figre 4. Dt Acqisition Instrmenttion Dierentil mnometer Ventrimeter Pitot tbe Pressre tp Pressre trnsdcer Sttic Simple mnometer Stgntion Pressre trnsdcer Simple mnometer Pressre trnsdcer Lbvie Lbvie Lbvie Figre4. Mnl nd tomted mesrement systems sed in the experiment

2 All pressre tps on the pipes, ventrimeters nd pitot probes hve 0.635cm dimeter qick copler connections tht cn be hooked p to the pressre trnsdcers.. Dt redction (DR) eqtions In lly developed, xi-symmetric pipe lo, the xil velocity ( = (r)) t rdil distnce r rom the pipe centerline, is independent o the direction in hich r is considered (Figre 5). Hoever, the shpe o the velocity proile is dierent or lminr nd trblent los. Lminr nd trblent lo regimes re distingished by the lo Reynolds nmber deined s VD 4Q Re = ν πdν = () Where, V is the verge pipe velocity, D is the pipe dimeter, Q is the pipe lo rte, nd ν is the kinemtic viscosity o the lid. For lly developed lminr lo (Re < 000), nlyticl soltion or the dierentil eqtions o the lid lo (Nvier-Stokes nd continity) cn be obtined. For trblent pipe los (Re > 000), there is no exct soltion, hence semi-empiricl ls or velocity distribtion re sed insted. The pipe-hed loss de to riction is obtined rom the Drcy-Weisbch eqtion: L V R R r mx V () V mx (b) Prbolic crve (r) (r) R r da A Figre 5. Velocity distribtions or lly developed pipe lo: ) lminr lo; b) trblent lo h = () D g here, is the (Drcy) riction ctor, L is the length o the pipe over hich the loss occrs, h is the hed loss de to viscos eects, nd g is the grvittionl ccelertion. Moody digrm provides the riction ctor or pipe los ith smooth nd rogh lls in lminr nd trblent regimes. The riction ctor depends on Re nd reltive roghness k/d o the pipe (or lrge enogh Re, the riction ctor is solely dependent on the reltive roghness). Velocity distribtions in the pipes re mesred ith Pitot tbes hosed in glss-lled boxes (Figre 3). The dt redction eqtion (DRE) or the mesrement o the velocity proiles is obtined by pplying ernolli s eqtion or the Pitot tbe [ () r ] g ( r) = SM Stg SM Stt here, (r) is the velocity t the rdil position r, g is the grvittionl ccelertion, SM (r) is the stgntion pressre Stg hed determined by the Pitot probe locted t rdil position r, SM Stt is the sttic pressre hed in the pipe, eql to tht o the mbient pressre inside the glss-lled box. The redings o the pressre heds in Eqtion (3) re in height o liqid colmn (t o ter)., is the density o ter nd is the density o ir. DRE or the riction ctor is one o the Drcy Weisbch eqtion orms (Roberson & Croe, 997) 5 gπ D = ( SM SM ) (4) i j 8LQ here, L is the pipe length beteen the tps i nd j, nd SM i SM is the dierence in pressre beteen the tps i nd j. j The lo rte Q is directly mesred sing the clibrtion eqtions or the Ventri meters (Rose, 978) Q / = Cd At g DM (5) here, C d is the dischrge coeicient, A t is the contrction re, DM is the hed drop cross the Ventri, mesred in height o liqid colmn (t o ter) by the dierentil mnometer or the pressre trnsdcer. Appendix A lists Ventri meter chrcteristics. Alterntively, the lo rte cn be determined by integrting the mesred velocity distribtion over the pipe cross-section. Q i r = π ( r) rdr (6) 0 (3) dh

3 3. Experimentl Process Test Set-p Dt Acqisition Dt Redction Uncertinty Anlysis Dt Anlysis Fcility & conditions Airlo pipe system Prepre experimentl procedres Set bloer speed Sttisticl nlysis Remove otliers Estimte bis limits Compre reslts ith benchmrk dt, CFD, nd /or AFD Instll model Clibrtion Prepre mesrement systems N/A N/A Initilie dt cqisition sotre Set vlves in proper positions Open Lbvie progrm Dt redction eqtions Evlte Eq. 3 Evlte Eq. 4 Evlte Eq. 5 Evlte Eq. 6 Tble Estimte precision limits Evlte Eq. 9 Evlte Eq. 3 Use Fig 8 s reerence vle or velocity proile Use Fig 9 s reerence vle or riction ctor Plot experimentl velocity proile nd riction ctor on reerence dt Report dierence beteen experimentl nd reerence dt Ventrimeter Pressre trnsdcer Vlve mniold Rn tests & cqire dt Enter hrdre settings Estimte totl ncertinty Evlte Eq. 7 Evlte lid physics, EFD process nd UA Pitot tbe Micrometer Mesre room nd pipe tempertre Evlte Eq. Anser qestions in section 4 Mesre totl dischrge Prepre report Mesre pressre drop in pipe Mesre velocity proile Repet dischrge mesrement Store dt Write reslts to otpt ile Figre6. EFD Process 3.. Test-setp The experimentl mesrement systems or the mnl nd tomted conigrtions re shon belo: Mnl Dt Acqisition 3 Atomted Dt Acqisition Fcility (Figre ) Fcility (Figre ) Thermometers (room nd inside the setp) Thermometers (room nd inside the pipe) Ventri meter (Figre ) Ventri meter (Figre ) Pitot-tbe ssembly (Figre 3) Pitot-tbe ssembly (Figre 3) Micrometer or Pitot positioning (Figre 3) Micrometer or Pitot positioning (Figre 3) Simple mnometer DA (see Appendix ) Dierentil mnometer DA (see Appendix ) DA mniold DA mniold 3.. Dt Acqisition Ech stdent grop ill obtin velocity distribtions nd determine the riction ctor or one o the 5.08cm (rogh or smooth) pipes. Dt cqired ith the DA re recorded electroniclly nd sbseqently sed or dt redction. The Dt redction sheet ill be sed or dt redction. The experimentl procedre ollos the seqence described belo:. Strting ith the lo velocity initilly set, increse grdlly the lo rte ntil the desired Re (= 96,000) in the test section is ttined (the desired Re cn be chieved or both pper nd loer pipes, ith setting o 35% on the bloer motor controller nd control vlves lly open). Mke t lest ive lo rte mesrements ith the ventre-

4 meter o 5.08cm contrction dimeter. The other to ventre-meters re kept closed. For the ive mesrements, the bloer setting shold strt rom 5% nd rech 35%, ith 5% increment ech time (recommended settings: 5%, 0% 5% 30% 35%). Record yor redings rom both the mnometer nd pressre trnsdcer. The remining experiment is crried ot t 35% bloer settings. Use Lbvie to record the ventrimeter reding.. Tke tempertre redings ith the digitl thermometer (resoltion 0. F) or mbient ir nd inside the pipe or clclting the corresponding ter nd ir densities, respectively. Inpt the tempertre redings s reqested by DA sotre interce. Since the tempertre increses dring the experiment, tke three tempertre redings t the beginning, in the middle, nd t the end o the mesrements. 3. Velocity distribtion is obtined ith the DA by mesring stgntion heds cross the ll pipe dimeter long ith the redings o the sttic heds sing the pproprite Pitot-tbe ssembly. Mesre stgntion heds t rdil intervls no greter thn 5 mm (recommended spcing or hl dimeter o the pper nd loer pipes is 0, 5, 0, 5, 0, 3, nd 4 mm). Positioning o the Pitot tbe ithin the pipe is mde ith micrometer (resoltion o 0.0 mm). To estblish precision limits or velocity proiles, mesrements ner the pipe ll (t 4mm) shold be tken t lest 0 times. The sme procedre is sed or the pper (smooth) nd loer (rogh) pipes. 4. Keeping the bloer setting t 35%, mesre the pressre heds t pressre tps,, 3, nd 4 seqentilly s indicted in Figre sing the DA by connecting ech tp to the pressre trnsdcer. To estblish precision limits or the riction ctor, mesrements, preerbly t tps 3 nd 4 shold be repeted 0 times. The repeted mesrements shold be mde lterntively beteen tp 3 nd 4. It is importnt to note tht the pressre in the pipe system lcttes hen opening or closing mniold vlves, hence it is necessry to it e seconds beteen consective mesrements, or the pressre lcttion to settle don. The dt cqisition procedre is sme or both rogh nd smooth pipes. 3.3 Dt Redction Dt redction incldes the olloing steps:. Using the verge tempertres, T nd T to determine,, nd ν rom lid property tbles. Determine the lo rte (Q) in the individl pipes sing Eqtion (6) nd Re sing Eqtion (). The method or clclting lo rte (Eqtion 6) in individl pipes is explined in the Dt redction sheet.. Compre the lo rte redings tken ith the mnometer nd pressre trnsdcer. 3. Clclte velocity distribtion proiles or the tested pipe sing Eqtion (3). Plot the mesred velocity proile inclding the velocity totl ncertinties clclted or centerline nd ner the ll mesrements. Compre the mesred velocity distribtion ith the benchmrk dt provided in Figre Clclte the riction ctor or the tested pipe sing Eqtion (4). Use redings t tps 3 nd 4, here the lo is lly developed. Compre ith benchmrk dt, inclding ncertinty bnd or the mesred. 3.4 Uncertinty Anlysis Uncertinties or the experimentlly mesred velocities nd riction ctor ill be evlted. The methodology or estimting ncertinties ollos the AIAA S-07 Stndrd (AIAA, 995) s smmried in Stern et l. (999) or mltiple tests (M = 0). The block digrms or error propgtions in the mesrements re provided in Figre 7. Elementl errors or ech o the mesred independent vrible in dt redction eqtions shold be identiied sing the best vilble inormtion (or bis errors) nd repeted mesrements (or precision errors). We ill consider in the nlysis only the lrgest bis limits nd neglect correlted bis errors. The spredsheet or evlting the ncertinties is provided in Dt redction sheet. The spredsheet incldes bis limit estimtes or the individl mesred vribles. The DRE or the velocity proile, Eqtion (3), is o the orm: ( r) = F( g,,, SM stg, SM stt ). We ill only consider bis limits or SM stg nd SM stt. The totl ncertinty or velocity mesrements is U = + P (7) The bis limit,, nd the precision limit, P, or velocities re given by j = θ i i = θ Z SM stg Z + θ SM stg i= 4 Z SM stt Z SM stt P = KS / M (9) here the coeicients θ re clclted sing men vles or the independent vribles (8)

5 Θ ZSM stg = SM stt ( ) SM stg 0.5g ( s ); Θ Z SM stt = ( ) SM stg g SM stt ( s ) (0) nd S is the stndrd devition o the repeted velocity mesrements. K = or (M =) 0 repeted mesrements. The DRE or the riction ctor, Eqtion (4), is o the orm: = F g, D, L, Q,,,, ). We ( SM i SM j ill only consider bis limits or SM i nd SM j. The totl ncertinty or the riction ctor is: U = + P () The bis limit,, nd the precision limit, P, or the reslt re given by j i= = θ i i = θ SM i + θ SM i SM j SM j () P = KS / M (3) here, the coeicients θ re clclted sing men vles or the independent vribles: 5 5 gπ D gπ D θ Z = () ( m ) θ = ( ) ( m ) SM i Z (4) SM j 8LQ 8LQ nd S is the stndrd devition o the repeted riction ctor mesrements. K = or (M =) 0 repeted mesrements. EXPERIMENTAL ERROR SOURCES EXPERIMENTAL ERROR SOURCES TEMPERATURE WATER TEMPERATURE AIR STAGNATION PRESSURE STATIC PRESSURE INDIVIDUAL MEASUREMENT SYSTEMS TEMPERATURE WATER TEMPERATURE AIR PIPE PRESSURE VENTURI PRESSURE INDIVIDUAL MEASUREMENT SYSTEMS T T,P T T T,P T SM stg, P SM stg SMstg SM stt, P SMstt SMstt MEASUREMENT OF INDIVIDUAL VARIALES T T,P T T T,P T SM, P SM SM DM, P DM DM MEASUREMENT OF INDIVIDUAL VARIALES = F(T ) = F(T ) ½ ( - ) g SMstg SMstt =F(,,, ) = SM SM stg stt DATA REDUCTION EQUATIONS = F(T ) = F(T ) Q=F( ) DM =F(,,,Q) = SM g D 8LQ 5 ( - ) SM i SM j DATA REDUCTION EQUATIONS,P EXPERIMENTAL RESULT, P EXPERIMENTAL RESULTS ) b) Figre 7. lock digrms or ncertinty estimtion: ) velocity; b) riction ctor Tble. is limits or the individl vribles inclded in the dt redction eqtions 3.5. Dt Anlysis Mesrements obtined in the experiments ill be compred ith benchmrk dt. The benchmrk dt or velocity distribtion is provided in nmericl nd grphicl orm in Figre 8. The benchmrk dt or riction ctor is provided by the Moody digrm (Figre 9) nd by the Colebrook-White-bsed orml (Roberson nd Croe, 997) 0.5 = k D 5.74 log Re (5) 5

6 κ The olloing qestions help to evlte lid physics, EFD process, nd ncertinty nlysis. The soltions to these qestions mst be inclded in the Dt nlysis section o the lb report. Use dt redction sheet nd ttch it to yor lb reports.. Comment on the dierences in lo rte redings obtined by the mnometer nd pressre trnsdcer.. Plot the velocity proile (r) obtined rom the experiment normlied by mximm velocity in pipe (/U mx ) ginst rdil distnce r, normlied by mximm rdis (r/r). Plot the Schlichting dt given in Figre 8 on the sme plot. Compre the to proiles. Choose point ner the ll here, the vle o r/r, is close to. Sho the totl percentge ncertinty t tht point sing n ncertinty bnd. 3. Plot the hed (in t o ir) t ech pressre tp s nction o distnce long the pipe. Comment on the pressre hed drop distribtion long the pipe nd comment on ncertinties nd ncconted error sorces. 4. Clclte the riction ctor nd compre reslts ith the Moody digrm. Sho the experimentl vle o the riction ctor on the Moody digrm long ith the ncertinty bnd. 5. Wht is the dvntge o sing non-dimensionl orms or vribles sch s those shon in Figres (8) nd (9)? r/r /U mx /Umx Schlichting Dt (Re = 0 5 ) r/r Figre 8. enchmrk dt or the velocity proile h Friction Fctor = (L/D)V /(g) Lminr Flo Lminr Flo = 64/Re Criticl Zone Trnsition Zone Hydrliclly Smooth Complete Trblence, Hydrliclly Rogh k /D = k /D = Reynolds Nmber, Re = VD ν Figre 9. enchmrk dt (Moody chrt) or pipe riction ctor Reltive Roghness, /D 4. Reerences Roberson, J.A. nd Croe, C.T. (997). Engineering Flid Mechnics, 7th edition, Hoghton Milin, oston, MA. Schlichting, H. (968). ondry-lyer Theory, McGr-Hill, Ne York, NY. Rose, H. (978). Elementry Mechnics o Flids, Dover Pblictions, Inc., Ne Yoirk, NY. Stern, F., Mste, M., eninti, L-M, Eichinger,. (999). Smmry o Experimentl Uncertinty Assessment Methodology ith Exmple, IIHR Report No. 406, Io Institte o Hydrlic Reserch, The University o Io, Io City, IA. APPENDIX A SPECIFICATIONS FOR THE EXPERIMENTAL FACILITY COMPONENTS Tble A. Pipe chrcteristics Experimentl Pipe Top Middle ottom Dimeter (mm) Internl Srce Smooth, k = 0.05 mm Smooth Rogh, k =0.04 mm Nmber o Pressre Tps Tp Spcing (t)

7 Tble A. Ventri meter chrcteristics Ventri speciictions Smll Medim Lrge Contrction Dimeter, D t (mm) Dischrge Coeicient, C d Pitot-Tbe Hosing Tested Pipe Sttic Pressre rom Pressre Tps To Atmosphere To Atmosphere DA DA Dierentil Mnometer Sttic Pressre Pressre Trnsdcer Vlve Mniold Stgntion Pressre Simple Mnometer Ventri Meter Retrn Pipe LEGEND Tygon Tbing Connections ) Photogrph o experimentl setp b) Schemtic o experimentl setp Figre A.. Lyot o the dt cqisition systems APPENDIX THE AUTOMATED DATA ACQUISITION SYSTEM (ADAS) Step : Initil Setp. Getting Strted ith DA Doble click on the shortct ond on the DA compter: Pipe_lov7.vi. A indo s shon in Figre. ill open. Hit Rn to rn the progrm.. Under Speciictions (see Figre.), TAs/stdents cn dd comments regrding the experiment i needed. (chrcteristics o pipe selected or the mesrements, trgeted Re, etc.). Figre.. Hit Rn to rn the progrm Figre.. Experiment Speciictions re 3. Type in the reding o the ir tempertre ( o C) in the cility in the Tempertre indo, s shon in Figre.3. Figre.3. Set pipe ir tempertre 7

8 Step : Dischrge Mesrements 4. Select the DPD men to mesre the lo dischrge in the pipe. To select it, click on the DPD tb s shon in Figre.4. Connect the lrgest ventrimeter in the loermost pipe directly to the pressre trnsdcer. 5. Click Acqire Pressre btton in the Mesrement indo on the right side o the interce to obtin reding o the hed drop on the Ventri meter (Figre.5). Note: Dischrge mesrements re tken t the beginning nd t the end o the experiment. The verge o the to dischrges is considered or the lb report to ccont or the vrition o the tempertre dring the experiment. Step 3: Velocity Distribtion Mesrements Velocity dt ill be mesred ith the pproprite pitot-tbe ccording to the instrctions given by the TA. Select the DPV tb, see Figre.6. Connect the stgntion point on the pitot probe to the high side o the trnsdcer nd leve the lo side open. Figre.4. Open DPD men Figre.5. Click on Acqire Pressre 6. Move the Pitot tbe in the hosing t the desired loction or the velocity mesrement (e.g. 0 mm rom the centerline). Click Acqire Pressre (Figre.7). The screen shon in Figre.7 ill then prompt the ser or the pitot-tbe loction. Enter Pitot-tbe position in the dilog box. Click OK to strt the mesrement. 7. Folloing step 7, the screen shon in Figre.8 ill pper. Open the stgntion point nd connect the sttic point rom the pitot probe to the high side o the trnsdcer, in this cse lso the lo side o the trnsdcer remins open. Click OK on the screen shon in Figre.8. Note: To estblish precision limits or the simple mnometer mesrements, mesrements shold be tken t lest 0 times. The repeted mesrements shold be mde sing n lterntive pttern to void sccessive mesrements t the sme loction. Velocities re displyed grphiclly in indo ter ech mesrement is tken. 8. Record inl mbient nd pipe ir tempertres s indicted in step 3. Figre.6. Click on DPV tp to mesre Dierentil Pressre or Velocity Figre.7. Enter position o pitot-tbe Figre.8. Click OK hen redy or sttic pressre mesrement 8

9 Step 4: Friction Fctor Mesrements 9. Select DPF tb in the min men (Figre.9). Choose the desired pressre tp tht is to be mesred nd connect it to the high side o the pressre trnsdcer nd leve the lo side open to tmosphere. 0. Then enter the pressre tp nmber in the indo shon in Figre.0. Click OK. Click on Acqire Pressre s shon t Step 7 to mke the mesrement. Close the inger vlve on the mniold nd open the vlve leding to the next mesrement loction. Note: The pressre drop long the pipe is shon on plot nd idelly liner crve shold be observed. Figre.9. Click on DPF tp to mesre Dierentil Pressre or Friction Fctor Figre.0. Enter or tp Z sm, or tp Z sm,...etc.. Write mesrements to ile. Click on Write Reslts (see Figre.). Figre.. Click on Write Reslts 3. The screen indicted in Figre. ill pper. Sve the reslt ile in the directory indicted by the TAs sing.txt extension or the ile nme. The dt is otptted in Excel comptible ile ormt. Units or the mesred vribles re speciied in the otpt ile. Figre.. Write reslts to ile 9