Flow Measurement Lab Report.docx

Comparison of Diff Different erent Flow Measurement Devices CHEG 2810 - Experiment 1

Danielle Valdivia, Travis Garlock, and Alex Maldonado October 22th, 2015

AB!"AC!

!he purpose of this e#periment was to calculate volumetric flow rates usin$ various flow measurement %evices an% compare their accurac& an% precision' !he three flow measurement %evices were( rotameter, orifice plate, an% ma$netic flow meter' As it turns out the most accurate an% precise flow meter was the ma$netic flow meter' !he ma$netic flow meter ha% an avera$e of  2'1) error while the orifice plate an% rotameter ha% a 1*'+) an% 2'*) error respectivel&' !he ma$netic flow meter an% rotameter were both accurate an% precise, but the orifice plate was neither' !his error was more than liel& to be cause% b& inefficienc& in the water collecte% from the output an% for the orifice plate the constant -umpin$ of pressures %i% not allow accurate rea%in$s' !hese results show that when precision is essential the rotameter or ma$netic flow meter shoul% be use%' Of these two when the flowrate nee%s to be imme%iatel& nown an% eas& to see chan$es the rotameter is the best choice'./!"ODC!.O/ an% BAC"O/D ./FO"MA!.O/ !he rotameter is a versatile process control %evice that can %emonstrate chan$es in flow of various materials3 in both $as an% li4ui% phases' !he %esi$n of the rotameter is %esi$ne% to e#ploit the opposition between the %ownwar% force of $ravit& an% the opposin$ force of the flowin$ flui%' !his force of the flowin$ flui% mainl& comes from the pressure %ifference the  bottom of the rotameter an% the si%es of the rotameter Basics of "otameters, 20026' 7hen the flui% approaches the bottom of the bob, the velocit& increases %ue to the contraction of the -et streams' 7hen there is a volumetric flow passin$ throu$h the meter, the velocit& of the -et is $iven b& the e4uation

u=

q C c a x

where 4 is the flow rate, Cc is the ratio narrowest part of the -et to the area of the area of the tube' .f we substitute Bernoulli8s law we $et  P1− P2=

 ρ 2

( ) q C c a x

Example

of the bob, an% a# as this in to

2

 which %emonstrates that the pressure

%ifference

cause% b& the -et stream contraction causes the buo&ant force' 7hen the flow rate is increase% an% the flui% an% rotameter sta& the same6 the pressure %ifference becomes $reater thus increasin$ the buo&ant force Di-stelber$en, 1+*96' 7hen the buo&ant force is the same as the $ravitational force of the bob ne$lectin$ the $ravitational force of the flui%6 the Rotameter in lab  bob reaches e4uilibrium' !his e4uilibrium stabili:es the hei$ht of the bob relative to the tube an% the velocit& of the flui% can be calculate% usin$ the e4uation u=

√

2 g V b

7here,

C Ab

(

∗

 ρb− ρ f   ρf 

)

• • • • • • •

u; ; volumetric flow rate Cm ; variable that contains constants from previous e4uation

!hese e4uations an% theor& show the useful an% versatile the rotameter is to measure flow rate' "otameters are still ver& popular amon$ in%ustrial applications because of cost effectiveness' !he& are relativel& ine#pensive an% provi%e a simple wa& to control flow for a wi%e variet& of substances' 7ith more comple# flowmeters the accurac& an% precision is $reatl& increase% but comes with a heft& price ta$' Overall rotameters are viable options when simplicit& an% cost effectiveness are priorities, an% when precision is top priorit& %ifferent flow meters are better options' Another wi%el& use% flow meter is calle% the orifice meter an% measures the flow of a li4ui% similar to that of a venturi meter, b& restriction' !he fi#e%?area flow is %ue to a finel& machine% concentric hole within a plate mounte%  perpen%icularl& between two flan$es' @ressure taps are place% before an% after the machine% plate an% connecte% to a manometer an%or a %ifferential pressure transmitter' !he cross sectional area of the pipe %iameter is re%uce%, increasin$ the velocit& hea% while %ecreasin$ the pressure hea% McCabe, 226'  !his re%uction in pressure hea% is what the connecte% %evice measures an% is correlate% to the li4ui% flow rate'

As the li4ui% approaches the orifice plate, a vena contracta forms' !his is where the flui% stream separates itself from the %ownstream si%e of the orifice plate an% forms a -et in the %ownstream li4ui% an% where the li4ui% is as its minimum cross section' !his is a $oo% location for the tap to  be place% so that the meter ma& measure the %ownstream velocit&' !his st&le of tap is calle% the vena contracta tap an% will have a static hole one?half to two pipe %iameters from the orifice  plate an% the other locate% at the vena contracta @err&, ?96' !hese t&pe of taps $ive the lar$est %ifferential hea% for a $iven flow rate' !he flow rate e4uation is $iven below' Q=

C d  A 2

√ ( ) 1−

 A 2  A1

2

√

2

( p

1

 p2 )

−

 ρ

7here • • • • •

p1?p26 ; the pressure %rop = ; the %ensit& A1 ; the pipe cross?sectional area A2 ; the orifice cross?sectional area C% ; the %ischar$e coefficient

!he %ischar$e coefficient chan$es with "e&nol%8s /umber at the orifice, base% on the orifice %iameter an% velocit& @err&, 10?1*6' !his number will increase with e%$e?roun%ness of the machine% hole in the plate' /ear the orifice plate on the %ownstream si%e of li4ui%, e%%ies form in the li4ui% %ue to lar$e friction losses' !hese friction losses account for the poor pressure recover& of an orifice meter an% its lar$est %isa%vanta$e' @ower losses nee% to be supplemente% with pumpin$ e4uipment' !he ma$netic flow meter is a more a%vance% %evice use% to measure the flow rate of a flui%' 7hen usin$ this %evice, a ma$netic fiel% is sprea% throu$hout the measurin$ tube3 the ions flowin$ within the flui% create a potential %ifference to be measure% b& the flow meter' !his potential %ifference is proportional to the flow velocit& of the flui%' .n or%er to use a ma$netic flow meter to measure a flow?rate, the flui% must be con%uctin$, an% the pipe must be insulatin$' Ma$netic flow meters are most useful in that the& are a non?contact, non?movin$ flow meter, which is ver& useful when measurin$ the flow rate of a %irt& li4ui% or wastewater material that is water?base%'  Theoretical Magnetic Flow Meter (Cadillac Meters, 2013)

!he ma$netic flow meter is base% on the principle of Fara%a&8s aw' !his states that the volta$e across a con%uctor as it moves perpen%icular to the ma$netic fiel% lines is proportional to the velocit& of that con%uctor Ma$netic Flow Meters, 20156' Fara%a&8s aw is represente% b& the e4uation(

 E=V ∗B∗ D

7here, • • • •

E ; volta$e $enerate% in a con%uctor, < ; velocit& of that con%uctor, B ; ma$netic fiel% stren$th, D ; len$th of the con%uctor bein$ measure%'

Each ma$netic flow meter is fitte% to a ma#imum flow that can be measure% b& that  particular flow meter' !he in%uce% potential an% the measure% flow are compare% to the ma#imum permitte% potential an% ma#imum measurable flow, respectivel& prin$stea%, 20156' !he %ispla&e% value on the ma$netic flow meter can either be the %irect flow measurement, or a percenta$e of the ma#imum measurable flow of the flow meter' Ma$netic flow meters are one of the most common t&pes of flow meters use% in in%ustr&' !he& are use% for their relative ease an% their nown accurac&' Ma$netic flow meters are much less cost effective than other flow meters but are much more e#act in their measurement' Ma$netic flow meters also come with the caveat that onl& con%uctin$ flui%s ma& be measure%, which proves them to be ina%e4uate in man& in%ustrial situations' enerall&, ma$netic flow meters are use% when precision is necessar&, an% when con%uctive flui%s are involve%'

ME!OD@"O!OCO Rotameter

7hen there is not a flow throu$h the rotameter, the bob is at the lowest point in the tube' Mar this point on a piece of tape on the si%e of the rotameter' !his will be the initial point when tain$ hei$ht measurements' Open the valves an% allowin$ a small flow throu$h the pipes an% observe the small increase in hei$ht of the bob' Allow the s&stem to fin% e4uilibrium from turbulent flow to more of a laminar flow' !ae a ruler an% measure from the initial point to the point where the  bob is when water is flowin$ throu$h' 7hile tain$ the bob hei$ht measurement, for five secon%s fill a bucet with the output water' !hen wei$h the bucet an% recor% the mass of the water' Orifice Plate

enerall&, a manometer will measure the pressure %rop b& correlatin$ it to the hei$ht of flui% in the two le$s of the manometer' owever, the %i$ital manometer use% in this lab will correlate the %ifference between the mechanical pressures on two trans%ucers locate% at the taps' !his will $ive a similar rea%in$ to the %ifferential pressure trans%ucer which will %ispla& as mA' !he lower the flow rate, the lower the mechanical pressure an% therefore, the lower the rea%in$ on  both meters' 7hen the e#periment is starte%, there is no flow throu$h the orifice plate an% both meters will rou$hl& rea% close to :ero' As the flow rate increases throu$h the pipin$ at each step interval, so too %oes the rea%in$ on each meter' Each time the flow rate is increase%, the s&stem is allowe% to e4uilibrate before flow measurements are taen with a bucet an% a stop watch' !he amount of water in the $iven time is then measure% for mass an% recor%e%, resultin$ in a flow rate versus pressure %rop $raph' Magnetic Flow Meter

First, ensure that the ma$netic flow meter rea%s :ero when there is no flow throu$h the pipe' !hen open the appropriate valves allowin$ a small flow throu$h the pipe that the flow meter is attache% to' Also mae sure that after the water passes throu$h the flow meter, the water continues throu$h the pipes an% into the output tan without flowin$ throu$h the other two flow meters' Once the s&stem has reache% e4uilibrium, recor% the percenta$e %ispla&e% on the flow meter3 this percenta$e represents a percent of the ma#imum measurable flow of the flow meter' As the measurement is recor%e%, for five secon%s fill a bucet with output water from %irectl& from the pipe' !hen wei$h the bucet an% recor% the mass of the water collecte%' Be sure to tare the bucet before each water sample is collecte%' .ncrease the flow of the s&stem, allow it to reach e4uilibrium, an% perform another sample collection an% measurement' Do this until there are between five an% ten %ata points'

"E! Avera$e Mass of Output 7ater  $6

ei$ht of  Bob cm6

0'2 1'5* 2'09 2'59 G'12 G'* 9'92

1'G G'2 9'1 5'G *'9 ' '+

Actual