Comparison of
Comparison of
Diff
Diff
erent
erent
Flow Measurement
Flow Measurement
Devices
Devices
CHEG 2810 - Experiment 1 CHEG 2810 - Experiment 1Danielle Valdivia, Travis Garlock, and Alex Maldonado
Danielle Valdivia, Travis Garlock, and Alex Maldonado
October 22
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$netic flow meter an% rotameter were both accurate an% precise, but the orifice plate was neither' !his error was more than liel& to be cause% b& inefficienc& in the water collecte% from the output an% for the orifice plate the constant -umpin$ 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$es the rotameter is the best
choice'
./!"ODC!.O/ an% BAC"O/D ./FO"MA!.O/
!he rotameter is a versatile process control %evice that can %emonstrate chan$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=C q
ca x
where 4 is the flow rate, Cc is the ratio of the
narrowest part of the -et to the area of bob, an% a# as
the area of the tube' .f we substitute this in to Bernoulli8s law we $et
P1− P2= ρ
2
(
q C ca x
)
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 $ravitational force of the flui%6 the
bob reaches e4uilibrium' !his e4uilibrium stabili:es the hei$ht of the bob
relative to the tube an% the velocit& of the flui% can be calculate% usin$ the e4uation
u=
√
2g V b C Ab∗(
ρb− ρf ρf)
7here, Example Rotameter in lab• u ; flow velocit& • < b; volume of the bob
• $ ; $ravitational acceleration constant • C ; %ra$ coefficient
• A b ; frontal area of the bob • = b; %ensit& of the bob • =f; %ensit& of the flui%
!his e4uation can calculate the velocit& in an& rotameter with an& incompressible flui%' 7hen usin$ the same rotameter an% flui%, most of the variables remain constant' 7hen usin$ a
rotameter, the selection of %esi$n can simplif& the e4uation further an% lineari:e it prin$stea%, 20156' Q=C m∗ y∗
√
ρb− ρf ρf =C m ' ∗ y 7here,• > ; 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, 226'
!his re%uction in pressure hea% is what the connecte% %evice measures an% is correlate% to the li4ui% flow rate'
Theoretical Magnetic Flow Meter (Cadillac Meters, 2013)
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&, ?96' !hese t&pe of taps $ive the lar$est
%ifferential hea% for a $iven flow rate' !he flow rate e4uation is $iven below'
Q= C d A2
√
1−(
A2 A1)
2√
2(
p1− p2)
ρ 7here• p1?p26 ; the pressure %rop • = ; the %ensit&
• A1 ; the pipe cross?sectional area • A2 ; the orifice cross?sectional area • C% ; the %ischar$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%'
!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 tain$ 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' !ae a ruler an% measure from the initial point to the point where the bob is when water is flowin$ throu$h' 7hile tain$ the bob hei$ht measurement, for five
secon%s fill a bucet with the output water' !hen wei$h the bucet 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 taen with a bucet 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$h the pipe that the flow meter is attache% to' Also mae sure that after the water passes throu$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$e represents a percent of the ma#imum measurable flow of the flow meter' As the measurement is recor%e%, for five secon%s fill a bucet with output water from %irectl& from the pipe' !hen wei$h the bucet an% recor% the mass of the water collecte%' Be sure to tare the bucet 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 Actual <olumetric Flow "ate(
m 3 s)
Measure% "otameter Flow "ate(
m 3 s)
@ercent Error 0'2 1'G 0'000199 0'0001G2 +'*) 1'5* G'2 0'000G12 0'000G1+ 1'+) 2'09 9'1 0'00090+ 0'00090 0'G) 2'59 5'G 0'00050+ 0'000525 G'1) G'12 *'9 0'000*25 0'000*G9 1'9) G'* ' 0'000G 0'000*1 1'5) 9'92 '+ 0'0005 0'0000 0'*) Rotameter.n theor& the rotameter shoul% be the least accurate of three teste% flow measurement %evices' owever it finishe% as the secon% most accurate %evice in this e#periment' !here are several reasons for this specific apparatus which will be covere% in the orifice plate section of the results' .n the chart to the ri$ht, the actual volumetric flow rate is the calculate% flow rate from the water output' !his is calculate% b& usin$ the mass of water an% %ensit& of the water which is affecte% b& the temperature which was 1 ⁰C for all rotameter trials' V
(
m3
)
= M ( Kg)ρ( Kg
m3) !his is the total
volume of the output water which when %ivi%e% b& the time the water was collecte% $ives us the flow rate' For this e#periment each sample was collecte% for five secon%s' An e#ample
calculation woul% be as follows,
Q= M ρ t = 2.04kg 998.6 kg m3 5s = 0.002043m3 5s =0.000407 m3 s
sin$ the hei$ht of the bob when collectin$ the output water we can $raph how the volumetric flow rate affects the hei$ht of the bob' Fin%in$ the linear relationship of the %ata set provi%es an e4uation to calculate the flow rate that hei$ht represents in the rotameter' For this %ata set, the linear re$ression e4uation with a " 2 value of 0'++ is,
Q=9.841∙10−5∗h+3.698∙10−6
!his can be use% to calculate the flow rate reporte% from the rotameter' !his is measure% flowrate in the above table an% the percent error is the %ifference in the actual an% e#perimental %ata'
Overall the rotameter was accurate an% precise with e#ception to the first trial which proves the reliabilit& of the rotameter'
0 1 2 3 4 5 6 7 ! 10 0 0 0 0 0 0 0 0 0 0 0
"(#) $ 0# % 0
&' $ 1
The &elationshi etween the *eight o" +o+ and ,ol-.etric Flow &ate
*eight o" o++er (c.) ,ol-.etric Flow &ate (.3/s)
Orifice Plate
!he orifice plate meter was actuall& the least accurate of the meters teste% partl& %ue to the
e%%ies formin$ where the %ownstream pressure sensor was locate%, causin$ constant fluctuation in the manometer an% %ifferential pressure $au$e' .n or%er to 4uantif& the accurac& of this meter, the actual flow rate an% the theoretical flow rates nee%e% to be compare% an% anal&:e% for
percenta$e error' !o %o this, the actual flow rate was measure% b& the amount of water e#itin$ the apparatus in a $iven amount of time'
Mass Output of 7ater $6 H@ressure6 Hmm$66 !heoretical <olumetric Flowrate mGs6 Actual <olumetric Flowrate mGs6 ) Error 2'2* 2'+5 0'00095G 0'00099912 * 2'1 G'90* 0'0009G 0'0005*0+ 15'+ 2' G'21 0'0005 0'000*+10G 1'+ 2'2 9'G2 0'000595 0'00051202 25'* G'G* 9'01 0'000*G 0'000299 1'+
B& tain$ the mass of the water comin$ out of the s&stem an% %ivi%in$ it b& the %ensit& of water, the volume of water can be calculate%' !his can then be %ivi%e% b& the amount of time taen to $ain that volume of water to arrive at the volumetric flowrate' !his volumetric flowrate will be
the actual flowrate use% to %etermine the accurac& of the flow meter when compare% to the theoretical %ata' !he theoretical %ata is $aine% from the e4uation(
where C% is assume% to be a constant' !his woul% be %one with all remainin$ samples an% the error calculate%' !he table below %epicts the calibration curve for the measure% %ata $aine% from the e#periment an% shows the tren%line an% "2 value for that tren%line'
Magnetic Flow Meter Mass of Output 7ater $6 @ercent of Ma#imum Flow Actual <olumetric Flow?rate mGs6 Measure% <olumetric Flow?rate mGs6 @ercent Error 0'*9 *' 0'00012205 0'00012+G* 0'5) 0' *'+ 0'000190229 0'0001G29 5'G1) 2'21 2G' 0'0009920 0'00095*0* G'02) 2'9 2'9 0'00059 0'00059*5GG 0'9G) G'0 G2'5 0'000*19+9 0'000*259G9 1'0) 9'1 92' 0'000G5GG 0'0002129 1'*G)
Base% on research an% on theor&, the results of the ma$netic flow meter were as we woul% e#pect, in that it was the most accurate of the three flow meters use% in this e#periment' !he %ispla& on the ma$netic flow meter rea%s out the percent of the ma#imum flow rate that is bein$ measure%' From this we nee% to calculate the ma#imum flow rate of our specific flow meter' .n or%er to %o this, we use the e4uation(
Fl! "at#= P#"c#$t fl!∗ Max % fl! "at#
7e %o this m& solvin$ for the ma#imum flow rate usin$ our recor%e% percent flows an% the flow rate that is obtaine% b& %ivi%in$ the volume of water collecte% b& the time it was collecte% in' A sample calculation is as follows(
Max% fl! "at#= fl! "at# p#"c#$t fl!= &l % f !at#" t'm# p#"c#$t fl! = 0.0007m3 5s#c 0.069 =0.00203327 m3 s#c
After performin$ all of the in%ivi%ual calculations, we tae an avera$e to %etermine the most appro#imate ma#imum flow rate' Our avera$e value was 0'001+29912 mIGs' 7e then use this e4uation a$ain onl& this time we solve for the flow rate usin$ the percent flow observe% an% the ma#imum flow rate we -ust calculate%' A sample calculation is shown below(
Fl! "at#= p#"c#$t fl!∗ Max % fl! "at#=0.069∗0.0019244 m
3
s#c=0.000132784 m3 s#c
!his calculation was %one on all measure% percent flows' !hen the& were compare% to the flow rates from the first e4uation an% a percent error was foun%' .n all of our sample observations, we can see that the ma$netic flow meter was a ver& accurate flow measurement %evice'
D.C.O/
Rotameter
!he theoretical or actual %ata woul% be the volumetric flow rate of the water output' As shown in the $raph below the e#perimental %ata is accurate an% precise' owever, there is some
%iscrepanc& in the %ata an% when there is nee% for e#tremel& precise measurement a rotameter shoul% suffice' 7hen simplicit& is of importance an% 4uic compairson of the chan$e in flow rate the rotameter is the best option'
0 1 2 3 4 5 6 7 ! 10 0 0 0 0 0 0 0 0 0 0 0
#eri.antal ata Co.ared to Theoretical ata
Theor #eri.ental
*eight o" o+ (c.) ol-.etric Flow &ate (.3/s)
Orifice Plate
!he orifice plate flow meter ha% a $reat amount of error when it came to theoretical an% actual flow rate comparison3 the $raph on the ne#t pa$e %epicts this %iscrepanc&' From the results section concernin$ the orifice meter, the calibration curve showe% a tren%line with the "2 value bein$ 0'+9* which, while close to 1, is much smaller a number than shoul% be for an accurate
rea%in$' !his is most liel& %ue to the e%%ies formin$ in the %ownstream pipin$ as these can cause a lar$e %ifferentiation of manometer rea%outs' !he manometer use% woul% fluctuate
consistentl&, main$ rea%out values more ran%omi:e% than accurate' !he four to five values that the manometer woul% rea% were avera$e% to mae a more realistic an% more accurate assumption of the values'
Magnetic Flow Meter
As we can %epict from the $raph below, our e#perimental %ata fits the theoretical %ata closel&' !here is ver& little error between the measure% volumetric flow rates an% the theoretical
volumetric flow rates' !his proves that our e#periment follows the research in that the ma$netic flow meter is the most accurate of the three flow meters in this e#periment' .f the precision of flow measurement is of utmost importance, then the ma$netic flow meter shoul% be the
0 5 10 15 20 25 30 35 40 45 0 0 0 0 0 0 0 0 0 0
#eri.ental ata s Theoretical ata
#eri.ental Theor
ercent o" Ma#i.-. Flow ol-.etric Flow &ate
CO/C.O/
Out of the three flow meters teste% throu$hout this e#periment, the ma$netic flow meter was foun% to be the most accurate while the orifice plate meter was the least accurate3 the rotameter was foun% to be somewhere in between but on the hi$her accurac& si%e of the spectrum' Each of these were not e#act forms of measurement as the& each ha% error when comparin$ theoretical to actual flow rates, which is to be e#pecte%' !he $reatest source of error came from the orifice plate meter with over 1*) error an% the smallest from the ma$netic flow meter at 2) err or'
ince the purpose of the e#periment was to calculate volumetric flow rates an% compare accuracies of the three meters, it woul% behoove a process plant to utili:e a ma$netic meter or rotameter in the fiel% rather than an orifice meter, strictl& on an accurac& stan%point' .f a flowrate was of imme%iate importance, a rotameter shoul% be use%'
"ECOMME/DA!.O/
.f we were to repeat this e#periment, there woul% be a couple of thin$s that we woul% %o
%ifferentl& to mae sure our e#periment ha% smaller error' !he first thin$ we woul% %o is to fi# all the pipin$3 the pipe that the orifice plate was attache% to ha% a lea in it' !his lea coul% throw off our measurements for flow an% increase our percent error' Another a%-ustment we woul% mae to this lab woul% be to use a more precise collection metho%' Althou$h the metho% we use% was ver& accurate, usin$ an automate% collection tool woul% allow us to collect output water for e#actl& five secon%s' 7ith our manual collection, there is alwa&s room for some error when timin$ an% hol%in$ the bucet' A thir% chan$e we woul% mae to this lab woul% be to increase the flow rate b& smaller increments' !his woul% allow us to tae more %ata points, which woul% &iel% a more reliable %ata tren%'
"EFE"E/CE
Di-stelber$en, ' 1+*96' "otameter %&namics' Chemical Engineering Science, 19, 5G?*5'
Ma$netic Flow Meters' 20156' Omega Engineering."etrieve% October 20, 2015, from
http(www'ome$a'compro%infoma$meter'html
Mechanical Flow Meters vs Ma$netic Flow Meters' 201G, Februar& 96' "etrieve% October 20, 2015, from http(ca%illacmeter'com201G0209mechanical?flow?meters?vs?ma$netic?flow? meters
prin$stea%, J' 20156' Data Ac4uisition an% an%lin$ aborator& Manual' !he Basics of "otameters' 2002, October 16' "etrieve% October 1*, 2015, from http(www'sensorsma$'comsensorsflowthe?basics?rotameters?10*
McCabe, 7arren ', Julian C' mith, an% @eter arriott' 20056' nit of Operations of Chemical En$ineerin$' th' /ew Kor( Mcraw?ill, p$ 22
@err&, "obert ' an% reen, Don 7' 1++6' @err&8s Chemical En$ineers8 an%boo' th' /ew Kor( Mcraw?ill' p$ ?9, 10?1*
A@@E/D.CE
Appendix A: ata c!llecti!n !" r!tameter.
ei$ht of "otameter cm6 Mass of 7ater Output $6 !emperature of 7ater Output ⁰C6 !ime of collecte% 7ater Output s6 Densit& of 7ater $mG6 1'G 0'2 1 5 ++'* G'2 1'5* 1 5 ++'* 9'1 2'09 1 5 ++'* 5'G 2'59 1 5 ++'* *'9 G'12 1 5 ++'* ' G'* 1 5 ++'* '+ 9'92 1 5 ++'*
Appendix #: Calc$lati!n% "!r the!retical r!tameter data
<olume of 7ater Output mG6
<olumetric Flow "ate of 7ater Output mGs6 0.72kg 998.6 kg m3 =0.000721 0.000721m 3 5s =0.000144 1.56kg 998.6 kg m3 =0.001562 0.001562m 3 5s =0.000312 2.04kg 998.6 kg m3 =0.002043 0.002043m 3 5s =0.000409 2.54kg 998.6 kg m3 =0.002544 0.002544m 3 5s =0.000509 3.12kg 998.6 kg m3 =0.003124 0.003124m 3 5s =0.000625 3.86kg 998.6 kg m3 =0.003865 0.003865m 3 5s =0.000773 4.42kg 998.6 kg m3 =0.004426 0.004426m 3 5s =0.000885
Appendix C: Calc$lati!n !" experimental "l!& rate !" r!tameter c!mpared t! act$al "l!& rate !" r!tameter
7hen plottin$ the e#perimental volumetric flow rate in respect to the measure% hei$ht of the bobber, we can use a linear re$ression tren% line to fin% an e4uation that calculates the volumetric flow rate from the hei$ht' !his e4uation is
Q=9.841∙10−5∗h+3.698∙10−6
7here,
• > ? <olumetric Flow "ate mGs6
• ? Chan$e in vertical hei$ht of bob from reference point cm6
An e#ample calculation for 9'1 cm woul% be
Q=9.841∙10−5∗(4.1)+3.698∙10−6=0.000407m
3
s
!he percent error is calculate% usin$
P#"c#$t E"""=
|
Exp#"'m#$tal−(h#"#t'cal(h#"#t'cal
|
∗100 Measure% Flow "ate mGs6 @ercent Error 0'0001G2|
0.000132−0.000144 0.000144|
∗100=9.6 0'000G1+|
0.000319−0.000312 0.000312|
∗100=1.90'00090
|
0.000407−0.000409 0.000409|
∗100=0.3 0'000525|
0.000525−0.000509 0.000509|
∗100=3.1 0'000*G9|
0.000634−0.000625 0.000625|
∗100=1.4 0'000*1|
0.000761−0.000773 0.000773|
∗100=1.5 0'0000|
0.000880−0.000885 0.000885|
∗100=0.6Appendix :
Appendix G: ata C!llecti!n !" 'agnetic (l!& 'eter
@ercent Ma#imum Flow Mass of 7ater Output $6 !emperature of 7ater Output C6 !ime of Collecte% 7ater Output s6 Densit& of 7ater $mIG6 *' 0'*9 1+ 5 ++'9 *'+ 0' 1+ 5 ++'9 2G' 2'21 1+ 5 ++'9 2'9 2'9 1+ 5 ++'9 G2'5 G'0 1+ 5 ++'9 92' 9'1 1+ 5 ++'9
Appendix H: Calc$lati!n% "!r )he!retical 'agnetic (l!& 'eter ata
<olume of 7ater Output mG6
<olumetric Flow "ate of 7ater Output mGs6 0.64kg 998.4 kg m3 =0.000641 0.000641m 3 5s =0.0001282 0.70kg 998.4 kg m3 =0.0007011 0.0007011m 3 5s =0.000140 2.21kg 998.4 kg m3 =0.002214 0.002214m 3 5s =0.0004427 2.74kg 998.4 kg m3 =0.002744 0.002744m 3 5s =0.0005489 3.07kg 998.4 kg m3 =0.003075 0.003075m 3 5s =0.000615 4.17kg 998.4 kg m3 =0.004177 0.004177m 3 5s =0.0008353
Appendix *: Calc$lati!n% "!r c!mparing experimental "l!& rate !" the magnetic "l!& meter t! the!retical "l!& rate !" the magnetic "l!& meter.
!he percent error is calculate% usin$ the same e4uation use% previousl& in this lab'
P#"c#$t E"""=
|
Exp#"'m#$tal−(h#"#t'cal(h#"#t'cal
|
∗100 Measure% Flow "ate mGs6 @ercent Error 0'00012+G*|
0.000129−0.000128 0.000128|
∗100=¿ 0'0001G29|
0.0001330.000140−0.000140|
∗100=1.9 0'00095*0*|
0.0004560.000443−0.000443|
∗100=0.3 0'00059*5GG|
0.0005460.000549−0.000549|
∗100=3.1 0'000*259G9|
0.0006250.000615−0.000615|
∗100=1.4 0'0002129|
0.0008220.000835−0.000835|
∗100=1.5Appendix +: Ori"ice ata "r!m experimentati!n
@ressure mm$6 Mass of 7ater $6 !emperature of 7ater C6 !ime s6 5'1 2'2* 1+ 5 9' 2'1 1+ 5 'G 2' 1+ 5 '9 2'2 1+ 5
11'G G'G* 1+ 5
Appendix : Calc$lated Ori"ice ata @ressure6 Hmm$66 Denist& of 7ater <olume of 7ater mG6 <olumetric Flow "ate mGs6 Measure% Flow "ate ms6 @ercent Error 2'+5 ++'9 0'0022*G*22 0'00095G 0'00099912 * G'90* ++'9 0'0021G9+9 0'0009G 0'0005*0+ 15'+ G'21 ++'9 0'0029*15 0'0005 0'000*+10G 1'+ 9'G2 ++'9 0'00229G5+ 0'000595 0'00051202 25'* 9'01 ++'9 0'00GG*5G5 0'000*G 0'000299 1'+
