Mapua Institute of Technology School of Chemical Engineering and Chemistry
Chemical Engineering Laboratory Experiment No. 4
Friction Factor (Fluid Flow Set-Up) Kim, Sung Mina, Lopez, Essene Qumran a, Santacruz, Margarette Louise a a
Bachelor of Science Science in Chemical Engineering, Mapua Institute Institute of Technology, Technology, School School of Chemistry and Chemical Engineering Engineering
A RT I CL E I N FO
ABSTRACT
Keywords: Keywords: Fluid Flow Surface oughness elati!e oughness oughness Friction Factor Factor eynolds "um#er "um#er $ate su#mitted: su#mitted: % "o!em#er &'(%
lui! "lo# in pipelines are important in many process in!ustries. $ut #hen "lui! "lo#s in pipes, mechanical energy is lost !ue to "riction bet#een the "lui! "lo#ing an! the pipe. rictional losses !epen! on the properties o" the pipe in #hich the "lui! "lo#, the properties o" the "lui!, an! the beha%ior o" the "lui! "lo# itsel". or "lui! "lo# through a straight pipe #ith uni"orm !iameter, "actors such as %elocity, !ensity an! %iscosity o" the "lui!, an! !iameter, length an! roughness o" pipe play a signi"icant role in buil!ing up "riction losses. &he ob'ecti%es o" this stu!y are( to !etermine the "riction "actor o" the "lui! "lo#ing through a small pipe) an! to !etermine the e""ect o" *eynol!s number an! relati%e roughness on the "riction "actor o" the "lui! "lo#. Comparing the %alues ac+uire! "or the experimental an! theoretical %alue "or the "riction "actor, the percentage errors compute! are -./ an! -.- percent "or trials 0 an! 1 respec respecti% ti%ely ely.. %arying %arying the the *eynol *eynol!2 !2ss number number or relati relati%e %e roughness has an e""ect to the "riction "actor o" the "lui! "lo#. $ase! on e+uation 4, the "ollo#ing may be obser%e!( 3" the relati%e roug roughn hnes esss remai remaine ne!! cons consta tant nt an! an! the the *eyno *eynol! l!ss numb number er is increase!, the "riction "actor that may be obtaine! #ill !ecrease) 3" the *eynol!s number remaine! constant, an! the relati%e roughness o" the material increase!, the "riction "actor that may be obtaine! #ill also increase. s such, it may be sai! that the "riction "actor is in%e in%ers rsely ely prop propor ortition onal al to the the *eyno *eynol! l!ss numb number er an! an! !ire !irect ctly ly proportional to the the relati%e roughness o" the the material.
INTRODUCTION
lui lui!! "lo# "lo# thro throug ughh pipe pipeliline ness is an important important proces processs in many in!ustri in!ustries. es. lui! "lo# may be classi"ie! as internal or external "lo# 56ni%ersitetet i 7slo, n.!. n.!.8.8. 3n this this stu!y, stu!y, internal "lo# is o" concern, in #hich the con!uit is "ille! #ith the "lui! an! "lui! "lo#s because o" Experiment :1;
pressure !i""erence. lui! "lo#s in channels because o" a !ri%ing "orce #hich ma9es the "lui! ha%e 9inetic energy. &he 9inetic energy o" the "lui! "lui! ma9es ma9es the "lui! "lui! to ha%e pressur pressure. e. &he &he pressure o" the "lui! loses its magnitu!e as "lui! "lo#s through the the con!uit. &his pressure pressure may be sai! as a mechanical energy. ( of )
3n actual "lui! "lo# through pipes, mechanical energy is lost because o" "riction 5
an!boo9 5an!boo9 5agenA =oiseuille e+uation f =
16
ℜ
e+n. 0
turbulent "lui! "lo# in rough pipes, the "riction "actor may be expresse! implicitly in the "orm o" 1
√ f
=−4 log
[
ϵ
3.7 D
+
1.256 ℜ √ f
] e+n. B
as the Colebroo9 "ormula, or explicitly in the "orm o"
[
( ) ] e+n. 4
1 0.27 ϵ 7 =−4 log + ℜ D √ f
0.9
as the Churchill e+uation, both #hich can approximate the "riction "actor #hen the *eynol!s number is greater than 4:::. 3n this stu!y, in or!er to compute "or the theoretical "riction "actor, e+uation 4 #ill be use!. 3n or!er to compute "or the "riction "actor using experimental !ata, the anning e+uation may be use! 5
2 f u L F = gc D
e+n. /
here( D "lui! "riction loss through the pipe " D anning "riction "actor u D %elocity o" the "lui! L D length o" the pipe
may be use! to approximate the "riction "actor in the "lo# o" a "lui! #hen the *eynol!s number is less than 10::) &he "riction "actor may be approximate! using the $lasius e+uation, f =
0.079
ℜ
0.25
e+n. 1
"or turbulent "lui! "lo# in smooth pipes #hose *eynol!s number is bet#een 4::: to 0: /) s "or Experiment :1;
? D insi!e !iameter o" the pipe gc D "orceAmass con%ersion "actor &he ob'ecti%es o" the stu!y are( to !etermine the "riction "actor o" the "lui! mo%ing through a straight pipe) an! to !etermine the e""ect o" *eynol!s number an! relati%e roughness on the "riction "actor o" the "lui! "lo#.
& of )
E!ERI"ENTAL SECTION
Isolate piping system
prime and start-up
Collection of water
determine temperature
Compute
compute % error repeat procedure for remaining trials
igure 0. lo# ?iagram o" =roce!ures i.
?etermination o" *eynol!s number
3n or!er to !etermine the *eynol!s number an! its e""ect, #e "irst !o the "irst step #hich is to isolate the piping system an! then begin to prime an! startAup the pump an! by allo#ing the #ater to pass through the pipeline, #ith these #e shoul! obtain the length o" the pipeline 5in terms o" m8 an! then measure the amount o" #ater 5in Experiment :1;
terms o" mB8 that has "lo#n in a certain amount o" time, #hich is in this case one minute. &he %elocity o" #ater can be obtaine! by !i%i!ing the length by the gi%en time. $y getting the temperature o" the #ater, properties o" it li9e, !ensity an! %iscosity are obtaine!. ith these !ata, the *eynol!s number is then compute!. i.
?etermination o" "riction "actor an! relati%e roughness
3n or!er to compute "or the theoretical "riction "actor an! relati%e roughness, the "lo# shoul! "irst be classi"ie! as laminar or turbulent. ith the rea!ing o" the manometer, #e shall be able to sol%e the mechanical energy lost !ue to "riction, using e+uation F =
−∆
ρ
p
= R m
(
ρ Hg ρ
−1
)( ) e+n. g gc
n! lasty sol%e "or the relati%e roughness o" the pipe an! also the experimemtal "riction "actor using e+uation / in or!er to compute "or the F error obtaine!. Six 58 trials #ere ma!e, each trial laste! "or : secon!s. &he secon! column o" the table #as obtaine! by ta9ing the a%erage o" the trials ma!e.
RESULTS AND DISCUSSION
&able 0. ?ata an! *esults Golumetric lo# *ate o" the .BBx0:A4 mB@s ater, G Gelocity o" the ater, u 11.0 m@s 3nsi!e ?iameter o" the pipe, ?
:.:: m
&emperature o" the ater
1/oC
?ensity o" the ater, H
.4/ 9g@mB
* of )
Giscosity o" the ater, I
:.:0/ x 0:AB c=
*eynol!s Number, N*e
04.:1
Manometer *ea!ing, * m
4./ cm>g
Mechanical energy lost !ue to "riction, Length o" the straight pipe, L *oughness o" the =ipe, Ɛ *elati%e *oughness o" the =ipe, Ɛ@? Experimental anning "riction "actor, " experimental &heoretical anning "riction "actor, " theoretical F error
//14.4 J@9g :.4 m :.::::4/ m .0x0:AB :.:/04 -.-1 x 0:AB -./F
s may be seen in table 0, the theoretical an! the experimental %alues o" the "anning "riction "actor #as obtaine!. &he "irst obser%e! %alue in the table is the %olumetric "lo# rate. &his #as obtaine! experimentally by getting the %olume o" #ater !ischarge! at a certain amount o" time. ?i%i!ing this %olumetric "lo# rate by the crossA sectional area o" the pipe in #hich the "lui! "lo#s, the %elocity o" the "lui! may be calculate!. &he temperature o" #ater #hich #as "lo#ing through the pipe #as also obtaine! in or!er to get its !ensity an! %iscosity. 6sing the insi!e !iameter o" the pipe use!, !ensity, %iscosity, an! the %elocity o" "lui! "lo#ing, the *eynol!s number #as then obtaine!. &he *eynol!s number "or both trials #ere "oun! to be greater than 4:::, #hich means the "lui! "lo# is in the turbulent region. Since the "lo# is turbulent an! the pipe is consi!ere! to ha%e roughness, e+uation 4 may then be use! in or!er to compute "or the theoretical "riction "actor. 3n or!er to calculate the theoretical "riction "actor using e+uation 4, the roughness, ϵ, shoul! also be 9no#n. &he %alue "or the roughness #as
Experiment :1;
obtaine! "rom =erry2s Chemical Engineering >an!boo9 &able A0 #hich may be seen in table 1 in this report. &he roughness o" the pipe use! is assume! to be e+ual to the roughness o" a commercial steel #hich #as "oun! out to be :.:4/ mm. 3n or!er to obtain the experimental %alue "or the "riction "actor, e+uations / an! shoul! be use!. &he manometer rea!ing #as also obtaine! experimentally. Comparing the percentage errors o" the theoretical an! experimental "riction "actors, the percentage errors that #ere compute! #ere -./ an! -.- percent "or trials 0 an! 1 respecti%ely. Causes o" errors may be( inaccurate rea!ing, human errors, e+uipment error, an! "lui! lea9age. 3t shoul! also be note! that %arying the *eynol!2s number or relati%e roughness has an e""ect to the "riction "actor o" the "lui! "lo#. $ase! on e+uation 4, the "ollo#ing may be obser%e!( 3" the relati%e roughness remaine! constant an! the *eynol!s number is increase!, the "riction "actor that may be obtaine! #ill !ecrease) 3" the *eynol!s number remaine! constant, an! the relati%e roughness o" the material increase!, the "riction "actor that may be obtaine! #ill also increase. s such, it may be sai! that the "riction "actor is in%ersely proportional to the *eynol!s number an! !irectly proportional to the relati%e roughness o" the material. &able 1. =erry2s Chemical Engineering >an!boo9 51::-8 &able A0( Galues o" Sur"ace *oughness "or Garious Materials Material ?ra#n tubing 5brass, lea!, glass, an! the li9e8 Commercial steel or #rought iron sphalte! cast iron
% of )
Sur"ace * :.::0/1 :.:4/ :.011 :.0/1 :.1/ :.0-BA:. :.B:/AB.:
*i%ete! steel REFERENCES
CONCLUSION
&he theoretical an! experimental %alues "or the "riction "actor o" "lui! "lo#ing through straight pipe #ere obtaine!. Comparing the %alues ac+uire! "or the experimental an! theoretical %alue "or the "riction "actor, the percentage errors compute! are -./ an! -.- percent "or trials 0 an! 1 respecti%ely. 3t shoul! also be note! that %arying the *eynol!2s number or relati%e roughness has an e""ect to the "riction "actor o" the "lui! "lo#. $ase! on e+uation 4, the "ollo#ing may be obser%e!( 3" the relati%e roughness remaine! constant an! the *eynol!s number is increase!, the "riction "actor that may be obtaine! #ill !ecrease) 3" the *eynol!s number remaine! constant, an! the relati%e roughness o" the material increase!, the "riction "actor that may be obtaine! #ill also increase. s such, it may be sai! that the "riction "actor is in%ersely proportional to the *eynol!s number an! !irectly proportional to the relati%e roughness o" the material.
Experiment :1;
0 eun!a 3nc. 51:048. =ipe =ressure Loss. *etrie%e! "rom( http(@@###.e"un!a.com@"ormulae@"lui!s@ calcpipe"riction.c"m 1 an!boo9, -th E!ition. 4 ishing 51::8. ?arcy riction actor. *etreie%e! "rom( http(@@###."sl.orst.e!u@geo#ater@B@h elp@->y!raulic*e"erence@?arcyrict ionactor.htm / =ipe lo# So"t#are 51:048. riction actor Calculations. *etrie%e! "rom( http(@@###.pipe"lo#.com@pipeApressureA !ropAcalculations@pipeA"rictionA"actors
) of )
