CAPE PENISULA UNIVERSITY OF TECHNOLOGY BELLVILLE CAMPUS DEPARTMENT OF CHEMICAL ENGINEERING ND : CHEMICAL ENGINEERING FLUID FLOW SUBJECT
:
CHEMICAL PLANT III
LECTURER
:
Mr L. Kloppers, Mr. W Maree
STUDENT
:
Richardt Johan Loots
STUDENT NO. NO.
:
214196585
Topic Topic
Mark allocation
Title Page Page
5
Synopsis
5
Intro!ction
5
Literat!re "e#ie$ an T%eory &incl!ing in te't re(erencing)
*+
E'periental Set-!p an Proce!re
*+
Mark
"es!lts an isc!ssion
5+ Calc!lations Concl!sions
5
/i0liograp%y
*+
Total Total
*++
I certi(y t%at t%is report is y o$n !naie $ork, e'cept (or t%e assistance recei#e (ro (ro t%e teac%ing sta1. sta1. I !nertake !nertake not to pass t%is report report onto any ot%er st!ent
Contents List o( Sy0ols........................................................................................................................................................ii I.Synopsis.................................................................................................................................................................i# *.Intro!ction...........................................................................................................................................................* 2.Literat!re "e#ie$ "e#ie$ an T%eory....................................................................................................................... T%eory....................................................................................................................... ........ 2 2.* 3l!i 4elocity........................................................................................................... 4elocity............................................................................................................................................... .................................... ... 2 2.2 "eynols n!0er...........................................................................................................................................2 2.2.* Lainar o$...........................................................................................................................................2 2.2.2 T!r0!lent 3lo$.................................................. 3lo$............................................................................................................................ .......................................................................................2 .............2 2.2.6 Transitional o$...................................................................................................................................... o$...................................................................................................................................... 2 2.6 Hea Losses....................... Losses................................................................................................. .................................................................................................................... .......................................... ....... 6 2.6.* 3riction Losses........................................................................................................................................6 2.6.2 S%ock Losses.......................... Losses..................................................................................................... .................................................................................................................7 ......................................7 6.E'periental 6.E'periental Proce!re................................... Proce!re............................................................................................................. ......................................................................................... ............... ......... ... 8 6.* E'periental E'periental Set!p.............................. Set!p......................................................................................................... ..........................................................................................................8 ...............................8 6.2 Apparat!s................................................................................... Apparat!s....................................................................................................................................................... .................................................................... 8 6.2.* Pipes !se............................... !se.......................................................................................................... ................................................................................................................ ..................................... 8 6.2.2 4al#es !se............................................................................................................................................. !se............................................................................................................................................. 8 6.6 Proce!re........................................................................ Proce!re.................................................................................................................................................... ............................................................................ ... 9 :. "es!lts an isc!ssion........................................................................................................... isc!ssion................................................................................................................................... ........................ ...... ; :.* "ecore "ecore 4al!es................................. al!es............................................................................................................ ............................................................................................................ ................................. ; :.2 Calc!late 4al!es........................................................................... 4al!es......................................................................................................................................... .............................................................. *+ :.6 isc!ssion....................................................................................................................................................** :.6.* Pipes.....................................................................................................................................................** :.6.24al#es....................................................................................................................................................** :.6.6 "eccoenations......................... "eccoenations.................................................................................................... .......................................................................................... ............... ......... ..... *2 5. Concl!sions.................. Concl!sions............................................................................................ .......................................................................................................................................*2 .............................................................*2 7."e(erences...........................................................................................................................................................*6 Appeni'...................................................................................................................................................................A Pipe Calc!lations............................................................................................................................. Calc!lations............................................................................................................................................... .................. ... A
List of Symbols Symbol
Description
Unit
2
Cross-sectional area o( pipe
2
d
Pipe iaeter
f
3riction (actor
iensionless
g
=ra#itational acceleration constant
>s2
h
Hea
Δh
C%ange in Hea
Δhf
3riction Hea loss in a pipe syste
H2?
K
Minor loss coe@cients (or 0ens an ttings
iensionless
L
Pipe lengt%
P
Press!re
kPa or H 2?
A
ΔP
Press!re rop
kPa or H 2?
Q
4ol!etric o$ rate
6>s
"e
"eynolBs N!0er
#
3l!i #elocity
iensionless >s
Greek symbols ε
μ ρ
Pipe ro!g%ness
3l!i #iscosity
Pa.s
ensity
kg>6
Subscripts E
Cali0rate #al!es Incl!ing error (actor
F
3anning
H2O
Properties o( $ater &!i)
arcyBs
6
I.Synopsis
1.Introduction 3l!i o$ or !i ec%anics is t%e !nerstaning o( $%at in!ences t%e o$ o( !is or gases It is 0ase on t%e analysis o( t%e 0e%a#io!r o( !is an gases $%ic% is 0ase on t%e (!naental la$s o( ec%anics an t%eroynaics $it%in a a close syste. T%e li(e-cycles o( stars, t%e creation o( atosp%eres, t%e so!ns $e %ear, t%e #e%icles $e ri#e, t%e systes $e 0!il (or ig%t, energy generation an prop!lsion all epens in an iportant $ay on t%e ec%anics an t%eroynaics o( !i o$ an t%e interaction o( t%e !i $it% its s!rro!nings. In t%is practical it $as set o!t to eterine t%e losses occ!rre $it%in a close syste o( o$. T%e losses $it%in a pipe epens on t%e "eynols n!0er an o$ rate o( t%e !i 0eing eas!re. /y kno$ing t%e "eynols n!0er it can 0e eterine $%at type o( o$ is present an t%e losses can 0e calc!late accoringly In t%e in!strial sense or in t%e processing o( !is an transport o( !is t%ese #al!es are o( !tost iportance an can in!ence #ario!s (actors s!c% as t%e aterials o( constr!ction, t%e sies o( t%e pipes, lengt%s o( pipes, $%ere !is 0!st 0e coole or %eate, $%en !is !st 0e i'e etc. /y kno$ing all t%is t%e ost e@cient an econoical plant can 0e 0!ilt accoring to t%e specications an reD!ireents o( t%e !i or gas 0eing processe. T%e #ario!s (actors t%at play a role on t%e 0e%a#io!r o( a !i or gas $ill 0e isc!sse in t%e ne't section to o0tain a 0etter !nerstaning o( %o$ !is 0e%a#e $it%in a certain syste an %o$ t%e aterials a1ect t%e o$ o( t%e !i.
:
2.Literature Review and Teory 2.1 !luid "elocity 3lo$ #elocity in !is is t%e #ector el t%at pro#ies t%e #elocity o( !is at a certain tie an position. T%e #elocity o( a !i is epenant on #ol!etric o$rate an t%e area o( t%e pipe. T%e i1erence in press!re ca!se 0y a p!p ca!ses a !i to o$ in a pipe.
v=
$%ere,
v =velocity
´Q
F*G
A
( ) m s
3
´ = volumetric flowrate( m ) Q s
2
A = area of pipe ( m )
2.2 Reynolds number In !i ec%anics, t%e "eynols n!0er, "e, is a iensionless n!0er t%at gi#es a eas!re o( t%e ratio o( inertia (orces to #isco!s (orces an D!anties t%e relati#e iportance o( t%ese t$o types o( (orces (or gi#en o$ conitions N ℜ=
W%ere,
ρ v d μ
ρ = density of the fluid
v =Velocity of fluid
.F2G
( )= kg
3
m
μ viscosity of the fluid ( Pa. s )
( ) m s
d = diameter of the pipe
( ) m s
Wit% t%e "eynols n!0er T%e type o( o$ can 0e eterine 0y t%e (ollo$ing 5
2.2.1 Laminar #ow ?cc!rs $%en t%e !i o$s in parallel layers, $it% no i'ing 0et$een t%e layers. W%ere t%e center part o( t%e pipe o$ t%e (astest an t%e cyliner to!c%ing t%e pipe isnBt o#ing at all. T%e o$ is lainar $%en "eynols n!0er is less t%an 26++. 2.2.2 Turbulent !low In t!r0!lent o$ occ!rs $%en t%e liD!i is o#ing (ast $it% i'ing 0et$een layers. T%e spee o( t%e !i at a point is contin!o!sly !nergoing c%anges in 0ot% agnit!e an irection. T%e o$ is t!r0!lent $%en "eynols n!0er greater t%an :+++. 2.2.$ Transitional #ow Transitional o$ is a i' o( lainar an t!r0!lent o$, $it% t!r0!lent o$ in t%e centre an lainar o$ near t%e eges o( t%e pipe ."eynols n!0er is in 0et$een 26++ an :+++ (or transitional o$.
2.$ %ead Losses Hea losses occ!r $%en t%ere is a resistance o( o$ present , $%ic% is al$ays present in pipes, t%is ca!ses a press!re rop $%ic% can 0e eas!re $it% anoeters in t%is case it $as eas!re in H 2? Factors afecting head loss
• • • • • • • •
3lo$ "ate Pipe iaeter Pipe lengt% 4iscosity "o!g%ness o( pipe $all Corrosion an scale eposits Pipe ttings an 0ens Pipe linearity or straig%tness &Hyroatic.co, 2+*5)
2.$.1 !riction Losses
3riction losses occo!r !e to t%e nat!re o( t%e aterial it is tra#elling t%ro!g% as entione a0o#e t%is can 0e !e to t%e ro!g%ness o( a pipe, (riction !e to eposits in t%e pipe etc. Calc!lating press!re losses in lainar o$ is ac%ie#e $it% 2 anoetric t!0es an t$o isplaceent sensors, $%earas calc!lationg press!re losses in t!r0!lent o$ is ac%ie#e $it% t$o press!re sensors. T%e calc! lation can 0e one $it% t%e arcyBs (or!la 7
∆ h f =
4 f F v
2
2 gd
.F6G
∆ h f = head loss due ¿ f riction( m )
W%ere,
= engthof pipe ( m) m v =velocity of the fluid ( ) s d = diameter of pipe ( m) f F =fanning factor g= gravitational constant (
m s
2
)
Wit% t%is (or!la t%e %ea loss can 0e calc!late, in o!r case $e calc!late t%e (anning (actor. The Moody Chart
W%en t%e (riction (actor is !nkno$n it can 0e eterine $it% a ooy c%art gi#en t%at yo! kno$ t%e "eynols n!0er&N "E), t%e iaeter o( t%e pipe&) an t%e relati#e ro!g%ness & ! / " ) o( t%e pipe. T%is $ill yiel a t%eoretical (riction (actor i1erent (ro t%e one eterine $it% a kno$n %ea loss.
Absolute roughness( ! )
A0sol!te Pipe "o!g%ness is a eas!re o( pipe $all irreg!larities o( coercial pipes. ?t%er t%an pipes, it is also !se (or representing ro!g%ness o( ot%er eD!ipent $alls. a0sol!te ro!g%ness %as iensions o( lengt% an is !s!ally e'presse in illieter &). &Enggcyclopeia.co, 2+*5) /elo$ is a ta0le listing a0sol!te ro!g%ness o( soe coon aterials
8
Table 1 & 'bsolute Rou(ness)
Surface Maer!a"
A#$%"ue R%u&'(e$$ C%eff!c!e( ) * !( ++
Aluminum, Lead
0.001 - 0.002
ra!n "rass, ra!n #o$$er
0.0015
Aluminum, Lead
0.001 - 0.002
%&#, %lastic %i$es
0.0015
'i(er)lass
0.005
*tainless steel
0.015
*teel commercial $i$e
0.045 - 0.09
P4C pipes $ere !se in t%e practical
Relatie Roughness ( ! / " )
"elati#e "o!g%ness o( a pipe $all can 0e ene as t%e ratio o( a0sol!te ro!g%ness to t%e pipe noinal iaeter. &Enggcyclopeia.co, 2+*5) #elativeroughness =! / " .F:G
I( t%e relati#e ro!g%ness an a "eynols n!0er is kno$n t%e (riction (actor can t%en 0e eterine (ro t%e ooy c%art.
9
2.$.2 Soc* Losses
S%ock losses is inor losses !e to ttings, #al#es an 0ens in pi pes. W%en a pipe is connecte to a 0en, #al#e or tting ,to connect one pipe to anot%er, inor losses $ill 0e present !e to irreg!lar s%ape or geoetry t%at c%anges t%e irection o( t%e o$ $%ic% ca!ses t!r0!lence T%is is !e to t%e (act t%at all !is %a#e $eig%t an t%!s %a#e oent!. I( a c%ange in s!r(ace occ!rs in a pipe s!c% as a #al#e or tting t%e irectional oent! $ill 0e c%ange, t!r0!lence occ!rs an t%!s s%ock losses occ!rs. W%en a !i o$s aro!n a 0en,t%e !i %as to c%ange irection 0!t its oent! carries it to t%e o!ter ege o( t%e 0en, t%is e1ecti#ely ecreases t%e pipe iaeter an increases t%e o$rate an t%is ca!ses an increase in %ea &Coecogs.co, 2+*5) T%e general eD!ation (or t%e %ea loss !e to an o0str!ction is as (ollo$s ∆ h = $
v
2
2g
........F5G ∆ h =headl oss due ¿ shock
$%ere,
$ = shock constant m v =velocity of the fluid ( ) s g= gravitational constant (
m s
2
)
$it% t%is (or!la t%e %ea loss can 0e calc!late. Again in o!r case $e calc!late t%e e'periental s%ock constant K Shock Constants (!)
T%e K-#al!e represents t%e !ltiple o( #elocity %eas t%at $ill 0e lost 0y !i passing t%ro!g% a tting or #al#e. /elo$ is a ta0le o( s%ock constants (or ttings !se in t%e practical
;
Table 2 & Soc* loss constants
"alve type
Soc* Constant
=ate 4al#e, 3!lly ?pen
+.*5
=ate 4al#e, *>: Close
+.27
=ate 4al#e, *>2 Close
2.*
=ate 4al#e, 6>: Close
*8
/all 4al#e, 3!lly ?pen
+.+5
/all 4al#e, *>6 Close
5.5
/all 4al#e, 2>6 Close
2++
iap%rag 4al#e, ?pen
2.6
iap%rag 4al#e, Hal( ?pen
:.6
iap%rag 4al#e, *>: ?pen
2*
$.+,perimental -rocedure $.1 +,perimental Setup
*+
!i(ure 1 & +dibon computer controlled #uid #ow benc
$.2 'pparatus $.2.1 -ipes used
*. Soot% pipe &P4C) $it% an e'ternal iaeter o( 2+ an an internal iaeter o( *7.5. 2. Soot% pipe &P4C) $it% an e'ternal iaeter o( 62 an an internal iaeter o( 27.5. $.2.2 "alves used
*. =ate #al#e $it% inner iaeter o( 2+. 2. iap%rag #al#e $it% inner iaeter o( 2+. 6. /all #al#e $it% inner iaeter o( 2+.
**
$.$ -rocedure *. T%e t!0es 0et$een t%e %yra!lic 0enc% an t%e !i o$ 0enc% $ere c%ecke to ens!re t%at t%ey $ere in orer. It $as iportant t%at t%e t!0e (ro t%e !i o$ 0enc% raine onto t%e tank o( t%e %yra!lic 0enc%. 2. T%e $iring o( t%e !nit $as c%ecke to ens!re t%at it $as connecte an t!rne on. 6. T%e p!p $as s$itc%e on. :. T%e 42 #al#e $as opene an it $as iportant to $ait !ntil all t%e air $as e'pelle (ro t%e pipe. 5. A pipe, to 0e !se in t%e e'perient, $as ientie an t%e inner iaeter $as note. 7. T%e press!re taps o( t%e corresponing anoeter $as connecte to t%e inlet an o!tlet o( t%e pipe. T%e anoetric t!0es $ere c%osen $%en t%e $ater col!n i1erences $ere lo$er t%an 9++ . 8. T%e o$ rate an press!re rops across t%e pipe $as recore. 9. Steps 7 8 $as repeate (or t%ree i1erent o$ rates. ;. Steps 5 9 $ere repeate (or se#eral pipes. *+.T%e gate #al#e $as ientie an t%e press!re taps o( t%e corresponing anoeter $ere connecte to t%e inlet an o!tlet o( t%e gate #al#e. T%e anoetric t!0es $ere c%osen $%en t%e $ater col!n i1erences $ere lo$er t%an 9++ . 7 an 8. **.T%e o$ rate an press!re rop across t%e gate #al#e $as recore (or t%ree i1erent o$ rates. *2.Steps *+ an ** $ere repeate (or t%e iap%rag #al#e an 0all #al#e.
*2
/. Results Discussion
0r.
/.1 Recorded
and
-
"alues
run
3l4min 5
m 9 8 1 6 . 6 7 1 D
*
68.6
+.:
2
7*.;
6.:
6
8:.:
5.8
m 9 8 2 6 . 6 7 2 D
*
69.*
-*
2
75.2
-+.;
6
87.;
-+.5
3dm%265
Table $ & Recorded -ipe "alues
Table / & Recorded "alve "alues
*6
run
e v l a " e t a :
m ( a r p a i D
/.2 "alues
-
3l4min5
3dm%265
*
69.5
-*.*
2
75.6
-+.;
6
87.9
-+.7
*
62
-+.*
2
56.*
2.*
6
77.:
:.6
Calculated e v l a " l l a ;
Table 9 & "alues
*
65.;
-*
2
5;.9
-+.;
6
8:.9
-+.7
calculated variables
e,perime ntal values
calibrated values
Calculated -ipe
teoretical values
J
4
"e
A
%(
( 3
%(
( 3
(
6>s
>s
"eynols Nr.
2
H2 +
-
H2 +
-
ooy
+.+2+*
m 9 8 * 1 6 +.+++7 . 2 6 7 1 D
2 +.++*+
6
( 3
-
+.+++ 2* 2.;+ ;
56;28.;5 9
+.+: +
+.+++ 69
+.67 +
+.++6: :
:.92 8
9;:;:.69 7
+.6: +
+.++* *9
+.;7 +
+.++66 6
*:
+.++5 +6
+.+*9; +.++:
86
6 +.++*2
:
5.9+ 2
*+8577.8 59
+.58 +
+.++* 68
*.:2 +
+.++6: *
*
+.+++7 :
*.*5 2
6:2;8.;5 2
+.*+ +
+.++; 9+
+.+9 +
+.++89 :
m 9 8 2 6 . 2 +.++*+ ; 6 7 2 D
*.;8 *
597;6.7+ 9
+.+; +
+.++6 +*
+.*+ +
2.62 5
7;227.+5 +
+.+5 +
+.++* 2+
+.*9 +
6 +.++*2
9
+.+++ 55
*5
+.+*66
+.++6 66
+.+26+
+.++5 85
+.++66 5
+.+2+:
+.++5 *
+.++:6 6
+.+*;8
+.++: ;6
Table 8 & Calculated valve "alues
/.$ Discussion T%e (riction (actors an s%ock constants o0taine is in close range o( t%e t%eoretical #al!es $%ic% leans to$ars correct calc!lations. T%ese res!lts $ere only o0taine !e to t%e application o( a correction (actor $%ereas i( no correction (actor $as !se a negati#e %ealoss $o!l 0e o0taine $%ic% is is not possi0le e'cept i( ot%er e'ternal (orces $ere present or energy
calculated variables
e,perimental values
Calibrated values
teoretical values
"
'
f
*
f
*
*
6>s
>s
2
H2+
-
H2+
-
-
+.+++
2.+: 25
-+.**+
-+.5*86*
+.+7
+.292*7 7
6.:7 ::
-+.+;+
-+.*:8*6
+.*
+.*76:8 :
+.++*
:.+8 :5
-+.+7+
-+.+8+;*
+.*7
+.*9;+; 2
+.+++
*.7; 88
-+.+*+
-+.+79+8
+.27
*.87;;+ *
+.2*+
+.5*;*77
+.8
*.86+55 2
* 7:
e v l a " 2 +.++* +; e t a :
6 29
* 56
m ( a +.+++ r 2 9; p a i D
2.9* 8*
+.+++6* :*5
+.++*
6.52 28
+.:6+
+.78;9:2
*.*:
*.9+268 2
+.+++
*.;+ :7
-+.*++
-+.5:+97
+.+9
+.:627;
6.*8 27
-+.+;+
-+.*85:6
+.*
+.*;:;2 9
6.;7 9:
-+.+7+
-+.+8:85
+.*7
+.*;;66 ;
6 **
* 7+
e v l a +.++* " 2 ++ l l a ; +.++*
6 25
*7
+.*5
2.6
+.+5
$as ae to t%e syste. T%e !ncali0rate #al!es $ill not 0e incl!e in t%e isc!ssion. /.$.1 -ipes
3or t%e soot% P4C pipes it can rsly 0e seen t%at $it% a increase in o$rate t%ere is a increase in t%e "eynols n!0er an t%at t%e o$ is t!r0!lent. Concerning pipe *, $it% a iaeter o( +.+*75 t%e cali0rate res!lts (or (anning (riction (actor is 0asically constant $it% increase in #elocity, $%ereas t%e t%eoretical #al!es s%o$ a ecrease in (anning (riction (actor, t%is res!lt can ay 0e !e to incorrect calc!lation or incorrect eas!reent ?t%er reasons co!l 0e t%at t%e error (actor applie $as not correct or t%at t%ere $as air trappe in t%e pipe. Concerning pipe 2 $it% a iaeter o( +.+275 it can 0e seen t%at t%at t%e rate o( increase in #elocity is a0o!t %al( o( pipe one $%ic% is !e to t%e i1erence in iaeter. Coparing t%e cali0rate an t%eoretical (anning (actors it can 0e seen t%at 0ot% s%o$ an o#erall ecrease in (anning (actor $it% a increase in !i #elocity an "eynols an yet a increase in %ea loss. So it can 0e sai t%at $it% a increase in #elocity an "eynols t%ere is a ecrease in (riction (actor, ree0ering t%at e#en t%o!g% t%ere is a ecrease in (riction (actor , (riction losses is still increasing. T%is ay 0e !e to t%e (act t%at $it% a increase in #elocity t%e o$ o( t%e !i tens to t%e centre o( t%e pipe t%!s ecreasing (riction in t%e centre 0!t a increase in total (riction losses is still present collecti#ely. It ay also 0e sai t%at t%e %ig%er t%e "eynols n!0er, t%e ore constant t%e (riction (actor. ?#erall it can 0e seen t%at ost e'periental (anning (actors is lo$er t%an t%e t%eoretical #al!es o0taine an soe %ig%er $%ic% leas to t%e (act t%at t%ese #al!es are not in per(ect agreeent. /.$.2"alves
T%e e'periental (anning (riction (actors o0taine (or t%e #al#es is in close ostly in close pro'iity o( t%e t%eoretical #al!es e'cept (or t%e 0all #al#e $%ere t%e #al!es are as !c% as 9 tie %ig%er t%an preicte 0y t%eory. W%en coparing t%e 0all #al#e s%ock constants (ro ta0le 2 it can 0e seen t%at i( it is *>6 close t%e constant is 5.5 $%ic% leas e to 0elie#e t%at t%e #al#e $as not opene (!lly or t%at t%e #al#e is e(ecti#e an co!l not 0e opene (!lly. T%is co!l also 0e !e to iper(ections o( t%e 0all an or #al#e. It can 0e seen t%at $it% a increase in #elocity t%ere is an o#erall ecrease in t%e s%ock constant an a increase in %ea loss.
*8
/.$.$ Reccomendations
Most iportantly is to $ork $it% a syste t%at is properly cali0rate an to alreay e'perientally kno$ t%e (riction (actors an s%ock coeecients, t%is ay 0e one 0y repetiti#e e'periental testing or it ay 0e kno$n (ro t%e an!(act!rerBs specications. Seconly is to ens!re t%at t%ere is no leaks or air entering t%e syste $%ic% co!l res!lt in press!re losses an increase !npreicta0ility. Lastly, to eliinate all roo (or error $%en taking reaings an oing calc!lations, 0y staying (oc!se on t%e s!0ect at %an
9. Conclusions T%e practical $as an s!ccess, t%e t%eory 0e%in t%e (anning (actor an s%ock constants is no$ properly !nerstoo an T%e role it plays in %ea losses T%e e'periental an t%eoretical #al!es (or (anning (actor an s%ock coe@cients $as s!ccess(!lly calc!late an copare to one anot%er 0y isc!ssion Alt%o!g% soe #al!es $ere inconsistent $it% t%eoretical #al!es it $as seen t%at $it% a increase in #elocity t%ere $as an increase in "eynols n!0er, a increase in %ea losses an a ecrease in (riction coe@cients. It $as isc!sse t%at t%is ecrease in t%e (riction coe@cient is ostly !e to t%e (act t%at !is tens to t%e centre o( a pipe as #elocity is increase an s%ear stress is ecrease on t%e 0!lk o( t%e !i 0!t still occ!rs at a increase rate on t%e !i at t%e o!terost point o( t%e pipe. It ay also 0e concl!e t%at t%e %ig%er t%e "eynols n!0er t%e saller t%e c%ange in (riction coe@cients is $it% a increase in o$. T%is is !e to t%e increase in oent! o( t%e !i.
*9
8.References F*GStreeter, 4. Wylie, E. *;8;. Fluid mechanics. Ne$ ork Mc=ra$-Hill.
F2GHyroatic.co,. 2+*5. Hea Loss in Piping Systes - Tec%In(o. %ttp>>$$$.%yroatic.co>"esientialPageOtec%in(opageO%ealoss.asp' *+ ?cto0er 2+*5.
F6GEnggcyclopeia.co,. 2+*5. A0sol!te Pipe "o!g%ness Enggcyclopeia. %ttp>>$$$.enggcyclopeia.co>2+**>+;>a0sol!te-ro!g%ness> *+ ?cto0er 2+*5.
F:GCoecogs.co,. 2+*5. Hea Loss - Pipes - 3l!i Mec%anics - Engineering N!erical Coponents in C an CQQ. %ttp>>$$$.coecogs.co>li0rary>engineering>!iOec%anics>pipes>%eaOloss>in e'.p%p ** ?cto0er 2+*5.
'ppendi,
´ =38.1 Q
l ∗1 min=60 s min 3
-ipe Calculations
0064
m /s
1000 l
<;ased on pipe 2 3D76.6289m5 run 1
´ =¿ Q 0.0 3
=1 m
¿ ρ & ' = 2
Uncalibrated friction factor
1? Area o" pipe D76.6289m
A =
% "
v=
2
´Q A
4
A =
% 0.0265
3
m /s v= 2 0.00055 m 0.00064
2
4
v =1.152 m / s 2
A = 0.00055 m
Fluid #elocity
*;
1000 kg
m
3
s 1.152 m
¿
$ead loss
/¿
¿ 0.080 m( 2 ( 9.81 m / s ( 0.0265 m f F = ¿ 4 ( 1 m(
2
∆ h f =−1 dm & 2 ' / 10
RTa0le 6
#al!es
2
f F =0.00784
∆ h f =−0.1 m & 2 '
Teoretical friction factor $? len(t 7 1m
∆ h f =
4 f F v
2?
μ & ' 2
7
2
6.666@A -a.s
2 gd
N ℜ= f F =
<
∆ hf 2 gd 4 v
ρ v d μ
2
N ℜ=
1000 kg
0.00089 Pa . s
s 1.152 m /¿
3
/m ( 1.152 m / s ( 0.0265 m
N ℜ=34297.95
¿
4 ( 1m (¿ 2
− 0.1 m( 2 ( 9.81 m / s ( 0.0265 m f F = ¿
2
R(ro eD!ation : an ta0le ta0le *-P4C
##=
f F =−0.00980
! 0.0015 = =0.00006 " 0.0265
Calibrated friction factor
f F =0.0230
∆ h f =(−1 dm & 2 ' + 1.4 ) ( 2 )>*+ ∆ h f = 0.080 m & 2 '
"alve Calculations
2+
∆ h f =−0.1 m & 2 '
Uncalibrated Soc* constant
Area o" ale
+.+2+ Rapparat!s 2
A =
% "
A =
% 0.020
9?
4
2
∆ h = $
4
A = 0.00031415 m
$ =
l ∗1 min=60 s min 3
m /s
2g
∆ h 2 g v
❑
2
−0.1 ( 2 ( 9.81 m / s ❑ 2
$ =
0060
2
2
Fluid #elocity
´ =35.9 Q
v
1000 l
´ =¿ Q 0.0
1.9046
2
$ =−0.54086
3
=1 m
¿ ρ & ' = 2
Calibrated soc* constant 1000 kg
m
<'rea and velocity is constant
3
∆ h f =((−1 dm & 2 '+ 1.4 ) ( 2)/ 10 1?
v=
v=
∆ h f = 0.08 m & 2 '
´Q A 0.00060 m
3
$ =
/s
0.00031415 m
2
/s ❑ 2
2
1.9046
$ = 0.43269
v =1.9046 m / s
Teoretical soc* constant
$ead loss
∆ h f =−1 dm & 2 ' / 10
0.08 ( 2 ( 9.81 m
RTa0le 6
$ = 0.05 for )all valve
#al!es 2*
22
26
2:
