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8/6/2019 Pipe Flow for Environmental Engineers
1/22
Ynyo jc`| agh ynyo gox|`tmr
Ht' Amoyaxn R' Tohh~
Xfayat _gnzotrnx~
Yaxnaca &Y_GEAD. 18< 998
NGHNA
8/6/2019 Pipe Flow for Environmental Engineers
2/22
Cxy fful
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fC ;fC ;
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foah ruyycnoh d~ a yukyfoah ruyycnoh d~ a yuky
foah lnzog x` a xutdngofoah lnzog x` a xutdngo
foah c`rr dox|oog robxn gr 1 agh 4foah c`rr dox|oog robxn gr 1 agh 4
Dotg`uccn Oquaxn`g agh OLC * FLC
b`grxy
l
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Zoc`bnx~ foah
Ocozaxn`g foah lflfy
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_gcorr ogotl~ nr ahhoh# OLC kurx rc`yo h`|g|ath ng xfo hntobxn`g `j jc`|
\fog |axot nr ax torx OLC agh FLC b`ngbnho agh cno ax xfo jtoo |axot rutjabo
FLC jaccngl doc`| xfo haxuk cngo nghnbaxor golaxnzo ytorruto ax xfax y`ngx
ulZyOLC !4
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yFLC !
8/6/2019 Pipe Flow for Environmental Engineers
3/22
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Ogotl~ Ltaho CngoOgotl~ Ltaho Cngo
F~htaucnb L CF~htaucnb L Czoc`bnx~ foahzoc`bnx~ foah
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8/6/2019 Pipe Flow for Environmental Engineers
4/22
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8/6/2019 Pipe Flow for Environmental Engineers
5/22
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8/6/2019 Pipe Flow for Environmental Engineers
6/22
Ogotl~ &foah. C`rr
X|` x~yor5
kae`t c`rr &jtnbxn`gac foah c`rr.
kng`t c`rror &foah c`rr huo x` `uxcox# ngcox#doghr# ocd`|r# zaczor# ynyo rno bfaglor.
X`xac ogotl~ c`rr ; kae`t c`rr ycur ruk `j acckng`t c`rror
Kae`t &jtnbxn`gac. foah c`rr Falog+Y`nrouncco j`tkuca j`t cakngat jc`|
tolnko
Hatb~+\onrdabf j`tkuca j t xtagrnxn`gac aghxutducogx jc`| tolnkor
Hatb~+\onrdabf j`tkuca bag do |tnxxog j`tcakngat jc`| xft`ulf oquaxngl xfo x|` foahc`rr j`tkucao agh jnghngl j
To nr To~g`ch gukdot agh hojngoh ar
4
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Hatb~+\onrdabf j`tkucaHatb~+\onrdabf j`tkuca
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Hatb~+\onrdabf j`tkuca
j`t cakngat jc`| tolnko
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8/6/2019 Pipe Flow for Environmental Engineers
7/22
K``h~ hnaltak agh jtnbxn`g jabx`t j
K``h~ hnaltak bag do uroh j`t
mg`|ngl xfo jtnbxn`g jabx`t j
_ro `j K``h~ hnaltak toquntor ynyo
t`ulfgorr jabx`t &.# ynyo
hnakoxot agh To~g`ch gukdot &To.
_rngl xfo butzo ryobnjnb x` xfo /Hjtnbxn`g jabx`t j b`ttory`ghngl x`
xfo To nr toah jt`k xfo K``h~
hnaltak
K``h~ hnaltak bag do uroh |fog
To nr 72v192
agh /H nr 34v19+4
Jtnbxn`g jabx`t j j`t cakngat jc`|
tolnko `gc~ To nr toquntoh agh j
nr toah jt`k xfo K``h~ hnaltak
b`ttory`ghngl x` xfo To~g`ch
gukdot To
ynyo kaxotnacynyo kaxotnacynyo t`ulfgorr
&kk.
ynyo t`ulfgorr
&kk.
lcarr# hta|g dtarr# b`yyotlcarr# hta|g dtarr# b`yyot 9'991?9'991?
b`kkotbnac rxooc `t |t`ulfx nt`gb`kkotbnac rxooc `t |t`ulfx nt`g 9'98?9'98?
aryfacxoh barx nt`garyfacxoh barx nt`g 9'149'14
laczagnoh nt`glaczagnoh nt`g 9'1?9'1?
barx nt`gbarx nt`g 9'4:9'4:
b`gbtoxob`gbtoxo 9'16+9':9'16+9':
tnzox rxooctnzox rxooc 9'>+>'99'>+>'9
b`ttulaxoh koxacb`ttulaxoh koxac 8?8?
YZBYZB 9'149'14
8/6/2019 Pipe Flow for Environmental Engineers
8/22
K``h~ Hnaltak
8/6/2019 Pipe Flow for Environmental Engineers
9/22
To~g`chr gukdot
A hnkogrn`gcorr gukdot toytorogxnglxfo taxn` `j ngotxna j`tbor x` znrb`urj`tbor
To~g`chr gukdot j`t bntbucat ynyorjc`|ngl jucc
To~g`chr gukdot j`t ynyor |nxf g`g+bntbucat bt`rr robxn`gr
FotoZ nr koag zoc`bnx~
H nr hnakoxot `j xfo ynyo
T nr f~htaucnb tahnur
nr mngokaxnb znrb`rnx~ &k4/rob'.
nr cnqunh hogrnx~
nr adr`cuxo/h~gaknb znrb`rnx~ &Ya Rob'.
TQ
Z HZHZT
o
TQ
Z ZTTZT
o
.8&.8&!!
yotnkoxot\oxxoh
atoaxn`gacBt`rr
T
rob
!
8/6/2019 Pipe Flow for Environmental Engineers
10/22
8/6/2019 Pipe Flow for Environmental Engineers
11/22
Foah c`rr5 Fauog+\nccnakr j`tkuca
ugnxrRN:
8/6/2019 Pipe Flow for Environmental Engineers
12/22
Kng`t C`rror
l
ZMfk
4
4 fk foah c`rr ng jnxxngl
M tornrxagbo b`ojjnbnogx j`t jnxxngl
Foah c`rr huo x` `uxcox# ngcox# doghr# ocd`|r# zaczor# ynyo rno bfaglor
Ogotl~ C`rr ng Zaczor
Jugbxn`g `j zaczo x~yo agh zaczo y`rnxn`g B`kycov jc`| yaxf xft`ulf zaczor torucx ng fnlf foah c`rr &`go `j xfo
yuty`ror `j a zaczo nr x` btoaxo foah c`rr |fog nx nr g`x jucc~ `yog!.
Zaczo M Coq/H
Laxo zaczo# |nho `yog 9'1? 99
Lc`do zaczo# |nho yog
8/6/2019 Pipe Flow for Environmental Engineers
13/22
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aglco &_.
99'19'49'29'89'?9':9'9# jcagloh 9'2
Tolucat >9# xftoahoh 1'?
C`gl tahnur >9# jcagloh 9'4
C`gl tahnur >9# xftoahoh 9'
Dtagbf jc`|# jcagloh 1'9
Dtagbf jc`|# xftoahoh 4'9
B`ky`gogx MC_gn`g# xftoahoh 9'6
Zaczor
Lc`do# jucc~ yog 19
Aglco# jucc~ yog 4
Laxo# jucc~ yog 9'1?
Laxo# bc`roh 9'4:
Laxo# bc`roh 4'1
Laxo# bc`roh 19t ocd`| 9'>
8?t ocd`| 9'8
X+eugbxn`g 1'6
Laxo zaczo 9'4? + 4?
8/6/2019 Pipe Flow for Environmental Engineers
20/22
Kucxnyco ynyo r~rxokr
241
241
JJJ
QQQQ
!!
!
Jtnbxn`gac foah c`rr ng Yataccoc ynyor
241DA
241
JJJJ
QQQ
!
!!
Jtnbxn`gac foah c`rr ngynyor ng rotnor
8/6/2019 Pipe Flow for Environmental Engineers
21/22
Oqunzacogx ynyor agh yataccoc ynyor
B`ky`ugh ynyor5
ynyor `j rozotac rnor ng rotnor
Dtagbfngl ynyor5
x|` `t k`to ynyor dtagbfngl `ux agh g`x b`kngl x`loxfot alang
h`|grxtoak
Oqunzacogx ynyo5
J`t a lnzog foah c`rr# xfo rako jc`| nr yt`huboh ng xfo oqunzacogx
ynyo
@jxog a b`kycov ynyngl r~rxok nr toycaboh d~ a rnglco oqunzacogxynyo
C``yngl ynyor &acr` mg`|g ar yataccoc ynyor.5
x|` `t k`to ynyor dtagbfngl `ux agh b`kngl x`loxfot alang
h`|grxtoak
8/6/2019 Pipe Flow for Environmental Engineers
22/22
Y`|ot j`t yukyngl
X`xac foah `j xfo yuky agh hnrbfatlo ato goohohj`t y`|ot toquntokogx bacbucaxn`g
X`xac foah ngbcuhor rxaxnb foah agh h~gaknb foah
b`ky`gogxr &`g d`xf rubxn`g agh hnrbfatlornhor.
H~gaknb foah c`rr `g onxfot rubxn`g rnho `t `ghnrbfatlo rnho ngbcuhor d`xf kae`t c`rror agh
kng`t c`rror
Ovytorrn`g `j kng`t c`rror ng xotkr `j oqunzacogxynyo coglxf kamor xfo foah c`rr bacbucaxn`gr oar~