3 minor losses

8/19/2019 3 Minor Losses

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CE- 342MINOR LOSSES

M


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Piping system

Most pipe systems, howeve!onside#$%y moe th#n st#

&hese #ddition#% !omponen$ends, tees, #nd the %i(e) #ove#%% he#d %oss o" the sys%osses #e gene#%%y tem


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Losses

O"ten it is ne!ess#y to detemine the he#d %oss, hL, th#t o!

pipe +ow so th#t the enegy e*#tion !#n $e *sed in #n#%ye+ow po$%ems.

&he ove#%% he#d %oss "o the pipe system !onsist o"

&he he#d %oss d*e to viscous efects in the st#ight pipesmajor loss #nd denoted hLmajor , #nd

&he he#d %os in the v#io*s pipe !omponent, temed the mi#nd denoted hLminor .

&h#t is hL = hLmajor + hLminor


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Minor losses

&he he#d %oss in %ong, st#ight se!tions o" pipe !#n !#%!*%#ted $y *se o" the riction actor o$t#ined "oeithe

the Moody !h#t o

the Co%e$oo( e*#tion.

Losses occur in straight pipes (major losses) an

pipe system components (minor losses).

&he he#d %oss in"om#tion "o essenti#%%y #%% !omponenis given in dimension%ess "om #nd $#sed e/peiment#% d#t#.


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Mino %osses

&he most !ommon method *sed to detemine thesehe#d %osses o pess*e dops is to spe!i"y the loss

coecient , 0 L, whi!h is de1ned #s

Lossys

comareo coe

•The pressure drop across a component that has a loss coefficient of K L = 1

is equal to the dynamic pressure, ρV 2 /2.

•For a given value of K L the head loss is proportional to the square of

velocity.

whee hL is the additional

irreversible he#d %oss in the pipingsystem !#*sed $y insetion o" the!omponent, #nd is de1ned #s


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PL


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ow t o*g #v#%ve

e#d %oss in # v#%ve is to dissip#tion o" the (inenegy o" the %#ge-ve%o+*id ne# the v#%ve se#t

&he he#d %oss #sso!i#ted with +ow tho*gh # v#%ve is # !ommon mino esist#n!e o he#d %oss tho*gh the v#%ve m#y $e # signi1!#nt potion o" ththe system. 5ith the v#%ve !%osed, the esist#n!e to the +ow is in1nite. 5ith open the e/t# esist#n!e d*e to the pesen!e o" the v#%ve m#y o m#y not $


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5hen the pipe di#mete downste#m o" the !omponent chdetemin#tiono" the mino %oss is even moe !omp%i!#ted.In #%% !#ses, howeve, it is $#sed on the additional ievesio" me!h#ni!#% enegy th#t wo*%d othewise not e/ist i" the %oss !omponent wee not thee

the !omponentin+*en!es the+ow"o seve#% pipedi#metesdownste#m.


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!he loss coecient, L &he #!t*#% v#%*e o" K L is stong%y dependent on the geometr

!omponent !onsideed.

It m#y #%so $e dependent on the +*id +ow !ondition K L = Φ (Geometry, Re)

6s the Reyno%ds n*m$e is large enough so th#t the +ow!omponent is domin#ted $y inertia efects, with vis!o*s e7se!ond#y impot#n!e.

In # +ow th#t is domin#ted $y inertia efects #the th#n vis!is *s*#%%y "o*nd th#t pess*e dops #nd he#d %osses !oe%#tethe dyn#mi! pess*e.

&his is the e#son why the "i!tion "#!to "o vey %#ge Reyn"*%%y deve%oped pipe +ow is independent o" the Reyno%ds s#me !ondition is "o*nd to $e t*e "o +ow tho*gh pipe !omp

&h*s in most !#ses o" #!ti!#% inteest the %oss !oe8

"or most loss coe

independ


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Equivalent length

Mino %osses #e #%so e/pessed in tems o" the

equivalent length Le&uiv , de1ned #s

9


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!otal 'ead Loss

On!e #%% the %oss !oe8!ients #e #v#i%#$%e, the tot#% he#dpiping system is detemined "om Total head loss (genera

whee i epesents e#!h pipe se!tion with !onst#nt di#meepesents e#!h !omponent th#t !#*ses # mino %oss. I" thpiping system $eing #n#%yed h#s # !onst#nt di#mete :9#ve#ge ve%o!ity


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6ny !h#nge in +ow #e# !onti$*tes %osses th#t #e not #!!o*"*%%y deve%oped he#d %oss !#%!*%#tion 'the "i!tion "#!to).

M#ny pipe systems !ont#in

v#io*s t#nsition se!tionsin whi!h the pipe di#mete!h#nges "om one sie to#nothe.S*!h !h#nges m#y o!!*#$*pt%y o #the smooth%ytho*gh some type o" #e#!h#nge se!tion.

&he e/teme !#ses invo%ve+ow into # pipe "om #esevoi 'an entrance) oo*t o" # pipe into # esevoi

'#n e/it).

Transition sections


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Entrance fow conditions and loss coecient.E#!h geomety h#s #n #sso!i#ted %oss !oe8!ient

(a) Reentrant, K L = 0.8 () shar!edged,

(c) slightl# rounded, K L = 0.$(d ) well!rounded,


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enacontracta

I" the e/it is not # smooth, we%%-!onto*edno%e, $*t #the # +#t p%#te, the di#mete o"the =et,d

=

, wi%% $e %ess th#n the di#mete o"the ho%e, dh.

&his phenomenon, !#%%ed # vena contractae7e!t, is # es*%t o" the in#$i%ity o" the +*id tot*n the sh#p >;? !one indi!#ted $y thedotted %ines in the 1g.

!he venacontracta efect isa unction o thegeometry o theoutlet*


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E#!h geomety h#s #n #sso!i#ted %oss !oe8!ient.

& vena contracta region 'a# result $e!#*se the +*id !#nno# sh#p ight-#ng%e !one.

&he +ow is s#id to sep##te "om the sh#p !one.


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%ow p#tten #nd pess*e disti$*tion "o # sh#pedged ent#n!e

&he e/t# (ineti! enegy o" the +*id #t se!tion '2) is p#ti#%%y %ost $eviscous dissipation so th#t the pess*e does not et*n to thev#%*eBB.

iscous dissipation ievesi$%e po!ess $y me#ns o" whi!h done $y the +*id on #d=#!ent %#yes d*e to the #!tion o" sheis t#ns"omed into he#t is de1ned #s viscous dissipation

&he m#=oity o" this %oss is d*e to inertia efects th#t #e edissip#ted $y the she# stesses within the +*id.

On%y # sm#%% potion o" the %oss is d*e to the $all shear stress $entrance region.

Minor hoten adissipa

inetic


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Ent#n!e %oss !oe8!ient #s # "*n!tion o" o*ndingthe in%et edge

6n o$vio*s w#y to ed*!e the ent#n!e %oss is to o*nd tent#n!e egion thee$y ed*!ing o e%imin#ting the ven#

!ont#!t# e7e!t.ipeentrancelossescan erelativelyeasily

reduced roundingthe inlet

Ent#n!e +ow !onditions #nd %oss


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Ent#n!e +ow !onditions #nd %oss!oe8!ient#- Reent#nt, 0 L 9 ;. $- sh#p edged,

0 L 9 ;.A

!- s%ight%y o*nded, 0 L 9 ;.2 d- we%%-o*nded,

0 L 9 ;.;4


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Loss !oe8!ient "o # s*dden !ont#!tion

&he %oss !oe7. 0 L is # "*n!tion o" the #e# #tio, 62D6.


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S*$meged o*t%et

!his is true, regardless o the shapeo the e-it.!hereore, there is no need to roundthe pipe e-its.

&he %oss !oe8!ient "o # s*$meged pipe e/it is o"ten %isted in h#nd$oo(s #s

6t #ny s*!h e/it, whethe %#min# o t*$*%ent, the +*id %e#ving the pipe, %osits (ineti! enegy #s it mi/es with the esevoi +*id #nd event*#%%y !omes to

tho*gh the ievesi$%e #!tion o" vis!osity.

E/it +ow !onditions #nd %oss


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E/it +ow !onditions #nd %oss!oe8!ient

In these !#ses the entie kinete/iting +*id 've%o!ity


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- Contin*

- Momen

-Eneg

h t th f i *0 + d d th i t d l


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haracter o the fow in a *0 +end and the associated loss co

Ch##!te o" the +ow$end #nd the #sso!i#!oe8!ient#) 5itho*t g*ide v#n$) G)with g*ide v#ne


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6 piping system m#y h#ve m#ny mino %osses whi!h #e #%% !to 2D2g

S*m them *p to # tot#% system %oss "o pipes o" the s#me di#

∑+=∑+=m

mm

m f L K D

L f

g

V hhh

2

2

EHL HL "o Losses in # Pipe


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EHL HL "o Losses in # Pipe

•Ent#n!es, $ends, #ndothe +ow t#nsitions!#*se the EHL to dop #n#mo*nt e*#% to thehe#d %oss pod*!ed $ythe t#nsition.•EHL is steepe #t

ent#n!e th#n it isdownste#m o" theewhee the s%ope is e*#%the "i!tion#% he#d %oss inthe pipe.• &he HL #%so dops

sh#p%y downste#m o"


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E-a'le!/ ead Loss and 1ressure Rise during 2raE-ansion

A !cm!diameter hori"ontal #ater pipe e$pands gradually to a %!cm!diameter

of the e$pansion section are angled &'( from the hori"ontal. The average veloc

of #ater )efore the e$pansion section are *m+s and 1'-a, respectively./etermine the head loss in the e$pansion section and the pressure in the larger!

Assumptions 1- The flo# is steady and incompressi)le. 2 -The flo# at section

developed and tur)ulent #ith 01 = 02 = 1.'.

Properties e ta-e the density of #ater to )e

= 1''' -g+m&

. The loss coefficient for graduale$pansion of u '( total included angle is

K L = '.'*.

E-a'le!$


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E-a'le!$

5#te is to $e withd#wn "om # 3-m-high w#te esevoi# .A-!m-di#mete ho%e #t the $ottom s*"#!e.

:iseg#ding the e7e!t o" the (ineti! enegy !oe!tion "#detemine the +ow #te o" w#te tho*gh the ho%e i" 'a) tho" the ho%e is we%%-o*nded #nd 'b) the ent#n!e is sh#p-

&ssu'tions3 &he +ow is ste#dy #nd in!ompessi$%e.$ &he esevoi is open to the #tmospheeso th#t the pess*e is #tmosphei!pess*e #t the "ee s*"#!e.4 &he e7e!t o" the (ineti! enegy!oe!tion "#!to is diseg#ded, #nd th*sJ 9 .0 L 9 ;.A '"o the sh#p ended ent#n!e)

0 L 9 ;.;3 '"o the we%%-o*nded ent#n!e)

%


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E/#mp%e-3

6 hoiont#% pipe h#s #n #$*pt e/p#nsion "om ! 9 !m to !2 9 &he w#te ve%o!ity in the sm#%%e se!tion is ; mDs #nd the +ow is t

&he pess*e in the sm#%%e se!tion is " 9 3;; (P#.

(ing the (ineti! enegy !oe!tion "#!to to $e .;K #t $oth the inthe o*t%et, detemine the downste#m pess*e "2, #nd estim#te thth#t wo*%d h#ve o!!*ed i" Geno*%%is e*#tion h#d $een *sed.

E/#mp%e-4


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E/#mp%e-4

6 3-m-di#mete t#n( is initi#%%y 1%%ed with w#te 2 m #$ove the !# sh#p-edged ;-!m-di#mete oi1!e.

&he t#n( w#te s*"#!e is open to the #tmosphee, #nd the oi1!

d#ins to the #tmosphee tho*gh # ;;-m-%ong pipe. &he "i!tion !oe8!ient o" the pipe !#n $e t#(en to $e ;.;A #nd e7e!t o" the (ineti! enegy !oe!tion "#!to !#n $e neg%e!ted.

:etemine 'a) theiniti#% ve%o!ity "om

the t#n( #nd 'b) thetime e*ied toempty the t#n(.


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Ne/t %esson- *i


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E %


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E/#mp%e

29E:/ &he !%osed-!i!*it wind t*nne% in whi!h #i #t st#n!onditions is to +ow tho*gh the test se!tion $etween se

#nd 'K) with # ve%o!ity o" K mDs. &he +ow is diven $y # "#n th#t essenti#%%y in!e#ses the spess*e $y the #mo*nt p./p0 th#t is needed to ove!ome%osses e/peien!ed $y the +*id #s it +ows #o*nd the !i!

Esti'ate the v#%*e o" p./p0 #nd the hosepowe

s*pp%ied to the +*id $y the "#n.

1ie ;low E-a'les


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&he #pp%i!#tion o" the petinent e*#tions st#ight"ow#d, with #the simp%e !#%!*%#tions thgive #nswes to po$%ems o" engineei

impot#n!e. &he m#in ide# invo%ved is to #pp%y tenegy e*#tion $etween #ppopi#te %o!#tiowithin the +ow system, with the he#d %oss wittentems o" the "i!tion "#!to #nd the mino %o!oe8!ients.

5e wi%% !onside two !%#sses o" pipe systems

those !ont#ining # sing%e pipe 'whose %ength m$e inte*pted $y v#io*s !omponents), #nd

those !ont#ining m*%tip%e pipes in p##%%e%, seieo netwo( !on1g*#tion

Si % i


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Sing%e pipes

&hee #e $#si!#%%y thee types o" po$%emsinvo%ved with *ni"om +ow in # sing%e pipe . :etemine the he#d %oss, given the (ind

#nd sie o" pipe #%ong with the +ow #te, 9 6Q<

2. :etemine the +ow #te, given the he#d(ind, #nd sie o" pipe

3. :etemine the pipe di#mete, given thetype o" pipe, he#d, #nd +ow #te

Sing%e pipes


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Sing%e pipes In # &ype I po$%em we spe!i"y the desied +ow#te o #ve#

ve%o!ity #nd detemine the ne!ess#y pess*e di7een!e ohe#d %oss. o e/#mp%e, i" # +ow#te o" .K %Dmin is e*ied# dishw#she th#t is !onne!ted to the w#te he#te $y # givpipe system, wh#t pess*e is needed in the w#te he#te

In # &ype II po$%em we spe!i"y the #pp%ied diving pess*e#%ten#tive%y, the he#d %oss, #nd detemine the +ow#te. oe/#mp%e, how m#ny g#%min o" hot w#te #e s*pp%ied to thedishw#she i" the pess*e within the w#te he#te is 44(P#nd the pipe system det#i%s %ength, di#mete, o*ghness othe pipeT n*m$e o" e%$owsT et!.#e spe!i1ed

In # &ype III po$%em we spe!i"y the pess*e dop #nd the+ow#te #nd detemine the di#mete o" the pipe needed. e/#mp%e, wh#t di#mete o" pipe is needed $etween the w#the#te #nd dishw#she i" the pess*e in the w#te he#te i4(P#, detemined $y the !ity w#te system, #nd the +owis to $e not %ess th#n .K %Dmin ,detemined $y them#n*"#!t*e


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Pipe +ow po$%ems !#n $e !h##!teied $y wh#tp##metes #e given #nd wh#t is to $e !#%!*%#ted

&ypes o" pipe +ow po$%ems


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yp p p p

Hiven :T LT < ')T UT VT W. Comp*te the he#d %oss " opess*e dop 'he#d %oss po$%ems).C#%!*%#te Re #nd U D: "om given d#t#

O$t#in " "om the Moodys !h#t Hiven :T LT " UT VT W. Comp*te the ve%o!ity < o "%ow#t

C#%!*%#te UD: "om given d#t# #nd Re Xse Co%e$oo( "om*%# #nd the #$ove #nd E. o$t#in O$t#in Re "om Moodys !h#t #nd hen!e

Hiven T LT " T UT VT W. Comp*te the di#mete : o" the

'sie po$%ems) 6ss*me # s*it#$%e v#%*e o" " #nd !#%!*%#te : "om :#

5eis$#!h e*#tion 5ith this ti#% v#%*e o" :, !#%!*%#te UD: #nd Re 5ith this UD: #nd e, !#%!*%#te " "om Moodys !h#t

Repe#t the po!ess ti%% " $e!ome s#me

2+1

2

23e

=

LV

D ghVD f

f

ν

2iven Li*id in pipe h#s E/'-o()


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2iven Li*id in pipe h#sγ 9 (NDm3. 6!!e%e#tion9 ;.

! 9 !m, µ 9 3/;-3 N-mDs2.

;ind Is +*id st#tion#y,

moving *p, o movingdown 5h#t is the me#nve%o!ity


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Hiven 0eosene '#9;.>4,µ9.>NsDm2). oiont#% ;-mpipe. $92/;-3 m3Ds. 9.A mTd9 2!m.

ind Pess*e dop pe ; m o"pipe.


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ind Estim#te thee%ev#tion e*ied in the*ppe esevoi to pod*!e# w#te dis!h#ge o" ; !"sin the system. 5h#t is theminim*m pess*e in the

pipe%ine #nd wh#t is thepess*e thee


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the system shown is 2 !"s,wh#t hosepowe is thep*mp s*pp%ying to thew#te &he 4 $ends h#ve ##di*s o" 2 in #nd the K-inpipe is smooth.

ind osepowe


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omewo( #ssignment-

Oi% with W 9 >;; (gDm3 #nd Y 9 ;.;;;; m2Ds, +owm3Ds tho*gh A;;m o" 2;;-mm di#mete !#st i:etemine #) the he#d %oss #nd $) the pess*ethe pipe s%opes down #t ;F in the +ow die!tion.


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omewo( #ssignment-2

6 !omme!i#% new g#%v#nied ion sevi!e pipew#te m#in is e*ied to de%eveed 2;;LDs od*ing # 1e. I" the %ength o" the sevi!e pipe is 3#%%ow#$%e he#d %oss in the pipe is A;m #nd the (vis!osity o" w#te #t 2;F! is .;;/;-K m2Dse!, whpipe di#mete to $e *sed "o this p*pose


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omewo( #ssignment-3

6 A;-mm di#mete g#%v#nied ion sevi!e !onne!ted to # w#te m#in in whi!h the pess*(P# g#ge. I" the %ength o" the sevi!e pipe to # "4; m #nd the "#*!et is .2m #$ove the m#in, ethe +ow#te when the "#*!et is "*%%y open.

3 minor losses

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