2_friction loss unguided(1)

8/12/2019 2_Friction Loss Unguided(1)

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DOC. REF SOE/CE/LS018

EFF. DATE 1-SEP-2012

REVISION NO. 1

MECHANICAL ENGINEERING

FRICTION LOSS ALONG A PIPE

AIM:

The aims of the e!e"ime#ts a"e to $emo#st"ate the %ha#&e i# the 'a( of "esista#%e )the

"e'atio#shi! *et(ee# i a#$ +, a#$ to esta*'ish the %"iti%a' R.

APPARATUS:

1, Sto! at%h.

2, Vo'+met"i% $"a+'i% e#%h.

, F"i%tio# Loss a'o#& a !i!e.

INTRODUCTION:

The f"i%tio#a' "esista#%e to (hi%h f'+i$ is s+*e%te$ as it f'o(s a'o#& a !i!e "es+'ts i# a%o#ti#+o+s 'oss of e#e"& o" tota' hea$ of the f'+i$. Fi&+"e 1 i''+st"ates this i# a sim!'e %ase3

the $iffe"e#%e i# 'e4e's *et(ee# !ie5omete"s A a#$ "e!"ese#ts the tota' hea$ 'oss h i# the

'e#&th of ' of !i!e. I# h$"a+'i% e#&i#ee"i#& it is %+stoma" to "efe" to the "ate of 'oss of tota'

hea$ a'o#& the !i!e6 $h/$' 6 * the te"m h$"a+'i% &"a$ie#t6 $e#ote$ * the sm*o' i 6 so that7

idl

dh= )1,

Fi&+"e 17 Dia&"am i''+st"ati#& the h$"a+'i% &"a$ie#t.





REVISION NO. 1

Os*o"#e Re#o'$s6 i# 1886 "e%o"$e$ a #+m*e" of e!e"ime#ts to $ete"mi#e the 'a(s of

"esista#%e i# !i!es. i#t"o$+%i#& a fi'ame#t of $e i#to the f'o( of (ate" a'o#& a &'ass !i!e

he sho(e$ the eiste#%e of t(o $iffe"e#t t!es of motio#. At 'o( 4e'o%ities the fi'ame#t

a!!ea"e$ as a st"ai&ht 'i#e (hi%h !asse$ $o(# the (ho'e 'e#&th of the t+*e i#$i%ati#& 'ami#a"

f'o(. At hi&he" 4e'o%ities6 the fi'ame#t6 afte" !assi#& a 'itt'e (a a'o#& the t+*e6 s+$$e#'

mie$ (ith the s+""o+#$i#& (ate"6 i#$i%ati#& that the motio# ha$ #o( *e%ome t+"*+'e#t.

E!e"ime#t (ith !i!es of $iffe"e#t $iamete"s a#$ (ith (ate" at $iffe"e#t tem!e"at+"e 'e$

Re#o'$s to %o#%'+$e that the !a"amete" (hi%h $ete"mi#es (hethe" the f'o( sha'' *e 'ami#a"

o" t+"*+'e#t i# a# !a"ti%+'a" %ase is7

µ

ρ uD R = )2,

i# (hi%h R $e#otes the Re#o'$s N+m*e" of the motio#.

ρ $e#otes the $e#sit of the f'+i$

+ $e#otes the 4e'o%it of f'o(D $e#otes the $iamete" of the !i!e

µ $e#otes the %oeffi%ie#t of 4is%osit of the f'+i$

This motio# is 'ami#a" o" t+"*+'e#t a%%o"$i#& as the 4a'+e to R is 'ess tha# o" &"eate" tha# a

%e"tai# %"iti%a' 4a'+e. If e!e"ime#ts a"e ma$e (ith i#%"easi#& "ates of f'o(6 this 4a'+e of R

$e!e#$s o# the $e&"ee of %a"e (hi%h is ta9e# to e'imi#ate $ist+"*a#%es i# the s+!!' a#$

a'o#& the !i!e. O# the othe" ha#$6 if e!e"ime#ts a"e ma$e (ith $e%"easi#& f'o(6 t"a#sitio#

f"om t+"*+'e#t to 'ami#a" f'o( ta9es !'a%e at a 4a'+e of R (hi%h is 4e" m+%h 'ess $e!e#$e#t

o# i#itia' $ist+"*a#%es. This 4a'+e of R is a*o+t 20006 a#$ *e'o( this the f'o( *e%omes

'ami#a" s+ffi%ie#t' $o(#st"eam of a# $ist+"*a#%e6 #o matte" ho( se4e"e it is.

Diffe"e#t 'a(s of "esista#%e a!!' to 'ami#a" a#$ to t+"*+'e#t f'o(. Fo" a &i4e# f'+i$ f'o(i#&

a'o#& a &i4e# !i!e6 e!e"ime#ts sho( that7

fo" 'ami#a" motio# i ∝ + ),

fo" t+"*+'e#t motio# i ∝ +# ):,

# *ei#& a# i#$e (hi%h 'ies *et(ee# 1.; a#$ 2.0 )$e!e#$i#& o# the 4a'+e of R a#$ o# the

"o+&h#ess of the (a'' of the !i!e,. E<+atio# is i# a%%o"$a#%e (ith Poise+i''e=s e<+atio#

(hi%h %a# *e ("itte# i# the fo"m7

2

12

gD

ui

ρ

µ = )>,

The"e is #o simi'a" sim!'e "es+'t fo" t+"*+'e#t f'o(7 i# e#&i#ee"i#& !"a%ti%e it is %+stoma" to

+se Da"%=s e<+atio#7

g D

fui

2

: 2

= ),

i# (hi%h f $e#otes a# e!e"ime#ta'' $ete"mi#e$ fa%to" (hi%h 4a"ies (ith R a#$ !i!e

"o+&h#ess.

;





REVISION NO. 1

?eas+"eme#ts of i i# the 'ami#a" "e&io# is +se$ to fi#$ the %oeffi%ie#t of 4is%osit a#$

meas+"eme#ts i# the t+"*+'e#t "e&io# is +se$ to fi#$ the f"i%tio# fa%to" f. Com!a"e the

f"i%tio# fa%to" o*tai#e$ f"om the e!e"ime#t (ith the 'asi+s=s e<+atio#.

DESCRIPTION:

Fi&+"e 27 Dia&"ammati% A""a#&eme#t of A!!a"at+s fo" ?eas+"i#& F"i%tio# Loss

A'o#& a Pi!e.

Fi&+"e 2 sho(s the a""a#&eme#t i# (hi%h (ate" f"om a s+!!' ta#9 is 'e$ th"o+&h a f'ei*'e

hose to the *e''-mo+the$ e#t"a#%e to a st"ai&ht t+*e a'o#& (hi%h the f"i%tio#a' 'oss is

meas+"e$. Pie5omete" ta!!i#& a"e ma$e at a# +!st"eam se%tio# (hi%h 'ies a!!"oimate' :>t+*e $iamete"s a(a f"om the !i!e e#t"a#%e6 a#$ at a $o(#st"eam se%tio# (hi%h 'ies

a!!"oimate' :0 t+*e $iamete"s a(a f"om the !i!e eit. These %'ea" 'e#&ths +!st"eam a#$

$o(#st"eam of the test se%tio# a"e "e<+i"e$ to !"e4e#t the "es+'ts fo"m *ei#& affe%te$ *

$ist+"*a#%es #ea" the e#t"a#%e a#$ eit of the !i!e. The !ie5omete" ta!!i#& a"e %o##e%te$ to

a# i#4e"te$ @-t+*e ma#omete"6 (hi%h "ea$s the $iffe"e#tia' !"ess+"e $i"e%t' i# mm of (ate"6

o" a @-t+*e (hi%h "ea$s i# mm of me"%+".

The "ate of f'o( a'o#& the !i!e is %o#t"o''e$ * a #ee$'e 4a'4e at the !i!e eit6 a#$ is

meas+"e$ * timi#& the %o''e%tio# of (ate" i# a meas+"i#& %'i#$e" )the $is%ha"&e *ei#& so

sma'' as to ma9e the +se of the $"a+'i% e#%h (ei&hi#& ta#9 im!"a%ti%a*'e,.

8





REVISION NO. 1

BACKGROUND:

Derivation of Poiseuille's Equation.

Fi&+"e 7 De"i4atio# of Poise+i''e=s E<+atio#.

To $e"i4e Poise+i''e=s e<+atio# (hi%h a!!'ie$ to 'ami#a" f'o( a'o#& a t+*e6 %o#si$e" the

motio# i#$i%ate$ o# Fi&+"e . O4e" ea%h %"oss-se%tio# of the t+*e the !ie5omet"i% !"ess+"e is

%o#sta#t6 a#$ this !"ess+"e fa''s %o#ti#+o+s' a'o#& the t+*e. S+!!ose that *et(ee# %"oss-

se%tio# A a#$ se!a"ate$ * 'e#&th ' of the t+*e6 the fa'' i# !"ess+"e is !. The# the fo"%e

ee"te$ * this !"ess+"e $iffe"e#%e o# the e#$s of a %'i#$e" ha4i#& "a$i+s "6 a#$ its ais o#

the %e#t"e 'i#e of the t+*e6 is !π" 2. O4e" a# %"oss-se%tio# of the t+*e6 the 4e'o%it 4a"ies (ith

"a$i+s6 ha4i#& a maim+m 4a'+e of + o at the %e#t"e a#$ fa''i#& to 5e"o at the (a''3 'et the

4e'o%it at "a$i+s " i# a# %"oss-se%tio# *e $e#ote$ * +" . The# the shea" st"ess τ 6 i# the

$i"e%tio# sho(# o# Fi&+"e 6 $+e to 4is%o+s a%tio# o# the %+"4e$ s+"fa%e of the %'i#$e"6 is

&i4e# *7

dr

dur

µ τ = );,

)Note thatdr

dur is #e&ati4e so that the st"ess a%ts i# the $i"e%tio# sho(# i# Fi&+"e ,. The

fo"%e o# the %'i#$e" $+e to this st"ess is rl dr

dur π

µ 2. . Si#%e the f'+i$ is i# stea$ motio#

+#$e" the a%tio# of the s+m of !"ess+"e a#$ 4is%o+s fo"%es3

02. 2

=+ rl dr

dur p r π µ π

The"efo"e7 µ l

pr

dr

dur

2−= )8,

+" 0 (he# " a

( )22

:r a

l

pur −=

µ )B,

This "es+'t sho(s that the 4e'o%it $ist"i*+tio# a%"oss a se%tio# is !a"a*o'i%6 as i#$i%ate$ o#

Fi&+"e 6 a#$ that the 4e'o%it o# the %e#t"e 'i#e6 &i4e# * !+tti#& " 0 i# E<+atio# B is

B





REVISION NO. 1

µ l

pauo

:

2

= )10,

The $is%ha"&e "ate ma #o( *e %a'%+'ate$. The f'o( "ate δ th"o+&h a# a##+'+s of "a$i+s "

a#$ (i$th δ" is

r r uQ r δ π δ 2=

I#se"ti#& +" f"om E<+atio# B a#$ i#te&"ati#&

( )dr r r al

pQ

a

∫ −=0

122

:π

µ

The"efo"e µ l

ppaQ

8

:

= )11,

No( the mea# 4e'o%it + o4e" the %"oss se%tio# is6 * $efi#itio#6 &i4e# *7

2. auQ π = )12,

a#$ e'imi#ati#& *et(ee# e<+atio# 11 a#$ 12 &i4es7

µ µ l

pD

l

pau

128

22

== )1,

(hi%h ma *e ("itte# i# the fo"m7

2

12

gD

ui

ρ

µ = )>,

* +se of the s+*stit+tio#s7 ρ&h !

a#$ il

h=

Derivation of Darcy's Equation

If the f'o( is t+"*+'e#t6 the a#a'sis &i4e# a*o4e is i#4a'i$ate$ * the %o#ti#+o+s mii#&

!"o%ess (hi%h ta9es !'a%e. A%"oss the %+"4e$ s+"fa%e of the %'i#$e" ha4i#& "a$i+s " i# Fi&+"e

6 this mii#& is ma#ifest as a %o#ti#+o+s +#stea$ a#$ "a#$om f'o( i#to a#$ o+t of the

%'i#$e"6 so that the a!!a"e#t shea" st"ess o# this s+"fa%e is &"eate" tha# the 4a'+e &i4e# i#

E<+atio# ;. e%a+se of the mii#& the $ist"i*+tio# of 4e'o%it o4e" a %"oss se%tio# is mo"e

+#ifo"m tha# the !a"a*o'i% sha!e $e$+%e$ fo" 'ami#a" f'o(6 as i#$i%ate$ o# Fi&+"e :.

10





REVISION NO. 1

Fi&+"e :7 De"i4atio# of Da"%=s E<+atio#.

A'tho+&h it is #ot !ossi*'e to !e"fo"m a %om!'ete a#a'sis fo" t+"*+'e#t f'o(6 a +sef+' "es+'t

ma *e o*tai#e$ * %o#si$e"i#& the (ho'e %"oss se%tio# as sho(# i# Fi&+"e :. It is "easo#a*'e

to s+!!ose that the shea" st"ess oτ o# the (a'' of the t+*e (i'' $e!e#$ o# the mea# 4e'o%it

+3 'et +s ass+me fo" the !"ese#t that7

22/1. u f o ρ τ = )1:,

i# (hi%h 1/2ρ+2 $e#otes the $#ami% !"ess+"e %o""es!o#$i#& to the mea# 4e'o%it +6 a#$ f

is a f"i%tio# fa%to" )#ot #e%essa"i' %o#sta#t,. Si#%e τo a#$ 1/2ρ+2 ea%h ha4e $ime#sio#s of

fo"%e !e" +#it a"ea6 f is $ime#sio#'ess. The fo"%e o# a %'i#$e" of 'e#&th l $+e to this st"ess

is al u f π ρ 2.2/1. 2

a#$ the fo"%e $+e to the fa'' i# !"ess+"e is !.πa26 so that7

al u f a p π ρ π 2.2/1.. 22

=

S+*stit+ti#&7 p gh = ρ

il h =

a#$

2

Da =

'ea$s to the "es+'t g

u

D

f i

2.

: 2

= ),

(hi%h is a fo"m of Da"%=s e<+atio#.

The f"i%tio# fa%to" f (hi%h o%%+"s i# this e<+atio# (as $efi#e$ * e<+atio# 1: a#$ is #ot

#e%essa"i' %o#sta#t. The "es+'ts of ma# e!e"ime#ts sho( that f $oes6 i# fa%t6 $e!e#$ o#

*oth R6 the Re#o'$s N+m*e"6 a#$ o# the "o+&h#ess of the !i!e (a''. At a &i4e# 4a'+e of R6 f

i#%"ease (ith i#%"easi#& s+"fa%e "o+&h#ess. Fo" a &i4e# s+"fa%e "o+&h#ess6 f &e#e"a''$e%"eases s'o(' (ith i#%"easi#& R. This mea#s that if R is i#%"ease$ * i#%"easi#& + a'o#& a

&i4e# !i!e6 f (i'' $e%"ease s'o(' (ith i#%"easi#& +6 so that the !"o$+%t f+2 o# (hi%h i

11





REVISION NO. 1

$e!e#$ i# e<+atio# (i'' i#%"ease some(hat 'ess tha# +2. I# fa%t6 o4e" a fai"' (i$e "a#&e6 it is

ofte# !ossi*'e to "e!"ese#t the 4a"iatio# of i (ith + * the a!!"oimatio#7

nkui =

(he"e 9 a#$ # a"e %o#sta#t fo" a &i4e# f'+i$ f'o(i#& a'o#& a &i4e# !i!e6 # ha4i#& a 4a'+e

*et(ee# 1.; a#$ 2.0.

The f"i%tio# fa%to" e<+atio# (hi%h (as !"o!ose$ * 'asi+s fo" t+"*+'e#t f'o( i# smooth !i!e

is e!"esse$ as7

2>.00;B.0

−

= R f

PROCEDURES:

Notes7 1, The hei&ht of the (ate" 'e4e' i# the ma#omete" ma *e "aise$ to a s+ita*'e 4a'+e *

a''o(i#& ai" to es%a!e th"o+&h the ai" 4a'4e at the to!6 o" * !+m!i#& ai" th"o+&h the

4a'4e.

2, D+e to the 'a"&e "a#&e of hea$ $iffe"e#%es6 the "ea$i#&s sho+'$ *e "e%o"$e$ i# t(o

sets. Those fo" 'o(e" 4e'o%it f'o( "ates6 (ith the (ate" ma#omete"6 a#$ those fo"

hi&h 4e'o%it (ith the me"%+" ma#omete".

Desi&# a#$ !e"fo"m a# e!e"ime#t to %ate" fo" the aims of the e!e"ime#t. It sho+'$ *e #ote$

that t(o t!es of f'o( "e&imes (i'' *e a!!a"e#t a#$ as s+%h6 "ea$i#&s sho+'$ %omfo"ta*'%o4e" the (ho'e of the 'ami#a" "e&io# a#$ the t"a#sitio# to t+"*+'e#t f'o(. P"ese#t the "es+'ts

o*tai#e$ i# a# a!!"o!"iate fo"mat a%%o+#ti#& fo" a# e""o"s )if s+ita*'e,.

@sef+' Data

Le#&th of !i!e *et(ee# !ie5omete" ta!!i#&6 I >2: mm

Nomi#a' $iamete" of !i!e6 D mm

C"oss-se%tio# a"ea of !i!e ;.0 mm2

REFERENCES:

1. ?e%ha#i%s of F'+i$s. ?asse6 S6 Va# Nost"a#$ Rei#ho'$6 1B8B

2. F'+i$ ?e%ha#i%s6 hite F ?6 ?%"a(-i''6 "$ E$. 1BB:

. A# A'*+m of F'+i$ ?otio#6 Va# D9e ?. Pa"a*o'i% P"ess6 1B82.

:. Chemi%a' E#&i#ee"i#& Vo'+me 16 Co+'so# Ri%ha"$so#6 +tte"(o"th-ei#ema##

12

2_friction loss unguided(1)

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