UNIVERSITI TENAGA NASIONAL COLLEGE OF ENGINEERING DEPARTMENT OF CIVIL ENGINEERING
CEWB121 MECHANICS OF FLUID LABORATORY OPEN ENDED EXPERIMENT REPORT EXP. TITLE
: HEAD LOSS DUE TO FRICTION AND PIPE FITTING IN ROUND SMOOTH PIPE
EXP. NO
:5
STUDENT NAME
: NUR FAREHA FAREHA BINTI ABDUL ABDU L GHAFAR
STUDENT ID
: CE096508
SECTION
: 01
GROUP
: 02
GROUP MEMBERS:
1. AZRUL AFFAN AFFAN BIN MUHAMAD RASHIDI CE096502 2. HARIGARAN A/L KANDASAM CE09650! ". MOHAMMAD OMAR HAMID #AGIEALLA CE09$089
INSTRUCTOR
Performed Date
: PROF. IR. DR. MARLINDA BINTI ABDUL MALEK
Due Date 10 AU AUGUST 2015 TH
Submitted Date 10 TH AUGUST 2015 1
TABLE OF CONTENT
TITLE O%&'()*+'
PAGE "
T,'-
"$
A)*(*3)'4 R'7)
8 10
A33)
11 12
P-('4'
1"15
D3)3 O%'+3)*- 34 R'7)
16 21
D*(*-
22
C-(7*-
2"
C*)*'
2"
R'''('
2"
A'4*;
2!
2
OBJECTIVE
T,' -' - ),* ';'*<') * )- <'3' ,'34 7- * *' - 4*'') =3)' 7-= 3)' 34 *' 4*3<')'. T,' ';'*<') * 37- (-4()'4 )- ')*<3)' ),' +37' - 7- (-'*(*') - *' - 4*'') 7-= (-4*)*- 34 4*3<')' 34 4')'<*' ),' ''() - 44' (,3>' * *' 4*3<')' 34 7-= 4*'()*- - ),' )-)37 ''> - ,'34 7-' * *'. THEORY
I B'-77*? '3)*- , ''') ),' ,'34 7- 4' )- *()*- %')='' ),' 7*4 34 ),' *)'37 3(' - ),' (-)3) 4*3<')' *' 3 ='77 3 ),' *()*- %')='' ),' 34&3(') 7*4 73' 1/ρ> @ 12/2> @ Z1 2 / ρ> @ 22/2> @ Z2 @ ,
1
T,* =*77 '7) * 3 (-)*- (,3>' - ''> -< 3 +373%7' <'(,3*(37 -< (, 3 *')*( - -)')*37 ''>*' )- 3 7' +373%7' ),'<37 -< ),3) * ,'3). T,* (,3>' - ''> * 377 '''4 )- 3 *()*- ,'34 7- =,*(, ''') ),' 3<-) - ''> (-+')'4 *),'3) ' *) ='*>,) - 7*4 .
T,' ,'34 7-' , * *' 4' )- *()*- (3 %' 4')'<*'4 *> D3(#'*%3(, '3)*- T%7') 7-=, ! L2 2 >D
2
#,'': L > D
F F *()*- 3()- L'>), M'3 +'7-(*) /A G3+*) C-)3) 4*3<')'
T,' *()*- ,'34 7- - %-), 73<*3 34 )%7') 7-= (3 %' ';''4 % *<*73 -<73 37),->, ),' -*>*37 4'*+3)*- - '3(, -' * 4*''): h f
= f L V
2
D 2 g
"
"
In laminar ow, the frition fator i! onl" a funtion of #e"nold! #e"nold! number while for turbulent ow it i! a funtion of #e"nold! $# e% number and the relati&e rou'hne!! of the (i(e) R '
=
ρ AD AD
!
µ
=,'' ρ: 4'*) : 3+'3>' +'7-(*) +'7-(*) D: *' **4' 4*3<')' µ: +*(-*). B3'4 - ),' 3)' - ),' 7-= *()*- 3()- (3 %' ')*<3)'4 *> ),' -77-=*> (-'73)*- L3<*3 7-=
6! R '
Turbulent *low
5
+ 0)1#e0)25
6 E3)*- 6 * B73* E3)*- 34 -7 +37*4 - <--), *' 34 "000 R' 105. T,' +37' - f - )%7') 7-= (3 %' -%)3*'4 ';'*<')377 ';'*<')377 -< ),' M--4 M--4 C,3). M-'-+' - )%7') 7-= ),' '73)*-,* %')='' , 34 34 )3' ),' -<
hf + .) /n
$%
where . i! a lo!! oeient and n ran'e! from 1) to 2)0 $de(endin' on the &alue of #e and !3D%)Thi! e4uation an be written a! o' hf + o' . 6 n o' /
$7%
in order to 8nd . and n e9(erimentall", u!in' 'ra(h :9(erimentall", one an obtain the head lo!! b" a((l"in' ener'" e4uation between an" two (oint! alon' a on!tant diameter (i(e) Thi! i! done in :4) 1 and b" notiin' that the (i(e i! hori;ontal and the diameter i! on!tant) The (re!!ur (re!!ure e head! of of a uid between between 2 (oint! (oint! , h1 and h2, are mea!ured b" u!in u! in' ' Pie;o ie;om meter eter tube tube! !) The total otal head ead lo! lo!! an an be dete deterrmined ined e9(erimentall" e9(erimentall" b" a((l"in' the , P1 P2 /ρ> ,1 ,2
9
E'> 7-' 3' --)*-37 )- ),' +'7-(*) ,'34 - ),' 7*4 3 *) 7-= 3-4 3 '7%-= ),->, 3 '73>'<') - (-)3()*- - ),' 7-= '()*- - ),->, 3 +37+'. E;'*<')37 +37' - ''> 7-' 3' 377 '-)'4 * )'< - 3 '*)3(' - 7- (-'*(*') K (-'*(*') K 3 -77-=:
!
hL
=
KV 2
2g
10
=,'' ,L * ),' <*- <*- 7- 7- K * ),' '*)3( '*)3('' - 7- (-'*( (-'*(*' *') ) 34 * ),' 3+'3>' 3+'3>' +'7-(*) - 7-= * ),' *' * ),' +*(**) =,'' ),' <*- 7- -((. T,' '*)3(' '*)3(' - 7- (-'*(*') * 4*<'*-7' %'(3' *) ''') 3 (-)3) - --)*-37*) %')='' ),' ''> 7- 34 ),' +'7-(*) ,'34. T,' <3>*)4' - ),' '*)3(' (-'*(*') 4''4 - ),' >'-<') - ),' 4'+*(' ),3) (3' ),' 7- 34 -<')*<' - ),' +'7-(*) - 7-=. Minor o!!"! #$ !%&&"n "n#r'"("n$ "n#r'"("n $
#,' 3 7*4 7-= -< 3 <377' *' *)- 3 73>' *' ),->, 3 44' '73>'<') *) +'7-(*) 3%)7 4'('3' (3*> )%7'(' =,*(, >''3)' 3 ''> 7-.
=,'' 1 +'7-(*) 3) <377 (-'()*- )'3< 2 +'7-(*) 3) 73>' (-'()*- 4-=)'3< T,' <*- 7- ,L 4' )- 44' '73>'<') - ),' *' (3 %' ')*<3)'4 % *)'>3)*> ),' <-<')< (-)**) 34 B'-77* '3)*- %')='' -*)*- 1 34 2 )- >*+' h L
=
(V − V ) 1
2
2
2 g
11
S%)*))*> 3>3* - ),' (-)**) '3)*- )- >') 3 ';'*- *+-7+*> ),' )=- 3'3 *.'. 21A1/A2 >*+' h L
=
KV 1
2
2 g
#,'' K = 1 −
A1 A2
2
D = 1 − D
1 2
2
12
2
5
Minor o!!"! #$ !%&&"n )on$r#)$ion
#,' 3 7*4 7-= 7-= -< 3 73>' *' *)- 3 <377' <377' *' ),->, 3 44' (-)3()*(-)3()*- ),' 7*4 7*4 )'3< )'3<7* 7*' ' =*77 =*77 (-+' (-+'> >'' &) &) 4-=) 4-=)' '3< 3< - ),' ),' <377 <377' ' *' *' -= -= 3 +'3 +'3 (-)3()*- (-)3()*- ,'-<'3 ,'-<'3 ('3)*> 3 )%7'(' )%7'(' '>*- -< ),' ,3 (-' (-' - ),' <377' <377' *' 34 ';)'4 3) ),' ), ' +'3 (-)3()3 =,*(, %'')7 %'')7 >''3)' 3 ''> 7-.
I 3 44' (-)3()*- 7-= (-)3() -< -*) 1 )- -*) 1? -<*> 3 +'3 (-)3()*-. I) * -*%7' )- 3<' ),3) ''> 7-' -< 1 )- 1? 3' '>7*>*%7' - '33)*- -(( * (-)3()*> 7-= %) ),3) <3&- 7-' -(( %')='' 1? 34 2 3 ),' 7-= ';34 3>3*
I ),' +'3 (-)3()3 3'3 * A1A( ),' ),' <*- 7- ,L (3 %' ')*<3)'4 ')*<3)'4 % *)'>3)*> *)'>3)*> ),' <-<')< (-)**) 34 B'-77* '3)*- %')='' -*)*- 1 34 2 )- >*+' h L
A = 1 − C A 2
2
V 22
1"
2 g
T,' 3%-+' 3%-+' '3)*- '3)*- * (-<<-7 (-<<-7 ';''4 3 3 ()*- - 7- (-'*(*') (-'*(*') K K 34 ),' ),' 3+'3>' +'7-(*) 2 * ),' <377' *' 4-=)'3< -< ),' (-)3()*- 3 -77-= h L
=
KV 2
2
2 g
AC K = 1 − A 2
2
1!
6
Minor Lo!!"! #$ "*o+ or *"n& ,i,"
L-' * *))*> (, 3 '7%-= +37+' ')( ,3+' %'' -4 )- %' --)*-37 )- ),' +'7-(*) ,'34 - ),' 7*4 7-=*>. T,' ''> 7- * ';''4 * ),' >''37 -<
hL
=
KV 2
2g
15
=,'' K 7- (-'*(*') 4''4') 4''4') - ),' 3)*- - )-)37 3>7' - %'4*> )- 34* - %'4*> R/4 - ),' (+' 3 ),' %'4*> -((
E-,"ri("n$# &"$"r(in#$ion &"$"r(in#$ion o $o$# /"#& o!!
In the e9(eriment the (re!!ure head! before and after a uid under'oin' !udden han'e in (i(e diameter or ow diretion, h1 and h2, are mea!ured b" u!in' Pie;ometer tube!) The total head lo!! $ma?or and minor lo!!e!% an be determined e9(erimentall" b" a((l"in' the P1/ρ> @ 7 2 / 2 > @ Z1 P2/ρ> @ 2 2 / 2 > @ Z2 @ ,L
16
,7 @ 7 2 / 2 > @ Z1 ,2 @ 2 2 / 2 > @ Z2 @ ,L
1$
34 *(' Z1 Z2
),'
h L
=h −h + 1
2
V 12
− V
2
2
2 g
18
ANTICIPATED ANTICIPATED RESULT
$
F- ),* ';'*<') ),' '4*()'4 '7) * ),' '7) ),3) =' (37(73)'4 *> ),' -+*4'4 -<73 =,*(, * 37- ''*> )- ),' ),'-')*(37 '7). S- ),' ),'-')*(37 '7) - HEAD LOSS DUE TO PIPE F- P*' D*3<')' 1*(,: 0.025!< *low #ate, @ $l3min%
Theoretial Head o!!
10 15 20 25 0
0 )0 0 0 )0 1 7 0 )0 0 )0 B 5 0 )0 - 2
F- P*' D*3<')' "/!*(,: 0.0191 < *low #ate, @ $l3min%
Theoretial Head o!!
10 15 20 25 0
0 )0 5 0 )0 1 0 )1 1 0 )1 0 )2
F- P*' D*3<')' 1/2*(,: 0.012$ < *low #ate, @ $l3min% 10 15 20 25 0
Theoretial Head o!! 0 )2 B 0 )B 0 )7 1 1 )2 0 1 )- 5
HEAD LOSS DUE TO ALES P*' 4*3<')': J * 0.0191<
8
G3)' +37+' *low #ate, @ $l3min% 10 15 20 25 0
Theoretial Head o!! 0 )0 5 0 )0 1 0 )1 1 0 )1 0 )2
B377 +37+' *low #ate, @ $l3min% 10 15 20 25 0
Theoretial Head o!! 0 )0 5 0 )0 1 0 )1 1 0 )1 0 )2
HEAD LOSS FOR ELBO# P*' 4*3<')': J * 0.0191<
*low #ate, @ $l3min% 10 15 20 25 0
Theoretial Head o!! 0 )0 5 0 )0 1 0 )1 1 0 )1 0 )2
9
HEAD LOSS DUE TO SUDDEN ENLARGEMENT
*low #ate, @ $l3min% 10 15 20 25 0
Theoretial Head o!! C0)002 C0)00 C0)00B C0)005 C0)00
HEAD LOSS DUE TO SUDDEN CONTRACTION
*low #ate, @ $l3min% 10 15 20 25 0
Theoretial Head o!! 0)000122 0)0002 0)000B70)0005 0)0010B
10
APPARATUS
HF1"5 P**> L- T') T') S') S)-=3)(, H437*( B'(,
D'(*)*- - A33) T'' PC P*' J S)3*>,) 7-= T'' PC P*' J L*' 90 %'4 PC P*' N- 1: D*3<')' 1* 0.025!< PC P*' N- 2: D*3<')' J * 0.0191< PC P*' N- 1: D*3<')' * 0.012$<
T,' ';'*<') ';'*<') =*77 %' '-<'4 '-<'4 *> 3 *' 7-= ') 3 ,-= * *>' 3%-+'. T,* * 3 '7 (-)3*'4 =3)' (*(73)*> *) - 3 )4 - *()*- 7-' * *' *' *))*> *))*> 34 +37+' 34 )- 4')'<*' 4')'<*' ),' (-'*(*') (-'*(*') - 4*(,3>' - *<3 7-= <'3*> 4'+*(' 3) +3*- 7-= 3)'. T,' *) (-*) - 3 < 3 )-3>' )3 34 3 3'7 - =,*(, 377 *()**()*- 7- (-<-') (-<-') 34 ),' 7-= <'3*> <'3*> 4'+*(' 4'+*(' 3' 33>'4. 33>'4. F*()* F*()*- - 7- * <'3'4 <'3'4 % 3 '' 4- 34 (-'*(*') - 4*(,3>' * 4')'<*'4 4')'<*'4 -< 3 '' 4- 34 3 7-= 3)'. F7-= 3)' * <'3'4 *> 3 (-)3) 7-= 3)' 7-= <')' 34 ),' '' 4- * <'3'4 *> 3 <3-<')'. P'' )3 3' (-'()'4 % 7';*%7' ,-' )- 3 ') - '(*377 33>'4 <3*-74 (, ),3) 4*'')*37 '' 3(- 3 (-<-') (3 %' <'3'4 *<7 % -'*> +37+' =*),-) '<-+*> ),' ,-'.
11
T,' '*<') (-*) - ),' -77-=*>: F*()*- C-<-') T,' (-<-') 3' 33>'4 - 3 3'7 34 *(74': Lin"#r ,i,"! L'>), - P*' : 1250 << T'' PC P*' J S3*>,) F7-= T'' T'' PC P*' J L*' 90 - B'4 PC : "/! * 1/2 * 34 1 *. E*o+! #n& *"n&! R'>73 '7%-= !5 '7%-= S,-) 34* %'4 L-> 34* %'4 V#0"! G3)' +37+' G7-%' +37+' B377 +37+' C,'( +37+' O$/"r i$$in'! S44' ';3*- 34 (-)3()*- T'' T'' '()*- M"#!%rin' D"0i)"! F7-= 3)' <')' I)377'4 - ),' 3<' 3'7 3 1.1 #3)' <3-<')' =*), 3 ,34 3* <: 2 )%' 950 << 1 << >343)*- M'( <3-<')': 2 )%' 950 << 1 << >343)*-
12
PROCEDURE To T"!$ $/" H"#& Lo!! &%" $o Pi," Fri)$ion 1. 2. ". !. 5. 6.
T,' 7-= 7-= (-)-7 +37+' * 77 -''4 34 *-73)*> +37+' * *7'). T,' >3)' +37+' 34 >7-%' >7-%' +37+' 3' (7-'4. T,' <3* =*)(, - ,437*( ,437*( %'(, 34 4*>*)37 '' '' *4*(3)- * -. -. T,' -)7') (-)-7 +37+' * -''4. -''4. T,' *-73)*> *-73)*> +37+' * -' - ),' )') *' N-. 1. T,' )=- <3-<')' )%' -< 4*>*)37 '' '' *4*(3)- * *')'4 *)- ),' )3*> +37+' - *' N-. 1. $. T,' < - ,437*( %'(, * =*)(,'4 -. 8. T,' =3)' =3)' 7-= * 7') ),->, ),' )'< - 3 =,*7'. =,*7'. 9. T,' '34*> '34*> - ),' 4*'')*37 4*'')*37 '' *4*(3)- * '(-4'4. 10. T,' 43* * (7-'4 34 3 )-=3)(, * '4 )- <'3' ),' )*<' )3' - ! 7*)' - =3)' )7-= *)- ),' <'3*> )3 11. T,' 43* * -''4 -(' *) * 4-' 34 ),' =3)' * 7') )- 7-= *)- ),' < )3. 12. T,' 7-= 3)' - =3)' * (,3>'4 % 34&)*> -)7') (-)-7 +37+' ) - >') 4*'') 4*'')*37 '' '34*>. 1". A>3* A>3* ),' 4*'')*37 '' '34*> * )3' 34 ),' )*<' )3' )- (-77'() ),' =3)' * '(-4'4. 1!. F*+' '34*> - +3*- 7-= 3)' * '4. 15. S=*)(, - ),' < 34 ,) ),' *-73)*> +37+' - )') *' N-. 1. 16. T,' 3%-+' -('4' 3' ''3)'4 - )') *' N-. 2 ''3) -('4' ! )- 1!. 1$. T,' < * =*)(,'4 - 34 ),' *-73)*> +37+' * ,) 4-= - )') *' N-. 2. 18. S)' <%' 1$ * ''3)'4 - )') *' N-. ".
PROCEDURE To T"!$ $/" H"#& Lo!! #$ $/" 0#0"! G#$" #n& B# 0#0"!
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
N- 1 )- " * * ''3) ''3)'4 '4 3) ),' B377 B377 3 37+' *' *' 5 '()* '()*-. -.
1"
PROCEDURE To T"!$ $/" H"#& Lo!! #$ $/" "*o+
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o T"!$ $/" S%&&"n En#r'"("n$
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
1!
PROCEDURE To T"!$ $/" S%&&"n Con$r#)$ion
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
15
Calculations ( Take Table 1 for example of calculation) T/" Fo+ R#$"3 R#$"3 4 i! )#)%#$"& )#)%#$"& *5 $/" oo+in' or(%#6 4 7
5.0 ; T/" Ar"#3 A i! )#)%#$"& *5 $/" oo+in' or(%#6 Ar"# o ,i,"
1.26$ ;
T/" V"o)i$53 V i! o*$#in"& *56
V"o)i$53 0
7
0.986
T/" R"5no& N%(*"r3 R " i! )#)%#$"& *5 $/" oo+in' or(%#6
R =
7
ₑ
2!51".8$ T/" Fri)$ion #)$or3 f #)$or3 f $/"o $/"o i! )#)%#$"& *5 $/" oo+in' or(%#6 f
+ 0)1#e0)25 + 0)1$2B51)7%0)25
+ 0)025 T/" Fri)$ion #)$or 3 f "-,"ri("n$# i! )#)%#$"& *5 $/" oo+in' or(%#6
f =
2 Dgh f 8';
LV 2
20.012$9.810.0!1
1.250.9862
0.01680
16
T/" T/"or"$i)# T/"or"$i)# H"#& Lo!! i! )#)%#$"& *5 $/" oo+in' or(%#6 7 f
T/"or"$i)# T/"or"$i)# /"#& o!!3
0.025"
0.062 T/" P"r)"n$ Error i! )#)%#$"& *5 $/" oo+in' or(%#6
P"r)"n$#'" "rror3 8
; 100
7
7
; 100
"".!8
*(The other calculations are done using the same steps.)
1$
DISCUSSION
18
