FACULT FACULTY Y OF CHEMICAL CHEM ICAL ENGINEERING ENGINEE RING CHE MICAL UNIVERSITI TEKNOLOGI MALAYSIA
FLUID MECHANICS LABORATORY
TITLE OF EXPERIMENT FRICTION LOSSES IN PIPE (E1) Name Matri N!" Gr!#$ % Se&ti!' S#$eri!r Date !* E$erime't Date !* S#+mii!' Mar, !+tai'e- (.)
1
1"/
O+0e&tie
The objectives of this experiment are i. ii. iii. iii. iv. iv.
"/
To measur measuree head head loss loss in pipes pipes for for differ different ent water water flow flow rates, rates, pipe pipe diame diameter terss and and pipe roughness. To estima estimate te the values values of loss loss coeffi coefficie cient nt for pipes pipes of differ different ent flow flow condit condition ions, s, diameters and roughness. To study study the the effect effect of of the veloci velocity ty of the flui fluid, d, the the size size (insi (inside de diame diameter ter)) of the the pipe, the roughness of the inside of the pipe on the values of loss coefficient. To study study the effect effect of sudden sudden change change in pipe pipe diam diamete eterr and flow flow direct direction ion on the total energy or head losses in pipes
I'tr!-#&ti!'
s an incompressible incompressible fluid fluid flows through through a pipe, a friction friction force along along the pipe wall is created against the fluid. The frictional resistance generates a continuous loss of energy or total total head in the fluid and hence decreases decreases the pressure pressure of the the fluid fluid as it moves through the pipe. There are four factors that determine determine friction losses in pipe i. ii. ii. iii. iii. iv.
The The vel velocit ocity y of the flui fluid. d. The The siz sizee (in (insi side de dia diame mete ter) r) of of the the pipe pipe The The rou rough ghne ness ss of the the ins insid idee of the the pip pipee The length of the pipe
!n addition to energy or head loss due to friction, there are always head losses in pipes due to an enlargement or contraction of the flow section, bends, junctions, valves etc., which are commonly "nown as minor or small losses. #hen the direction of flow is altered or distorted, energy losses occur which are not recovered are dissipated in eddies and additional turbulence and finally lost in the form of heat. $owever, this energy must be supplied if the fluid is to be maintained in motion, in the same way, as energy must be provided to overcome friction. !n practice, in long pipe lines of several "ilometres the %
effect of minor losses may be negligible. &or short pipeline the losses may be greater than those for friction.
'
2"/
T3e!r4
!n ernoullis e*uation as shown below, hf represents the head loss due to friction between the fluid and the internal surface of the constant diameter pipe as well as the friction between the adjacent fluid layers p1+ρg -1%+%g 1 / p% + ρg -%%+%g % hf
(1)
This will result in a continuous change of energy from a valuable mechanical form (such as "inetic or potential energies) to a less valuable thermal form that is heat. This change of energy is usually referred to as friction head loss, which represents the amount of energy converted into heat per unit weight of fluid.
The head losses (hf ) in pipe due to friction can be determined using 0arcy#eisbac" e*uation2 Turbulent flowhf / 3 f4-%
(%) % g0
hf / '% f45%
4aminar flow
%
(')
6
π g0 #here7 f 4 g 0
/ / / / /
&riction factor 4ength 8ean velocity (5+) 9ravity :onstant diameter
The friction head loss for both laminar and turbulent flows can be expressed by similar formulas although the original derivation of each one is different7 h f
= f
L V
%
D % g
(3)
In laminar fow, the riction actor is only a unction o Reynolds number while or turbulent fow it is a unction o Reynolds (R e) number and the relative roughness o the pipe. ; e
=
ρ -0 µ
(6)
where ρ7 density, -7 average velocity, 07 pipe inside diameter, µ7 viscosity.
3
ased on the nature of the flow, friction factor (f ) can be estimated using the following correlations 4aminar flow
f
/ <3
(<)
; e Turbulent &low
f / =.'1< x ; e =.%6
(>)
?*uation (>) is lausius ?*uation and only valid for smooth pipe and '=== @ ;e@ 1=6. The value of for turbulent flow can be obtained experimentally from the 8oody :hart. 8oreover, for turbulent flow, the relationship between hf and - ta"es the form
(!)
h = K. n
where K is a loss coe"cient and n ranges rom #.$ to %.& (depending on the value o Re and 's).*his e+uation can be written as og h = og K - n og
()
in order to /nd K and n e0perimentally, using graph 10perimentally, one can obtain the head loss by applying energy e+uation between any two points along a constant diameter pipe. *his is done in 1+. # and by noticing that the pipe is hori2ontal and the diameter is constant. *he pressure heads o a fuid between % points , h# and h%, are measured by using 3ie2ometer tubes. *he total head loss can be determined e0perimentally by applying the 4ernoulli5s e+uation as ollows6 hf / (A1 A%) +ρg / h1 h%
(1=)
?nergy losses are proportional to the velocity head of the fluid as it flows around an elbow, through an enlargement or contraction of the flow section, or through a valve. ?xperimental values for energy losses are usually reported in terms of a resistance or loss coefficient K as follows7 hL
=
KV 2 2g
(11)
where h4 is the minor loss, K is the resistance or loss coefficient, and - is the average velocity of flow in the pipe in the vicinity where the minor loss occurs. The resistance or loss coefficient is dimensionless because it represents a constant of proportionality 6
between the energy loss and the velocity head. The magnitude of the resistance coefficient depends on the geometry of the device that causes the loss and sometimes on the velocity of flow. Mi'!r 5!e at #--e' e'5ar6eme't
#hen a fluid flows from a smaller pipe into a larger pipe through a sudden enlargement, its velocity abruptly decreases, causing turbulence, which generates an energy loss.
where, -1 / velocity at small crosssection (upstream) -% / velocity at large crosssection (downstream) The minor loss (h4) due to sudden enlargement of the pipe can be estimated by integrating the momentum, continuity and ernoulli e*uations between positions 1 and % to give h L
=
(V 1 − V % ) %
% g
(1%)
Bubstituting again for the continuity e*uation to get an expression involving the two areas, (i.e. -%/-1(1+%) gives h L
=
KV 1
%
% g
#here , K = 1 −
%
A% A1
(1')
%
D1 % = 1 − D%
Mi'!r 5!e at #--e' &!'tra&ti!'
#hen a fluid flows from a larger pipe into a smaller pipe through a sudden contraction, the fluid streamlines will converge just downstream of the smaller pipe, "nown as vena contraction phenomena, creating a turbulence region from the sharp corner of the smaller pipe and extends past the vena contracta, which subse*uently generates an energy loss.
<
!n a sudden contraction, flow contracts from point 1 to point 1, forming a vena contraction. !t is possible to assume that energy losses from 1 to 1 are negligible (no separation occurs in contracting flow) but that major losses occur between 1 and % as the flow expands again
!f the vena contracta area is 1C/c, then the minor loss (h 4) can be estimated by integrating the momentum , continuity and ernoulli e*uations between positions 1 and % to give
h L
A = 1 − C A %
%
%
V %
% g
(13)
>
The above e*uation is commonly expressed as a function of loss coefficient (D) and the average velocity (-%) in the smaller pipe downstream from the contraction as follows2 h L
#here
=
KV %
%
% g
AC K = 1 − A %
(16)
%
s the difference in pipe diameters gets large ( 1+% =) then this value of D will tend towards =.6 which is e*ual to the value for entry loss from a reservoir into a pipe. The value of D depends upon the ratio of the pipe diameters ( D%+ D1) as given below2
0%+01 D
= =.6
=.1 =.36
=.% =.31%
=.' =.'F
=.3 =.'<
=.6 =.''
=.< =.%E
=.> =.16
=.E =.16
=.F =.=<
1.= =
Mi'!r L!e at e5+!7 !r +e'- $i$e
4osses in fittings such as elbow, valves etc have been found to be proportional to the velocity head of the fluid flowing. The energy loss is expressed in the general form, hL
=
KV 2 2g
(1<)
where, D / loss coefficient (dependent on the ratio of total angle of bending to radius of bending (;+d) of the curves as the bending occurs)
E
E$erime'ta5 -etermi'ati!' !* t!ta5 3ea- 5!
In the e0periment the pressure heads beore and ater a fuid undergoing sudden change in pipe diameter or fow direction, h # and h%, are measured by using 3ie2ometer tubes. *he total head loss (ma7or and minor losses) can be determined e0perimentally by applying the 4ernoulli5s e+uation as ollows6 A1+ρg -l % + % g 1 / A%+ρg -% % + % g % h4
(1>)
hl -l % + % g 1 / h% -% % + % g % h4
(1E)
%
and since 1 / % ,
then
h L
= h1 − h% +
V 1
− V %% % g
(1F)
F
8"/
A$$arat#
1=
4inear Aipe 1 %
Bection (rough)
0iameter (mm) %6.=
4ength (mm) 1='=
(smooth) (rough)
%'.6 13.=
1='= 1='=
(smooth)
1'.'
1='=
Gote 17 5 (m'+s) / 5 (1+min) x 1.<<> x 1= 6 Gote % 7 ;eynold Gumber for linear pipe assumed at room temperature Aipe 17 ; e / %F.% x 1=' x -
Aipe %7 ; e / 1<.3 x 1=' x -
Aipe 17 ; e / %>.6 x 1=' x -
Aipe %7 ; e / 16.6 x 1=' x -
Ta+5e !* 9ater D4'ami& Vi&!it4 a'- De'it4 at Di**ere't Tem$erat#re
Tem$erat#re ( !C)
;"/
(,6%m2)
( 1/:2 N"%m2)
=
FFF.E
1.>E1
6
1===.=
1.61E
1=
FFF.>
1.'=>
16
FFF.1
1.1'F
%=
FFE.%
1.==%
%6
FF>.=
=.EF=
'=
FF6.>
=.>FE
3=
FF%.%
=.<6'
6=
FEE.=
=.63>
<=
FE'.%
=.3<<
>=
F>>.E
=.3=3
E=
F>1.E
=.'63
F=
F<6.'
=.'16
1==
F6'.3
=.%E%
E$erime'ta5 Pr!&e-#re
11
Hpen all outlet valves of pipes 1, % and 3 (valves are in parallel with the pipes). 8a"e certain that the control valve in closed position (turn cloc"wise). Bwitch on the pump and slowly open the control valve (turn countercloc"wise) until maximum, and wait for a while in order to remove any air bubble in the flowing pipe. Im$!rta't N!te< To identify which inlet flowing pressure ($1) and outlet flowing pressure ($%) during installation of water manometer rubber tube, determine the direction of water inflow and outflow through the pipe. A)
B)
E$erime't 7it3 Pi$e A< R!#63 S#r*a&e
1.
:onnect rubber tube of water manometer at inlet flowing pressure ($1) and outlet flowing pressure ($ %) for rough surface of Aipe %.
%.
;educe the flow rate (5) by slowly closing the control valve (turn cloc"wise) until flow rate of %< liter+minute is achieved. Then, rise both water manometer rubber tubes at inlet flowing pressure ($1) and outlet flowing pressure ($%) while at the same time close the outlet valves of pipes 1 and 3 (turn cloc"wise) but let only the outlet valve of pipe % open . t this moment the flowing system is for pipe % of rough surface. 0uring the process, if air bubbles present in the flowing pipe, the air will move through the water manometer rubber tube. ir bubbles will move to the pea" of the higher tube. ;emove the air bubbles up to the manometer glass tube.
'.
;eadjust the flow rate to %< liter+minute, and determine 6 (five) flow rates 5 from value of %< liter+minute to the lowest value 1% liter+min (let the increment as large as possible). ;ecord the values of $1 and $% in millimeter (mm) of the inlet and the outlet of water manometer flowing pressures as 5 is changed.
E$erime't 7it3 Pi$e B< Sm!!t3 S#r*a&e
1.
8ove manometer rubber tube from the outlet flowing pressure ($%) of the rough surface of pipe % to inlet flowing pressure ($ 1) of smooth surface of pipe %. The system is now flowing through pipe % (smooth surface).
%.
;ise both water manometer rubber tubes at inlet flowing pressure ($1) and outlet flowing pressure ($ %) while at the same time slowly open the control valve (turn countercloc"wise) until flow rate 5 reaches %< liter+minute. 0uring the process, if air bubbles present in the flowing pipe, the air will move through the higher end of water manometer rubber tube. ;emove the air bubbles up to the manometer glass tube.
1%
'.
C)
D)
0etermine 6 (five) flow rates (5), similar to Aipe % (rough surface). ;ecord the values of $1 and $% in millimeter (mm) of the inlet and the outlet of water manometer flowing pressures as 5 is changed.
E$erime't 7it3 Pi$e 1A< R!#63 S#r*a&e
1.
8ove both manometer rubber tubes of inlet ($1) and outlet ($%) flowing pressures of pipe % (smooth surface) to the section of pipe 1 (rough surface).
%.
Hpen the outlet valve of pipe 1 (turn countercloc"wise), and close the outlet valve of pipe % (turn cloc"wise). The system is now flowing through pipe 1 (rough surface).
'.
;ise both water manometer rubber tubes at inlet flowing pressure ($1) and outlet flowing pressure ($ %) while at the same time slowly open the control valve (turn countercloc"wise) until flow rate 5 reaches maximum value 3% liter+min. 0uring the process, if air bubbles present in the flowing pipe, the air will move through the higher end of water manometer rubber tube. ;emove the air bubbles up to the manometer glass tube.
3.
;eadjust the flow rate to appropriate maximum value 3% liter+min, and determine 6 (five) different flow rates 5 from manimum value to the lowest value 1% liter+min (let the increment as large as possible). ;ecord the values of $1 and $% in (mm) of the inlet and the outlet of water manometer flowing pressures as 5 is changed.
E$erime't 7it3 Pi$e 1B< Sm!!t3 S#r*a&e
1.
8ove the manometer rubber tubes from outlet ($%) flowing pressures of pipe 1 (rough surface) to inlet ($1) flowing pressure of pipe 1 (smooth surface). The system is now flowing through pipe 1 (smooth surface).
%.
;ise both water manometer rubber tubes at inlet flowing pressure ($1) and outlet flowing pressure ($ %) while at the same time slowly open the control valve (turn countercloc"wise) until flow rate 5 reaches maximum value 3% litter+min. 0uring the process, if air bubbles present in the flowing pipe, the air will move through the higher end of water manometer rubber tube. ;emove the air bubbles up to the manometer glass tube.
'.
0etermine 6 (five) different flow rates 5 similar to pipe 1 (rough surface). ;ecord the values of $1 and $% in (mm) of the inlet and the outlet of water manometer flowing pressures as 5 is changed.
1'
E)
F)
E$erime't 7it3 Pi$e 8< S#--e' E'5ar6eme't
1.
8ove both manometer rubber tubes of inlet ($1) and outlet ($%) flowing pressures of pipe 1 (smooth surface) to the section of pipe 3 (Budden ?nlargement).
%.
Hpen the outlet valve of pipe 3 (turn countercloc"wise), and close the outlet valve of pipe 1 (turn cloc"wise). The system is now flowing through pipe 3 (Budden ?nlargement).
'.
;ise both water manometer rubber tubes at inlet flowing pressure ($1) and outlet flowing pressure ($ %) while at the same time slowly open the control valve (turn countercloc"wise) until flow rate 5 reaches '= liter+minute value. 0uring the process, if air bubbles present in the flowing pipe, the air will move through the higher end of water manometer rubber tube. ;emove the air bubbles up to the manometer glass tube.
3.
;eadjust the flow rate to '= liter+min, and determine 6 (five) flow rates 5 from value of '= liter+minute to the lowest value 1% liter+min (let the increment as large as possible). ;ecord the values of $1 and $% in millimeter (mm) of the inlet and the outlet of water manometer flowing pressures as 5 is changed.
E$erime't 7it3 Pi$e 8< S#--e' C!'tra&ti!'
1.
8ove the manometer rubber tubes from the inlet flowing pressure ($1) of pipe 3 (sudden enlargement) to the outlet flowing pressure ($%) of pipe 3 (sudden contraction). The system is now flowing through pipe 3 (sudden contraction).
%.
;ise both water manometer rubber tubes at inlet flowing pressure ($1) and outlet flowing pressure ($%) while at the same time slowly open control valve (turn countercloc"wise) until flow rate 5 reaches value '= liter+minute. 0uring the process, if air bubbles present in the flowing pipe, the air will move through the higher end of water manometer rubber tube. ;emove the air bubbles up to the manometer glass tube.
'.
;eadjust the flow rate to appropriate value '= liter+minute, and determine 6 (five) different flow rates 5 from value '= liter+minute to the lowest value 1% liter+min. (let the increment as large as possible). ;ecord the values of $1 and $% in millimeter (mm) of the inlet and the outlet of water manometer flowing pressures as 5 is changed.
13
G)
H)
E$erime't 7it3 Pi$e 8< =/ ! Be'-
1.
8ove the manometer rubber tube from the inlet flowing pressure ($1) of pipe 3 (sudden contraction) to the outlet flowing pressure ($%) of pipe 3 (F=o bend). The system is now flowing through pipe 3 (F=o bend).
%.
;ise both water manometer rubber tubes at inlet flowing pressure ($1) and outlet flowing pressure ($ %) while at the same time slowly open the control valve (turn countercloc"wise) until flow rate 5 reaches value '= liter+minute. 0uring the process, if air bubbles present in the flowing pipe, the air will move through the higher end of water manometer rubber tube. ;emove the air bubbles up to the manometer glass tube.
'.
;eadjust the flow rate to appropriate maximum value '= liter+min, and determine 6 (five) different flow rates 5 from value '= liter+min to the lowest value 1% liter+min. (let the increment as large as possible). ;ecord the value of $1 and $% in millimeter (mm) of the inlet and the outlet of water manometer flowing pressure as 5 is changed.
E$erime't 7it3 Pi$e 8< E5+!7
1.
8ove the manometer rubber tube from the inlet flowing pressure ($1) of pipe 3 (F=o bend) to the outlet flowing pressure ($%) of pipe 3 (elbow). The system is now flowing through pipe 3 (elbow).
%.
;ise both water manometer rubber tubes at inlet flowing pressure ($1) and outlet flowing pressure ($ %) while at the same time slowly open the control valve (turn countercloc"wise) until flow rate 5 reaches value '= liter+minute. 0uring the process, if air bubbles present in the flowing pipe, the air will move through the higher end of water manometer rubber tube. ;emove the air bubbles up to the manometer glass tube.
'.
;eadjust the flow rate to appropriate maximum value '= liter+minute, and determine 6 (five) different flow rates 5 from value '= liter+minute to the lowest value (let the increment as large as possible). ;ecord the value of $1 and $% in millimeter (mm) of the inlet and the outlet of water manometer flowing pressure as 5 is changed.
16
>"/
Pi$e
A
B
E$erime'ta5 -ata a'- a'a54i
? (1%mi')
? 1/:8 (m2%)
31 (mm)
3 (mm)
A (m 1/:8)
V (m%)
R e ( 1/2)
f theo
h f.theo
(E@ > !r E@" !r M!!-4 -ia6ram)
(E@" 8)
h f.exp 331:3) (m)
f exp (E@" 1/)
f =
% Dgh f ,exp
%<
3.''
F%=
'6
3.F1
=.EE%
13.3<
=.1<%
=.3>'
=.EE6
=.'='
%%
'.<>
>>=
166
3.F1
=.>3>
1%.%6
=.1
=.'6%
=.<16
=.%F3
1E
'.==
<<=
%3=
3.F1
=.<11
1=.=%
=.1>>
=.%3E
=.3%=
=.'==
13
%.''
6<6
'%=
3.F1
=.3>6
>.>F=
=.1EF
=.1<=
=.%36
=.%F=
1%
%.==
6'=
'6=
3.F1
=.3=>
<.<>=
=.1F<
=.1%%
=.1E=
=.%EF
%<
3.''
F16
1E6
3.'3
=.FFE
16.3>
=.16F
=.<%6
=.>'=
=.1E<
%%
'.<>
>E=
%36
3.'3
=.E3<
1'.11
=.1<<
=.3
=.6'6
=.1EF
1E
'.==
<<=
'==
3.'3
=.
1=.>1
=.1>3
=.'%E
=.'<=
=.1F1
13
%.''
6>=
'6=
3.'3
=.6'>
E.'%=
=.1E6
=.%11
%.%%=
=.1F'
1%
%.==
6'6
'>=
3.'3
=.3<1
>.16=
=.1F'
=.1<%
=.1<6
=.1F>
LV %
1<
Pi$e
1A
1B
? 1/:8 (m2%)
? (1%mi')
31 (mm)
3 (mm)
A (m 1/:8)
V (m%)
R e (1/2)
f theo
h f.theo
(E@ > !r E@" !r M!!-4 -ia6ram)
(E@" 8)
h f.exp 331:3) (m)
f exp (E@" 1/)
f =
% Dgh f ,exp
%E
3.<>
'F=.%
'==
3.F1
=.F61
%E.''
=.1'>
=.%<=
=.=F
=.=3>
%3
3.==
'>'
'16
3.F1
=.E16
%3.%F
=.13%
=.1FE
=.=<
=.=3'
%=
'.''
'<=
''=
3.F1
=.<>E
%=.%=
=.13F
=.133
=.='
=.='1
1<
%.<>
'6'
'3=
3.F1
=.633
1<.%1
=.16>
=.=FE
=.=1'
=.=%1
1%
%.==
'3F
'36
3.F1
=.3=>
1%.1'
=.1
=.=6F
=.==3
=.=11
%E
3.<>
'E3
'=6
3.'3
1.=><
%F.6F
=.1'6
=.'3F
=.=>F
=.='1
%3
3.==
'>=
'16
3.'3
1.1
'%.1%
=.1'%
=.3=%
=.=66
=.=1E
%=
'.''
'<6
'1>
3.'3
1.3=%
'E.6<
=.1%<
=.66'
=.=3E
=.=11
1<
%.<>
'<'
'%=
3.'3
1.>3F
3E.1=
=.1%=
=.E%=
=.=3'
=.==<
1%
%.==
'<6
'%6
3.'3
%.''6
<3.%1
=.111
1.'6%
=.=3
=.=='
LV
%
Ta+5e *!r Data !* S#--e' E'5ar6eme't Pi$e
5 (1+min)
5x1=3 (m'+s)
h1 (mm)
h% (mm)
∆h (m)
1 (m%x1=3)
% (m%x1=3)
-1 (m+s)
-% (m+s)
h4,theo (m) ?*. %
h4,exp (m) ?*. F
D h4,exp +(-1%+%g)
1>
%E
3.<>
6'6<
6%6
=.=1
1.'F
3.%<
'.'<=
1.=F<
=.%<1
=.6%3
=.F11
%3
3.==
3F=
3E6
=.==6
1.'F
3.%<
%.E>E
=.F'F
=.1F%
=.'E%
=.F=6
%=
'.''
336
33=
=.==6
1.'F
3.%<
%.'F<
=.>%E
=.1''
=.%<<
=.F=F
1<
%.<>
3=6
3==
=.==6
1.'F
3.%<
1.F%1
=.<%>
=.=E6
=.1>'
=.F%=
1%
%.==
'<6
'<'
=.==%
1.'F
3.%<
1.3'F
=.3
=.=3E
=.=F<
=.F1=
D
Ta+5e *!r Data !* S#--e' C!'tra&ti!' Pi$e
5 (1+min)
5x1=3 (m'+s)
h1 (mm)
h% (mm)
∆h (m)
% (m%x1=3)
% (m%x1=3)
-1 (m+s)
-% (m+s)
h4,theo (m) ?*. 6
h4,exp (m) ?*. F
h4,exp +(-%%+%g)
%E
3.<>
E36
%E=
=.6<6
3.%<
1.'F
1.=F<
'.'<=
=.%EE
=.=61
=.=EF
%3
3.==
><6
'==
=.3<6
3.%<
1.'F
=.F'F
%.E>E
=.%11
=.=EE
=.%=E
%=
'.''
<'6
''6
=.'==
3.%<
1.'F
=.>E%
%.'F<
=.13<
=.='F
=.1''
1<
%.<>
6<=
'3=
=.%%=
3.%<
1.'F
=.<%>
1.F%1
=.=F3
=.=6%
=.%><
1%
%.==
3E6
'<=
=.1%6
3.%<
1.'F
=.3
1.3'F
=.=6'
=.='1
=.%F3
(m+s)
h4,theo (m) ?*. <
h4,exp (m) ?*. F
D
Ta+5e *!r Data !* =/ ! Be'- Pi$e
5 (1+min)
5x1=3 (m'+s)
h1 (mm)
h% (mm)
∆h (m)
% (m x1=3)
h4,exp +(-%+%g)
1E
%E
3.<>
E%6
%%=1
=.<=6
1.%>
'.<>>
=.%<%
1.%F3
1.E>E
%3
3.==
>'6
%6=
=.3E6
1.%>
'.16=
=.1F%
=.FF1
1.F<=
%=
'.''
<3=
%F6
=.'36
1.%>
%.<%%
=.1''
=.
1.FE'
1<
%.<>
66=
''=
=.%%=
1.%>
%.1=%
=.=E<
=.336
1.F><
1%
%.==
3>6
'66
=.1%=
1.%>
1.6>6
=.=3E
=.%3<
1.F3<
D h4,exp +(-%+%g) %.1'%
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1. Bee handout (4aboratory ;eport &ormat) %. dditional report re*uirement
i. ii.
3lot a graph o f theo and f exp versus Re on the same graph and comment on the results. 3lot a graph between e0perimental h and on a log8log paper to obtain the values o K and n in e+. () or turbulent fow in a pipe. 9se log8log paper and remember that n, the slope o the straight line, is given as n = (log hf 1 - log hf 2 ) / (log V 1 - log V 2 ). *he y8 intercept gives the value o log K. a. :alculate the value of n. Theoretically, the head loss due to friction is proportional to the velocity of the flow (i.e. hf / "-%+%). :omment on the obtained value of n. b. 0iscuss the effect of fluid velocity, pipe roughness and pipe diameter on the value of loss coefficient (D) and hence friction loss in pipe.
iii.
iv.
3lot (h)th and (h )e0p versus : on the same graph. ;ompare the di
v.
riefly discuss factors contributing to errors or inaccuracy in experimental data and propose recommendation to improve the results
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n = (log h # 8 log h % ) (log # 8 log % ) pipe %7 (log =.E3 J log =.'%)+ (log =.E3 J log =.3<) / 1.36 J log =.=1)+ (log =.F J log =.6) / =.1<1% pipe 17 (log =.=6 J log =.=3)+ (log =1.'6 J log %.1) / =.=%'3
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