Flow Measurement in Closed Conduit
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Transcript of Flow Measurement in Closed Conduit
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CHEMICAL ENGINEERING LAB
Flow Measurement in Closed Conduit
& Centrifugal Pump Characteristics
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Part I
Flow Measurement inClosed Conduit
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Summary
The objectives of this experiment were to get familiarized with various flow
measuring devices, such as venturi meter, orifice plate, rotameter, etc, for measurement
of discharge in closed conduits and to determine the loss coefficients for the various
fittings in the s!stem
The loss coefficient, " was found b! ma#ing use of the following expression
$
$V K
P g c=
∆
ρ
where %P is the pressure drop, is the densit! of fluid and v is the velocit! of the fluid
The pressure drop across a particular device was measured at different flow rates to
obtain the various loss coefficients of the various devices
'nce the various loss coefficients were obtained, the flow rate across each line
when all three lines were opened was calculated, and the sum of the flow rates was found
to be close to the actual flow rated used which showed that the loss coefficients obtained
were rather accurate as well
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CONTENTS
Part I Flow Measurement in Closed Conduit
Se!tions Pa"e
Title (
)ummar! $
* *ntroduction +
** Theoretical ac#ground -
*** .xperimental set up and procedures /
*0 1esults and 2nal!sis 3
0 4iscussion $+
0* Conclusion 55
0** 1eferences 55
2ppendices
Part II Centri#u"al Pum$
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I Introdu!tion
The objectives of the experiments were to6
( To get familiarized with various flow measuring devices, such as venturi meter,
orifice plate, rotameter, etc, for measurement of discharge in closed conduits
$ To determine the loss coefficients for the various fittings in the s!stem
5 To determine to individual flow rates in each line when all 5 lines were opened
Flow rate measurements are important not onl! in the laborator! but also in the
industrial plants, serving as a basis for proper monitoring and control 2s a result, we
must be able to account for the losses due to pipe material, pipe fittings as well as the
flow measuring devices in the s!stem ! measuring pressure, elevation and sometimes
velocit!, measurement of losses can be accomplished
The aim of this experiment is to get familiarized with the different flow measuring
devices, such as the venturi meter, orifice meter and rotameter, which are often used forthe measurement of discharge in closed conduits The choice of a flow meter is
influenced b! the accurac! re7uired, range, cost, ease of reading and service life The
simplest and cheapest device that gives the desired accurac! is then appropriatel! chosen
The various fittings8 loss coefficients are being investigated The flow in a piping
s!stem ma! be re7uired to pass through a variet! of fittings, bends or abrupt changes in
area 2dditional head loss arises as a result of flow separation For flow through pipe
bends and fittings, the loss coefficient, " is found to var! with pipe size 9diameter: in
much the same manner as the friction factor, f , for flow through a straight pipe Pressure
at different points of the closed conduits is measured and the results are then used for the
determination of the loss coefficient, " for the various fittings in the s!stem
For a good plant design, it is essential to #now the values of head losses as well as to
account for them in the design ;iven the wide range of flow meters available nowada!s,
it is also important for engineers to possess #nowledge of the relative advantages and
disadvantages, as well as limitations, of the different t!pes of flow measuring devices
available 'ften, the simplest and most economical device that will be able to cope with
the desired accurac! range will be preferred
The stud! of loss coefficients for the various fittings in a piping s!stem is an essential
re7uirement for understanding the flow behavior within the s!stem
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II T%eoreti!al Ba!&"round
o
bend, a (?>o bend, and a 3>o elbow
*t can be closed or opened b! the control of the isolation valve
=ine $ consists of6
4iaphragm valve, ball valve, globe valve and needle valve
*t can be closed b! the control of an! one valve or opened b! all the valves
=ine 5 consists of6
'rifice meter and venturi meterThe closure and open of this line is controlled b! the isolation valve
The combined flow passed through a rotameter and then flowed bac# to the
holding vessel
*n pipe lines, the total head loss is made up of both the frictional head loss and the
head loss due to fittings 9eg valves, elbows:
9h=:total @ 9h=:frictional A 9h=:fittings
where 9h=:frictional @ frictional head loss @ $f f =V $B4g
9h=:fittings @ head loss due to fittings @ ∆PBρ @ " V $B$ gc
*n this experiment, we are onl! concerned about the head loss due to fittings
9h=:fittings @ ∆PBρ @ " V $B$gc
The loss coefficient, " is defined as follows6
$
$V
K P g c=
∆
ρ
where
∆P @ Pressure drop
ρ @ 4ensit! of fluid
V @ 0elocit! of the fluid
" @ =oss coefficient
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For a particular device, if the pressure drop and the flow rate are #nown, the loss
coefficient can be found b! plotting 9gc ∆PBρ: against V 2B$: The slope is then the loss
coefficient, "
'nce the various loss coefficients are obtained for the various devices, the flow
rates in each individual line can be calculated b! finding out V , the velocit! of the fluid
using the same e7uation above The total flow rates of the 5 lines should be e7ual to the
actual flow rate used if the loss coefficients are accuratel! obtained
III E'$erimental Pro!edure
Flow Chart of .xperimental Procedures
6
'pen all 5 lines and ta#e pressurereadings for + different flow rates
Close the b!pass valve partiall!, andadjust the #nob of the rotameter to set
a desired flowrate
efore starting the pump, ensure that
the b!pass is opened
)witch on the power for the digital pressure gauge and the pump
1epeat the same procedure for line $9with lines ( and 5 closed: and line 59with lines ( and $ closed:
0ar! the flow rate to ma#e at least +different runs
'pen the gate valve for line (, andclose the valves for lines $ and 5
Ta#e the reading for all the pressuretap points in line (
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5( 4etailed Procedures
The different apparatus and the apparatus under investigation is listed below
Pi$in"s
( )mooth bore pipe
$ rough bore pipe
(al)es
5 diaphragm valve
+ ball valve
- globe valve
/ needle valve
isolation valve
Ot%er $i$e #ittin"s
? gradual expansion
3 sudden contraction
(> bend
(( elbows
Meters
($ orifice meter
(5 venturi meter (+ rotameter
Ot%ers
(- holding vessel
(/ pump
( digital pressure gauge
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The apparatus was set up as shown in the diagram below
Fi"ure * E'$erimental Set+u$
)witch on the power for the digital pressure gauge and the pump 'pen the gate valve for
( The b!pass was ensured to be opened and the pump started$ The gate valve for line ( was opened while the valves for line $ and 5 were
closed
5 The b!pass valve was closed partiall! and the #nob of the rotameter adjusted to a
flow rate of (> lBmin
+ The pressure readings at tap points (D(>, $( and $$ were ta#en down and
recorded
- The flow rate was varied covering the range of flow rates from (> lBmin to
/- lBmin to obtained + different runs
/ The same procedure for line $ 9with line ( and 5 closed: was repeated and
pressure readings at tap points ((D(-, $( and $$ were ta#en down and recorded
The same procedure for line 5 9with line ( and $ closed: was repeated and
pressure readings at tap points (/D$$ were ta#en down and recorded
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? 2ll three lines were opened and pressure readings at all tap points were ta#en
down and recorded
3 The flow rate was varied covering the range of flow rates from $> lBmin to
- lBmin to obtain + different runs
5$ Precautions Ta#en
• 2ll valves in the lines other that the one to be studied were ensured to be
closed
• The flow rate through lines $ and 5 were #ept below 5> lBmin to prevent
damage to the valves in the lines
I( Results and Analysis
Line ,e)i!e Internal ,iameter- I, .m/
*
1ough ore Pipe >>$>>
(?>o end >>$$(
)udden Contraction >>5(
;radual .xpansion >>5(
3>o .lbow >>$$(
3>o end >>$$(
)mooth ore Pipe >>$$(
0
4iaphragm 0alve >>(//
all 0alve >>(//
;lobe 0alve >>(//
Eeedle 0alve >>(//
1'rifice Meter >>($
0enturi Meter >>($
1otameter >>$$(Ta2le * ,iameters o# )arious de)i!es
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)et Eumber
( $ 5 +
Flowrate
9lBmin:
(> 5> -> /-
Point Pressure 9psi:( $$/>$ (?$5 ($-$ //??$ $$/++ (3>5 (+/5$ (>$35 $$/? (3(5$ (+?// (>$+ $$/-( (3$3/ (-$/5 ((53-- $$/(/ (3$$ (-($5 ((>5/ $$/( (35-? (-$?- ((555 $$/-3 (3+(/ (-$ ($>$5? $$/3 (3+- (-?( ($$$-3 $$$+ (3-/+ (/>?$ ($/--(> $$5 (3// (/5>( (5>$3
$( $$-$$ (?5 ((+5$ +?$$ $$$$5 ($- (>-35 5/?
Ta2le 0 Pressure readin"s #or line * o$en
)etnumber
( $ 5 +
Flow rate9lBmin:
(> $> $- 5>
Point Pressure 9psi:(( $$+- $>3 $>-> (33+/($ $(53- (??$$ (?5$( (-/--(5 $(55( (?--+ ($$$ (--?(+ $((/ ( ($>3 (5++$(- (355$ (5+(? 3/+3 (-($( $>55- (-$5/ (>+?/ 3$$$$ $>>(5 (->+/ (>>+- ?+$3
Ta2le 1 Pressure readin"s #or line 0 o$en
)et number ( $ 5 +
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Flow rate9lBmin:
(> $> $- 5>
Point Pressure 9psi:(/ $$5>? $(?35 $>$?? (3?( $$$ $>/-5 (??$ ((?-(? $$$3- $>$5 (?>$ (35//
(3 $$(>? $>53+ (?/>+ (3>?-$> $$$-- $>/>$ (?5 (3(+/$( $$$/ $$-35 (3?5 (3(5($$ $(3-3 $>$>$ (35? (?/>+
Ta2le 3 Pressure readin"s #or line 1 o$en
)et number ( $ 5 +Flow rate
9lBmin:$> +> /> -
Point Pressure 9psi:
( $>3++ (/?5 (5>/ 3-+($ $(>>3 (?3- (+$$- (>+?5 $(>$( (3// (+5$ (>-??+ $(>$5 (3?+ (++>/ (>3+- $(>>? (3$ (+5$ (>>/ $(>($ (33( (++$- (>? $(>$- (?>$- (+--5 (>33? $(>5 (?>5 (+-/- ((>++3 $(>+( (?>-/ (+/(3 ((($5(> $(>-? (?>?$ (+/3 (($($(( $(> (?(3( (+3/( (((+($ $(>$5 (?>+3 (+/>3 (((+$(5 $(>(/ (?>55 (+-+3 ((>/3(+ $>3? (3/ (++5 (>?+$(- $>3>- (->5 (5->$ 35$(/ $(>++ (?$$- (+3>/ (($(( $>?3- (55? (5/// ?+>5(? $>3 (-? ($?>$ 3-$$(3 $>?+( ((+( (5-(( ?(>3
$> $>3++ (-(5 ($-5( 3$?5$( $>?5> ((/- ($5( ?>>?$$ $>+-/ (/->$ ((($ ?+??
Ta2le 4 Pressure readin"s #or all 1 lines o$en
Cal!ulation o# loss !oe##i!ient
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The loss coefficient, ", is defined b! the following expression6
$
$V
K P g c=
∆
ρ
where P6 pressure drop
6 densit! of fluid
V 6 velocit! of the fluid
There are two methods to calculate the value of the loss coefficient "
First Met%od
=et G be the flow rate set in the lines
Hence, V @ GB2 where 2 is the area
>> I >$?>3:
@ $>/$
Se!ond Met%od
Plot a graph of P vs V $
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The gradient obtained from the graph @ " B $
>> #g m D5 , " can be found
.g6
1ough ore Pipe 9diameter @ >>$>>m: with G @ (> lBmin
From the best fit line, the e7uation is found be to ! @ $>3+$x K 3>$+/
Hence, ;radient @ $>3+$ @ " B $Therefore, " @ $>3+$ I $ B (>>>
@ +(?
For line *
Rou"% Bore Pi$e
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G 9lBmin: G 9m5Bs: P( 9psi: P$9psi: P 9psi: P 9Pa: 0 9mBs: " 9mtd (:
(>(/ x (>D+ $$/>$ $$/++ >>+$ $?3/ >-5 $>/$
5> -x (>D+ (?$5 (3>5 >? --(-? (-3 +5/+->
?55 x (>D+ ($-$ (+/5$ $(>- (+-(5+ $/- +(55/-
(>? x (>D5 //?? (>$3 5/>$ $+?5+? 5+- +(5A)era"e 5 16781
*899 Bend
G 9lBmin: G 9m5Bs: P$ 9psi: P59psi:
P9psi:
P 9Pa: 0 9mBs: " 9mtd(:
(> (/ x (>D+ $$/++ $$/? $$/++ $$/? >+5 $-5-
5> -x (>D+ (3>5 (3(5$ (3>5 (3(5$ (5 >+?(
-> ?55 x (>D+ (+/5$ (+?// (+/5$ (+?// $( >/?-
/- (>? x (>D5 (>$3 (>$ (>$3 (>$ $?$ >+/A)era"e 5 *6**0
Sudden Contra!tion
G 9lBmin: G 9m5Bs: P5 9psi: P+9psi:
P9psi:
P 9Pa: 0 9mBs: " 9mtd(:
(> (/ x (>D+ $$/? $$/-( D>>$ D(?/(/ >$( D?++5
5> -x (>D+ (3(5$ (3$3/ >(/+ ((5> >/5 -/3?
-> ?55 x (>D+ (+?// (-$/5 >53 $5$ (>/ +?$
/- (>? x (>D5 (>$ ((53- >/- +/-53 (5 +3-3A)era"e 5 46*:711
Gradual E'$ansion
G 9lBmin: G 9m5Bs: P+ 9psi: P-9psi:
P9psi:
P 9Pa: 0 9mBs: " 9mtd(:
(> (/ x (>D+ $$/-( $$/(/ D>>5- D$+(5$ >$( D(>3++
5> -x (>D+ (3$3/ (3$$ D>>/3 D+-+ >/5 D$53
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-> ?55 x (>D+ (-$/5 (-($5 D>(+ D3-$$/ (>/ D(/3-
/- (>? x (>D5 ((53- ((>5 D>5$$ D$$$>( (5 D$5//A)era"e 5 (/(-
;99 El2ow
G 9lBmin: G 9m5Bs: P/ 9psi: P9psi:
P9psi:
P 9Pa: 0 9mBs: " 9mtd(:
(> (/ x (>D+ $$/( $$/-3 >>+$ $?3/ >+5 5(55
5> -x (>D+ (35-? (3+(/ >>-? 5333 (5 >+5
-> ?55 x (>D+ (-$?- (-$ >+5- $333$ $( ($+
/- (>? x (>
D5
((555 ($>$5 >/3 +-+ $?$ ((3/A)era"e 5 *64*;
;99 Bend
G 9lBmin: G 9m5Bs: P 9psi: P?9psi:
P9psi:
P 9Pa: 0 9mBs: " 9mtd(:
(> (/ x (>D+ $$/-3 $$$3 >> +?$/ >+5 (+3$
5> -x (>D+ (3+(/ (3+- >>5+ $5++ (5 >$
-> ?55 x (>D+
(-$ (-?( >>3 /$>- $( >$/+
/- (>? x (>D5 ($>$5 ($$$- >$>$ (53$ $?$ >5-A)era"e 5 964;7
Smoot% Bore Pi$e
G 9lBmin: G 9m5Bs: P? 9psi: P(>9psi:
P9psi:
P 9Pa: 0 9mBs: " 9mtd(:
(> (/ x (>D+ $$$3 $$5- >>>/ +(5 >+5 5?>5
5> -x (>D+
(3+- (3// >$( (+3/$ (5 ((
-> ?55 x (>D+ (-?( (/5>( >+3( 55?-5 $( (+5?
/- (>? x (>D5 ($$$- (5>$3 >?>+ --+5+ $?$ (53+A)era"e 5 06*90
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Rotameter
G 9lBmin: G 9m5Bs: P$( 9psi: P$$9psi:
P9psi:
P 9Pa: 0 9mBs: " 9mtd(:
(> (/ x (>D+ $$-$$ $$$$5 >$33 $>/(- >+5 $$$33
5> -x (>D+ (?5 ($- >->? 5->$- (5 +(+-
-> ?55 x (>D+ ((+5$ (>-35 >?53 -?+ $( $+-
/- (>? x (>D5 +? 5/? ((?5 ?(-/+ $?$ $>-(A)era"e 5 :6:18
Ta2le 7 Ta2ulation o# results #or Line * ,e)i!es
Fi"ure 0 Plot o# Pressure ,ro$ (s FLow Rate #or line * de)i!es6 .Only t%e rou"% 2ore $i$e is $lotted
on t%e se!ondary a'is/
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Fi"ure 1 Plot o# Pressure ,ro$ (s (elo!ity
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G 9lBmin: G 9m5Bs: P(( 9psi: P($9psi: P 9psi: P 9Pa: 0 9mBs: " 9mtd (:
(> (/ x (>D+ $$+- $(53- (>/$ 5$$$> > $+>>
$> 555 x (>D+ $>3 (??$$ $(+? (+?>3?3 (-+ ($+?3
$- +( x (>D+ $>-> (?5$( $(?/ (->(?3 (3$ ?(
5> ->> x (>D+
(33+/ (-/-- +$3( $3-?-5 $5( ((>?3A)era"e 5 *36**3
Ball (al)e
G 9lBmin: G 9m5Bs: P($ 9psi: P(5 9psi: P 9psi: P 9Pa: 0 9mBs: " 9mtd(:
(> (/ x (>D+ $(53- $(55( >>/+ ++($/$3 > (+??
$> 555 x (>D+ (??$$ (?--+ >$/? (?+?3 (-+ (--?
$- +( x (>D+ (?5$( ($$$ (>33 -5($ (3$ +(((
5> ->> x (>D+ (-/-- (--? >>- -((>- $5( >(3+
A)era"e 5 *6818
Glo2e (al)e
G 9lBmin: G 9m5Bs: P(5 9psi: P(+ 9psi: P 9psi: P 9Pa: 0 9mBs: " 9mtd(:
(> (/ x (>D+ $(55( $((/ >(/+ ((5>5/ > 5?(+
$> 555 x (>D+ (?--+ ( > -5-$>? (-+ +-(?
$- +( x (>D+ ($$$ ($>3 >>(5 ?3/5(-5 (3$ >>+3
5> ->> x (>D+ (--? (5++$ $(5? (++>3+ $5( --$-
A)era"e 5 367*;
Needle (al)e
G 9lBmin: G 9m5Bs: P(+ 9psi: P(- 9psi: P 9psi: P 9Pa: 0 9mBs: " 9mtd(:
(> (/ x (>D+ $((/ (355$ (?5- ($/-(?+ > +$/?
$> 555 x (>D+ ( (5+(? +5-3 5>>-+(+ (-+ $-5+-
$- +( x (>D+ ($>3 3/+3 -/ -$($+(? (3$ $?$3
5> ->> x (>D+ (5++$ (-( ((/3( ?>/>/55 $5( 5>$($
A)era"e 5 1*6708
Rotameter
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G 9lBmin: G 9m5Bs: P$( 9psi: P$$ 9psi: P 9psi: P 9Pa: 0 9mBs: " 9mtd(:
(> (/ x (>D+ $>55- $>>(5 >5$$ $$$>(>+ > $+>(+
$> 555 x (>D+ (-$5/ (->+/ >(3 (5>3333 (-+ 5+/(
$- +( x (>D+
(>+?/ (>>+- >++( 5>+>- (3$ -((?5> ->> x (>D+ 3$$ ?+$3 D>-> D5+3-/5 $5( D+(5
A)era"e 5 86*38
Ta2le 8 Ta2ulation o# results #or Line 0 ,e)i!es
Fi"ure 3 Plot o# Pressure ,ro$ (s FLow Rate #or line 0 de)i!es6
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Fi"ure 4 Plot o# Pressure ,ro$ (s (elo!ity
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For Line 1
Ori#i!e Meter
G 9lBmin: G 9m5Bs: P(/ 9psi: P(9psi: P 9psi: P 9Pa: 0 9mBs: " 9mtd (:
(> (/ x (>D+ $$5>? $$$ >>5? $/(3333 (5( >5>-
$> 555 x (>D+
$(?35 $>/-5 ($+ ?-+3+/3 $/5 $+$
$- +( x (>D+ $>$?? (??$ (+(/ 3/$3+$ 5$3 (?>+
5> ->> x (>D+ (3? ((?- $-35 (??>+ 53- $$3$
A)era"e 5 *6:*8
(enturi Meter
G 9lBmin: G 9m5Bs: P(? 9psi: P$> 9psi: P 9psi: P 9Pa: 0 9mBs: " 9mtd(:
(> (/ x (>D+ $$$3- $$$-- >>+ $-?35 (5( >5$(
$> 555 x (>D+ $>$5 $>/>$ >($( ?5+$/$ $/5 >$+(
$- +( x (>D+ (?>$ (?5 >(3 (5>3333 5$3 >$+$
5> ->> x (>D+ (35// (3(+/ >$$ (-(/?+( 53- >(3+
A)era"e 5 96049
Rotameter
G 9lBmin: G 9m5Bs: P$( 9psi: P$$ 9psi: P 9psi: P 9Pa: 0 9mBs: " 9mtd(:
(> (/ x (>D+ $$$/ $(3-3 >5>( $>-5(- (5( $(+53
$> 555 x (>D+ $>-35 $>$>$ >53( $/3-?+( $/5 ($5
$- +( x (>D+ (3?5 (35? >+-$ 5((/+(3 5$3 -$+/
5> ->> x (>D+ (3(5( (?/>+ >-$ 5/55-$+ 53- +5>>
A)era"e 5 ;640:
Ta2le *9 Ta2ulation o# results #or Line 1 ,e)i!es
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Fi"ure 7 Plot o# Pressure ,ro$ (s FLow Rate #or line 1 de)i!es .Only t%e )enturi meter is $lotted on
t%e se!ondary a'is/
Fi"ure : Plot o# Pressure ,ro$ (s (elo!ity
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,e)i!e E=uation o# Lines in Fi" 7 Gradient 5 .mtd 0/
'rifice Meter ! @ ((3?x D (5?/3 ((3? $53/
0enturi Meter ! @ 3$>/-x A ($? 3$>/- >(?+
1otameter ! @ (>5/?x A (??3 (>5/? $>+
Ta2le ** Gradients o# t%e $lot #or line 0 de)i!es
Ta2le *0 (alues o# 5 #or )arious de)i!es
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,e)i!e 5 .mtd */ 5 .mtd 0/ 5 a)e
1ough ore Pipe 5/?5 +(?? 535/
(?>> bend ((($ >$3 >3$(
)udden Contraction -(/ -($( -(+3
;radual .xpansion (/(- $(> (?/(3>> .lbow (-(3 ($+> (53
3>> end >-3/ >$- >+$
)mooth ore Pipe $(>$ (5?5 (+$
4iaphragm 0alve (+((+ ?>/ ((+(>
all 0alve (?5? >/3/ ($/
;lobe 0alve +/(3 +>> +//>
Eeedle 0alve 5(/$? $?35/ 5>$?$
'rifice Meter ((? $53/ $>-
0enturi Meter >$-> >(?+ >$(
1'tameter 5? ?(+? 3-$ (--( /$+5 $>+ -??>
( ,is!ussion
(
From the pressure drop versus flow rate graphs as illustrated in figure (, 5 and -,
it can be observed that generall! pressure drop increases as flow rate increases This is
because pressure drop is directl! proportional to the s7uare of the velocit! as seen in the
e7uation$
$V
K P g
c=
∆
ρ *ncreasing flow rate also increases the velocit! as the diameter
of respective devices is fixed
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The loss coefficient is obtained b! the e7uation based calculation 9method (: and
graphical determination 9method $: *n method (, " was calculated using the e7uation,
$
$V
K P g c=
∆
ρ where 0$ is determined b! the flow rate used The " is than evaluated at
all the flow rate used and arithmetic " average is found *n method $, P versus 0$ was
plotted using the best fit method 9b! linear regression: and the gradient of the line was
obtained
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Ori#i!e
meter
( Cheap, small and convenient
$ .as! to install and maintain
5 ;reater flexibilit! to change
throat to pipe diameter ratio to
measure a larger range of flow
rates
+ .xtensive industrial use
( =arge power consumption in the
form of irrecoverable pressure loss
$ High permanent pressure loss due to
the uncontrolled expansion
downstream from the metering
5 4eposits near the orifice plate ma!
decrease the lifespan of the meter
+ Has a small and simple geometr!,
which cannot be used to measure
large flows(enturi
meter
( 0er! accurate for large range of
flows and has ver! little
frictional loss
$ Has a conical diffuser section,
which reduces head loss
Therefore, onl! small pressure
drop is re7uired
( Heav! and bul#! hence ma#ing
installation more difficult
$ *t onl! has a limited range of
pressure drop because it is onl!
constructed for certain flow rates
5 *t is expensive
Rotameter ( )imple device that can be mass
manufactured out of cheap
materials$ 1e7uires no external power or
fuel, it uses onl! the inherent
properties of the fluid, along
with gravit!, to measure flow
rate
5 2llows the flow rate to be
adjusted
( Heav!, bul#! and unsuitable for
large flow rates$ 4ue to its use of gravit!, a rotameter
must alwa!s be verticall! oriented
and right wa! up, with the fluid
flowing upward
3. *s not easil! adapted for reading b!
machine
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saddleDli#e structure of the valve =i#ewise, this causes a greater disturbance in fluid flow
hence having a reasonable loss coefficient However, both the ball valve and globe valve
have relativel! low loss coefficients due to the rounded interiors which do not
significantl! obstruct the fluid flow and reduces energ! loss
Comparison of " between discharge measuring devicesThe " value for the orifice meter was much higher than the one for the venturi meter 9(>
times larger: This result can be attributed to the structural design of the discharging measuring
device
The cross sectional expansions and contractions are gradual in venturi meter which gives
rises to small loss coefficients as fluid flow is not significantl! disrupted and reducing energ!
loss
However, in the orifice meter, the position of the orifice plate collides with the fluid flow
head on *n addition, the formation of edd! currents at the downstream of the orifice meter alsocontributes to the head loss
5
$
$V
K P g
c=
∆
ρ DDDDDDDDDDDDD 9(:
.7uation ( can be rearranged to express the e7uations in terms of 0Therefore,
0i @ 9gc∆P I $: B 9"Iρ:
Gi @ 0i I 2 where i refers to individual device
G( average @ 9 N Gi : B N i
GT @ G( A G$ A G5
>T ? :4 l@min ? 9699*04 m1@s
4evice P 9Pa: "ave 0$ 9m$BsD$: 09mBs: 2 9m$ : Gi
Line *
1ough ore Pipe /++(- 535/ 5$3 (?( >>>>5(+ -> x (>D+
(?> bend ++/5 >3$( (/$ ($ >>>>5?+ +?? x (>D+
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)udden Contraction (+$>5$ -(+3 >-- >+ >>>>?3 -?/ x (>D+
;entle .xpansion D-33?+ (?/( D D >>>>5?+ D
3> elbow (5$53 (53 (3$ (53 >>>>5?+ -5$ x (>D+
3> end ++?(/ >+$ $(> (+- >>>>5?+ --/ x (>D+
)mooth ore pipe ((-?5$ (+$ (55 ((- >>>>5?+ ++$ x (>D+
G( 2verage 6 -$3 x (>D+
Line 0
4iaphragm 0alve 53+53 ((+( >/3 >?5 >>>>$(/ (?> x (>D+
all 0alve ->55$ ($ >3 >?3 >>>>$(/ (35 x (>D+
;lobe 0alve (-/-(> +// >/ >?$ >>>>$(/ ( x (>D+
Eeedle 0alve (>+35? 5>$? >/3 >?5 >>>>$(/ (?> x (>D+
G$ 2verage (?5 x (>D+
Line 1
'rifice Meter $$?/$ $>/ $$$+ +$ >>>>($ -3? x (>D+
0enturi Meter (/+?+ >$$ (-(3 53> >>>>($ +3+ x (>D+
G5 2verage -+/ x (>D+
Ta2le *1 Cal!ulations o# indi)idual #low rates #or #low o# :4 l@min
GT @ G( A G$ A G5
@ -$3 x (>D+ A (?5 x (>D+ A -+/ x (>D+
@ >>>($-? m5Bs
>T ? 79 l@min ? 9699* m1@s
4evice P 9Pa: "ave 0$ 9m$BsD$: 09mBs: 2 9m$ : Gi
Line *
1ough ore Pipe 5-?5 53+ (?$ (5- >>>>5(+ +$+ x (>D+
(?> bend /-->> >3$ (+$ ((3 >>>>5?+ +- x (>D+
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)udden Contraction -3$3- -(- >$5 >+? >>>>?3 53 x (>D+
;entle .xpansion D$5++$ (?/ D D >>>>5?+ D
3> elbow ??$-5 (5? ($? ((5 >>>>5?+ +5+ x (>D+
3> end ?$+ >+5 >53 >/$ >>>>5?+ $53 x (>D+
)mooth ore pipe ?/>> (+ >3> >3- >>>>5?+ 5/+ x (>D+
G( 2verage 6 5?5 x (>D+
Line 0
4iaphragm 0alve $+$/3- ((+( >+5 >/- >>>>$(/ (+( x (>D+
all 0alve +(5/? ($ >/- >?( >>>>$(/ (- x (>D+
;lobe 0alve $$( +// >55 >-? >>>>$(/ ($- x (>D+
Eeedle 0alve /++/-? 5>$? >+5 >/- >>>>$(/ (+( x (>D+
G$ 2verage (+- x (>D+
Line 1
'rifice Meter ?-+3+ $>/ ?5( $?? >>>>($ 5/- x (>D+
0enturi Meter (?/?+ >$$ ($$ +(- >>>>($ -$/ x (>D+
G5 2verage ++/ x (>D+
Ta2le *3 Cal!ulations o# indi)idual #low rates #or #low o# 79 l@min
GT @ G( A G$ A G5
@ 5?5 x (>D+ A (+- x (>D+ A ++/ x (>D+
@ >>>>3+ m5Bs
>T ? 39 l@min ? 9699977: m1@s
4evice P 9Pa: "ave 0$ 9m$BsD$: 09mBs: 2 9m$ : Gi
Line *
1ough ore Pipe (+/(/? 53+ >+ >?/ >>>>5(+ $( x (>D+
(?> bend +?3-5 >3$ (>/ (>5 >>>>5?+ 53/ x (>D+
)udden Contraction ($+(( -(- >>- >$$ >>>>?3 (5 x (>D+
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;entle .xpansion D535>> (?/ D D >>>>5?+ D
3> elbow $5++$ (5? >5+ >-? >>>>5?+ $$+ x (>D+
3> end ?$+ >+5 >53 >/$ >>>>5?+ $53 x (>D+
)mooth ore pipe 5(>$/ (+ >5/ >/> >>>>5?+ $$3 x (>D+
G( 2verage 6 $-- x (>D+
Line 0
4iaphragm 0alve 33>- ((+( >( >+( >>>>$(/ ?3/ x (>D-
all 0alve ((>5$ ($ >( >+$ >>>>$(/ 3>5 x (>D-
;lobe 0alve ->55$ +// >$$ >+/ >>>>$(/ (>( x (>D+
Eeedle 0alve 5(->?3 5>$? >$( >+/ >>>>$(/ 3? x (>D-
G$ 2verage 3+? x (>D-
Line 1
'rifice Meter /((-/5 $>/ -3- $++ >>>>($ 5>3 x (>D+
0enturi Meter +/(3- >$$ +$/ $>/ >>>>($ $/( x (>D+
G5 2verage $?- x (>D+
Ta2le *4 Cal!ulations o# indi)idual #low rates #or #low o# 39 l@min
GT @ G( A G$ A G5
@ $-- x (>D+ A 3+? x (>D- A $?- x (>D+
@ >>>>/5- m5Bs
>T ? 09 l@min ? 96999111 m1@s
4evice P 9Pa: "ave 0$ 9m$BsD$: 09mBs: 2 9m$ : Gi
Line *
1ough ore Pipe ++?(/ +(3 >$( >+/ >>>>5(+ (+- x (>D+
(?> bend ?$+ >5 >$5 >+? >>>>5?+ (?5 x (>D+
)udden Contraction (53 -($ >>( >> >>>>?3 -3 x (>D-
;entle .xpansion D(>5+$ $(( D D >>>>5?+ D
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3> elbow ?3/5 ($+ >(+ >5? >>>>5?+ (+/ x (>D+
3> end ((>5$ >$/ >?/ >35 >>>>5?+ 5-- x (>D+
)mooth ore pipe (($( (5? >( >+( >>>>5?+ (-? x (>D+
G( 2verage 6 (+ x (>D+
Line 0
4iaphragm 0alve 5$5$ ?( >>3 >$3 >>>>$(/ /55 x (>D-
all 0alve +?$/ >> >(+ >5 >>>>$(/ ?>/ x (>D-
;lobe 0alve $+?$( +> >(( >5$ >>>>$(/ >5 x (>D-
Eeedle 0alve -((> $?3+ >>+ >(3 >>>>$(/ +>3 x (>D-
G$ 2verage /5? x (>D-
Line 1
'rifice Meter (>$5$ $+> >?/ >35 >>>>($ (( x (>D+
0enturi Meter $$-5 >(? $+ (- >>>>($ (33 x (>D+
G5 2verage (-? x (>D+
Ta2le *7 Cal!ulations o# indi)idual #low rates #or #low o# 09 l@min
GT @ G( A G$ A G5
@ (+ x (>D+ A /5? x (>D- A (-? x (>D+
@ >>>>53/ m5Bs
GT 9 m5Bs: G( 9m5Bs: G$ 9m5Bs: G5 9m5Bs: GT 9Calculated: 9m5Bs: O error
>>>($- -$3 x (>D+ (?5 x (>D+ -+/ x (>D+ >>>($-? >/+
>>>( 5?5 x (>D+ (+- x (>D+ ++/ x (>D+ >>>>3+ D$/
>>>>// $-- x (>D+ 3+? x (>D- $?- x (>D+ >>>>/5- D->+
>>>>555 (+ x (>D+ /5? x (>D- (-? x (>D+ >>>>53/ (-3>
)ince the percentage errors are relativel! small, the approximate individual flow rate in
each line can be ta#en as the summarized values in the table above The relative low
percentage errors suggest that the " values obtained earlier on were rather accurate
Ta2le *: Com$arison o# a!tual #low rates and !al!ulated #low rates
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(I Con!lusion
The loss coefficients for the various fittings and devices were calculated from the
experimental data The " values obtain were then used to calculate the flow rate through
each fitting The results obtained were then compared with the flow rate recorded b! the
rotameter 2s discussed in 7uestion 5 of the discussion section, the flow rates calculatedare sufficient close to the recorded values The percentage errors were found to be rather
low Thus we can conclude that the experiment was fairl! accurate
From this experiment, we learned how the geometr! of a fitting affects the head
loss *n general, it was observed that if there was a sudden increase or decrease in the
cross sectional area of the pipe, the loss coefficient would be greater than if these changes
were gradual The needle valve was found to be the device which posses the highest "
value
2 better understanding of the various devices and the various flow meters was
achieved Familiarization of the applications and limitations of the flow meters was also
obtained
(II Re#eren!es
( Fox, 1+:
$ (:
5 ;erhart, PM & ;ross, 1, SFundamentals of Fluid MechanicsS, 2ddisonD
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Appendix
Needle Valve
From the above picture, it can be seen that the needle lie plun!er !ives rise
to si!ni"cant constriction #uid #o$ !ivin! rise to the lar!est loss coe%cient.
&http'(($$$.tpub.co m(content(doe(h1018v2(css(h1018v2)54.htm *
Diaphragm Valve
35
http://www.tpub.com/content/doe/h1018v2/css/h1018v2_54.htmhttp://www.tpub.com/content/doe/h1018v2/css/h1018v2_54.htmhttp://www.tpub.com/content/doe/h1018v2/css/h1018v2_54.htmhttp://www.tpub.com/content/doe/h1018v2/css/h1018v2_54.htmhttp://www.tpub.com/content/doe/h1018v2/css/h1018v2_54.htmhttp://www.tpub.com/content/doe/h1018v2/css/h1018v2_54.htm
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+he diaphra!m valve closes b a diaphra!m, $hich actuall sits on top o- a
saddlelie structure o- the valve $hich obstructs does not obstruct the #uid
#o$ as si!ni"cantl as b the needle valve.
&http'(($$$.romech.co.u(/elated(alves.html )
Globe valve
+he rounded structure reduces
ener! loss.
&http'(($$$.valve dia!nostics.com(medi
a(pictures(!lobe. !i- *
Ball Valve
36
http://www.roymech.co.uk/Related/Valves.htmlhttp://www.roymech.co.uk/Related/Valves.htmlhttp://www.valvediagnostics.com/media/pictures/globe.gifhttp://www.valvediagnostics.com/media/pictures/globe.gifhttp://www.roymech.co.uk/Related/Valves.htmlhttp://www.valvediagnostics.com/media/pictures/globe.gifhttp://www.valvediagnostics.com/media/pictures/globe.gifhttp://www.valvediagnostics.com/media/pictures/globe.gifhttp://www.valvediagnostics.com/media/pictures/globe.gif
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/ounded sur-ace o- the ball reduces ener! loss hence !ivin! rise to a small
loss coe%cient.
&http'(($$$.spirasarco.com(resources(steamen!ineerin!tutorials(pipeline
ancillaries(isolationvalvesrotarmovement.asp*
Venturi Meter
+he !radual epansions and contractions in the venturi meter can be
observed above.
37
http://www.spiraxsarco.com/resources/steam-engineering-tutorials/pipeline-ancillaries/isolation-valves-rotary-movement.asphttp://www.spiraxsarco.com/resources/steam-engineering-tutorials/pipeline-ancillaries/isolation-valves-rotary-movement.asphttp://www.spiraxsarco.com/resources/steam-engineering-tutorials/pipeline-ancillaries/isolation-valves-rotary-movement.asphttp://www.spiraxsarco.com/resources/steam-engineering-tutorials/pipeline-ancillaries/isolation-valves-rotary-movement.asp
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&http'(($$$.#o$meterdirector.com(ima!es(#o$meter)pro-)001.!i- *
Orifce Meter
+he -ormation o- edd currents !ives rise to a lar!er loss coe%cient.
&http'((instrumentation.co.a(rticles(20nstrumentation2020ontrol
2020ublished20b20+echne$s(77c123b.pn! *
Part II
38
http://www.flowmeterdirectory.com/images/flowmeter_prof_001.gifhttp://instrumentation.co.za/Articles/SA%20Instrumentation%20&%20Control%20-%20Published%20by%20Technews/77c123b.pnghttp://instrumentation.co.za/Articles/SA%20Instrumentation%20&%20Control%20-%20Published%20by%20Technews/77c123b.pnghttp://www.flowmeterdirectory.com/images/flowmeter_prof_001.gifhttp://instrumentation.co.za/Articles/SA%20Instrumentation%20&%20Control%20-%20Published%20by%20Technews/77c123b.pnghttp://instrumentation.co.za/Articles/SA%20Instrumentation%20&%20Control%20-%20Published%20by%20Technews/77c123b.png
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Centri#u"al Pum$
C%ara!teristi!s
39
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Summary
The objective of this experiment was to determine the performance curve of the pump and
to verif! pump laws *n this experiment, centrifugal pump was selected as the experimental
s!stem and water was used as the fluid medium .xperiment was carried out at / different pump
speeds 2t each speed, flow rate of water through the pump was varied between the minimum and
maximum possible flow rate The recorded reading was then used to plot the performance curve
of the pump and to verif! the pump laws
For our experiments, we have concluded that centrifugal pump behaves ideall! according to
Pump 2ffinit! =aw at higher pump speed
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CONTENTS
Part II Centri#u"al Pum$
Pa"e
Title 5+
)ummar! 5-
* *ntroduction 5
** Theoretical ac#ground 5?
*** .xperimental set up and procedures ++
*0 1esults and 2nal!sis +/
0 4iscussion -5
0* Conclusion --
0** 1eferences --
2ppendices
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I6 Introdu!tion
*n chemical industr!, engineers often face the problems of pump failures Thus in order to
protect the pumps and to choose the right s!stem for use in the industr!, it is important for
engineers to have a good understanding of the process as well as having thorough #nowledge of
the mechanics of the s!stems 'n top of that, the! also need to have the abilit! to observe the
performance of the s!stem over times This can be done b! conducting experiment to obtain the
performance curve of the pump, which is one of our main objectives of the experiment
2nother objective of this experiment was to verif! pumps laws Pumps law is the general
law that the centrifugal pump is obe!ing This law states that the flow rate of li7uid is directl!
proportional to the pump speed, thus the pump speed in the industr! is adjusted according to this
law Therefore it is ver! important this law is verified so that the s!stem designed in industr!
would not be under or overDestimated from the ideal s!stem
*n our experiment, we varied the pump speed for six times For each pump speed, we
varied the flow rate six times as well using the control valve 1eadings recorded were then used
to plot performance curve and to verif! the pump law
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II6 T%eoreti!al 2a!&"round
Centrifugal pump
2 centrifugal pump is made up of two main components6
( 2 rotating component made up of an impeller and a shaft
$ 2 stationar! component made up of a casing, casing cover and bearings
Fi"ure 8General !om$onent o# a Centri#u"al Pum$
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Fi"ure ; General !om$onent o# a Centri#u"al Pum$
Centrifugal pump converts the input power from turbine or electric motor into #inetic
energ! in the li7uid This is done b! accelerating the li7uid with turbine or electric motor which
acts as the revolving device, also #nown as impeller The #inetic energ! is then changed into
pressure energ! of li7uid that is being pumped "inetic energ! in the li7uid is obstructed b!
creating a resistance in the flow The first resistance is created b! the pump volute 9casing: which
serves as an obstruction to the flow of li7uid and thus slows the flow of li7uid The #inetic that
decreased as li7uid flow decreases is converted into pressure energ!
Me!%anisms
Fi"ure *9 Li=uid #low $at% in a !entri#u"al $um$
Generation o# Centri#u"al For!e
The fluid medium enters through the suction nozzle into the center of the impeller 2s the
impeller rotate, fluid is being rotated in between the vanes as well and thus centrifugal
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acceleration resulted 2s fluid leave the center of impeller, a region of low pressure is then
created This will induce more fluid to flow in from a higher pressure region This will thus
ensure the continuous flow of fluid into the impeller 2s the impeller blades are curved, the fluid
is made to move in a tangential and radial direction due the centrifugal force .nerg! of li7uid
generated b! this centrifugal force is termed as #inetic energ!
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out of the impeller with relative velocit! tangential to the blades The velocit! triangles for the
fluid particles entering and leaving the impeller are as shown
Fi"ure 8*
2ngular momentum of fluid entering and leaving the impeller6
Hi @ r (m9u(cosθ(: and
Ho @ r $m9u$cosθ$: respectivel!
where
m 6 mass of fluid flowing through the impeller
u( 6 the fluid velocit! at the impeller inlet
u$ 6 the fluid velocit! at the impeller outlet
U( 6 the angle between u( and the tangential direction at the blade
U$ 6 the angle between u$ and the tangential direction at the blade
The tor7ue acting on the fluid, , is the rate of change of angular momentum with time,
? Ho + Hi
@ m9r $ u$cosθ$ D r ( u(cosθ(:
Therefore, the power re7uired is
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P @ τω
@ m9r $ u$cosθ$ D r ( u(cosθ(: ω
where ω is the 9angular speed: rotational speed of the impeller
The fluid output power is6
Pf @ m g h
where h is the theoretical head of the fluid
Compare P with Pf 6
h @ 9(Bg:9r $ u$cosθ$ D r ( u(cosθ(: V D 9.uler8s .7uation:
2ssuming there is no preDrotation at the impeller inlet, r (@>, the above e7uation is further
simplified to6
h @ r $ u$ cos U$ V B g 9(:
From the velocit! triangle at the outlet of the impeller,
u$ cos U$ @ ut$ D ur$ B tan 9W$:
and since ur$ is directl! proportional to the flow rate G,
u$ cos U$ @ ut$ D C G 9$:
where C is a constant for the pump
Combining both e7uation 9(: and 9$:6
h @ r $ V 9ut$ D C G: B g 95:
2 plot of the above e7uation will results a linear relationship between H and G 9.uler =ine:
However the actual characteristics curve of the centrifugal pump shows a sharper decline of the
head H over the increase of flow rate G This is shown in the figure below6
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Fi"ure *0 E'$e!ted $lot o# H )s >
The possible factors that might bring about the sharp decrease of the head H are6
( Prerotation of fluid on entering the impeller
$ *nterblade rotation of the fluid
5 =osses at entrance of the impeller and in the subse7uent diffusing process
+ =ea#age through the impeller
Pump 2ffinit! =aws
The performance of a centrifugal pump is affected b! the change in speed of pump as wellas the diameter of impeller The techni7ue dimensional anal!sis is applied to the stud! of the
characteristics of the centrifugal pump operation to produce useful results The basic 7uantities
involved in the pump operation with similar geometrics are6
G 6 Flow rate
E 6 1otational )peed
4 6 *mpeller 4iameter
6 Fluid 4ensit!
X 6 0iscosit! of the fluid
H 6 *ncrease in fluid head
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The general function of the pump operation will have the form6
f 9 G, E, 4, r, X, H: @ >
2ppl!ing dimensional anal!sis, we obtain the following relations6
G @ C( x E x 45
H @ C$ x E$ x 4$ x
and since power re7uired for the pump is directl! proportional to the product of G and H 6
P @ C5 x E5 x 4- x
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III E'$erimental Pro!edure
Flow Chart of .xperimental Procedures
50
Fine tune the inverter output so that the
tachometer displa indicates a speed o- 1450
once the pump has accelerated to a stead
lose the control valve at the dischar!ed
side and -ull open the control valve at
the suction side o- pump
et the initial readin! o- the
load cell to ero
et the -re:uenc output o- the
inverter to a ratio o- approimatel
50
et the control s$itch o- theinverter to run position.
et the control s$itch to o;
position and s$itch on the po$er
su l
ontrol the #o$ o- the pump
/epeat the above steps $ith di;erent
pump speeds
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16* ,etailed Pro!edures
( The control valve at the discharge side was closed and the control valve at the suction
side of pump was full! opened
$ The initial reading of the load cell was set to zero b! pressing the mode and zero #e!
simultaneousl!
5 The fre7uenc! output of the inverter was set to a ratio of approximatel! ->O
+ The control switch was set to off position
- The power suppl! to the electrical panel was switched on
/ The control switch of the inverter was set to run position
'nce the pump had accelerated to a stead! state, the inverter output was fine tuned so
that the tachometer displa! indicated a speed of (+-> rpm
? The flow of the pump was controlled b! graduall! opening the control valve at the
discharge side at small steps
3 The readings of the measured values were ta#en down
(> The above steps were repeated with pump speed changed to (->, $>->, $5->, $/-> and
$3>> rpm respectivel!
2pparatus used6
( .lectrical Panel
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160 Pre!autions Ta&en
( .nsure that the control valve at the suction side of the pump was full! open and the valve at
discharge side was closed before !ou switch on the pump
$ )tand clear of the motor and pump when setting the control switch of the inverter to QrunR
position *f the pump does not run after switch on, switch it off immediatel! and inform thelab demonstrator
5 4o not touch an! moving parts when the pump is running
+ *f water is spilled around the electrical points, inform the lab demonstrator immediatel!
I( Results and Cal!ulation
*mpeller diameter, 4 @ >((m
Tor7ue arm length, = @ >(+m
gc @ ( #gm m B E B s$ @ 3?( #gm m B #gf B s$
E9revBmin: @ (+->
F9#g:
G 9m5Bh:P>
9#gf Bcm$:Pi
9mmHg:Hs
9m:H
9m:Pf
9 5/> >$>> D(>> 55/ 55/ 5$3- >-- (-(3> ?5-- 53++
>5? 5>> >$$- D(>> 5/( 5/( $3-> >-$ (-(3> ?33 55-
>5/ $>> >$-> D(>> 5?/ 5?/ $(>5 >+3 (-(3> ++5 $?$/
>5+ (>> >$- D(>> +(( +(( (($> >+ (-(3> (53 (-/?
Ta2le *88 Measured and !al!ulated )alues at *349r$m
E9revBmin: @ (->
F9#g:
G 9m5Bh:P>
9#gf Bcm$:Pi
9mmHg:Hs
9m:H
9m:Pf
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>-+ ->> >5>> D($- +> +> /+>$ >+ (?555 (5-// +(3
>-> +>> >5-> D(>> +?/ +?/ -$3/ >/3 (?555 ($/-> +(?
>/> 5>> >+>> D(>> -5/ -5/ +5?( >?$ (?555 (->55 $3(+
>++ $>> >+$- D(>> -/( -/( 5>- >/> (?555 ((>>> $3
Ta2le *; Measured and !al!ulated )alues at *:49r$m
E9revBmin: @ $>->
F9#g:
G 9m5Bh:P>
9#gf Bcm$:Pi
9mmHg:Hs
9m:H
9m:Pf 9> >+$- D(-> /$3 /$3 (>$?$ >3( $(+/ (3-+5 -$/(
>/$ ->> >->> D($- /> /> 3($ >?- $(+/ (?$-- ->>>
>-? +>> >--> D(>> /?/ /?/ +/ >?> $(+/ ((?( +5-$
>-+ 5>> >/>> D(>> 5/ 5/ />(/ >+ $(+/ (-?3$ 5?/
Ta2le 09 Measured and !al!ulated )alues at 0949r$m
E9revBmin: @ $5->
F9#g:
G 9m5Bh:P>
9#gf Bcm$:Pi
9mmHg:Hs
9m:H 9m: Pf 9> >-- D(-> 3 3 (+?- ((- $+/(3 $?5($ -$+>+ ->> >$- D($- ?3- ?3- ($(35 (>$ $+/(3 $-((( +?-/
>// 5>> >?$- D(>> 3/( 3/( ?-- >3( $+/(3 $$+>5 5->/
>-? (>> >3>> D- (>>$ (>>$ $5> >?> $+/(3 (3/3- (5?/
Ta2le 0* Measured and !al!ulated )alues at 0149r$m
E9revBmin: @ $/->
F9#g:
G 9m5Bh: P>9#gf Bcm$:
Pi9mmHg:
Hs9m:
H 9m: Pf 9 ?>> >-> D$>> (>$$ (>$$ $$$- (5 $/$ 5?>5+ -?-
>3> />> >3$- D(-> (($3 (($3 (?+- ($+ $/$ 5++$- -5/(
>?> +>> (>-> D(>> ((?/ ((?/ ($3$/ ((> $/$ 5>-5? +$55
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>> $>> (($- D(>> ($/( ($/( /?$ >3/ $/$ $//-$ $-?
Ta2le 00 Measured and !al!ulated )alues at 0749r$m
E9revBmin: @ $3>>
F9#g: G 9m5Bh:
P>9#gf Bcm$:
Pi9mmHg:
Hs9m: H 9m: Pf 9> >?>> D$-> ((+> ((+> 5(>-? (/$ 5>5?( +3$( /5((
((> ?>> (>>> D$>> ($$ ($$ $$- (-( 5>5?( +-?- />++
>3? />> ((- D(-> (53 (53 $$-++ (5- 5>5?( +(>(+ -+3
>?/ +>> (5>> D(>> (+5/ (+5/ (-/-( ((? 5>5?( 5-?-> +5//
Ta2le 01 Measured and !al!ulated )alues at 0;99r$m
Cal!ulation
Sample calculation of first experimental run
4 @ >(( m, G @ (>>> m5Bhr 9max value:
Fluid 0elocit!, v @ +G B J4$
@ >$3$ mBs
Fluid 0elocit! Head, Hv @ v$ B $g
@ +5-x (>D5 m 9negligible compared to Hs:
)uction Pressure, Pi @ D(>> mmHg
@ D(>> x (B/> x (>(5$- x (>- B (>> B (>> B 3?(
@ D>(5/ #gf B cm$
4ischarge Pressure, Po @ >$>> #gf B cm$
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Fluid )tatic Head, Hs @o i P P
g ρ
−
×9 @ (>>> #gBm5 for water, g @ 3?( mBs$:
@ Z>$>> K 9D>(5/:[ x 3?( x (>+ B 9(>>> x 3?(:
? 55/ m \\ Hv
Fluid Total Head, H @ Hs A Hv ] Hs @ 55/ m
Fluid Power, Pf @5/>>
Q H g ××× ρ
@ (>>> x 3?( x 55/ x 5/> B 5/>>
@ 5$3/ <
= @ >(+ m, F @ >+> #g
Tor7ue, Y ? F x =
@ 9>+> x 3?(: x >(+
@ >-- EDm
E @ (+-> rpm
2ngular velocit!, V @ $ x $$B x Erpm/>
rps(×
@ $ x$$B x (+-> B />
@ (-(3> rad B sec
Pump Power, P p @ Y x V
@ >-- x (-(3>
@ ?5-- <
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Pump .fficienc!, . @ O(>>× p
f
P
P
@ 5$3- B ?5-- x (>>O
@ 53++O
Fi"ure *; Plot o# H a"ainst >
Pump 2ffinit! =aws
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Tabulation and iscussion
E@(+->rpm E@(->rpm E@$>->rpm
GBE HBE$ GBE HBE$ GBE HBE$
>>>$+?$? (-3/+.D>/ >>>$?-(+ (-5+5.D>/ >>>$3$/?5 (+3/53.D>/
>>>$>/3 ((/--.D>/ >>>$$?-( (-?//5.D>/ >>>$+53>$ (-3+>(.D>/
>>>(535 (?5-+/.D>/ >>>((+$3 (+3?3.D>/ >>>(3-($$ (/5$(5.D>/
>>>>/?3 (3-+5/.D>/ >>>((+$?/ (?5(-5.D>/ >>>(+/5+( (-(((.D>/
Ta2le 03 Ta2ulation o# >@N and H@N0
E@$5->rpm E@$/->rpm E@$3>>rpm
GBE HBE$ GBE HBE$ GBE HBE$
>>>$3? (+(>55.D>/ >>>5>(?? (+-->-.D>/ >>>5++?$? (5--$-.D>/
>>>$($ (/$>+5.D>/ >>>$$/+(- (/>+3.D>/ >>>$-?/$ (-($$/.D>/
>>>($// (533?.D>/ >>>(->3+5 (/??$.D>/ >>>$>/?3 (/53-+.D>/
>>>>+$-- (?(+$.D>/ >>>>-+$ (3--$.D>/ >>>(535( (>5?.D>/
Ta2le 04 Ta2ulation o# >@N and H@N0
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Fi"ure **9 Plot o# >@N a"ainst H@N0
iscussion
2s can be observed from Figure / above, the curves did converge but did not converge to
one curve The curves are relativel! closer to each other at lower values of HBE$
This deviation at higher values could be due to s!stematic and experimental error
The graph of GBE against HBE$ should converge due to the following reason6
G @ C( x E x 45
H @ C$ x E$ x 4$ x , according to the affinit! laws
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1earranging the above e7uations6
GBE @ C( x 45
9C( is the pump constant and 4 is the impeller diameter:
HBE$@ C$ x 4$ x
9C$ is the pump constant, 4 is the impeller diameter:
Therefore, a plot of GBE and HBE$ should converge as the! are independent of pump
speed Figure / ,hence, verified the first and second pump affinit! laws The third pump affinit!
law 9P @ C5 x E5x 4- x : is thus also verified as it is directl! proportional to the product of G and
H which are the first and second pump affinit! laws
G @ C( x E x 45
H @ C$ x E$ x 4$ x
P @ C5 x E5
x 4-
x
The above 5 pump affinit! laws are useful as the! allow us to predict the effect of var!ing
pump speed, fluid densit! and etc on the flow rate, head and power of the pump For example, if
pump speed was increased b! (>O 9#eeping all other variables constant:
Flow rate, G will increase b! (( times
Head, H will increase b!6 9((:$
@ ($( times
Power, P will increase b!6 9($:5 @ (55( times
Error Analysis
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The experimental data deviates from the ideal case due to the following inevitable s!stematic and
experimental errors
( The pump efficienc! laws are based on ideal fluid which has no viscosit! *naccurac! of
data could have arised from the nonDidealit! of water
$ Constant fluctuations in the readings of E and flow rates were observed This could be
due to the turbulent flow in the s!stem which affected the sensitivit! of the tachometer
and rotameter 2n average reading was ta#en and hence this could compromise the
accurac! of the data collected
5 *t was prone to parallax error while ta#ing the readings of pressure and flow rates 2lso,
the scale of the pressure gauge was large and it could onl! be used to read for a multiple
of $- These errors could have been minimized with the usage of digital pressure meters
+ *t was also noted when the flow rate was varied, the pump speed also changed
These fluctuations might have affected the accurac! of the collected data
( ,is!ussion
From the experimental plot of H against G, it is observed that the curve of H against G
concaves downwards Hence the curve deviates from the theoretical .uler8s linear line This is
because experimental total heat loss includes the loss due to preDrotation of the fluid entering
impeller, interDblade rotation and frictional losses during diffusion of the fluid whereas the
theoretical head loss does not account for such losses The following figure shows the t!pes of
losses within the centrifugal pump which accounts of the deviation
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Fi"ure *** E##e!ts o# losses on t%e $um$ %ead a"ainst #low rate !ur)e
These losses were resulted due to the following reasons
( )hoc# losses arise from the turbulence created b! the impact of the fluid against the
blades, friction between the fluid and the boundaries, recirculation of a small fluid
amount after lea#age through the clearance spaces outside the impeller
$ .ddies ma! result in some bac# flow into the inlet pipe, causing the fluid to have a whirl
before entering the impeller
5 H!draulic losses due to pipe friction and pipe connection such as valves and meters
*t is also observed that as the rotating speed of the pump increases, the curves shift outwards
This is because higher rotating speed results in fluid with higher angular speed and momentum,
this in turn, result in higher fluid output power and hence a larger head value
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Fi"ure **0 Pum$ e##i!ien!y !ur)es
This is not the case in our experimental plot as the range of flow rates was not large
enough to form the complete curves 'nl! half of the efficienc! curves was obtained during our
experiment and the best efficienc! point could not be determined
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were #ept constant for all experimental readings Thus, the 5 pump affinit! laws were verified and
found to be accurate
(II Re#eren!es
(