Flow Measurement in Closed Conduit

8/18/2019 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


24/65

,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


27/65

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

$:


28/65


29/65

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+

28


30/65

)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


Line *

1ough ore Pipe 5-?5 53+ (?$ (5- >>>>5(+ +$+ x (>D+

(?> bend /-->> >3$ (+$ ((3 >>>>5?+ +- x (>D+

29


31/65

)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


Line *

1ough ore Pipe (+/(/? 53+ >+ >?/ >>>>5(+ $( x (>D+

(?> bend +?3-5 >3$ (>/ (>5 >>>>5?+ 53/ x (>D+

)udden Contraction ($+(( -(- >>- >$$ >>>>?3 (5 x (>D+

30


32/65

;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+


GT @ G( A G$ A G5

@ $-- x (>D+ A 3+? x (>D- A $?- x (>D+

@ >>>>/5- m5Bs

>T ? 09 l@min ? 96999111 m1@s


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

31


33/65

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+


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

32


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35/65

(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


36/65

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


37/65

+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


38/65

/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


39/65

&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


40/65

Centri#u"al Pum$

C%ara!teristi!s

39


41/65

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

40


42/65

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

41


43/65

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


44/65

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$onent o# a Centri#u"al Pum$

43


45/65

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

44


46/65

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!


47/65

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

46


48/65

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

47


49/65

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

48


50/65

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


51/65

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


52/65


53/65

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

52


54/65

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

9


55/65

>-+ ->> >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

54


56/65

>> $>> (($- 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 @ >$>> #gf B cm$

55


57/65

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

(

Flow Measurement in Closed Conduit

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