calc example blank

8/11/2019 Calc Example Blank

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TOTAL HEAD, N.P.S.H. AND OTHER CALCULATION EXAMPLESJacques Chaurette p. eng.,

www.lightmypump.comJune 2003


2/41

Total head, N.P.S.. and other calculations!2

Figure 1 Calculation example flow schematic.

Situation

"ater at #$0 % is to &e pumped 'rom a collecting tan( located at the &asement le)el

*ele)ation 2+00 a&o)e sea le)el-. oth the suction and discharge tan(s ha)e a squareti */ /" #0 - th 'l l l i t + ' th & tt ' th t ( Th


3/41


6our tas( is to7

#. Calculate the total head and select the pump.2. Calculate the NPS a)aila&le and chec( with respect to the NPS required.3. Calculate the speci'ic speed and predict the pump e''iciency. Calculate the

suction speci'ic speed and Thoma num&er and chec( the prediction o' theThoma num&er regarding ca)itation.

8. Calculate the temperature rise o' the 'luid within the pump and compare with thema1imum recommended.

$. Calculate the pressure ahead o' the control )al)e using method # which uses the'low data &etween points # and the control )al)e inlet point 9 *see %igure 3- andmethod 2 which uses the 'low data &etween points 2 and the control )al)e inletpoint 9 *see %igure 3-.


4/41


CALCULATIONS

1. Calculate the total head and elect the !u"!

Total head is gi)en &y 'ormula :#;. %or the meaning o' the )aria&les see thenomenclature in ta&le 20. ' you would li(e to (now more a&out how this equationwas deri)ed see J. Chaurettes &oo(


5/41

Total head, N.P.S.. and other calculations!$

SECTION #LO$%U&al'"in(

DIA%in(

)ELOCIT*%+t'(

H#P'L

%+t'1 +t !i!e(

L%+t(

H#P%+t +luid(

#238$/Su&Btotal

%P#B99Total

%P#B2Table 1 Friction loss for all pipe segments.


6/41

Total head, N.P.S.. and other calculations!/

Sa"!le calculation +o- line e&"ent L1

The 'riction loss in 'eet o' 'luid 'or #00 'eet o' pipe 'rom the ta&le in %igure / is #./8.

The 'riction loss is then7

06.0100

464.1)( == fluidftHFP

P-eu-e head lo due to +ittin& +-iction

The 'riction loss 'or 'ittings is gi)en &y 'ormula :3;.

tableseeKforsftg

sftvKfluidftH FF

)/(2

)/()(

2

22

=:3;

The D 'actors 'or the di''erent 'ittings type is gi)en in the 'orm o' graphs *see %igures

+ and E which are e1tracts o' the ydraulic Fngineerings Standards &oo(,www.pumps.org-. se these 'igures 'or the D 'actors in equation :3; 'or 'ittings andmanual )al)es.

SECTION #LO$%U&al'"in(

T*PE T* DIA%in(

)ELOCIT*%+t'(

/0'0&%+t +luid(

H##%+t +luid(

#

#233


7/41


Sa"!le calculation +o- line e&"ent L1

The D )alue 'or the entrance loss is #. The 'riction loss is then7

5.0)/(17.322

)/(67.51)(

2

22

=

=sft

sftfluidftHFF

Pressure head loss due to equipment

SG

psipfluidftH

)(31.2)( =

:8;

The pressure drop across the 'ilter is gi)en &y the manu'acturer, 3 psi at $00 gpm. "ecan calculate the pressure head loss &y using equation :8;. The )alue o' the speci'icgra)ity SG is )ery close to one, 'or water this )alue changes with the temperature *see

%igure #2-. 5 similar approach is ta(en 'or the heat e1changer whose pressure drop isgi)en as $ psi.

The control )al)e is a di''erent matter, i' this is a new system we will ha)e to assume areasona&le )alue 'or a pressure drop that is consistent with good practice. Consultantsha)e 'ound that in general i' one assumes a pressure head drop o' #0 't o' 'luid it willalways &e possi&le to select a )al)e o' a reasona&le si=e that will pro)ide good control.' the system is e1isting then the manu'acturers data will ha)e to &e used to calculate

the pressure drop 'or that speci'ic )al)e at $00 gpm.


8/41

Total head, N.P.S.. and other calculations!+

P-eu-e head lo due to the chec3 /al/e

To calculate the pressure head drop across the chec( )al)e we use the C o' the )al)e.

The )al)e 'low coe''icient *C- is used as an indicator o' the pressure drop across a)al)e under speci'ic 'low conditions and is 'ormally de'ined as the num&er o' gallons perminute o' room temperature water that will 'low through the )al)e with a pressure dropo' # psi across the )al)e *see equation :$;-. The )alue 'or the chec( )al)e C can &e'ound in the ta&le o' %igure $.

SG

psip

USgpm

C! )(

)(

=:$;

"e can o&tain the )alue o' the pressure drop *p- across the chec( )al)e &y using

equation :/; which is equation :$; with the pressure drop term isolated on the le't handside o' the equation.

SG

psi

gpmC!

gpmpsip

=

2

2/1

)()(

:/;

T*PE #LO$%U&al'"in(

T* DIA%in(

S2 C) %&!"'!i1'0 (

!

%!i(

Hchec3%+t +luid(

Tilting disc


9/41

Total head, N.P.S.. and other calculations!E

)elocit6 head di++e-ence 7et8een the outlet and inlet o+ the 6te"

)#and )2are respecti)ely the )elocities o' the 'luid particles at the inlet o' the system

and the outlet. The inlet o' the system is at the position o' the sur'ace o' the liquid in thesuction tan(. The )elocity *)#- o' the 'luid particles at the sur'ace is quite low and smallenough to &e considered nil. The outlet o' the system is at the position o' the sur'ace o'the liquid in the discharge tan(. The )elocity *)2- o' the 'luid particles at the sur'ace isquite low and small enough to &e considered nil.Notice that the discharge end o' the pipe is su&merged, the 'luid particles will tra)el 'romthe discharge pipe end to the liquid sur'ace in the discharge tan(. ' the pipe were notsu&merged then the outlet o' the system would &e located at the discharge pipe end

and the )elocity )2would &e the )elocity at the end o' the pipe.

/1 /0 /10'0& /00'0& /

00'0& 9 /1

0'0& %+t +luid(

Tan( pressure head di''erence &etween the outlet and inlet o' the system

' the suction tan( were pressuri=ed with pressure p#, there would &e a correspondingpressure head #. Since the tan( is not pressuri=ed and is open to atmosphere then thepressure p#is =ero and there'ore #is =ero. The same applies to the discharge tan(.

Calculation -eult %total head(

Ta&le $ &rings together all the pre)ious calculations and the result is the total headrequired o' the pump.

H1 H0 H09 H1 %+t +luid(


10/41

Total head, N.P.S.. and other calculations!#0

:-a3e ho-e!o8e-*determine the pump e''iciency 'rom the pump per'ormance cur)e prior to doing thiscalculation-

The power a&sor&ed &y the pump is gi)en &y equation:9; *see re'erence #-7

pump

Ppump

galUSfluidftHSG"pP

=

3960

min)/()()(

:9;

SPECI#IC2RA)IT*S2

TOTALHEAD

HP%+t +luid(

#LO$;%U&al'"in(

PUMPE##ICIENC*

:RAEHORSEPO$ERP%h!(

Table 2ower to the pump shaft calculation results.


11/41

Total head, N.P.S.. and other calculations!##

PUMP SELECTION DATA

This ta&le lists the important in'ormation on the pump that was selected to meet the

process requirements.

Pump anu'acturer

Pump odel

Type

Suction dia. *in-

4ischarge dia. *in-

mpeller speed *rpm-

Aperating head *'t-

Aperating %low *sgpm-

Pump e''iciency *M-

Predicted e''iciency *M-

Speci'ic speed

Suction speci'ic speed

Temperature rise *%-

%luid typeiscosity *cSt-

Temperature *%-

Speci'ic gra)ity

Speci'ic heat *tu?l&B%-

ra(e horsepower *hp-

Selected horsepower *hp-

%rame

Pump shutBo'' head *'t-

System high point *'t- =high L =#


12/41


0. Calculate the N.P.S.H. a/aila7le and chec3 a&aint the N.P.S.H. -e;ui-ed.

ost o' the data required 'or the N.P.S.. a)aila&le has already &een calculated.

S*see equation :+a;- is the pressure head at point S or the pump suction. TheN.P.S.. a)aila&le is the )alue o' the pressure head a)aila&le at point S * S- plus theatmospheric pressure minus the )apor pressure o' the liquid.

va#Savail HHHabsfluidftHSP$ +=).(.... . :+a;

The )alue o' the pressure head *S- at point S *see equation :+&;- will depend on thepipe and equipment loss &etween points # and S plus the )elocity head at point #and plus the ele)ation di''erence the two same points. ' you would li(e to (nowmore a&out how this equation was deri)ed see re'erence #.

)(2

)( 1

2

111 1 Hzz

g

vHHH

SSEQSFS ++++= :+&;

y replacing the )alue o' Sin equation :+&; into equation :+a; we o&tain the N.P.S..a)aila&le *see equation :+c;-.

SEQSFavail Hzzg

vHHabsfluidftHSP$

S ++++= (

2)().(....

2

111. 1

:+c;


13/41


P-eu-e head lo due to !i!e +-iction

SECTION #LO$

%U&al'"in(

DIA

%in(

)ELOCIT*

%+t'(

H#P'L

%+t'1 +t !i!e(

L

%+t(

H#P

%+t +luid(#2Total

%P#BSTable 4


SECTION T*PE T* #LO$%US&al'"in(

DIA%in(

)ELOCIT*%+t'(

/0'0&%+t +luid(

H##

%+t+luid(

##2

Total%%#BSTable #

P-eu-e head lo due to e;ui!"ent

SECTION T*PE T* #LO$

%US&al'"in(

!

%!i(

S2 !

%+t +luid(

HE15S

%+t +luid(2Ta&le #0


14/41


At"o!he-ic !-eu-e head

The atmospheric pressure in the en)ironment o' the pump depends on the ele)ation

a&o)e sea le)el or the plant ground 'loor ele)ation which is considered precise enough.The chart in %igure ## gi)es the pressure in psia corresponding to the pumps ele)ation.sing equation :8; we can calculate the corresponding pressure head.

!A%!ia( S2 HA%+t +luid a7.(

)a!o- !-eu-e head

The )apor pressure o' the 'luid depends on its temperature. The ta&le in %igure ##gi)es the )apor pressure in psia corresponding to the temperature. sing equation :8;we can calculate the corresponding pressure head.

!/a%!ia( S2 H/a%+t +luid a7.(

Calculation -eult %N.P.S.H. a/aila7le(

Co"!onent Si&n %+t +luid( Reult

Pipe 'riction head loss B %P#BS

%ittings 'riction head loss B %%#BS

Fquipment 'riction head loss B FH#BS

Suction static head K =#B=STan( pressure head K #

elocity head K )#2?2g

5tmospheric pressure head K


15/41

Total head, N.P.S.. and other calculations!#$

3. Calculate the !eci+ic !eed, uction !eci+ic !eed and Tho"a nu"7e- and

chec3 the !-ediction o+ the Tho"a nu"7e- -e&a-din& ca/itation

S!eci+ic !eed %NS(

Speci'ic speed is a num&er that pro)ides an indication o' the speed o' the impeller, the'low rate and the head produced. The num&er is low, &elow 2000 *see %igure #3- 'orpumps o' radial design that pro)ide high head and low 'low. t is large, o)er #0000, 'orpumps that pro)ide high 'low and low head. 5long with the suction speci'ic speed, it can&e used to predict ca)itation.

75.0)(

)()(

fluidftH

USgpmQrpm$$S

=

:E;


16/41

Total head, N.P.S.. and other calculations!#/

_____________________

_______________=

=S$

:Ea;

P-edict the !u"! e++icienc6

The pumps e''iciency is directly related to its speci'ic speed. F''iciency increases asspeci'ic speed increases. 5lso, as shown in %igure #8, the e''iciency increases as 'lowrate increase, this means that larger pumps at the same speci'ic speed are moree''icient. . %or impeller si=es larger than #0> the e''ect o' si=e or increased 'low rate issmall and generally insigni'icant. %or impeller si=es 8> and less , the penalty 'or smallersi=es is se)ere.

The e''iciency predicted &y the chart in is %igure #8 is @@@@@@@.

Suction !eci+ic !eed %S(

Suction speci'ic speed is a num&er that is dimensionally similar to the pump speci'icspeed and is used as a guide to pre)ent ca)itation.

75.0)(....

)()(

fluidftHSP$

USgpmQrpm$S

#

=

:#0;

nstead o' using the total head o' the pump , the N.P.S..5*Net Positi)e Suction eada)aila&le- is used. 5lso i' the pump is a dou&le suction pump then the 'low )alue to &eused is one hal' the total pump output.

The ydraulic nstitute recommends that the suction speci'ic speed &e limited to +$00.Some pump manu'actures limit this )alue to #0,000B#2,000.

_________________

=S:#0a;


17/41


Tho"a ca/itation !a-a"ete-

H

HSP$ ....=

:##;

The Thoma ca)itation parameter is non dimensional and has &een used to predict theonset o' ca)itation *see %igure #/-. se this num&er to )eri'y that this pump will ha)esu''icient N.P.S..5. to operate properly.

___________________

________.....===

H

#HSP$

:##a;


18/41

Total head, N.P.S.. and other calculations!#+

$. Calculate the !-eu-e ahead o+ the cont-ol /al/e uin& "ethod 1

t is important to (now the pressure Oust at the inlet o' a control )al)e. This in'ormation is

required to si=e the )al)e and ensure that it will control properly and a)oid ca)itation.

Method 1

ethod # consists o' calculating the pressure at the inlet o' the control )al)e &y ma(inguse o' the total head o' the pump and the 'riction loss and ele)ation di''erence &etweenthe inlet o' the system and point 9, the inlet o' the )al)e.

*see equation :#3;- is the pressure head o' any point we choose on the dischargeside o' the pump *see re'erence #-.

H H H Hg

v v z H z ' P F ' EQ ' ' '= + + + + ( ) ( ) ( )1 1 12 2

1 1

1

2

:#3;

n our case point will &e point 9 or the point Oust at the inlet o' the control )al)e.

)()(2

1)( 711

2

7

2

171717 zHzvvgHHHHEQFP ++++= :#8;


19/41

Total head, N.P.S.. and other calculations!#E

The )alue o' the pressure head at point 9 depends on the total head o' the pump minusthe pipe and equipment head loss &etween points # and 9 minus the di''erence in)elocity head &etween points # and 9 and minus the ele)ation di''erence &etween the

two same points.

Ance again most o' the data required to calculate the pressure at point 9 has already&een calculated.

P-eu-e head lo due to !i!e +-iction

SECTION #LO$

%US&al'"in(

DIA

%in(

)ELOCIT*

%+t'(

H#P'L

%+t'1 +t !i!e(

L

%+t(

H#P%+t +luid(

#238$/

Total%P#B9Table 1$


SECTION #LO$%US&al'"in(

T*PE T* DIA%in(

)ELOCIT*%+t'(

/0'0&%+t +luid(

H##

%+t +luid(

##2


20/41



SG

psip

fluidftH

)(

31.2)( =


T*PE T* !

%!i(

S2 !

%+t +luid(

HE%+t +luid(

2 $00 %ilter # 3 0.E+ 9.09 9.09

3

TotalFH#B9Table 1'

P-eu-e head lo due to the chec3 /al/e

SG

psi

gpmC!

gpmpsip

=

2

2/1

)()(

T*PE #LO$%US&al'"in(

T* DIA%in(

C)%&!"'!i1'0 ( S2 !

%!i(

Hchec3%+t +luid(

Tilting discTable 1


21/41

Total head, N.P.S.. and other calculations!2#

Calculation -eult %"ethod 1 9 !-eu-e at the cont-ol /al/e inlet(

The sign in the second column 'ollows the signs o' the terms in equation :#/;.


Total head K P

Pipe 'riction head loss B %P#B9

%ittings 'riction head loss B %%#B9

Fquipment 'riction head loss B FH#B9

Chec( )al)e head loss B CFCD

Total static head K =#L =9elocity head di''erence K )2#?2g L )9

2?2g

Tan( pressure head K #

Pressure head at the control )al)e *'t 'luid- I 9

Pressure at the control )al)e *psig- I p9Table 1 ummary of the results of the pressure calculation at point 3.


22/41


$. Calculate the !-eu-e ahead o+ the cont-ol /al/e uin& "ethod 0

Method 0

ethod 2 consists o' calculating the pressure at the inlet o' the control )al)e &y ma(inguse o' the 'riction loss and ele)ation di''erence &etween the outlet o' the system andpoint 9, the inlet o' the )al)e.

*equation :#9; is the pressure o' any point we choose on the discharge side o' thepump.

)()(21

22

22

222 ''EQ'F'' zHzvvg

HHH ++++= :#9;

n our case point will &e point 9 or the point Oust at the inlet o' the control )al)e.

)()(2

1722

2

7

2

227277 zHzvvg

HHH EQF ++++= :#+;

The )alue o' the pressure head at point 9 will depend on the pipe and equipment loss&etween points 9 and 2 *the outlet- plus the di''erence in )elocity heads &etween points2 and 9 and plus the ele)ation di''erence &etween the two same points. Notice that withthis method we do not consider the total head o' the pump.

The pressure at point 9 is dictated &y the 'low rate. The 'luid particles that are ahead o'point 9 do not (now that they ha)e gotten to that point than(s to the energy supplied &ythe pump, all that they see is that they ha)e arri)ed at point 9 with a certain amount o'

pressure and )elocity. "e can there'ore do an energy &alance &etween points 9 and 2and 'ind out what the pressure at point 9 has to &e to maintain the pressure and )elocityenergy at this point.


23/41



SECTION #LO$

%US&al'"in(

T*PE T* DIA

%in(

)ELOCIT*

%+t'(

/0'0&

%+t +luid(

H##>50

%+t +luid(9Total

%%9B2Table 14


SG

psipfluidftH

)(31.2)( =


T*PE T*

!

%!i(

S2

!

%+t +luid(

HE>50%+t +luid(

9Total

FH9B2Table 1#

Total tatic head

4> 40 4054>%+t +luid(

)elocit6 head di++e-ence 7et8een !oint > and 0

/> /0 />0'0& /00'0& /

00'0& 9 />

0'0& %+t +luid(


24/41


Calculation -eult %"ethod 0 9 !-eu-e at the cont-ol /al/e inlet(

The sign in the second column 'ollows the signs o' the terms in equation :#+;.


Pipe 'riction head loss K %P9B2

%ittings 'riction head loss K %%9B2

Fquipment 'riction head loss K FH9B2

Static head K =2L =9elocity head di''erence K )22?2g L )9

2?2g

Tan( pressure head K 2

Pressure head at the control )al)e *'t'luid-

I 9

Pressure at the control )al)e *psig- I p9Table $( 7esults of the pressure calculation at point 3.


25/41

Total head, N.P.S.. and other calculations!2$

S6"7ol

)a-ia7le no"enclatu-e I"!e-ial 6te"

%#PS unit(

Met-ic 6te"

%SI unit(

head 't *'eet- m *meter-

P total tead 't *'eet- m *meter-

FH#B2 equipment 'riction head loss

&etween points # and 2

't *'eet- m *meter-

%#B2 'riction head loss in pipes &etween

points # and 2

't *'eet- m *meter-

5 atmospheric pressure head 't *'eet- m *meter-

)a )apor pressure head 't *'eet- m *meter-

p pressure psi *pound per squareinch-

(Pa *(iloPascal-

SG speci'ic gra)ityQ ratio o' the 'luiddensity to the density o' water atstandard conditions

nonBdimensional

NS Speci'ic speed

S Suction speci'ic speed

cp Speci'ic heat T?l&B% DJ?(gBC

Thoma ca)itation parameter nonBdimensional

q 'low rate gpm *gals.?min- ?min *liters?mi-

) )elocity 't?s *'eet?second- m?s *meter?second-

g acceleration due to gra)ity, 32.#9

't?s2't?s2*'eet?second

squared-

m?s2*meter?second

squared-8 vertical position 't *'eet- m *meter-

Table $1 Variable nomenclature.


26/41

Total head, N.P.S.. and other calculations!2/

Re+e-ence

#. Pump System 5nalysis and Centri'ugal Pump Si=ing &y J. Chaurette pu&lished &yhttp7??www.lightmypump.com?pump@&oo(.htm, January2003

2. Standards &y the ydraulic nstitute, New Jersey www.pumps.org

3. The Cameron ydraulic data &oo( &y ngersoll Rand
http://www.lightmypump.com/pump_book.htmhttp://www.lightmypump.com/pump_book.htm


27/41



28/41

Total head, N.P.S.. and other calculations!2+


29/41

Total head, N.P.S.. and other calculations!2E


30/41


Fi 4 9 t h d l ffi i t %


31/41


32/41



33/41



34/41



35/41

Total head, N.P.S.. and other calculations!3$


36/41

Total head, N.P.S.. and other calculations!3/


37/41



38/41

Total head, N.P.S.. and other calculations!3+

Figure 1 pecific speed values for the different pump designs.

%source: the !ydraulic "nstitute tandards book6 see www.pumps.org&


39/41

Total head, N.P.S.. and other calculations!3E

Figure 1 The Thoma number vs. specific speed and suction specific speed to predictcavitation %source: the 2ump !andbook6 -c


40/41



41/41

igure 14 The -oody diagram6 friction factor vs. 7eynolds number for laminar and turbulent flow at various pipe roughness*values.

calc example blank

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