20651432 Fluid Flow Student Guide for Operations Training

8/13/2019 20651432 Fluid Flow Student Guide for Operations Training

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OPERATIONS TRAINING PROGRAM

STUDENT TEXT

Rev. 0

FLUID FLOW


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NOTICE: If you plan to use this material in a classroom

setting, then please purchase the exam bank and answer key

from the cribd store for !"#$$ or %isit marathon&ohnb at

cribd# The exam is gi%en at the end of the course and has

specific 'uestions for each chapter#

(O) T)*ININ+ E ON-.

The uncontrolled information contained in these training

materials is FOR TRAINING USE ON!. In no "a#should it $e inter%reted that the material contained herein

ma# $e su$stituted for facilit# %rocedures or SO&s. 'hen

co%ies of SO&s or %rocedures are given( the# are intended

as e)am%les and information onl#( and the latest revisionof the material in *uestion should $e o$tained for actualuse. If #ou have an# *uestions( contact #our su%ervisor.

ii of )ii Rev. 0


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Contents:///

Table of Contents:

NOTICE: If you plan to use this material in a classroom setting, then please purchase

the exam bank and answer key from the cribd store for !"#$$ or %isit

marathon&ohnb at cribd# The exam is gi%en at the end of the course and has

specific 'uestions for each chapter##############################################################################ii

Contents:///##########################################################################################################################iii

Chapter 0 INT)O1CTION TO (-I1######################################################################02

Introduction ###########################################################################################################################################02

1escription of (luids##############################################################################################################################03

4umidity#################################################################################################################################################0"

)elati%e 4umidity##################################################################################################################################0"

1ensity 56 and pecific 7olume 56#########################################################################################################0"

1ensity 1ifferences for Non/8ixable 5Non/8iscible6 (luids#############################################################09

pecific +ra%ity######################################################################################################################################0

;ressure 5p6 ############################################################################################################################################20

;ressure 8easurements#########################################################################################################################23

*bsolute, +age, and 7acuum ;ressure )elations###############################################################################3s ;rinciple#######################################################################################$2

(igure A/"< ;ing ;ong =all (loating in *ir tream#########################################################$3

(igure A/"0 *ir ;assing *bo%e and =elow *irplane @ing #############################################$3

(igure A/"2 *ir ;assing by a Thrown =aseball################################################################$"

(igure ?/"3 ;ipe ection with a )eduction in *rea########################################################0


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(igure /9< ;ressure 1rop and (luid (riction###############################################################00"

(igure /90 Energy Con%ersions in a Closed ystem#####################################################00?

(igure /92 * imple Closed -oop ystem#####################################################################00$

(igure /93 Closed -oop Example###################################################################################00$

(igure /9" ;ressure is ;roportional to Column 4eight###############################################02 of @0 Rev. 0

5ensities of Some 1ommon ,aterials+

,aterial5ensit#( gcm

helium/ ) 0

=3

air.< ) 0

= sho"s a t#%ical $ello"s t#%e

%ressure detector.

Other t#%es of %ressure detectors use

similar arrangements to measure the

difference $et"een an un2no"n %ressure

and the reference %ressure. &ressure

&age /3 of @0 Rev. 0

T.;IC*- ;)E,)E +*+E

,EASURE5 &RESSURE

4EO'

REFEREN1E

&RESSURE

IN5I1ATE5 P

I5IFFEREN1E 4ET'EE

,EASURE5 &R ESSURREFEREN1E&RESSURE and

(igure 0/9 Typical ;ressure +age

(igure 0/" ;ressure cales


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PERATI-S TRAI-I-. PR.RAMStudent .uide/ Fluid Flow Cha$ter 0/ Introduction to Fluids

gages referenced to atmos%heric %ressure indicate the amount of %ressure a$ove or $elo" atmos%heric

%ressure. The units for these %ressure gages are %sig 7l$fin/gage: for %ressure a$ove atmos%heric and

%siv 7l$fin/vacuum: for %ressure or vacuum $elo" atmos%heric.

Finall#( %ressures and

vacuums ma# $e e)%ressed

in terms of the height of a

li*uid column the %ressure

"ill su%%ort. These include

inches of "ater( feet of

"ater( and inches of

mercur#. ,illimeters of

mercur# is also a common

unit for measuring %ressure.

,illimeters of mercur# isalso given the name torr.

One torr e*uals one

millimeter of mercur#.

Figure .C sho"s thatatmos%heric %ressure at sea level( 3.@ %sia( "ould su%%ort a mercur# column /8.8/ inches high or a

"ater column


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atm @C0 torr

atm 0 0>. &aTable 0/3 Common ;ressure nits

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The follo"ing e)am%les utilie common %ressure units+

a. 1onvert 3.0 %sia to inches of "ater.

= 388.571 in H2O

$. 1onvert 3.@ in of -/O to %sia:

= 0.5296 psia

c. 1onvert >0 in -g to in of -/O+

= 682 in H20

d. 1onvert . Pa760 torr 1 atm

50 in Hg 1 atm 408 in H2O

29.92 in Hg 1 atm

14.7 in H2O 1 atm 14.7 psia

408 in H2O 1atm

14.0 psia 1 atm 408 in H20

14.7 psi 1 atm


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Referring to Table 1-3, estimate the following values. Then, using note paper (if needed), calculate each

value in the assigned units.

!amples' >answers on the following page?

a. 1onvert /@ %si+

Estimate Calculate

in H2O in H2O

in Hg in Hg

mm Hg mm Hg

torr torr

Pa Pa

$. 1onvert C %si+

Estimate Calculate

in H2O in H2O

in Hg in Hg

mm Hg mm Hg

torr torr

Pa Pa

d. 1onvert 3>> in -/O+

Estimate Calculate

in Hg in Hg

mm Hg mm Hg

psi psi

torr torr

Pa Pa

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+nswers-

a. 1onvert /@ %si+

Estimate 1alculate

a$out @>0 in -/O @38.> in -g >3.8>> in -g

a$out 300 mm -g (.893 mm -g

a$out 300 torr (.893 torr

a$out /)0>&a .9>>)0

>&a

$. 1onvert /C< in -/O

a$out 3 in -g &a 0.3>9)0

>&a

c. 1onvert />C %si+

Estimate 1alculate

a$out @000 in -/O @0>.00 in -g >/.0>>9 in -g

a$out


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*bsolute, +age, and 7acuum ;ressure )elations

A 2e# to understanding %ressure measuring is to understand "here these measurements originated. Gage

%ressure is the normal "a# the $od# o%erates. Though there is atmos%heric %ressure on the $od# the $od#

ignores itD so also "ith gage %ressure. ,ost o%erations can $e %erformed successfull# ignoring

atmos%heric %ressure so man# gages read in gage %ressure.J

1onverting a measurement of ero %si gage %ressure is e*ual to a measurement of 3.@ %si a$solute.Al"a#s add 3.@ %si to change gage %ressure to a$solute %ressure. Su$tract 3.@ %si to convert a$solute

%ressure to gage %ressure.

A %um% does "or2 to %ut a %ressure on the fluids in a %i%ing s#stem( $ut ma# also $e re*uired to %roduce

a vacuum to lift a fluid so the it ma# $e %um%ed. The %ressure %ushing the fluid is "or2 and the vacuum

lift is also "or2D $oth must $e done $# the %um%. 4oth of these are seen as %ositive amounts of "or2

%erformed $# the %um%. ?acuum lift is considered to $e a %ositive amount and the vacuum gage reads

%ositivel# under almost all situations.

Al"a#s convert gage %ressure to vacuum %ressure 7and vice versa: $# ta2ing the same amount of %ressureand reverse the sign 7i.e. from %ositive to negative or negative to %ositive:.

E*uations give the relationshi% $et"een a$solute %ressure( gage %ressure( and vacuum %ressure. 'e can

convert them using these e*uations. A$solute %ressure 7%sia: is e*ual to the atmos%heric %ressure 7%sia:

%lus the gage %ressure 7%sig:+

$a*solute2 $atm8 $"a"e

Absolute pressure (psia) is equal to atmospheric pressure (psia) minus vacuum pressure (psiv):

$a*solute2 $atm# $ac

Vacuum pressure is normally used for pressures below one atmosphere where it is a positive reading.

Vacuum pressure starts with zero at one atmosphere and reaches its maximum value of 14.7 psiv at a

perfect vacuum where absolute pressure is zero. The relationship between absolute pressure, gage

pressure and vacuum pressure is illustrated in Table 1-4.

Absolute Pressure Gage Pressure Vacuum Pressure

19.7 psia 5 psig Not Normally Used

14.7 psia 0 psig 0 psiv

0 psia -14.7 psig 14.7 psiv

Table 0/" *bsolute, +age and 7acuum ;ressure

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Example:

The %ressure indicated is /> %sig. 1alculate the a$solute %ressure.

$a$soluteM$atmP$gage

$a$soluteM 3.@ %sia P /> %sig$a$soluteM %sia. 1alculate the gage %ressure.

$a$solute M$atmP$gage$a$solute Q$atmM$atmQ$atmP$gage

$gage M$a$soluteQ$atm

$gageM /> %sia Q 3.@ %sia$gageM 0.< %sig

Example:

The %ressure indicated is /.> %siv. 1alculate the a$solute %ressure.

$a$soluteM$atm=$vac$a$soluteM 3.@ %sia = /.> %sig

$a$soluteM /./ %sia

Example:

The %ressure indicated is 0 %sia. 1alculate the vacuum %ressure.

$a$soluteM$atm=$vac$a$soluteP$vacM$atm=$vac P$vac$a$solute=$a$soluteP$vacM$atm=$a$solute$vacM$atm=$a$solute$vacM 3.@ %sia = 0 %sia$vacM 3.@ %siv

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Example:

The %ressure indicated is @> %sig. 1onvert the %ressure to torr.

Notice that torr is an a$solute %ressure. In order to do this conversion "e must first convert %sig to %sia.

Once the %ressure is converted to %sia it is in an a$solute scale and can $e converted to torr

$a$soluteM$atmP$gage$a$soluteM 3.@ %sia P @> %sig

$a$soluteM 98.@ %sia

M 3(C in of -/O. 1alculate the vacuum %ressure.

$a$soluteM$atm=$vac$a$soluteP$vacM$atm=$vac P$vac$a$solute=$a$soluteP$vacM$atm=$a$solute$vacM$atmQ$a$solute

=2.702 psia

$vacM 3.@ %sia = /.@0/ %sia

$vacM .889 %siv

=uoyancy

4uo#anc# is defined as the u%"ard force on an immersed o$ect. 'e have all o$served the $uo#ant

effects of a li*uid( $ut $uo#anc# also e)ists for gases. 'hen "e go s"imming( our $odies are held u% $#

the "ater. 'ood( ice( and cor2 float on "ater. 'hen "e lift a roc2 from a stream $ed( it suddenl# seems

heavier on emerging from the "ater $ecause it has $een $uo#ed u% "hile $eing su$merged in a fluid.

4oats rel# on this $uo#ant force to sta# afloat. A $alloon filled "ith a light gas rises in air( a heavier gas.

This $uo#ant force occurs $ecause there is a %ressure inside of a fluid that e)erts a force on an# $od#touching that fluid. This fact causes the u%"ard force on the $ottom of a su$merged o$ect to $e greater

than the do"n"ard force on its to% surface. The amount of this $uo#ant effect "as first com%uted and

stated $# the Gree2 %hiloso%her Archimedes.

Archimedes found( "hen he got into his $ath tu$ "hich "as filled "ith "ater to the rim( that "ater "as

dis%laced out of the tu$ and onto the floor. -e calculated that the volume of "ater dis%laced "as e*ual to

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the volume of his $od#. From these findings he determined that an# $od# com%letel# or %artiall#

su$merged in a fluid is $uo#ed u% 7%ushed u%: $# a force e*ual to the "eight of the amount 7volume: offluid dis%laced $# the $od#.J This is 2no"n as+rchimedes0 *rinciple.

If a $od# "eighs more than the li*uid it dis%laces( it sin2s $ut "ill a%%ear to lose an amount of "eight

e*ual to that of the dis%laced li*uid( as our roc2. If the $od# "eighs less than that of the dis%laced li*uid(the $od# "ill rise to the surface eventuall# floating at such a de%th that "ill dis%lace a volume of li*uid

"hose "eight "ill ust e*ual its o"n "eight. A floating $od# dis%laces its o"n "eight of the fluid in

"hich it floats.

If a diverKs $od# and diving e*ui%ment e*uals the "eight of the "ater that is dis%laced the diver hangs

sus%ended at an# location or de%th li2e a fish. If a diver and e*ui%ment "eigh less than the "ater

dis%laced the diver has a hard time su$merging and $o$s a$out on the surface li2e a $oat. 'ith a total

"eight of more than the "eight of the "ater dis%laced( a diver sin2s to the $ottom.

See Figure .@. A cu$ic foot of "ater "eighs C/.3 %ounds( and if a one %ound $all dis%laces a cu$ic footof "ater a %erson using the $all to aid them in floating is also $uo#ed u%. The more li*uid the $all

dis%laces the greater the amount of force e)erted on the s"immer. 'hen the $all is totall# su$merged it"ill e)ert an u%"ard force of C/.3 %ounds and "ith its o"n "eight of one %ound of force do"n"ard

canceling one of those %ounds "ill e)ert a force of C.3 %ounds u%"ard. This is true of an# immersedo$ect that dis%laces a cu$ic foot of li*uid.

Ever# $oat is s%ecificall# designed to dis%lace the amount of fluid "eight that is

e*ual to or greater than its o"n "eight.

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4ydrostatic ;ressure

An#one "ho dives under the surface of the "ater notices that the %ressure on their eardrums at a de%th of

even a fe" feet is *uite noticea$le and increases "ith de%th. ,easurements have sho"n that the

h#drostatic 7h#droJ M "ater( staticJ M non=movingD therefore+ h#drostatic M non=moving "aterJ :

%ressure "ithin a li*uid increases directl# "ith the de%th of the li*uid. The %ressure at an# de%th is thesame in all directions. A li*uid molecule does not move "hen the %ressure is the same( $ut sta#s in one

s%ot until a difference in%ressure causes it to move

a"a# from the higher %ressure

region to"ard the lo"er

%ressure region.

Figure .9 illustrates the

relationshi% $et"een li*uid

level and %ressure. If holes

are %laced in the tan2( the

li*uid in the tan2 "ill lea2 out.The lo"er in the tan2 the hole

is %laced( the greater the

velocit# of the li*uid as it

lea2s from the tan2 due to the

increased %ressure. The holes are 2no"n as deliver# %oints.J The greater the de%th( the greater the

%ressure and the greater the s%eed and volume of the li*uid flo"ing out of the tan2.

P total= P atmospheric+ PelevationP total= P atmospheric+ gz

The total %ressure measured at the $ottom of the tan2 is due to the %ressure of the atmos%here 73.@ %si at

sea level: %lus the %ressure due to the height of molecules stac2ed one a$ove another in the tan2. This

last %ressure is due to $oth the densit# 7 : of the li*uid( gravitational %ull of the earth on ever# molecule7g:( and the height of the stac2 of molecules in the tan2 7:. 7hJ re%resents several other %ro%erties so "e

use J to re%resent height.:

Oftentimes it is necessar# to o$tain the li*uid level in a vessel $# the e*uivalent %ressure that is measured.

A di%tu$e( 7a hollo" tu$e usuall# constructed of metal:( is inserted do"n the entire measura$le de%th ofthe vessel. The di%tu$e is onl# a fraction of the diameter of the vessel in "hich the %ressure is measured.

The actual diameter of the di$tu$e or of the vessel itself is not needed. The height of the li*uid in the

vessel( and an# %ressure that is e)erted on to% of the li*uid is the onl# re*uired %arameter to o$tain the

vessel level. The follo"ing e)am%le hel%s e)%lain "h# the tu$e siing 7or tu$e diameter: is not im%ortant

and does not effect the measurement.

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Example:

Recall that %ressure is the measure of an a%%lied force of a given area.

A

"V

A

m"

Area

'ei"ht

Area

Forceessure

====&r

where: hAV =

The volume is e*ual to the cross=sectional area 7A: times the height 7h: of li*uid.

Su$stituting this into the a$ove e*uation #ields+

h"A

"hA

A

"Vessure

=

== :7

&r

The a$ove e*uation tells us that the %ressure e)erted $# a column of "ater is directl# %ro%ortional to the

height of the column and the densit# of the "ater and is inde%endent of the cross=sectional area of the

column.

The pressure thirty feet below the surface of a one inch diameter standpipe is the same as the

pressure thirty feet below the surface of a large lakeL

Notice the vertical column of "ater sho"n on the left side in Figure .8 that e)tends from the $ottom of

the tan2. This column rises almost to the


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tatic headis the measure of the vertical distance from the "ater surface to the deliver# %oint and thisdistance has a direct relationshi% to the %ressure caused $# the "eight of "ater e)tending a$ove that %oint.

The calculations of the %ressure at 0 ft( /0 ft(and


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This is an alge$ra %ro$lem that can $e solved $# multi%l#ing $oth sides of the e*uation

$# the same num$er in the attem%t to eliminate ever#thing on the right side of thee*uation e)ce%t for

Solving for +

1anceling li2e=num$ers and li2e=units 7dimensions: in numerators and denominators

have+

So at 3.@ %si 7one atmos%here of %ressure: there is an e*uivalent de%th of li*uid of


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Example:

Using Figure 1-11, Fill in the table below: (answers are on the following page)

M depth Estimated

psig

Calculated

psig

Estimated

psia

Calculated

psia

< ft .< %sig C %sia

/ 0 ft

C C ft

@ @ ft

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PERATI-S TRAI-I-. PR.RAM

Student .uide/ Fluid Flow Cha$ter 0/ Introduction to Fluids

Answers to head and $ressure illustration/

M depth Estimated

psig

Calculated

psig

Estimated

psia

Calculated

psia

< ft a$out .> %sig .< %sig a$out C.> %sia C %sia

/ 0 ft a$out 3.> %sig 3. 3 ft a$out C %sig C.0C %sig a$out / %sia /0.@C %sia

C C ft a$out @ %sig C.8< %sig a$out /.@ %sia /.C< %sia

@ @ ft a$out < %sig s -aw 5the law of hydraulics6

4ecause li*uids are essentiall# incom%ressi$le( "hen "e %ressurie a li*uid( its densit# does not change.

In Figure ./( "e a%%l# a force F to the %iston on a confined li*uid. This results in an increase of

%ressure throughout the li*uid. This %ressure increase is the same ever#"here in the li*uid. &ascal6s

%rinci%le sa#s+

The pressure applied to a fluid confined in a container is transmitted undiminished throughout the

fluid and acts in all directions#

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Conditions and Results:

a %ressure is a%%lied to a fluid the fluid is enclosed the %ressure is transmitted "ithout loss the %ressure is measured the same in ever# direction the fluid and the "alls of the vessel receive the same measure of %ressure

This %rinci%le a%%lies to all li*uids and to man# gas=filled s#stems as "ell. It is the fundamental %rinci%le

of h#draulics( and is im%ortant for a%%lications in h#draulics( such as h#draulic valve o%erators or

h#draulic ac2s. This %rinci%le is also im%ortant in maintaining a static %ressure on a totall#contained

s#stem. uite often( an e)ternal %ressure is a%%lied to a s#stem to maintain the entire s#stem at a

minimum %ressure. 7e)am%les+ a %ressurier that hel%s to sto% cavitation $# increasing the %ressure in an

enclosed loo%( or a storage tan2 "ith a $ag 7$alloon: that maintains the %ressure on a "ater s#stem "hen

the %um% is tem%oraril# off.:

A force a%%lied to even a ver# small surface area is transmitted at the s%eed of sound 7s%eed of %ressure in

a fluid: throughout the fluid.

An# e*ual area an#"here "ithin the fluid "ill feelJ the same amount of force over its surface.

Referring to Figure =


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Example:

The h#draulic s#stem in Figure .3 consists of a small %iston at A( a large %iston at 4( and a

fluid=filled reservoir connecting the t"o c#linders.

The area of %iston A is in/( and the area of %iston 4 is ft

/. If "e a%%l# a force of 30 l$fto the

to% of %iston A( ho" much force can "e generate at %iston 4H

Pascal;s $rinci$le says that the

$ressure at A$Ais e7ual to the

$ressure at


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Gravit# and &um%s $oth %rovide -eadJ or &ressure

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Chapter 0 ummary

pecific %olume= amount of s%ace occu%ied $# unit of mass. =V

m or =

1

1ensity= amount of mass in a unit of volume. =m

Vor =

1

pecific gra%ity= the ratio of the densit# of a fluid to the densit# of a standard fluid

SG=liquidwater

and SG=gasair

T"o non=mi)a$le 7non=misci$le: fluids "ill se%arate "hen %laced in the same container. The fluid "ith

the highest densit# "ill sin2 to the $ottom.

&ressure is a force acting over an area.

$ 2F

A

atm M 3.@ %sia

atm M 309 in. of - O

atm M /8.8/ in -g

atm M @C0 mm -g

atm M @C0 torr

atm M &a

$a$sM$atmP$gage$a$sM$atm=$vac

From these findings he determined that an# $od# com%letel# or %artiall# su$merged in a fluid is $uo#ed

u% 7%ushed u%: $# a force e*ual to the "eight of the amount 7volume: of fluid dis%laced $# the $od#.J

This is 2no"n asArchimedes= Princi$le%

=uoyancyis the u%"ard force on an immersed o$ect.

The pressure of a liquid is directly proportional to the depth of the liquid. The area of a container of

liquid has no effect on the pressure; the depth and density of the liquid determines the pressure at the

bottom of the container.

Head is a measure of pressure in units of feet since it defines the depth at which a pressure is measured.

When converting pressure units change first to number of atmospheres.

&ascal6s la" states in effect that a %ressure a%%lied to a contained fluid is transmitted "ithout decreasing

throughout the container. It is e)%erienced $oth in the fluid as "ell as u%on the "alls of the container no

matter in "hat direction the measurement is ta2en.

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PERATI-S TRAI-I-. PR.RAMStudent .uide/ Fluid Flow Cha$ter 4/ Com$ression of Fluids

Chapter 2 Compression of (luids

Com$ressi*ility is the measure of the chan"e in olume a su*stance under"oes when a $ressure is e>erted

on the su*stance% This cha$ter coers the fundamental conce$ts of the Com*ined Ideal .as ?aw

and the com$ressi*ility and incom$ressi*ility of fluids%

TO 2#< Given the necessary fluid system parameters and using theombined %deal Gas Law, #!S7%9! the compressibility or

incompressibility of a fluid when a pressure is eerted

!O (." ST+T! the ombined %deal Gas Law

!O (.( SOL! for fluid parameter using the ombined %deal Gas Law

!O (. #!S7%9! when a fluid may be considered to be

incompressible

!O (.2 #!S7%9! the effects of a pressure or temperature change on

a confined fluid

!O (.5 !)*L+%& how to prevent over pressuri@ation accidents caused

by gas or li1uid confinement.

Compressibility

1om%ressi$ilit# is the measure of the change in volume a su$stance undergoes "hen a %ressure is e)erted

on the su$stance. i*uids are generall# considered to $e incom%ressi$le. For instance( a %ressure of

C(300 %sig "ill cause a given volume of "ater to decrease $# onl# > from its volume at atmos%heric

%ressure. Gases on the other hand( are ver# com%ressi$le. The volume of a gas can $e readil# changed

$# e)erting an e)ternal %ressure on the gas

The Combined +as -aw

The com$ined gas la" relates to the %ro%erties of a 7non=e)istent: so=called idealor$erfect "as. An ideal

gas has the same %ro%erties at ever# %oint throughout its mass and is not influenced $# chemical or

e)ternal forces. To $e mathematicall# correct( the com$ined gas la" can onl# $e used on gases of lo"

densities that do not undergo a change to solids or to li*uids. In addition( a$solute tem%eratures and

%ressures must al"a#s $e used during these calculations or the calculations "ill $e incorrect. 7See

e)am%le on follo"ing %age:

The com$ined gas la"( as its name im%lies( is a com$ination of t"o la"s of nature o$served $# the

%h#sicists( 1harles and 4o#le. 1harles determined that at constant lo" %ressures( the volume of a gas( V(is directl# %ro%ortional to the a$solute tem%erature( T( of the gas. At an# time the ratio of volume toa$solute tem%erature remains the same(


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Student .uide/ Fluid Flow Cha$ter 4/ Com$ression of Fluids

V1

T1=

V2

T2(

"hereV

1 andT

1are the initial volume and a$solute tem%erature( andV

2 andT

2 are the final volumeand a$solute tem%erature.

4o#le determined that at lo" %ressures the %roduct of volume and %ressure of constant tem%erature gas is

al"a#s the same.

P1V1= P2V2

These t"o la"s are com$ined to $e stated as+

$or a given mass of any gas, the product of the absolute pressure and volume occupied by the gas,divided by its absolute temperature, is a constant.

1om$ined Gas a"+ a constantJ.

'here+

&M initial a$solute %ressure(

?M initial volume

TM initial a$solute tem%erature( in a$solute terms R or

L 7degrees Ran2ine( or Lelvin :

&/M final a$solute %ressure

?/M final volume

T/M final a$solute tem%erature( R or L

This means that the ratio of a$solute %ressure times volume "hen com%ared to a$solute tem%erature

al"a#s #ields a num$er that does not change. The ratio does not change "ith an# change in an# varia$le.

Example:

9usin" the En"lish System in de"rees Ran(ine:

30F air is charged into a tan2 until its %ressure is C0 %sia 7%siaJ is the designation for a$solute

%ressure:. Over the course of the da# the air tem%erature cools so the gas in the tan2 slo"s do"n(

has less energ# and therefore e)erts less %ressure on the "alls of the tan2 as time goes on. 'hat"ill $e the tem%erature of the air( in degrees Fahrenheit( "hen the %ressure in the tan2 reaches

>0 %siaH Assume no air is added or removed from the tan2 during this time.


47/180



olution:

The ratio of the a$solute &ressure times ?olume divided $# the a$solute Tem%erature is an

unchanging constant num$er for a s%ecific gas that sa#s that the ratio at an# time "ill $e e*ual to

the ratio at an# other time for the same gas.

The com$ined gas la" is+P1V1

T1=

P2V2

T2= 1onstant(

and "e can choose to eliminate the M 1onstantJ %art of the e)%ression.

To ma2e things even sim%ler( the tan2 volume is constant( so ?and ?/are e*ual. This allo"s us

to see that ?and ?/are constant and ma# $e eliminated from the e*uation( allo"ing us to "rite

the e*uation as+P1

T1=

P2

T2

T/"ill $e the final tem%erature and Tthe initial tem%erature. 'e then decide to solve the

e*uation for final tem%erature T/+ T2=T1P2

P1.

1onverting the initial tem%erature to a$solute+ 7add 3C0F to an# Fahrenheit tem%erature to ma2e

it Ran2ine= a$solute:

TM 3C0 P 30F M C00R

Su$stitute and solve for final tem%erature+

T2=

(600 R)(150psi)

160psi =562.5

R

1onverting $ac2 to F+ T2= 562.5R 460 F= 102.5 F

Effects of ;ressure Changes on Confined (luids

Fluids ma# $e classified as com%ressi$le or incom%ressi$le. Gases are highl# com%ressi$le. A fluid is

considered incom%ressi$le "hen it is a li*uid( $ecause its volume and densit# remain essentiall# constant"ith changes in %ressure. It is this incom%ressi$ilit# that allo"s a h#draulic s#stem to o%erate.

Although li*uids are generall# considered to $e incom%ressi$le( in realit#( li*uids reall# do com%ress( $ut

the# com%ress so little that the# are still considered to $e incom%ressi$leJ. A ver# large %ressure must

$e a%%lied to see a significant change in volume and densit#. For e)am%le( a %ressure of C(300 %si "ill

cause a volume of "ater to decrease $# onl# > %ercent from its volume at atmos%heric %ressure. The fact

that li*uids donKt com%ress can have significance in our o%erations. For e)am%le( if "e enclosed a tan2

and fill it "ith "ater "ithout venting it "e can e)ceed %ressure limits %ossi$l# to the %oint of ru%turing

the tan2( valves( or vents. @orst Case Expected+ &ressure U% = -#draulic $ursting &ressure 5o"n Q

crum%le the tan2( or 7if the fluid %laced in the container is hot: u%on release of %ressure an e)%losion.


48/180



Gases( on the other hand( are ver# com%ressi$le. If a fluid increases its densit# significantl# "hen

%ressure is a%%lied( then the fluid is considered com%ressi$le. This occurs "ith fluids of ver# lo"

densities( such as gases. The volume of a gas can $e readil# changed $# a%%l#ing an e)ternal %ressure on

the gas. Gases ma# $e com%ressed until the# $ecome li*uids $ut at that %oint further attem%ts to reduce

volume ma# have catastro%hic results. @orst Case Expected+ &ressure U% Q Tan2 $ecomes a roc2et( or

e)%losion &ressure 5o"n Q 1rum%le the tan2 7im%losion:.

Gasses are 1O,&RESSI4E.

i*uids are IN1O,&RESSI4E.

If "e %ut %ressure on them and the# canKt flo" a"a# the# ma# $urst the confining vessel

Effects of Temperature Changes on Confined (luids

An increase in temperature will tend to decrease the density of many fluids as the molecules become more

active and bump into each other more often driving the molecules further away from one another. If

the fluid is confined within a container of fixed volume, the effect of a temperature change will depend on

the compressible nature of the fluid.

If the fluid in a closed container is a com%ressi$leJ gas( it "ill res%ond to a tem%erature change in the

same manner %redicted $# the ideal gas la". A > %ercent increase in a$solute tem%erature "ill cause a

corres%onding > %ercent increase in a$solute %ressureD a > %ercent decrease in a$solute tem%erature "ill

cause a corres%onding > %ercent decrease in a$solute %ressure.

@orst Case Expected+ Tem%erature U% Q Tan2 $ecomes a roc2et( or e)%losion Tem%erature

5o"n Q 1rum%le the tan2 7im%losion:.

If the fluid is an incom%ressi$leJ li*uid in a closed container( changes in tem%erature cause a much more

dramatic effect. If a container is filled "ith a li*uid as the tem%erature increases the li*uid attem%ts to

e)%and and change into a gas 7a decrease in densit#:. Since the li*uid is confined "ithin the container(

the "alls of the container are $um%ed into more oftenJ so %ressure increases. This results in a

tremendous increase in %ressure for a relativel# minor increase in tem%erature. This has a greater

%otential of causing an e)%losion.

@orst Case Expected+ Tem%erature U% Q Tan2 $ecomes a roc2et( or e)%losion( or $urst tan2 Tem%erature 5o"n Q Freee( and if "ater+ $urst tan2 since "ater e)%ands u%on freeing:

(illing and 7enting

&ro%er filling and venting techni*ues can %revent serious %ro$lems caused $# gas tra%%ed in closed

s#stems "hich ma# degrade s#stem %erformance. Air in %um%s can cause gas $inding. Air in heat

e)changers reduces the heat transfer ca%a$ilit# $ecause air effectivel# creates an insulation $arrier. Tan2

e)%losions ma# occur "ith over %ressuriation. A steam incident death at -anford could have $een

%revented if the o%erator had $een a$le to use %ro%er steam line drainingventing measures.


49/180



Gas and li*uid filled tan2s and lines are %ressure tested $# filling "ith cold li*uid onl#( since an h#draulic

over %ressuriation "ill sim%l# $urst the container. If a hot li*uid or a gas "ere used the container might

e)%lode and the e)%anding gas released might %ro%el shra%nel on the e)%anding "ave front at a rate faster

than the s%eed of sound.

'hen to $e 1oncerned

(illing a closed li'uid filled systemP pre%iously drained:

Over=%ressuriation accidents ma# $e eliminated $# o%ening high %oint vents to allo" gas to $e

forced from the s#stem. 'hen a stead# stream of li*uid issues from the vents( the high %oints are

then closed. After filling a s#stem( the %um% ma# $e ogged to circulate the li*uid for a fe"

seconds to attem%t to move gas in the lines to the high %oints "here the vents are again o%ened to

release an# gas that ma# have $een tra%%ed. 7See a%%endi)D 1ro"der e)%eriences:

1raining a closed li'uid filled system:

It is also im%ortant to o%en vent valves to allo" gas to enter "hen draining a s#stem. If ventvalves are not o%ened( all the li*uid ma# not $e a$le to drain from the s#stem. ater during

maintenance activities the tra%%ed and %erha%s heated or contaminated li*uid ma# $e released and

cause harm to %eo%le and e*ui%ment.

4eating a closed li'uid filled system:

If a confined li*uid is heated it "ill attem%t to e)%and and %ressure "ill $uild ver# ra%idl#. If

%ressure e)ceeds the limits of the "ea2est %ortion of the containment s#stem it "ill ru%ture or

e)%lode violentl#. Safet# or relief valves must $e maintained in %ro%er o%erating condition to

%rotect the s#stem.

Cooling and confining an open li'uid/filled system:

An o%en s#stem containing a heated li*uid "hich is then confined and cooled ma# also e)ceed

design limits and $# de%ressuriation cause the s#stem to im%lode. Also draining a 0(000 gallon

tan2 "ith the vents closed can *uic2l# turned it into a


50/180



Fluctuating flo" rates

Fluctuating motor currents

Increased noise levels

E)cessive e*ui%ment vi$ration

-igher than normal heat e)changer tem%eratures 7air $lan2et causing decease in

heat transfer: 4u$$les %resent in sight flo" indicators

Increasing levels in surge tan2s 7as li*uid is dis%laced $# gas:


51/180


52/180



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53/180

PERATI-S TRAI-I-. PR.RAMStudent .uide/ Fluid Flow Cha$ter 1/ -atural Circulation Flow

Chapter 3 N*T)*- CI)C-*TION (-O@

It is $ossi*le to desi"n some fluid systems in a manner that does not re7uire the $resence of $um$s to

$roide circulation% This cha$ter descri*es the mechanism for natural circulation flow of a fluid

TO 3#< $or any natural circulation fluid system, #!S7%9! themechanism that allows for fluid flow

!O ." L%ST the conditions necessary for natural circulation to occur

!O .( !)*L+%& how fluid flows in natural circulation fluid systems

Natural Circulation

The head 7or %ressure: re*uired to com%ensate for the head losses is created $# densit# gradients and

elevation changes. Flo" that occurs under these circumstances is called natural circulation. Natural

circulation is circulation of a fluid "ithout the use of mechanical devices( such as %um%s. The driving

force for natural circulation flo" is the difference in densit# $et"een t"o $odies or areas of fluid.

Thermal driin" head is the force that causes natural circulation to ta2e %lace. It is caused $# the

difference in densit# $et"een t"o $odies or areas of fluid. In the figure $elo" this force causing the

$alloon to rise is a result of a difference in densit# $et"een the hot air inside the $alloon and the cooler air

surrounding it. This is an e)am%le of *uoyancy.

-eat added to the air in the $alloon ma2es it less dense or lighter than the surrounding air. Since the air in

the $alloon is less dense( gravit# has less effect on it. The result is that the gas in the $alloon "eighs less

than the surrounding air. Gravit# tends to %ull cooler air do"n into the s%ace occu%ied $# the $alloon.

W ar m A ir

Co ld Air Co ld Air

(igure 3/09 *ir =aloon =uoyancy


54/180


Student .uide/ Fluid Flow Cha$ter 1/ -atural Circulation Flow

This do"n"ard movement of cooler air ma# force the $alloon out of the s%ace it occu%ied and the $alloon

ma# rise if the "eight of the material of the $alloon is light enough. i2e a $u$$le in "ater the gas

$u$$le 7$alloon: tends also to rise in air.

Conditions )e'uired (or Natural Circulation

Natural circulation "ill onl# occur if the correct conditions e)ist. Even after natural circulation $egins(

removal of an# one of these conditions "ill sto% natural circulation. The conditions for natural circulation

are+

Tem%erature difference 7-eat sin2M"here the heat goesD -eat sourceM"here the heat comes from: -eight difference Fluids are in contact "ith each other

There must $e t"o $odies of fluid at different tem%eratures. This could also $e one $od# of fluid "ith

areas of different tem%eratures. The difference in tem%erature is necessar# to cause a densit# difference

in the fluid. The densit# difference is the driving force for natural circulation flo".

The difference in tem%erature must $e maintained for the natural circulation to continue. Addition of heat

$# a heat source must e)ist at the high tem%erature area. 1ontinuous removal of heat $# a heat sin2 must

e)ist at the lo" tem%erature area. Other"ise( the tem%eratures "ould e*ualie and no further circulation

"ould occur.

The "arm area must $e at a lo"er elevation than the cool area. As seen $# the e)am%les of the $alloon

and the closed loo%( a "armer fluid is less dense and "ill tend to rise and a cooler fluid is more dense and

"ill tend to sin2. To ta2e advantage of the natural movement of "arm and cool fluids( the heat source

and heat sin2 must $e at the %ro%er elevations.

Hot air rises

Cooler air

Ele%ation

(igure 3/0A 4eat ource G 4eat ink


55/180



The hot and cold areas must $e in contact so that flo" $et"een the areas is %ossi$le. If the flo" %ath is

o$structed or $loc2ed( then natural circulation cannot occur. A va%or $u$$le ma# $e caught at one %oint

causing a va%or loc2 7"here a gas $u$$le is created at a hot s%ot and sto%s the li*uid from "hich it "as

created from flo"ing:( or a valve ma# $e closed.


56/180



Chapter 3 ummary

Natural circulation flo" is the circulation of a fluid "ithout the use of mechanical devices 7i.e. %um%s.

etc.:.

The driving force for natural circulation is the difference in the densities $et"een t"o $odies or la#ers of

fluid.

For natural circulation to occur the s#stem must have all the follo"ing conditions+

Tem%erature difference 7causing densit# difference:-eight difference 7heat source located $elo" the heat sin2 = cooling:

Fluids are in contact 7flo" %ath e)ists $et"een the "arm fluid and cold fluid:

Natural circulation "ill occur "ith the conditions state a$ove $ecause+

-otter fluids tend to $ecome less dense and rise

1older fluids tend to $ecome more dense and sin2


57/180

PERATI-S TRAI-I-. PR.RAMStudent .uide/ Fluid Flow Cha$ter 5/ Volumetric and Mass Flow Rate

Chapter " 7O-8ET)IC *N1 8* (-O@ )*TE

@nderstandin" the 7uantities measured *y the olumetric flow rate and mass flow rate is crucial to

understandin" other fluid flow to$ics% This cha$ter calculates the olumetric and mass flow rates

of fluids to determine arious fluid $arameters%

TO "#< /sing fluid system volumetric and mass flow rates, SOL! forunknown fluid parameters values to predict fluid system

characteristics

!O 2." #!$%&! the fluid flow terms ABass $low 7ate0 and

Aolumetric $low 7ate0 to include their typical units

!O 2.( Given the necessary fluid parameters, #!T!7B%&! the mass

flow rate or the volumetric flow rate of a given fluid system

!O 2. #!$%&! the fluid flow term ASteady-State0

!O 2.2 !)*L+%& the Law of onservation of Bass and !nergy as

pertains to a fluid flow system

!O 2.5 Given a steady-flow system, +**LC the ontinuity !1uation to

determine fluid system parameters

7olume 576

?olume is the amount of s%ace occu%ied $# a

fluid or an o$ect. ,athematicall#( volume is

the length of an o$ect times its cross=sectional

area. See Figure 3..

arealen"thV =

Fluids are usuall# in %i%es or c#lindrical tan2s.

'e "ill focus on c#linders. The area A of a

c#linder is+

A 2 r 2+

4 2

+

5

4

4 4

VOLUME

Space Occupied By A T!ee"Di#e$%i&$a' O()ec*

UNITS + LENGT, -UBED + I$ / 0* / #

!

'

1

Vrectan"le 2 l w h

Vcircle 2r h

(igure "/0? 7olume of an Ob&ect


58/180


The volume of a c#linder is+

V 2 l r 2 l+

4 2

l +

5

4

4 4

.

Example:

1onsider the follo"ing sections of %i%es+

In $oth of the a$ove %i%e sections( A of fig 3=/ and 4 of fig 3=


59/180


60/180


V 2 A

flo" flo"

'here+

V

M volumetric flo" rate( m


61/180


? M / feet in length ) < s*uare foot cross=sectional area e*uals C cu$ic feet of volume+

/ ft < ft/M C ft


62/180


Su$stituting values+

A 21

4

A 2B

5

A 2 %D33

4

4

4

ft

ft

ft

Su$stitute the values for area and fluid velocit# into the volumetric flo" rate formula+

V

M @.0C9C ft/> fts

Solve for volumetric flo" rate+

V

M .


63/180


So( mathematicall#+

7Area ?elocit#:

?olumetric Flo" Rate

'here+ V

M volumetric flo" rate( ft


64/180


Summation+

?olumetric flo" rate( V

MVolume

TimeD can ta2e four forms+

V

=V

t

V

=A

V

= 3.14 d

2

2

V

= 3.14r2

'here+

is volumetric flo" rate in cu$ic feet %er second

d is inner diameter of a %i%e in feet

r is inner radius of a %i%e in feet is fluid velocit# in feet %er second

7 is volume in cu$ic feet

t is time in seconds

* is area in s*uare feet

8ass, 1ensity, and pecific 7olume

,ass is the amount of matter in a su$stance. The densit# of a material relates mass to the volume it

occu%ies.

The amount of mass in a volume is determined $# multi%l#ing the densit# of the material times the

volume it occu%ies.


65/180


In e*uation form+

'here+m M mass in g( 2g( or l$m

M densit# in gcms ;rinciple

-ave #ou ever "ondered "h# a car6s converti$le to% $ulges u%"ard at high s%eeds or "h# smo2e goes u%

a chimne#H These are e)am%les of a %rinci%le discovered $# 5aniel 4ernoulli 7@00=@9/:. 4ernoulli6s%rinci%le sa#s that "here the velocit# of a fluid is high( the %ressure is lo"( and "here the velocit# is lo"(

the %ressure is high. 74ernoulli "as a S"iss mathematician "ho "as the first to stud# this %henomena in

@


93/180


Student .uide/ Fluid Flow Cha$ter 3/ Forms of Ener"y ) The .eneral Ener"yE7uation

Example:

A %ing %ong $all can $e made to float a$ove a $lo"ing et of air( see Figure C.


94/180


95/180



PE1+KE

1+FE

1+U

1+Q

in+W

in=PE

2+KE

2+FE

2+ U

2+Q

out+W

out

Sim%lification &rocess+

PE1+KE

1+FE

1+U

1+Q

in+W

in= PE

2+KE

2+FE

2+ U

2+Q

out+W

out

0 0

Note+ does not change from %oint one to %oint t"o( therefore it is the same and ma# $e

canceled out. This onl# occurs $ecause an ideal fluid has no viscosit# 7or friction:( therefore no

changeJ occurs in the internal energ# of the fluid.

PE1+KE

1+FE

1+U

1+Q

in+W

in= PE

2+KE

2+FE

2+ U

2+Q

out+W

out

0 0 0 0

independent of one another

Also 7$oth in and out: $ecomes ero for an ideal fluid. No heat is transferred to or from the

fluid. 7O%erators control real fluids $# o%erating heaters to add heat or $# o%erating heat

e)changers to ta2e heat out. Either action ma# ta2e %lace "ith or "ithout the other. An o%erator

can add heat "ithout ta2ing it out and vise versa.:

PE1+KE

1+FE

1+ U

1+Q

in+W

in= PE

2+KE

2+FE

2+ U

2+Q

out+W

out

0 0 0 0 0 0

independent of one anotherindependent of one another

Also @7$oth in and out: $ecomes ero for an ideal fluid. No "or2 is transferred to or from the

fluid. 7O%erators control real fluids $# o%erating com%ressors and %um%s to add "or2 or $#

o%erating tur$ines and %addle "heels to ta2e "or2 out. An o%erator can add "or2 "ithout ta2ing

it out and vise versa.:


96/180


97/180



pecific flow energy 7fe: is the flo" energ# %er unit of mass. It is e*ual to the total flo" energ# divided

$# the total mass. Since s%ecific volume 7 : is e*ual to total volume divided $# mass( s%ecific flo"energ# is e*ual to %ressure times the s%ecific volume.

fe=FE

m=

PV

m= P

'here+

fe M s%ecific flo" energ#ftlbf

lbm

FE M flo" energ# ft lbf( )

? M volume ft3( ) m M mass 7l$m:

& M %ressure lb f / ft2( ) M s%ecific volume ft3/lbm( )

Su$stituting e*uivalent e)%ressions after dividing $# the mass of the s#stem gives the s%ecific energ#

form of the e*uation.

gz1

gc+

v12

2gc+ P11=

gz2

gc+

v22

2gc+ P2 2

Sim%lified 4ernoulli6s E*uation=S%ecific Energ# form

Each term in the a$ove E*uation re%resents a form of energ# %ossessed $# a moving fluid 7%otential(

2inetic( and flo" related energies:. The e*uation %h#sicall# re%resents a $alance of the %otential( 2inetic(

and flo" energies so that if one form of energ# increases( one or more of the others "ill decrease to

com%ensate( and vice versa.


98/180



Chapter A ummary:

&otential energ# is the energ# a fluid %ossesses due to its height 7%osition: relative to other $odies.

Linetic energ# is the energ# a fluid %ossesses due to its %elocity.

Flo" energ# is the energ# a fluid %ossesses due to its pressure and volume.

Internal energ# is the energy of the moleculesof a fluid due to rotation( vi$ration( translational motion

and intermolecular attractions.

-eat and 'or2 are $oth outside in%uts %erformed $# an o%erator for the %ur%ose of increasing or

decreasing the four fluid energies listed a$oveD their use "ill $e discussed in greater de%th in the heattransfer course.

Rather than tal2 a$out the total energ# in the s#stem "e can then tal2 a$out the energ# in a single mass

unit of the fluid. 5ividing an energ# $# mass turns it into a specific energy#

The a" of 1onservation of ,ass and Energ# statesD Energ# can neither $e created nor destro#ed( onl#

altered in form.J This la" includes all energies in the universe.

The General Energ# E*uation includes onl# those energies %ertinent to conventional engineering %ractice(

and is an incom%lete mathematical e)%ression of the la" of conservation of mass and energ#+PE

1+KE

1+FE

1+ U

1+Q

in+W

in=PE

2+KE

2+FE

2+ U

2+Q

out+W

out

5ividing mass out of the General Energ# E*uation gives the s%ecific form of the General Energ#

E*uation+

pe1 +ke1+ fe1 + u1+ qin+ win= pe2+ke2+fe2+u2+qout +wout

All energ# has units of 4tuKs or Force times 5istance.


99/180

PERATI-S TRAI-I-. PR.RAMStudent .uide/ Fluid Flow Cha$ter / Ener"y Conersions in Ideal Fluid Systems

ENE)+. CON7E)ION IN I1E*- (-I1 .TE8

This cha$ter descri*es the arious ener"y conersions that can occur in Ideal Fluid Systems% An Ideal

Fluid System is one where no heat or wor( is transferred into or out of the fluid% Althou"h not in

real world a$$lications, the Ideal Fluid conce$t is fre7uently used to understand and $redict

system *ehaior%

TO ?#< G%!& an %deal fluid system where no heat is transferred in or out,and no work is performed on or by the fluid, !)*L+%& the energy

conversions that occur

!O :." Given an %deal fluid system, #!T!7B%&! the energy

conversions that occur using arrow analysis

Energy Con%ersions in Ideal (luid ystems

As discussed earlier( energ# ma# neither $e created nor destro#ed. -o"ever( the %otential( 2inetic( andflo" energies in a fluid s#stem ma# $e converted from one form to another de%ending on the changes that

occur to the elevation or flo" area 7%i%e sie: of the %i%ing s#stem. 4ernoulli6s e*uation hel%s e)%lain

ho" these energ# conversions ta2e %lace and ho" the energ# $alance is affected. 75OE ?ol. III( %. /s e'uation discussed earlier.

gz1

gc+

v12

2gc+ P11=

gz2

gc+

v22

2gc+ P2 2

Remem$er( the a$ove e*uation assumes an ideal fluid and no heat transferred in or out 7%erfectl#

insulating:( and that no work is done on or by the system 7no com%ression( no decom%ression:( andtherefore( no change occurs in the internal energyof the s#stem 7no loses due to tur$ulence( no internal

friction:.

Since "e are concerned here onl# "ith a change in %i%e sie( "e do not consider a change in %i%e

elevation. 'ith no change in %i%e elevation( there is no change in %otential energ# 7nor s%ecific %otential

energ#:.

Since %otential energ# 7gz

gc: is the same at all %oints( it can $e canceled out of the e*uation.


100/180


Student .uide/ Fluid Flow Cha$ter / Ener"y Conersions in Ideal Fluid Systems

So the a$ove e*uation can $e sim%lified to+

v12

2gc

+ P11=v2

2

2gc

+ P22

From the %revious discussion of 4ernoulli6s %rinci%le( "e 2no" that as %i%e sie gets smaller or larger(

flo" velocit# increases or decreases( res%ectivel#. 9Remem*er how elocity increases as a rier "oes

throu"h a narrow "or"e and slows down as the rier widens a"ain%:

As the velocit# of a fluid increases( the 2inetic energ# of the fluid increases. The increase in 2inetic

energ# must come from some %lace. The onl# other energ# that can change in this e)am%le is flo"

energ# 7P :. Therefore( as 2inetic energ# increases( flo" energ# must decrease to offset the increase in2inetic energ#. This is in accordance "ith the conservation of energ# %rinci%le 7energ# can not $e created

nor destro#ed:. This relationshi% is sho"n $# the arro"s in the e*uation $elo".

Notes regarding use of arrow analysis+

An eas# "a# to get used to using arro" anal#sis is to remem$er that the anal#sis always looks back from point 2 to

where it was earlier at point 0( and it is a com%arison of the differencethat ta2es %lace.

Onl# three com%arisons can $e made( either increaseJ( decreaseJ( or no changeJ.

'hen the arro" %oints u%( ( it means an increase "hen loo2ing $ac2 from %nt / to %nt .

'hen the arro" %oints do"n( ( it means a decrease "hen loo2ing $ac2 from %nt / to %nt .

'hen the arro" %oints side"a#s( or ( it means no change "hen loo2ing $ac2 from %nt / to %nt .

It sho"s that as one form of energ# goes u%( the other must go do"n in order for the e*uation to remain in

$alance.

v1

2gc

2

+ P11=v2

2gc

2

+P 22

This means that( in this instance "here onl# the %i%e sie changes( a change in 2inetic energ# is e)actl#

offset $# a corres%onding change in flo" energ#. Or stated mathematicall#+

fe(e =

7'here the stands for the Gree2 d( delta( and means difference or change inJ.:

9The followin" e>am$les assume a continuously flowin" ideal fluid%:D


101/180



Example:

E)%lain the energ# conversions that occur $et"een %oints and / $elo".

Flo" energ# is converted to 2inetic energ#.

E)%lanation+

. Since %i%e elevation does not change( %otential energ# remains the same and is not a

consideration. Onl# 2inetic energ# and flo" energ# are involved./. Area is greater than area /.


102/180



. Since %i%e elevation does not change( %otential energ# remains the same and is not a

consideration. Onl# 2inetic energ# and flo" energ# are involved.

/. Area is smaller than area /.


103/180



Example:

E)%lain the energ# conversion that occurs as an ideal fluid flo"s from %oint to %oint /.

Flo" energ# is converted to %otential energ#.

E)%lanation+

. Since there is no %i%e area 7sie: change( there is no change in fluid velocit# so 2inetic

energ# remains the same and is not a consideration. Onl# %otential energ# and flo"

energ# are involved./. Elevation is lo"er than elevation /.


104/180



E)%lanation+

. Since there is no %i%e area 7sie: change( there is no change in fluid velocit# so 2inetic

energ# remains the same and is not a consideration. Onl# %otential energ# and flo"

energ# are involved./. Elevation is higher than elevation /.


105/180



Chapter ? ummary:

&otential energ# is the energ# a fluid %ossesses due to its height 7%osition: relative to another $od#.

If %otential energ# increases flo" energ# decreases( and if %otential energ# decreases flo" energ#increases. 7If$ethenfe; If$ethenfe:

&otential energ# increases "hen heightincreases( and decreases "hen heightdecreases.

Linetic energ# is the energ# a fluid %ossesses due to its velocit#.

If 2inetic energ# increases flo" energ# decreases( and if 2inetic energ# decreases flo" energ# increases.

7If (ethenfeD If (ethenfe)

4ernoulli6s %rinci%le sa#s + 'here the %elocityof a fluid is high( the %ressure is lo"D and "here the

%elocityis lo"( the %ressure is high.

?elocit# changes "ith %i%e sie changes. 7A reducer causes an increase in velocit# and a reduction in

%ressureD and vice versa.:

Flo" energ# is the energ# a fluid %ossesses due to its pressure and volume.

Flo" energ# ta2es the hit from %otential energ#( 2inetic energ# and internal energ#. 'hatever each of

these energies do flo" energ# com%ensates and does the o%%osite.

Advance information for com%arison and ease of revie"=

Internal energ# is the energy of the moleculesof a fluid due to rotation( vi$ration( translational motion

and intermolecular attractions.Internal energ# al"a#s increases and flo" energ# al"a#s com%ensates $# decreasing. 7uandfe

100% of the time) Internal energ# e)ists in a real fluid"here there is al"a#s viscosit# and fluidfriction due to intermolecular attractions.


106/180



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107/180

PERATI-S TRAI-I-. PR.RAMStudent .uide/ Fluid Flow Cha$ter / Ener"y Conersions in Real Fluid Systems

Chapter ? Energy Con%ersions in )eal (luid ystems

This cha$ter descri*es fluid friction as well as the use of arrow analysis to determine the arious ener"y

conersions that occur in real fluid systems where head loss is always $resent%

TO #< G%!& a 7eal fluid system, #!S7%9! the effects of fluid frictionto predict energy conversions

!O ;." #!$%&! the fluid flow term 3fluid friction4

!O ;.( %#!&T%$C the factors that effect fluid friction in 7eal fluid

systems

!O ;. #!$%&! the fluid flow term 3head loss4

!O ;.2 #!S7%9! the effects of fluid friction on a flowing fluid in a

piping system

!O ;.5 #!$%&! the fluid flow term 3throttling4

!O ;.8 #!S7%9! the effects of throttling on the fluid flow in a

piping system

!O ;.: /S! arrow analysis and the general energy e1uation to predict

energy conversions in a real fluid system

(riction

Friction is the force "hich o%%oses movement. Friction forces are created "henever t"o o$ects are

touching and there is movement in o%%osition to one another. If "e slide a $o) along the floor( some of

the mechanical energ# necessar# to move the $o) is converted into internal energ#. 'e measure this asan increase in the tem%erature of the $o) and the floor. 'hen #ou ru$ #our hands together( the friction

$et"een #our hands "ill cause an increase in the tem%erature #ou can feel.

(luid (riction

Fluid frictionis the force "hich o%%oses the movement of a fluid. A good e)am%le of fluid friction is theresistance "e feel "hen stirring %aint "ith a flat stic2. Fluid friction converts flo" energ# into internal

energ#.

Fluid friction occurs $et"een a fluid and the "alls of a %i%e( and $et"een each of the molecules of a fluid(

since each molecule hinders the movement of ever# other molecule it touches.


108/180


7iscosity

?iscosit# "as discussed in the cha%ter on T#%es of Flo". It is mentioned again here $ecause viscosit# is

often identified "ith fluid friction. ?iscosit# "as defined earlier as a measure of a fluid6s resistance to

flo". ?iscosit# is tied to the internal friction of a fluid "hich ma2es it resist flo"ing %ast a solid surface

or other la#ers of fluid. If there is no viscosit# there is no fluid friction and vice versa.

Factors Affecting Fluid Friction

The follo"ing factors "ill cause an increase in fluid friction+

Increase in fluid velocit# Increase in roughness of %i%e -igher viscosit# fluids Smaller diameter %i%e Increase in tur$ulent flo" Increase in %i%e length Increased num$ers of valves( fittings( and $ends

Energy Con%ersion by (luid (riction in )eal (luids

In a pre%ious chapter we assumed an ideal fluid# For an ideal fluid( there is no viscosit# and no fluid

friction and therefore( no change in internal energ# of the s#stem. =ut for a real fluid, the effects of

fluid friction must be considered#

This is 4ernoulli6s e*uation "ritten to include internal energ# u( assuming no "or2 is done on or $# the

s#stem( and no heat enters into or moves out of the s#stem 7 M0( 'M0:

pe1+ke

1+fe

1+u

1=pe

2+ke

2+fe

2+u

2

4ernoulli6s e*uation can $e a%%lied to a straight horiontal %i%e( "ith no change in elevation and no

change in %i%e sie 7Figure 9.:. These assum%tions eliminate the 2inetic and %otential energ# terms from

the e*uation so that it $ecomes+

fe1+u

1= fe

2+u

2


109/180


Fluid friction resists the fluid flo" and causes flo" energ# to $e converted to internal energ# as the fluid

flo"s through the %i%ing s#stem. Internal energ# is the energ# associated "ith the motion of the

molecules of a su$stance. Tem%erature is a measure of the molecular motion of molecules. An increase

in internal energ# "ill increase the tem%erature of the fluid.

Fluid friction causes internal energ# to increase( and flo" energ# to decrease. The change in internal

energ# in this e)am%le is e*ual to the change in flo" energ# or+

u= fe

The amount of flo" energ# converted to internal energ# $# fluid friction is called head loss# 7Also

e*uivalent to a %ressure loss since fe=P :.

4ernoulli6s e*uation can also hel% sho" the effect of friction on flo" in a %i%e that has changes in $oth

elevation and %i%e sie.

Example+

E)%lain "hat ha%%ens to the energ# levels and

tem%erature and %ressure of the s#stem sho"n

in figure 9./. as "ater flo"s from %oint to

%oint /H

olution+

4egin $# evaluating the energ# conversionsthat occur. In this case( the %i%e is not

horiontal and the %i%e sie changes. The three

factors to consider are changes to elevation(

%i%e sie( and the %resence of fluid friction.

;oint;oint

(igure /"? traight ;ipe ection

(igure /" ;ipe ection with Changes in

siFe and Ele%ation


110/180


;otential Energy: Goes u%. 4ecause elevation increases from %oint to %oint /( the %otential

energ# of the fluid increases. Flo" energ# "as converted to %otential energ#. This means

%ressure decreases due to the decrease infe#

Dinetic Energy: Goes u%. 4ecause the %i%e flo" area decreases from %oint to %oint /( thefluid velocit# increases( "hich increases 2inetic energ#. This increase came from flo" energ#.

&ressure decreases againdue to the decrease infe%

Internal Energy: Goes u%. 4ecause fluid friction is %resent( flo" energ# is converted to internal

energ#. This means %ressure decreases a third "a#( and tem%erature increases.

/*s a )esult/

(low Energy: Goes do"n. The changes in elevation( %i%e sie( and the %resence of friction all

contri$ute to dro%s in the flo" energ# 7%ressure decrease: at %oint /. This is characteristic of an

o%en flo" 7non recirculating: s#stem. A %um% must su%%l# enough %ressure to overcome the

%ressure decreases caused $# fluid friction and changes in %i%e elevation and %i%e sie.

In the e*uation $elo"( the arro"s sho" the net effect of the energ# conversions that too2 %lace in

this o%ennon=recirculating s#stem.

pe1+ ke1 + fe1+ u1= pe2 +ke2 +fe2 +u2

Su$stituting e*uivalent terms for s%ecific %otential( s%ecific 2inetic( and s%ecific flo" energies+

gz1

gc+

v 12

2gc+P11+u1=

gz2

gc +

v22

2gc +P2 2 +u2

Energy Con%ersion by (luid (riction

So far( in our discussions on energ# conversions for changes in area and elevation( "e assumed a

frictionlessfluid. For an ideal fluid( there is no fluid friction and no change in internal energ# of the

s#stem. (or a real fluid, the effects of fluid friction are real#

'e "ill start "ith the delta form of the general energ# e*uation.

$eP (eP uP 7P: P w2(netM 7net

Fluid friction %roduces a %ressure dro% and an increase in internal energ#. 'e can measure the %ressure

dro%. 'e can ta2e %ressure readings at $oth ends of a long %i%e run( for e)am%le. 'e can also ta2e%ressure readings on $oth sides of a valve or other com%onent.

'e "ould li2e to 2no" "hether "e can detect fluid friction as a change in fluid tem%erature. Recall that

;oule6s constantG is the relationshi% $et"een heat and mechanical "or2. 'e "ould li2e to ans"er the


111/180


follo"ing *uestion+ ho" much of a %ressure dro% is re*uired to %roduce a F increase in tem%eratureHThe ans"er to this *uestion is found using the mechanical e*uivalent of heat and some dimensional

anal#sis.

Example:

The %i%e sho"n in Figure 9.3 has a constant

flo" rate. There is no change in %i%e sie or

elevation.. 'hat is the %ressure dro% from

%oint to %oint /H

First "e "rite do"n the delta form of the

general energ# e*uation+

$eP (eP uP 7P : P w2(netM 7net

Then "e sim%lif# the general energ# e*uation

$# anal#sis+

w2(netM 0

7netM 0

$eM 0 (eM 0

This leaves us "ith

uP 7P : M 0

The change in internal energ# uis the change associated "ith the change in fluid tem%erature from@0 F to @ F.

In a se%arate -eat Transfer course( regarding sensi$le and latent heat( "e "ill find that the heat added to a

s#stem is given $#+

7M c T

"here+

7M heat %er unit mass in g

;orl$

4tu

m

c M s%ecific heat ca%acit# in1g

;or

Fl$

4tu

m

TM change in tem%erature in F or 1

For "ater at room tem%erature( cM .0Fl$

4tu

m. So for a F increase in tem%erature(

Pipe

1 2

T1= 70oF

p1=D1= 10 in

Z1= 50 ft

T2= 71oF

p2=D2= 10 in

Z2= 50 ft

(igure /"$ The ;ressure 1rop from a 0(Temperature )ise


112/180


q= cT=1.0Btu

lbmF1F

= 1Btu

lbm

This energ#==Y"hich is transferred as heat at the molecular levelZ==is converted from flo" energ#

7%ressure: to internal energ# 7tem%erature:. So "e are loo2ing for a %ressure dro% e*ual to 4tul$m.

'e do this $# dimensional anal#sis+

Btu 1 Btu 778 ftlbf 62.4 lbm 1 ft2

lbm lbm 1 Btu ft3 144 in21 =

Btu

lbm

1 = 337 psi

Although it6s %ossi$le to %rove that the densit# $elongs in this calculation( dimensional anal#sis gave us

the correct ans"er. 'e ust used unit conversion factors "hich too2 us in the right direction.

This sa#s that a F rise in fluid tem%erature corres%onds to a


113/180


If the area is constant( the velocit# can not change( in accordance "ith the continuit# e*uation. Since

s%ecific 2inetic energ# consists of the velocit# s*uared divided $# /( if the velocit# is constant the 2inetic

energ# must also $e constant

S%ecific %otential energ# consists of gravit# times height 7:. Gravit# does not change. Since there is no

change in elevation 7 sta#s constant:( there is no change in s%ecific %otential energ#.

In a real fluid s#stem that has viscosit# there is al"a#s friction. Friction A'A!S causes an increase in

the s%ecific internal energ#.

Since s%ecific internal energ# has increased and energ# can neither $e created nor destro#ed the energ#must $e transformed into another form. Since the s%ecific 2inetic energ# and the s%ecific %otential energ#

did not change( the onl# energ# form that can change is the s%ecific flo" energ#. Since s%ecific internal

energ# increased( the s%ecific flo" energ# must decrease. S%ecific flo" energ# consists of s%ecific

volume times %ressure. For an incom%ressi$le fluid the densit# and s%ecific volume remain constant. Ifthe s%ecific volume remains constant and the s%ecific flo" energ# decreases( the %ressure must also

decrease.

Remem$er( there are several factors "ill cause an increase in fluid friction in real fluids+

Increase in fluid velocit#

Increase in roughness of %i%e

-igher viscosit# fluids

Smaller diameter %i%e

&resence of tur$ulent flo" instead of laminar flo"

Increase in tur$ulence

&resence of valves( fittings( and $ends

ength of %i%e


114/180


Example:

The s#stem sho"n in Figure 9.> has a %ressure of

@0 %sig at %oint and a %ressure of 3> %sig at %oint

/. 'hat is the flo" energ# loss due to fluid

frictionH

As al"a#s( "e first "rite the delta form of the

general energ# e*uation+

$eP (eP uP 7P : P w2(netM 7net

Anal#ing the s#stem( "e find+

7netM 0

w2(netM 0

(eM 0

The general energ# e*uation then reduces to+

$eP uP 7P : M 0

'e identif# uas the flo" energ# loss due to fluid friction. So "e solve for u+

uM = $e= 7P:

Ne)t( "e get numerical values for & and $e.

;Since+ &/= &M 3> %sig = @0 %sig

&M =/> %sig M/

/>

in

l*f

=

1

=

1

62.4 lbmft 3

=0.01603ft3

lbm

therefore(

5P6

&M

& M =>@.@09m

f

l$

l$ft

D1= 6 in

V1= 500 gpm

Z1= 80 ftp1

= 70 psig

T1= 70 F

1

2

D2= 6 in

V2= 500 gpm

Z2= 125 ft

p2= 45 psig

T2= 70 F

Pipe

(igure /9< ;ressure 1rop and (luid (riction

0.0C0< ft1 =/> l$f

33 in4

l$min

4ft

4


115/180


No" solving for pe/

$eM"7!/=!: M ( )ftft

s

ft90/>

@.m

f

l$

l$ft

Since

uQ / pe/ 5P6Then(

uM 7>@.@09m

f

l$

l$ft : 3>

m

f

l$

l$ft

uM /.@09m

f

l$

l$ft

That is(

u/= uM /.@09m

f

l$

l$ft

The internal energ# at %oint / is greater than the internal energ# at %oint $# /.@09m

fl$

l$ft .

'e can convert this to 4tu or an e*uivalent %ressure dro%.

mff

f4tul$0C3.0

l$ft@@9

4tu

l$

l$ft@09./=

T= c7

Rearrange to solve for T +c

7=T

F0C3.04tu.0

Fl$

l$

4tu0.0C3T =

=

m

m

u4#u0M/

/

/

0@.>

in33

ft

ft

l$3.C/

l$

l$ft/.@09f

m

m

f=

M >.>0@ %si

ftl$fs

/

s/


116/180


The internal energy change due to friction is


117/180


E)%lain the energ# conversions and %ressure and tem%erature changes for the closedrecirculating

s#stem sho"n in Figure 9..

olution:

4egin $# considering the energ# conversions that occur and noting "hich conversions causeincreases in %ressure 7flo" energ#: and "hich cause decreases in %ressure 7flo" energ#:.

&oint to &oint / = (low energy 5pressure6 is con%erted to potential energy# ;ressure

decreases#

EV&ANATION+ As the fluid is elevated from %oint to %oint /( its %otential energ# is

increased. This increase in %otential energ# has to come from some"here. 7&er the a"of 1onservation of Energ# = #ou don6t get something for nothing:. The increased

%otential energ# comes from flo" energ# $eing converted to %otential energ#. Flo"

energ# 7%ressure times s%ecific volume( P : has decreased. Therefore( %ressure hasdecreased. The arro"s in the e*uation $elo" sho" the relative changes in energ# from

%oint to %oint /.

gz1

gc+

v12

2gc+ P11+ u1=

gz2gc

+v2

2

2gc+ P22+ u2

&oint / to &oint < = (low energy 5pressure6 is con%erted to kinetic energy# ;ressure

decreases#

EV&ANATION+ The %i%e sie decreases at %oint


118/180


gz1

gc+

v12

2gc+ P11+ u1=

gz2

gc+

v22

2gc+ P22+ u2

&oint < to &oint 3 = Dinetic energy 5%elocity6 is con%erted to flow energy# ;ressureincreases#

EV&ANATION+ The %i%e flo" area increases as the fluid leaves %oint ( its %otential

energ# is decreased. The decrease in %otential energ# is e*uivalent to the increase in

%otential energ# as the fluid moved from %oint to %oint /. The %otential energ# lost isconverted $ac2 to flo" energ# 7 P :. The %ressure therefore increases $# an amounte*ual to the %ressure decrease from %oint to %oint /.

gz1

gc+

v12

2gc+ P11+ u1=

gz2gc

+v2

2

2gc+ P22+ u2

Net Result+ No losses in &ressure 7e.g. ideal fluid: If we did not consider the effects offluid friction, the abo%e analysis would show that the pressure at point 0 and point 9

would be the same# The decrease in %ressure "hen the %i%e sie decreases is e)actl#

offset $# the increased in %ressure "hen the %i%e sie increases. The decrease in %ressure

"hen elevation increases is e)actl# offset "hen the fluid returns to the same elevation it

started from.

Fluid friction is %resent in all real fluids including all gases and li*uids. Fluid friction results in the

conversion of flo" energ# to internal energ#( as evidenced $# a decrease in %ressure and an increase in

tem%erature.

In the e*uation $elo" the arro"s sho" the net result of the energ# conversion in a real fluid that too2%lace in a closedrecirculating s#stem.

gz1

gc+

v12

2gc+ P11+ u1=

gz2

gc+

v22

2gc+ P 22+ u2

Flo" Energ# goes do"n and Internal Energ# goes u% $# the same amount.


119/180


Unli2e the %ressure dro% caused $# the changes in %i%e sie and elevation( fluid friction results in anunreco%ered pressure drop. This %ressure dro% is referred to as head loss. This dro% in %ressure must

$e re%laced $# "or2 on the fluid( usuall# %rovided $# a %um%( or the fluid "ill sto% flo"ing.

Fluid Friction results in an un-recovered pressure drop

et6s loo2 ne)t at another closed loo%. ,an# fluid s#stems are closed loo%s. A t#%ical closed loo% has a

%um% to su%%l# %ressure( some load

7li2e a heat e)changer:( andconnecting %i%ing. The s#stem in

Figure 9.C is a sim%le closed loo%.

'ater leaves the %um% at %oint ( flo"s through the loo%( and returns to the %um% at %oint /. Out in the

loo%( the s#stem e)%eriences changes in elevation

7:( %i%e sie7A:( and direction. It %ro$a$l#transfers heat. If it is a %o"er s#stem 7li2e a

h#draulic s#stem: it ma# also %erform "or2.

'e "ant to find out "hat the effect of fluid friction

is on this real s#stem.

Example:

Figure 9.@ sho"s the fluid %ro%erties of a s#stem. 5etermine the fluid friction energ# dro% in this

s#stem. The densit# of "ater at 03 F is C.8 l$mft

Documents

20651432 Fluid Flow Student Guide for Operations Training