t Fluid Flow

Chapter 1: Fluid Flow Rules of Thumb for Chemical Engineers, 5th Edition by Stephen all

This Excel workbook includes Visual Basic for Application function subroutines. Macros must be enabled for them to work. The following Text Text Boxes contain the syntax for the functions. Copy them to the worksheet where you want to use the functions for ready reference. Function Subroutines in S! "nits Function #ReS!!" #ReS! !" mu" d" #ptional ro" #ptional Tin" #ptional Mw" #ptional p$ % ! & 'lowrate in kg(h % mu & Viscosity in m)a*s % d & )ipe+, in mm % ro & density in kg(m- reuired for liuid$ % Tin & temperature" deg C reuired for gas$ * default /0 deg C % Mw & molecular weight reuired for gas$ * default /1 % p & pressure" k)a reuired for gas$ * default 2000 k)a

Function FrictionS!epsilon" FrictionS! epsilon" 34e" d$ % epsilon & 5urface roughness is in units m % d & )ipe+, is in units mm Function $%S!!" $%S! !" )in" )out" d" 6" f" #ptional ,ensity" #ptional Tin" #ptional Mw" #ptional 7amma" #ptional +sothermal$ % )ressure ,rop due to friction in a round pipe adiabatic for compressible flow$ % with the following arguments % 5pecify two of the following three8 function will compute the third % ! & mass mass flow flow rate" kg(h % )in & inlet" inlet" or upstream" pressure" k)a % )out & outlet" or downstream downstream pressure" k)a % )ipe properties % d & pipe diameter" diameter" mm % 6 & pipe length" m % f & ,arcy friction factor % 'luid properties % ,ensity optional$ optional$ ** specify specify for liuids" kg(m% Tin optional$ optional$ ** specify for for gas" inlet temperature" temperature" deg C default default to /0$ % Mw optional$ ** specify for gas" molecular molecular weight default to /1 for air$ air$ % 7amma optional$ ** specify for gas" ratio ratio of Cp(C9 Cp(C9 default to 2.:$ % +sothermal optional$ ** any 9alue results in isothermal compressible calc" if missing then adiabatic calc

ChemEng 5oftware sells an Excel template called )+)E5+;E. www.chemengsoftware.com )+)E5+;E si
Function Subroutines in "S "nits Function #Re"S!" #Re"S !" mu" d" #ptional ro" #ptional Tin" #ptional Mw" #ptional p$ % ! & 'lowrate in lb(h % mu & Viscosity in c) % d & )ipe+, in inches % ro & density in lb(ft- reuired for liuid$ % Tin & temperature" deg ' reuired for gas$ * default =0 % Mw & molecular weight reuired for gas$ * default /1 % p & pressure" psia reuired for gas$ * default 22>

Function Friction"Sepsilon" Friction"S epsilon" 34e" d$ % epsilon & 5urface roughness is in units feet % d & )ipe+, is in units inches Function $%"S!" $%"S !" )in" )out" d" 6" f" #ptional ,ensity" #ptional Tin" #ptional Mw" #ptional 7amma" #ptional +s % )ressure ,rop due to friction in a round pipe adiabatic or isothermal for compressible flow$ % with the following arguments % 5pecify two of the following three8 function will compute the third % ! & mass mass flow rate" lb(hr % )in & inlet" inlet" or upstream" upstream" pressure" pressure" psia % )out & outlet" outlet" or or downstream downstream pressure" pressure" psia % )ipe properties % d & pipe diameter" diameter" inches % 6 & pipe length" feet % f & ,arcy friction factor % 'luid properties % ,ensity optional$ ** specify specify for liuids" lb(ft% Tin optional$ optional$ ** specify for gas" inlet temperature" temperature" deg ' default default to =0$ % Mw optional$ ** specify for gas" molecular molecular weight default to /1 for air$ air$ % 7amma optional$ optional$ ** specify specify for gas" ratio of Cp(C9 Cp(C9 default to 2.:$ % +sothermal optional$ ** any 9alue results in isothermal compressible calc" if missing then adiabatic calc

thermal$

$roblem Statement: Calculate pressure drop per 200 m or 200 ft using the shortcut formula 5+ ?nits ?5 ?nits !nputs 'low 4ate Viscosity )ipe ,iameter ,ensity

kg(h m)a*s mm kg(m-

,elta )

Bar(200 m

20"000.0 2./ [email protected] 1=2.>

lb(h c) in lb(ft-

//"000.0 2./ 2.> =0.0

&utput 2.@-

psi(200 ft

@.01

$roblem Statement: Calculate 4eynolds 3umber using VBA function function call.

!nputs )arameter Mass 'low 4ate Viscosity )ipe ,iameter ,ensity Temperature Molecular !eight )ressure

?nits kg(h m)a*s mm kg(mC kg(kgmol k)a" absolute

4eynolds 3umber

dimensionless

6iuid 7as Example 2 Example / 20"000.0 2"/00.0 2./ 0.022 [email protected] /=.= 1=2.0 :0.0 2=.0: /"/00.0

&utput

&34e5+,@",1",20",22$

VA6?E

VA6?E

&34e5+E@"E1"E20""E2/"E2-"E2:$

?5 Customary ?nits ?nits lb(h c) in lb(ft' lb(lbmol psia

6iuid 7as Example 2a Example /a //"000.0 /"=:>.0 2./ 0.022 2.> 2.0: =0.0 20:.0 2=.0: -21.0

VA6?E

&34e?5+@"+1"+20"+22$

VA6?E

&34e?5D@"D1"D20""D2/"D2-"D2:$

$roblem Statement: Calculate ,arcy 'riction 'actor using VBA function function call.

!nputs

6iuid Example /10.0 2./ [email protected] 1=2.0

)arameter Mass 'low 4ate Viscosity )ipe ,iameter ,ensity Temperature Molecular !eight )ressure

?nits kg(h m)a*s mm kg(mC kg(kgmol k)a" absolute

)ipe 4oughness

m

4eynolds 3umber

dimensionless

VA6?E

,arcy 'riction 'actor

dimensionless

VA6?E

0.0000:>

&utput

&'riction5+,2=",21",20$

?5 Cus Custo tom mary ary ?ni ?nitts ?nits lb(h c) in lb(ft' lb(lbmol psia

6iu 6iuiid Example -a //"000.0 2./ 2.> =0.0

ft

0.0002>

VA6?E VA6?E

&'riction?5+2="+21"+20$

$roblem Statement: Calculate )ressure ,rop due to 'riction

!nputs

6iuid 7as Example : Example > 20"000.0 2"/00.0 00.0 /"/00.0

)arameter Mass 'low 4ate )ressure in upsteam$

?nits kg(h k)a" absolute

Viscosity )ipe ,iameter Eui9alent 6ength of )ipe ,ensity Temperature Molecular !eight Cp(C9

m)a*s mm m kg(mC kg(kgmol

)ipe 4oughness

m

4eynolds 3umber

dimensionless

VA6?E

VA6?E


dimensionless

VA6?E

VA6?E

VA6?E

VA6?E

2./ [email protected] :0.0 1=2.0

0.022 /=.= =0.0

0.0000:>

:0.0 2=.0: 2.-> 0.0000:>

&utput

)ressure #ut" gi9en Mass 'low and )ressure in

&),5+,@",1"",2/",2-",/:",2:$

&),5+E@"E1""E2/"E2-"E/:""E2>"E2="E2$

?5 Customary ?nits ?nits lb(h psia c) in ft lb(ft' lb(lbmol

6iuid 7as Example :a Example >a //"000.0 -"[email protected] 202.> -21.0

2./ 2.> 2-2.0 =0.0

0.022 2.0: 21.0

ft

20:.0 2=.0: 2.->

0.0002>

0.0002>

VA6?E

VA6?E

VA6?E

VA6?E

VA6?E

VA6?E

&),?5+@"+1""+2/"+2-"+/:"+2:$

&),?5D@"D1""D2/"D2-"D/:""D2>"D2="D2$

$roblem Statement: Calculate 'low 4ate gi9en upstream and downstream pressures

!nputs

7as )arameter 7?E55 Mass 'low 4ate )ressure in upsteam$ )ressure out downstream$ Viscosity )ipe ,iameter Eui9alent 6ength of )ipe


Example > 2/00 //00 2-:0 0.022 /=.= =0

Temperature Molecular !eight Cp(C9

C kg(kgmol

)ipe 4oughness

m

4eynolds 3umber

dimensionless

VA6?E


dimensionless

VA6?E

m)a*s mm m

:0 2=.0: 2.->

0.0000:>

&utput

Mass 'low" gi9en )ressure in and out

VA6?E

&),5+ "E1"E20"E2/"E2-"E/:"E2:"E2>"E "E1"E20"E2/"E2-"E/:"E2:"E2>"E2="E2$ 2="E2$ ,ifference between 7?E55 and ca calculated ra rate" E@*E/=

VA6?E

?s the tha C 3u 7u

7oal 5eek to find a 9alue for 7uessed flow rate Cell E@$ t euals the calculated flow rate ll E/=$. 3otice that 4eynolds mber is calculated using the ess.

?5 Cust Custom omar ary y ?nit ?nits s

7as 7as

?nits lb(h psia psia c) in ft

Example >a -"0@0.: -21.0 22= 0.022 2.0: 21.0

' lb(lbmol

ft

20:.0 2=.0: 2.-> 0.0002>

VA6?E VA6?E VA6?E

&),?5 "61"620"62/"62-"6/:""62>"62="6 "61"620"62/"62-"6/:""62>"62="62$ 2$ VA6?E

$roblem Statement: Compare pressure drop calculations using e ui9alent length and G*9alue methods for fittings.

!nputs )arameter Mass 'low 4ate )ressure in upsteam$


Viscosity )ipe ,iameter 6ength of )ipe ,ensity Temperature Molecular !eight Cp(C9

m)a*s mm m kg(mC kg(kgmol

)ipe 4oughness

m

Fittings

6iuid 7as Example : Example > 20"000.0 2"/00.0 00.0 /"/00.0 2/.0 >0.0 [email protected] 1=2.0 0.0000:>

0.022 /=.= =0.0 2-.= :0.0 2=.0: 2.-> 0.0000:>

uantity = / / 2

10 deg" welded r(, & 2 TEE" through branch as elbow$ )lug 9al9e" straight 5wing check" Vmin & -> roF0.>

&utput 4eynolds 3umber

dimensionless

VA6?E

VA6?E


dimensionless

VA6?E

VA6?E

VA6?E

VA6?E

)ressure ,rop" gi9en Mass 'low and )ressure in

Eui9alent length of fittings

m

2:.@0

.@

)ressure ,rop" eui9 length method

VA6?E

VA6?E

Mass flux Velocity

kg(m/*s m(s

2":2:.2 2.:

>11.@::./>

'itting pressure loss

kg(m/ k)a



)ressure ,rop" -*G method

VA6?E

VA6?E

)ressure ,rop" Crane method

VA6?E

VA6?E

E 6

6(,$e /0 /0 2@ 200

'low >0 200 >00 2000 /000 20000 -0000 >0000 0000

Gm

Gi @00 @00 -00 2>00

Gd 0.012 0./@ 0.0@: 0.:=

4egime 6aminar 6aminar 6aminar 6aminar 6aminar Turbulent Turbulent Turbulent Turbulent

: : -.1 :

Total 6(, 2/0 :0 -= 200 /1=

)ressure ,rop" )a Eui9 6 Crane G - *G 0.0=0 0. 0.0:0.0>2 0.2/0 0. 0.0@ 0.20/ 0.>1@ 0. 0.::= 0.>/> 2.21= 0. 0 .1/2 2.0@1 /.-1/ 2. 2 .1=0 /.--2 :2.01 ->.>0@ -@.: /@ /@:.2/1 /> / >.1-: /@.-2> 2 2=./=2 == = =-.12 2>.>/= 2" 2"-/@.1/@ 2" 2 "/:.-02 2"-::./:1

-*G Method total Gf Ex : Ex > VA6?E V VA6?E VA6?E VA6?E VA6?E V VA6?E VA6?E V VA6?E VA6?E VA6?E

?5 Customary Customary ?ni 6iuid 6iuid ?nits Example :a lb(h =-"000.0 psia 202.> c) in ft lb(ft' lb(lbmol

20.0 -.2 -2.> 22/.> 2/.0

ft

0.0002>

- nomina nominall si
Crane ft

Crane G

0.02 0.021/ 1/220.021/ 0.021/220.02 0.021/ 1/220.021/ 0.021/22

/.-2 /.-2 0. 0. 0.=1 0.=1 2.1/ 2.1/ >.=1

VA6? VA6?E E VA6? VA6?E E ,elta )" pipe Velocity f" full full turb turbul ulen ence ce

VA6?E -.00.02 0.02-2: 2:1@ 1@-

6e 10 Ell Branch tee 5wing check )lug 9al9e - x 2 reducer

,elta )" comparison

/ 2 2 2 2

20./>.22 />.> :.=0 @//.=@ @[email protected]

Crane G -*G 0.=1/>11 VA6?E 0. 0 .-:=- VA6?E 2.-2:1@ VA6?E 0.-22= VA6?E >.1/ >.1/ =2.00 VA6?E VA6?E

VA6?E

VA6?E

VA6?E

VA6?E

VA6?E

2

$roblem Statement: Calculate )ermanent )ressure ,rop Through #rifice =0 m !nputs

6iuid Example = 20"000.0 00.0 2./ [email protected] =0.0 1=2.0

)arameter Mass 'low 4ate )ressure in upsteam$ Viscosity )ipe ,iameter Eui9alent 6ength of )ipe ,ensity Temperature Molecular !eight Cp(C9

?nits kg(h k)a" absolute m)a*s mm m kg(mC kg(kgmol

)ipe 4oughness #rifice ,iameter

m mm

4eynolds 3umber

dimensionless

VA6?E


dimensionless

VA6?E

I )/ )-

Expansion factor #rifice discharge pressure )ermanent 6oss

k)a" absolute m(s m(s dimensionless dimensionless r dimensionless k)a" absolute k)a" absolute

VA6?E 20.2

H C

)ressure out downstream$ Velocity through orifice 5onic 9elocity #rifice diameter ratio #rifice Coefficient of ,ischarge

,elta)

)2*)-

k)a

)0

P0

)ipe Jeader at 00 k)a absolute

0.0000:> 21.2

&utput

)2 V2

0.> VA6?E

Stolz equation, Radius Taps

2.0 VA6?E VA6?E VA6?E

4esult G flow coefficient Eui9alent 6ength

dimensionless m

Compare eui9alent length ratio to pressure drop ratio )ipe 6 ( #rifice 6 )ipe )ressure ,rop ( #rifice )ressure ,rop



Close enough" alt

4#

" [email protected] mm +,

P2

P1 P3

hough not perfect

$roblem Statement: Calculate )ressure ,rop due to 'riction for !ater*5team !ater*5team Mixture

!nputs

5team*!ater 5team*!ater at 5aturated Conditions Total Mass 'lux kg(m/*s uality Mass 'raction Vapor +nlet )ressure Bar )ipe ,iameter mm Eui9alent 6ength of )ipe m )ipe 4oughness m

Calculations ' $roperty (oo)up )arameter Cross*sectional area Total Mass 'low 4ate +nlet )ressure Temperature Viscosity Molecular !eight ,ensity Cp(C9

?nits m/ kg(h k)a C m)a*s kg(kgmol kg(m-

!ater 2"->=.0 0.> 2.02 >.0 2.0 0.000002> 5mooth Tube Tube & 0.000002> m

Total as 6i Vapor )rops 0.000021=-> 1>.@ 202.0 1.: 0./@ 0.02/ [email protected] 11@. 0.= 2.-2

Mixture

0.0/2./

&utput

20000

2000

4eynolds 3umber

dimensionless

VA6?E

VA6?E


dimensionless

VA6?E

VA6?E


VA6?E

VA6?E

6iuid ), Multiplier

p hi phiF/


)ressure ,rop" /*)hase 'low

k)A

VA6?E

2.02 Bar =.@1 Bar -:.: Bar [email protected] Bar 20- Bar

200

2-@ Bar 2/ Bar /0 Bar //2./ Ba r

20

2 0

0.2

0 ./

0.-

0.:

0.>

0 .=

0.

0.@

0.1

2

/>0

/00

2>0

7&-1

7&2>=

200

>0

0 0

0.2

0./

0.-

0.:

0.>

0.=

0.

0.@

0.1

2

/>

/0

2>

Awad Dansse n

20

>

0 0

0.2

0./

Property Correlations

0.-

0.:

0.>

0.=

0.

0.@

0.1

2

for all correlations" t & deg C Vapor )ressureK logmm Jg$ & A * B ( tLC$

A 42/ 4// !ater

=.11 .0: @.-2

B [email protected] @>0.20 2"1@=.>0

C />-.-@ /:>.2@ /=@.:

4efe 4efere renc nceK eK

+)C/ +)C/00 00:* :*/ /2 2

$

Comparison Case 42/ /"000.0 0.1 =.00 >0.0 2.0 0.000002> 5mooth Tube & 0.000002> m$

Total as 6i Vapor )rops 0.0021=-:1>: 2:"2-./ =00.0 //.0 0./0 0.022/0.1 2"-/>./1.= 2.2

?ser in input puts a Temperature" correlation p worksheet$. assume assumed d tha the pressure. Calculations subrou subroutin tines es * subroutines

Mixture

Clicking on t macro that ru ru inputs" based +t seems like for 'igure   once" then re recomputing

0.02> -/.@

VA6?E

VA6?E

VA6?E

VA6?E

VA6?E VA6?E VA6?E VA6?E

)hiF/ uality 0 0.00.00.0> 0.0> 0.0@ 0.22 0.22 0.2> 0./ 0./ 0.0.-

2.02 2 :=.:2 :=.:2=:> =:>/1 /12 2 -.--.--//@ //@ 02 02 222.2@::/@: /@: 2:.2@>2 2:.2@>21>01>021-.:0/:/:1./:1.-=>/ =>/>/ >/@> @> ->. ->.=00 =002@ 2@>= >=

0.= 0.= =0.@ =0.@2: 2:/0 /0:> :> 0.@ 0.@ @>./ @>./::2 ::2>= >=-> -> 2 20@.0@1=0>

)hiF/ uality 0 0.2 0.2 0./ 0./ 0.0.0.: 0.: 0.> 0.> 0.= 0.= 0. 0.@ 0.@ 0.1 0.1 2

--1 2 /2.=> /2.=>-:/ -:/>0 >01> 1> [email protected]@ [email protected]@>0= >0=1: 1:@@ @@ >-.=1 >-.=1- -/@ /@/> /> =@./=@./-@-= @-=== ===/ =/ @/./@ @/./@>:: >::@0 @0/2 /2 1>.1@ 1>.1@=2/ =2/1 10 0 201 201.:/1/@0> @0> 2//.= 2//.=-0 -02@ 2@01 01 2->. 2->.>= >=0 0-> -> 2:@. 2:@.2/2 2/2@> @>/> />

)hiF/ uality 0 0.2 0.2 0./ 0./ 0.0.0.: 0.: 0.> 0.> 0.= 0. 0. 0.@ 0.@ 0.1 0.1 2

//@ 2 -.// -.//>02 >021> 1>=>> =>> >.->.--==/ ==/>2 >2/= /= .-@ .-@==0 ==0-/ -/@-: @-: 1.-1 1.-1@-= @-=0@ 0@1>1 1>1 22.-@: 2.-@:-= -==-= =-=2 2 2-. 2-.->2 ->211=21 =21 2>.-0 2>.-0>1: >1:: :0> 0> 2./: 2./:1- 1-@1 @1>/ >/ 21.2@ 21.2@:>0 :>0-1 1 /2.2 /2.22/1 2/1:2 :2=2 =2

6iuid ViscosityK lnc)$ & A L B ( CLt$

A @.$ @. $ /0.1 /0. 1 :.-: :.:

B >"2-:.>"2-:. :="2:-. :=" 2:-.> > ="1/. ="1 /.-/ -/

Vapor ViscosityK lnc)$ & A L B ( CLt$

C =1-.02 =1.02 /"0=:. /" 0=:.@1$ @1$ 2"--/. 2" --/.--$ --$

1.00$ 1.00$ -.:$ -. :$ :.1/$ :. 1/$

:"=22.@ :"=2 2.@=$ =$ /@. / @.:$ :$ /00.: /0 0.:1$ 1$

2"00@.@ 2"00@ .@$$ /@=.== /@=.== >0/.> >0 /.>$ $

re in 4E, " 9iscosity" and density are determined from rameters in lookup table down at the bottom of the hese are affected by the inlet pressure 9ariable. +t is t the temperature is the saturation temperature at . for 4e" f" and pressure drop a re performed in VBA * other worksheets in this workbook 9erify that those re correct. e 4e*4un All +nputs button at cell 6-> runs a ns the calculation on 9arious combinations of on the charts in +)C/00:*/2. the only way to get a straight line per the reference$ 4ow 2/-$ is to do the friction factor calculations calculate phi for a range of ualities 0 to 2$ without the mixture 9iscosity and density for each uality.

=.@1 2 @.//:=/@=@ @=@2: 2/.=:@-:1/ :1/21 [email protected]@0>1/ >1/2/ /:.1>/2=>=>-@1 -/.=@@@1->@/ :/.0 :/.0> >= =:/ :/-1 -1 =0.2@=0/2= /2=22

-:.: 2 /.:@22@1>/: -.:/--0= -0==1 :.@@0 @0@0@ =.20@-/@ -/@@-.@2@>>2 1.@1 1.@11 11> 1>//-= = 2-.1 -.1/=>=>-2=1

[email protected] 2 2./: /:/01 /.21-2 /.@1 @1@/> -.>>0 >>0/1= :.:/:2@= >.:1 >.:122--: -: .>=> >=>::>

202 2.: 2.:2/ 2/1-=-=2. 2.1: 1:2@/1 /1 /./ /./--@ --@:@10@ 10@ /.=@0/-2 -2: -./=>0:01:: -.1@ -.1@/2 /201 01>2 >2= = >.>.-@0@ @0@/->= ->=

2-@ 2 2.2.-:2/2 2/2:==/ 2.> 2.>=>> >>-0>: 2.@ 2.@1@=/ @=/:2/2 /.// ///>0/@ 0/@ /.=>1=02@/: -.21 -.2121 21-= -=2/ 2/2 2 :./-: /-:=2@:> @:>

2/ 2 2./=> /=>:-==: ==: 2.::0 ::010:>> :>> 2.0/ 0/0-:>= :>= 2.1=0 1=0@>--@ --@ /.-0/=>/./ /./>2 >2/0 /02 22 -.>>= >>=--0@/ 0@/

/0 2 2./2--@22 @22@ 2.->: ->:1-1-@ 1-@2 2.>== >==/@>@ @>@1 2.= =:2>/ 2>/= /.0>>0-@1> /.:0 /.:00= 0=1 1>@ >@  -.0@: 0@:/@>0 >0

//2./ 2 2.2 2.21=1: =1:: 2.2.-/> >> 2.> 2.>/-/ /-/ 2. 2.21 12 2.1=->> /./1 /./1: :/ / /.1 /.1--1: -1:2

22/.2/.- 02 02@@ @@2 2 />. />.:1-:1--1: 1:-= -= 2-.> 2-.>/2 /21@ 1@ 1.:0 1.:0>2 >2>: >:1 1@ @ ./: ./:>2 >2@@ @@@1 @1: : >.1= >.1=1/ 1/-= -=:1 :1 >.0@ >.0@:= :=1= 1=> >: : :.@0 :.@0:2 :2=1 =1 2:=. 2:=.- -2 22/> 2/>/ / -/. -/.11@> 11@>@ @@/ @/ 2.2.- = = 2/. 2/.00== 00==>> >>0= 0= 1.21 1.2120 20// //=2 =2: : .>.>-22-22-1 1 =.-@ =.-@> >> >@/ @/2 2 =.0/ =.0/::-@1 @1 2@0. [email protected]= 0=21 210 0:2 :2 :0. :0.:/0@ :/0@-1 -12/ 2/ /2.2 /2.2@@-= = 2:. 2:.>0= >0==/ =/@: @: 22.20 2.20==-22->= >= 1.0= 1.0=1 11> 1>-: -: .== .==0 0>1 >1/2 /2  .// .//> >1 1

5onic Velocity

U

max

2->= 2 //.12=:>22> :/.0>=:/-1 =0.2@=0/2=22 .@->-@2-@ 1>.211@=/=>: 22/.-02@@2 2/1.://>>@-1 2:=.-22/>/ 2=-./:>=->/> [email protected]=210:2

>:/: Mass 'lux , ,e ensity 2 11@.== /:.>//2:-@= >.@ :=.:21/10:= /.1: =.@=:0/-2@ 2.1= @1.20211: 2.: 220./-110=2 2.2@ 2-2.-0:/=// 0.1@ 2>/.-//@0.@: 2-.-0@:> 0.: 21:./0>>:1 0.== /2>./2-@-0.>1

=

√

Z γ R T M

)ipe flow area Velocity" m(s --1 0.-: >.> 22>.2 2/.>@ /-0.00 /@.:2 -::.@:0/./: :>1.== >2.0 >:.:@

:@1.:1 :@1.:1@// @//  m(s

0.000021=-> m/ 2->= 2.-= //-2.0/ :=0.= =10.-121.11 2"2:1.=> 2"-1.-0 2"[email protected]= 2"@-@.=/ /"0=@./@ /"/1.1:

>:/: kg(m/*s >.:1/:.0= IE66#! 2"@:/.=1 4E, N Ma /"=2.--"=1.1= :">1@.>1 >">2.// =":->.@> "->:.:@ @"/-.22 1"212.:

Mass 'lux 2 >.>  @ 1.> 22.>

,ensityK kg(m- & m t L b

m -.01$ -.0 1$ -./ ./0$ 0$ 2.> 2 .>=$ =$

b 2"-12" -1-.: .:0 0 2"/1 2" /1..-2"2>0 2" 2>0.: .:/ /

,ensityK lb(ft- & m t L b

m 0.2 0 .21$ 1$ 0./ 0 ./0$ 0$ 0.0 0 .0=$ =$

b @=.11 @=.11 1.@ 1. @ =:./: =:. /:

Molecular !eight 2/0.1 2/0 .12 2 @=.:@ @=. :@ [email protected] 2@. 00

Cp(C9 2.20 2.20 2./>0 2. />0 2.-20 2. -20

N Mach 0.h2

$roblem Statement: Calculate )ressure ,rop due to 'riction for 42/ at 5aturation

!nputs


Calculations ' $roperty (oo)up )arameter ?nits Cross*sectional area m/ Total Mass 'low 4ate kg(h +nlet )ressure k)a Temperature C Viscosity m)a*s Molecular !eight kg(kgmol ,ensity kg(mCp(C9 Velocity assuming a9g density$ m(s Critical Velocity m(s &utput 4eynolds 3umber dimensionless ,arcy 'riction 'actor

dimensionless

)ressure ,rop" gi9en Mass 'low and )ressure in 6ower Bound ?pper Bound A9erage . m ' a $ + t n e i d a r g e r u s s e r p l a n o i t c i r f

200"000

20"000

42/ 200.0 0.> 1.:0 20.0 2.0 0.000002> 5mooth Tube Tube & 0.000002> m

6iuid .@>-1@/E*0> 2:.2 1:0.0 -1./ 0.2 2/0.1 2"//.>

2:.2 1:0.0 -1.2= 0.02: 2/0.1 :-.@ 2.2 2.2@ 2>@.0

VA6?E

VA6?E

VA6?E

VA6?E

VA6?E

VA6?E

0.20.-: k)a & )a

Vapor

0.//-2.@-

2"000

200

20

2 20

2 00

mass flu* +)g'm,-s.

2000

4efe 4efere renc nceK eK +MEC +MECE/ E/00 00>* >*@2 @2:1 :1-

$


6iuid 0.0021=-:1>: 2":2-. =00.0 //.0 0./0 2/0.1 2"-/>.-

Vapor 2/"/-.> =00.0 //.0> 0.022/0.1 /1.= 2.-2 =2.0> 2=-./=

VA6?E

VA6?E

VA6?E

VA6?E

VA6?E

VA6?E

.= 2/.1: 20.-0

uality

0.>

Mass Mass 'lu 'lux x 6ower 6ower /0 @ @0 @= /00 :/> :00 2": 2":-2 =00 /"1 /"101 2000 2000 "2 "22/

5onic

A9erage 2: 2> @0 /"=/>"--2-"0-

?pper

2>@.02=

,ensity Velocity Velocity"" m(s /0 @:.= @:.=/ /  0./0./-==-/1 /1 //@ 0.1:>-2 2"2-: /.-=-/1/ -"@2> :./=>@> ">= .0@1@ 2@"1=/ 22.@2=:=

$roblem Statement: Calculate )ressure ,rop due to 'riction for 42/ at 5aturation

!nputs




42/ 200.0 0.> 1.:0 20.0 2.0 0.000002> 5mooth Tube Tube & 0.000002> m

6iuid .@>-1@/E*0> 2:.2 1:0.0 -1./ 0.2 2/0.1 2"//.>

Vapor

2:.2 1:0.0 -1.2= 0.02: 2/0.1 :-.@ 2.2


dimensionless

VA6?E

VA6?E


dimensionless

VA6?E

VA6?E


VA6?E

VA6?E

dp(d<

)a(m

VA6?E

VA6?E

'itting parameter

p

Total pressure drop

k)a(m

0.@ VA6?E

4efe 4efere renc nceK eK +MEC +MECE/ E/00 00:* :*=2 =2:2 :20 0

$


6iuid 0.0021=-:1>: 2":2-. =00.0 //.0 0./0 2/0.1 2"-/>.-

k)a(m

Vapor 2/"/-.> =00.0 //.0> 0.022/0.1 /1.= 2.-2

water 4eference article" 'igure !ater*Air >12.0 0.0-> 2.-0 /.0 2.0 0.000002> 5mooth Tu

6iuid 0.000>/>= 2"21.= 2-0.0 /0.0 0.-1 [email protected] 2"221.2"221.-

Vapor /0.= 2-0.0 /0.00 0.0/0 /1.0 2.>> 2.:0

VA6?E

VA6?E

VA6?E

VA6?E

VA6?E

VA6?E

VA6?E

VA6?E

VA6?E

VA6?E

VA6?E

VA6?E

VA6?E

VA6?E

VA6?E

VA6?E

0.- This method depends on fitting parameter" p VA6?E

0./> This metho VA6?E VA6?E

2

be & 0.000002> m$

depends on fitting parameter" parameter" p

$roblem Statement: Calculate )ressure ,rop due to 'riction for !ater*5team !ater*5team Mixture

!nputs




water 220.= 0.2 2:.@[email protected] -0.> 0.0000:>

6iuid 0.0022:0012@ -1/. 2":@/.@ 21. 0.2 [email protected] @:/.:

Vapor

=2.2":@/.@ 21.0 0.02: [email protected] =. = .@ 2.:0


dimensionless

VA6?E

VA6?E


dimensionless

VA6?E

VA6?E


VA6?E

VA6?E

6ockhart and Martinelli Method O dimensionless )hi*liuid dimensionless


Total )ressure ,rop" /*phase

m r e p a $ ) , p 0.20 o r %

k)a psi(200 ft

VA6?E VA6?E BrananK 0.:1 psi(200 ft 4ukanK 0./@ psi(200 ft

Comparison of o f Two-$hase Two-$hase /odels R1 R1, 0 ar pressure, 122 )g'm-s in 52 mm s

r . u s s e r 0.0@ $

0.0 0.0= 0.0> 0.0: 0.00.0/ 0.02 * 0

0.2

0./

m r e p a $ ) , p 2=0 o r % e r u 2:0 s s e r $

0.-

0.:

0.> 3uality

0.=

0.

0.@

Comparison of Two-$hase Two-$hase /odels R1, 0 ar ar pressure, 5222 )g'm-s in 52 mm mm s

2/0 200 @0 =0 :0 /0 * 0

0.2

0./

0.-

0.:

0.> 3uality

0.=

0.

0.@

4efere 4eference nceKK Branan Branan"" 4ules 4ules of Thum Thumb" b" :th Edit Edition ion

Comparison Case 42/ /"000.0 0.1 =.00 >0.0 2.0 0.000002>

6iuid 0.0021=-:1>: 2":2-. =00.0 //.0 0./0 2/0.1 2"-/>.-

Vapor 2/"/-.> =00.0 //.0> 0.022/0.1 /1.= 2.-2

VA6?E

VA6?E

VA6?E

VA6?E

VA6?E

VA6?E

VA6?E VA6?E VA6?E

ooth pipe

!allis

)hiF/" lo )hi" lo

/0.@1-0>2 :.>0@12 VA6?E

/ass Flu* 3u 3uality 4elocity omog Split 200 0 0.0> 0. 0.00 200 0.2 0.:0= 0.02 200 0./ 0.- 0.02 200 0.2.0=@ 0.0/ 200 0.: 2.-11 0.0/ 200 0.> 2./1 0.0200 0.= /.0=0 0.0-

0.00 0.02 0.0/ 0.00.00.0: 0.0>

Jomogeneou s 5plit Asymptotic Asymptotic 6ockhart

0.1

2

ooth pipe

Jomogeneou s 5plit Asymptotic Asymptotic 6ockhart

0.1

2

200 200 200 200 20 >0 200 /00 -00 :00 >00 =00 00 @00 2000 2000 2000 2000 2000 2000 2000 2000 2000 2000 2000 2000 /000 /000 /000 /000 /000 /000 /000 /000 /000 /000 /000 >000 >000 >000 >000 >000 >000 >000 >000 >000 >000 >000

0. 0.@ 0.1 2 0.> 0.> 0.> 0.> 0.> 0.> 0.> 0.> 0.> 0.> 0.> 0 0.2 0./ 0.0.: 0.> 0.= 0. 0.@ 0.1 2 0 0.2 0./ 0.0.: 0.> 0.= 0. 0.@ 0.1 2 0 0.2 0./ 0.0.: 0.> 0.= 0. 0.@ 0.1 2

/.-12 /.// -.0>/ [email protected]>1 0.1> 2.>10 -.21 :.=1 =.->1 .1:@ 1.>-@ 22.2/@ 2/ 2/.2 2>.@1 0.>> :.0=/ .-0 20.=@ 2-.1@= 2./1: /0.=02 /-.101 /./2 -0.>/> --.@-2.>01 @.2/> 2:.:0 /2.->= /.1/ -:.>@ :2./0:.@2@ >:.:-: =2.0>0 =.==> -./0.-2/ -=.@>2 >-.-10 =1.1/1 @=.:=@ 20-.00 221.>:= 2-=.0@> 2>/.=/: 2=1.2=-

0.0: 0.0: 0.0: 0.0> 0. 0.000. 0.0>2 0. 0.2= 0. 0.=22. 2./@> /. /.2@: -. -.-0: :. :.=:2 =.21: .1=2 2/ 2/.2-0 2 2 2 / / / : 0 / > =  1 20 22 22: / 22 21 /@ -= :: >/ =0 =@ =

0.0> 0.0> 0.0> 0. 0.00> 0. 0.0@: 0. 0./@: 0. 0.1>: 2. 2.1:0 -. -./01 :. :.:/ =. =.>/: @.>:> 20.1: 2> 2 >.1>2 0 2 2 / / / 0 / : > = @ 1 20 20 20 / 22 2@ /> -/ -@ ::@ >2 >2

symp 0.02 0.0/ 0.00.00.0: 0.0>

(oc)hart 0.0/ 0.00.0: 0.0> 0.0= 0.0

Fluid 42/ 42/ 42/ 42/ 42/ 42/ 42/

!nlet $res $ipe %iam E6ui7alen $i $ipe Roughne =.00 >0.0 2.0 0.000002> =.00 >0.0 2.0 0.000002> =.00 >0.0 2.0 0.000002> =.00 >0.0 2.0 0.000002> =.00 >0.0 2.0 0.000002> =.00 >0.0 2.0 0.000002> =.00 >0.0 2.0 0.000002>

0.0> 0.0= 0.0=

0.0@ 0.01 0.0@

0.00 0.0= 0.// 0.1:0 2.1:> -./:.12=.@>1 1.20> 22.=:@ 2.=2-

0.022 0.2/: 0.::2.>/ -.2> >.-22 .1=1 22.2/2:.=/ 2@.@@/ /@.>:/

2 2 / / : : :

2 / : : > = = =

/ : = @ 20 2/ 2: 2> 2=

:  20 22= 21 // /: /:

2: /: -> := >@ =1 1 @@ 1:

/> :2 >@ = 1222 2/= 2-@ 2:2

42/ 42/ 42/ 42/ 4// 4// 4// 4// 4// 4// 4// 4// 4// 4// 4// 42/ 42/ 42/ 42/ 42/ 42/ 42/ 42/ 42/ 42/ 42/ 42/ 42/ 42/ 42/ 42/ 42/ 42/ 42/ 42/ 42/ 42/ 42/ 42/ 42/ 42/ 42/ 42/ 42/ 42/ 42/ 42/ 42/

=.00 =.00 =.00 =.00 1.20 1.20 1.20 1.20 1.20 1.20 1.20 1.20 1.20 1.20 1.20 =.00 =.00 =.00 =.00 =.00 =.00 =.00 =.00 =.00 =.00 =.00 =.00 =.00 =.00 =.00 =.00 =.00 =.00 =.00 =.00 =.00 =.00 =.00 =.00 =.00 =.00 =.00 =.00 =.00 =.00 =.00 =.00 =.00

>0.0 >0.0 >0.0 >0.0 20.0 20.0 20.0 20.0 20.0 20.0 20.0 20.0 20.0 20.0 20.0 >0.0 >0.0 >0.0 >0.0 >0.0 >0.0 >0.0 >0.0 >0.0 >0.0 >0.0 >0.0 >0.0 >0.0 >0.0 >0.0 >0.0 >0.0 >0.0 >0.0 >0.0 >0.0 >0.0 >0.0 >0.0 >0.0 >0.0 >0.0 >0.0 >0.0 >0.0 >0.0 >0.0

2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0

0.000002> 0.000002> 0.000002> 0.000002> 0.000002> 0.000002> 0.000002> 0.000002> 0.000002> 0.000002> 0.000002> 0.000002> 0.000002> 0.000002> 0.000002> 0.000002> 0.000002> 0.000002> 0.000002> 0.000002> 0.000002> 0.000002> 0.000002> 0.000002> 0.000002> 0.000002> 0.000002> 0.000002> 0.000002> 0.000002> 0.000002> 0.000002> 0.000002> 0.000002> 0.000002> 0.000002> 0.000002> 0.000002> 0.000002> 0.000002> 0.000002> 0.000002> 0.000002> 0.000002> 0.000002> 0.000002> 0.000002> 0.000002>

ss

Jashi 0.: />0 2

m r e p a $ ) , p o r % e r u s s e r $ l a n o i t c i r F

R1, 0 ar C

=

>

:

-

/

2

*

0

m r e p a $ ) , 200.000 p o r % e r u s s 20.000 e

0.2

0./

0.-

0.

R, 891 

$

2.000

0.200

0.020

0.002

20

Comparison of Two-$hase /odels ressure, ressure , 1222 )g'm-s in 52 mm smooth pipe pipe

0.> 3uality

0.=

0.C

0.@

0.1

Comparison Comparis on of Two-$hase /odels r pressure, 295 3uality 3uality in 12 mm smooth tube

200 ass Flu*, )g'm-s

2000

6ockhart Asymptotic Asymptotic 5plit Jomogeneou s

2

6ockhart Asymptotic Asymptotic 5plit Jomogenous Jashi
$roblem Statement: Calculate )ressure ,rop Through an Elbow for ,ifferent 5team ualities

!nputs




!ater 2"->=.0 0.2 =.00 >0.0 2.0 0.000002> 5mooth Tube Tube & 0.000002> m

Total as 6i Vapor )rops 0.0021=-:1>: 1">@>.0 =00.0 2>@.0./2 [email protected] 10-. -.0

Mixture

0.0@: /1./


dimensionless

VA6?E

VA6?E


dimensionless

VA6?E

VA6?E


VA6?E

6iuid ), Multiplier

p hi phiF/


)ressure ,rop" /*)hase 'low

k)A

VA6?E

5onic Velocity

U

max

uality 0 0.02 0.02

=

√

Z γ R T M

:>.=

)ipe flow area 0.0021=-:1> Velocity" m(s ,ensity >:/: kg(m/*s 10-. 10-.> > =.00 =.00 //=.:0 //=.:0 /-.1= /-.1= IE66#! IE66#! & N Mach Mach 0.-

0.0/ 0.0/ 0.00.00.0: 0.0: 0.0> 0.0> 0.0= 0.0= 0.0 0.0 0.0@ 0.0@ 0.01 0.01 0.2 0.2 0.2 0.22 0.2/ 0.2/ 0.20.20.2: 0.2: 0.2> 0.2> 0.2= 0.2= 0.2 0.2 0.2@ 0.2@ 0.21 0.21 0./ 0./ 0./2 0./2 0.// 0.// 0./0./0./: 0./: 0./> 0./> 0./= 0./= 0./ 0./ 0./@ 0./@ 0./1 0./1 0.0.0.-2 0.-2 0.-/ 0.-/ 0.-0.--

2/1.:2 2/1.:2 10.= 10.=0 0 =1.= =1.=1 1 >=.= >=.=:.= :.=1 1 :2.2 :2.21 1 -=./ -=./: : -/.-/.-= = /1./ /1.//=.= /=.=> > /:.: /:.:1 1 //.= //.=> > /2.0 /2.0  21. 21.0 0 2@.: 2@.:1 1 2.: 2.:2=.: 2=.:@ @ 2>.= 2>.=/ / 2:.@ 2:.@= = 2:.2 2:.2= = 2-.> 2-.>2/.1 2/.1> > 2/.: 2/.:2 2 22.1/ 2.1/ 22.: 2.: 22.0> 2.0> 20.= 20.== = 20.20.-0 0 1.1= 1.1= 1.=: 1.=: 1.-: 1.-: 1.0= 1.0=

:2.12 :2.12 4E, 4E, N Mach Mach 2 >1.@ >1.@ .@.@1>.@ 1>.@ 22-.: 2-.: 2-2.= 2-2.=1 1 2:1.= 2:1.=> > 2=.= 2=.=2 2 2@>.> 2@>.>= = /0-.> /0-.>/ / //2.: //2.:  /-1.: /-1.:/>./>.-1 1 />./>.-: : /1-./1-.-0 0 -22. -22./> /> -/1./ -/1./2 2 -:.2 -:.2  -=>.2 -=>.2/ / [email protected] [email protected]@ @ :02.0 :02.0:[email protected] :[email protected] 1 :-=.1 :-=.1> > :>:.10 :>:.10 :/.@= :/.@= :10.@2 :10.@2 >0@. >0@.  >/=. >/=.>::. >::.=@ =@ >=/.= >=/.=: : >@0.> >@0.>1 1 >1@.> >1@.>> >

Property Correlations

for all correlations" t & deg C Vapor )ressureK logmm Jg$ & A * B ( tLC$

A 42/ 4// !ater

=.11 .0: @.-2

B [email protected] @>0.20 2"1@=.>0

C />-.-@ /:>.2@ /=@.:

$

Gm @00

m(s

m/

G

VA6? VA6?E E k)a VA6?E

Gi 0.012

VA6?E elbow

Gd :

VA6?E VA6?E VA6?E VA6?E VA6?E VA6?E VA6?E VA6?E VA6?E VA6?E VA6?E VA6?E VA6?E VA6?E VA6?E VA6?E VA6?E VA6?E VA6?E VA6?E VA6?E VA6?E VA6?E VA6?E VA6?E VA6?E VA6?E VA6?E VA6?E VA6?E VA6?E VA6?E

2/.00

20.00

@.00

=.00

:.00

/.00

*0.2

* */.>>>>=2>=/@1E*2

0.2

6iuid ViscosityK lnc)$ & A L B ( CLt$

A @.$ @. $ /0.1 /0. 1 :.-: :.:

B >"2-:.>"2-:. :="2:-. :=" 2:-.> > ="1/. ="1 /.-/ -/

Vapor ViscosityK lnc)$ & A L B ( CLt$

C =1-.02 =1.02 /"0=:. /" 0=:.@1$ @1$ 2"--/. 2" --/.--$ --$

1.00$ 1.00$ -.:$ -. :$ :.1/$ :. 1/$

:"=22.@ :"=2 2.@=$ =$ /@. / @.:$ :$ /00.: /0 0.:1$ 1$

2"00@.@ 2"00@ .@$$ /@=.== /@=.== >0/.> >0 /.>$ $

0./

0.-

,ensityK kg(m- & m t L b

m -.01$ -.0 1$ -./ ./0$ 0$ 2.> 2 .>=$ =$

b 2"-12" -1-.: .:0 0 2"/1 2" /1..-2"2>0 2" 2>0.: .:/ /

,ensityK lb(ft- & m t L b

m 0.2 0 .21$ 1$ 0./ 0 ./0$ 0$ 0.0 0 .0=$ =$

b @=.11 @=.11 1.@ 1. @ =:./: =:. /:

Molecular !eight 2/0.1 2/0 .12 2 @=.:@ @=. :@ [email protected] 2@. 00

Cp(C9 2.20 2.20 2./>0 2. />0

$roblem Statement: Compare the )anhandle and !eymouth formulas with the +sothermal gas calculation

!nputs

5+ ?nits 7as molecular weight Temperature C )ipe diameter mm )ipe length km +nlet pressure k)a abs #utlet pressure k)a abs Ele9ation difference m Efficiency A9erage compressibility compressibility factor

Value

?5 ?nits

2.: -.@ 20/ -/./ 2-"00 20"-00 -0.> 2 2

' in miles psia psia ft

Value

2.: 200 :.0/= /0 /"000 2">00 200 2 2

Constants Base temperature Base pressure )ipe roughness Calculations Isothermal Gas Calculation 4eynolds 3umber 'riction factor 'low 4ate 5tandard 9olumetric rate Intermediate Calcs 7as specific gra9ity A9erage temperature A9erage pressure Jead correction

C k)a abs m

kg(h MM m-(day

G k)a abs k)a

Weymouth 5tandard 9olumetric rate

MM m-(day

Panhandle A 5tandard 9olumetric rate

MM m-(day

Panhandle B 5tandard 9olumetric rate

MM m-(day

* 200 0.0000:>

/00"000 VA6?E VA6?E VA6?E

0.=0 -22 2/"0@0 :1

' psia ft

lb(h MM ft-(day

4 psia psi

=0 2:. 0.0002>

/00"000 VA6?E VA6?E VA6?E

0.=0 >=0 2"=/ 

MM ft-(day

20"2>2

:0/

MM ft-(day

2>"220

:/@

MM ft-(day

2="0-:

t Fluid Flow

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