Vessel_Volumes.xls

7/25/2019 Vessel_Volumes.xls

1/72

Art Montemayor Vessel Design TipsAugust 21, 2000Rev: 2(05-05-03

!age 1 o" #2$le%troni% &ile'ame: 30100)32*+ls

or./eet: 'otes $+perien%e

T/e "olloing are some guielines an e+perien%e /ints "or t/e esign an utiliation o" pro%ess vessels*

T/is in"ormation is never taug/t nor is%usse in 4niversity %ourses or a%aemi% %ir%les* t /as 6een

/istori%ally e+pe%te t/at grauate engineers ill learn t/is in"ormation using t/eir on e""orts*

1 Alays try to esign aroun e+isting or availa6le stanar materials su%/ as:

a* .tanar pipe %aps* T/ese are usually availa6le o""-t/e-s/el" in %ar6on steel, as ell as stainless,

in sies up to 27 an in various pipe s%/eule t/i%nesses*

6* .tanar seamless pipe* T/is is 6asi% material t/at %an 6e reaily "oun availa6le toay* Alaysmae t/is your "irst priority in sele%ting t/e vessel s/ell 6e%ause o" t/e %onvenien%e o" eliminating

any plate rolling, longituinal el seam, an reu%ing t/e possi6ility o" stress relie"* T/is

option s/oul 6e re8e%te only i" re9uire alloy, all t/i%ness, or iameter is not availa6le*

2

an6oo !u6lis/ing n%*; !*5; Tulsa,


2/72

Art Montemayor Vessel Design TipsAugust 21, 2000Rev: 2(05-05-03


or./eet: 'otes $+perien%e

C emisp/eri%al /eas are t/e strongest o" t/e "orme /eas "or a given t/i%ness* A sp/ere is t/e

strongest non vessel s/ape* oever, t/e main trae-o"" /ere is t/at all sp/eres /ave to 6e "a6ri%ate

as ele sp/eri%al segments* T/is re9uires more manual intensive or an results in a /ig/er %ost*

) Alays 6e %ogniant o" t/e nee "or vessel entry into a vessel as ell as vessel internal parts su%/ as

trays, 6a""les, agitators, ip pipes, on%omers, separator vanes, emister pas, et%* .ometimes t/ese

items ire%tly a""e%t not only t/e /eig/t o" a vessel, 6ut also t/e iameter* A %/emi%al engineer s/oul

tae t/ese "a%tors into %onsieration even t/oug/ t/ey normally are not %onsiere /ile oing pro%ess

%al%ulations an simulations*


3/72

Art Montemayor !artially-&ille oriontal VesselsMay 15, 1))C

Rev:1(01B22B00

!age 3 o" #2 $le%troni% &ile'ame: 30100)32*+lsor./eet: !artial-&ille oriontalVessel

VOLUMES IN PARTIALLY FILLED HORIZONTAL VESSELS

Name: General Purpose Tank

Item No: T-C-15 Vessel Volume

Flat Heads Unit

Case: Partial Vol

3,381,604 3,901,853

1,956.95 2,258.02

Tank Inside Dia. in = 126.00 14,638.9 gal 16,891.1

Cylindrical Length, in = 276

Liquid Height, in = 120.00 Hemi Heads Unit F & D Heads

L/D = 2.2

H/D = 0.9524 4,422,102 3,595,708

2,559.09 2,080.85

19,143.3 gal 15,565.8

Cylindrical radius = r = 63.00 in.

Chord Length = CL= 53.7

in.egment !rea = !seg = 12,252 U. S. Gallons

Cylindrical "olume = = 3,381,604 14,638.9

# $ Dished "olume = = 214,104 926.9

%lli&soidal "olume = = 520,249 2,252.2

&herical "olume = = 1,040,498 4,504.3

2:1 Ellip.

Heads

in3

ft3

in3

ft3

in'

"cyl in(

"FD in(

"ell in(

"sph in(

te&s:)*+ %nter the required inormation in the YELLOWcells-)'+ The calculated results a&&ear in REDnumers.


4/72

Art Montemayororiontal .torage Tan

Volume ali6ration'ovem6er 11, 1)))

Rev: 1(03B12B00

!age o" #2$le%troni% &ile'ame: 30100)32*+ls

or./eet: oriontal Tan .trapping

CALIBRATION DATA FOR HORIZONTAL TANK ITH FOR!"D H"AD#

Tank Inside Diameter (ID) in%/es $%&'&&& H 10*0000 "t

Tan lengt/, tanBtan "eet %('&&& H %)* in%/es

Tank HeadT+,e Pressure 1 .t* is/ (non-pressure I 15 psig 'ote: !la%e an 7+7 in only one o" t/e

2 Torisp/eri%al (A.M$ &D I 200 psig 5 /ea options availa6le* " more t/an

3 $llipsoial (2:1 J 200 psig - one option %ontains an 7+7, t/e

$llipsoial (non-st Varies program ill use t/e "irst one it "ins*

5 emisp/eri%al To .uit

ea type sele%te: %.$ "lli,soidal ea Volume H $(&'/& %u*"t*

nsie ept/ o" /ea (DD: in%/es %& '


5/72



Rev: 1(03B12B00



Li7uid De,th Li7uid Volu8e Content

n%/es entimeters 4. Gals Eiters

1 2*5 2*3C 1#*) >C

2 5*0C >*#C 50*) 1)2

3 #*>2 12*51 )3*) 355

10*1> 1)*33 15*0 5C

5 12*#0 2#*0C 203*1 #>C

> 15*2 35*># 2>#*5 1,011# 1#*#C 5*01 33#*> 1,2#>

C 20*32 55*05 12*) 1,5>1

) 22*C> >5*#5 )3*1 1,C>

10 25*0 ##*05 5##*) 2,1C

11 2#*) CC*)3 >>>*) 2,521

12 30*C 101*3 #>0*1 2,C#3

13 33*02 11*2# C5#*1 3,20

1 35*5> 12#*>) )5#*# 3,>20

15 3C*10 11*5C 1,0>1*C ,01

1> 0*> 155*)0 1,1>)*3 ,20

1# 3*1C 1#0*>> 1,2#)*) ,C3C

1C 5*#2 1C5*C2 1,3)3*> 5,2>C1) C*2> 201*3> 1,510*2 5,#0)

20 50*C0 21#*2) 1,>2)*# >,1>0

21 53*3 233*5# 1,#51*C >,>22

22 55*CC 250*1) 1,C#>* #,0)3

23 5C*2 2>#*15 2,003*> #,5#

2 >0*)> 2C*2 2,133*2 C,0>3

25 >3*50 302*00 2,2>5*0 C,5>2

2> >>*0 31)*C# 2,3))*0 ),0>C

2# >C*5C 33C*02 2,535*2 ),5C3

2C #1*12 35>*5 2,>#3* 10,105

2) #3*>> 3#5*13 2,C13*5 10,>35

30 #>*20 3)*0> 2,)55*5 11,1#231 #C*# 13*23 3,0))*3 11,#15

32 C1*2C 32*>3 3,2*C 12,2>5

33 C3*C2 52*25 3,3)1*) 12,C21

3 C>*3> #2*0C 3,50*> 13,3C

35 CC*)0 )2*11 3,>)0*) 13,)51

3> )1* 512*3 3,C2*5 1,525

3# )3*)C 532*# 3,))5*> 15,103

3C )>*52 553*32 ,1)*) 15,>C#

3) ))*0> 5#*0# ,305*5 1>,2#5

0 101*>0 5)*)# ,>2*3 1>,C>#

1 10*1 >1>*02 ,>20*2 1#,>

2 10>*>C >3#*22 ,##)*1 1C,0>53 10)*22 >5C*5 ,)3)*1 1C,>#0

111*#> >C0*00 5,100*0 1),2#C

5 11*30 #01*5# 5,2>1*# 1),CC)

> 11>*C #23*25 5,2*3 20,50

# 11)*3C #5*03 5,5C#*# 21,122

C 121*)2 #>>*)0 5,#51*C 21,#2

) 12*> #CC*C# 5,)1>*5 22,3>

50 12#*00 C10*)1 >,0C1*C 22,)C)

&t3


6/72



Rev: 1(03B12B00

!age > o" #2$le%troni% &ile'ame: 30100)32*+ls


51 12)*5 C33*03 >,2#*# 23,>1>

52 132*0C C55*20 >,1*0 2,25

53 13*>2 C##* >,5C0*C 2,C#5

5 13#*1> C))*#3 >,#C*0 25,50#

55 13)*#0 )22*0> >,)15*5 2>,10

5> 12*2 )*3 #,0C3*2 2>,##5

5# 1*#C )>>*C2 #,251*2 2#,0)

5C 1#*32 )C)*2 #,1)*3 2C,05

5) 1)*C> 1,011*># #,5C#*5 2C,>C1

>0 152*0 1,03*11 #,#55*C 2),31#>1 15*) 1,05>*55 #,)2*1 2),)53

>2 15#*C 1,0#C*)C C,0)2*3 30,5C)

>3 1>0*02 1,101*3) C,2>0* 31,22

> 1>2*5> 1,123*#) C,2C* 31,C5)

>5 1>5*10 1,1>*15 C,5)>*2 32,)3

>> 1>#*> 1,1>C*) C,#>3*> 33,12#

># 1#0*1C 1,1)0*## C,)30*C 33,#5C

>C 1#2*#2 1,213*01 ),0)#*> 3,3C)

>) 1#5*2> 1,235*1) ),2>3*) 35,01C

#0 1##*C0 1,25#*31 ),2)*C 35,>5

#1 1C0*3 1,2#)*35 ),5)5*1 3>,2#0

#2 1C2*CC 1,301*31 ),#5)*C 3>,C)2#3 1C5*2 1,323*1) ),)23*) 3#,512

# 1C#*)> 1,3*)# 10,0C#*3 3C,130

#5 1)0*50 1,3>>*>5 10,2)*) 3C,#

#> 1)3*0 1,3CC*22 10,11*> 3),35>

## 1)5*5C 1,0)*># 10,5#2*5 3),)>

#C 1)C*12 1,31*00 10,#32*5 0,5>)

#) 200*>> 1,52*1) 10,C)1* 1,1#0

C0 203*20 1,#3*2 11,0)*3 1,#>>

C1 205*# 1,)*15 11,20>*1 2,35)

C2 20C*2C 1,51*C) 11,3>1*# 2,)#

C3 210*C2 1,535*# 11,51>*1 3,531

C 213*3> 1,555*CC 11,>>)*1 ,10)C5 215*)0 1,5#>*10 11,C20*C ,>C2

C> 21C* 1,5)>*13 11,)#1*0 5,250

C# 220*)C 1,>15*)> 12,11)*# 5,C13

CC 223*52 1,>35*5C 12,2>>*) >,3>)

C) 22>*0> 1,>5*)C 12,12* >,)1)

)0 22C*>0 1,>#*15 12,55>*1 #,>2

)1 231*1 1,>)3*0C 12,>)C*1 #,)))

)2 233*>C 1,#11*## 12,C3C*3 C,52)

)3 23>*22 1,#30*1) 12,)#>* ),051

) 23C*#> 1,#C*3 13,112*> ),5>>

)5 21*30 1,#>>*22 13,2>*> 50,0#2

)> 23*C 1,#C3*#) 13,3#C* 50,5#1)# 2>*3C 1,C01*0# 13,50C*0 51,0>0

)C 2C*)2 1,C1C*02 13,>35*2 51,51

)) 251*> 1,C3*>5 13,#5)*) 52,012

100 25*00 1,C50*)3 13,CC2*0 52,#

101 25>*5 1,C>>*C5 1,001* 52,)25

102 25)*0C 1,CC2*0 1,11C*0 53,3>>

103 2>1*>2 1,C)#*5> 1,231*# 53,#)>


7/72



Rev: 1(03B12B00

!age # o" #2$le%troni% &ile'ame: 30100)32*+ls


10 2>*1> 1,)12*31 1,32*3 5,21

105 2>>*#0 1,)2>*> 1,)*C 5,>20

10> 2>)*2 1,)0*52 1,553*) 55,01

10# 2#1*#C 1,)53*) 1,>5*> 55,3)

10C 2#*32 1,)>>*C# 1,#51*5 55,#>1

10) 2#>*C> 1,)#)*2) 1,C*# 5>,113

110 2#)*0 1,))1*1> 1,)33*# 5>,50

111 2C1*) 2,002*# 15,01C*5 5>,##0

112 2C*C 2,013*1> 15,0)C*# 5#,0#3

113 2C#*02 2,023*20 15,1#*0 5#,35C11 2C)*5> 2,032*55 15,2*1 5#,>23

115 2)2*10 2,01*1 15,30C*5 5#,C>>

11> 2)*> 2,0C*C) 15,3>>*> 5C,0C>

11# 2)#*1C 2,055*#0 15,1#*C 5C,2#)

11C 2))*#2 2,0>1*3 15,>0*C 5C,2

11) 302*2> 2,0>5*C3 15,)3*C 5C,5>>

120 30*C0 2,0>C*22 15,511*> 5C,>3


8/72

Art Montemayororiontal ylinri%al Tan

!artial Volume DeterminationMay 5, 2001

Rev: 0

!age C o" #2 $le%troni% &ile'ame: 30100)32*+lsor./eet: !artial oriontal

Hori9ontal C+lindri1al Tank :ith "lli,soidal or He8is,heri1al Heads

Total tan volume H (Total volume in to /eas L (Total volume in %ylinri%al se%tion

H

26BD

e H

% H

!artial tan volume H

"(% H oriontal %yliner %oe""i%ient ("rom Doolittle ta6les

or,

"(e H $llipsoial %oe""i%ient ("rom Doolittle ta6les

or,

/ere,

&or $llipsoial 2:1 /eas,

6 H (1B D

1B2

; $5* K$D(< = ; $5> D%L /2(1*5 - / ***********************Volume o" 2:1 $llipsoial /ea, in 4. gallons

V

H 2 V$ll

***********************Volume o" emisp/eri%al /ea, in 4. gallons

/ere, / H ept/ o" li9ui %ontent in t/e /oriontal /ea, in* H insie iameter o" t/e /oriontal /ea, in*


14/72

Art Montemayor Doolittle "7uation 3or Pariall+Filled Vessel HeadsMay 2#, 1))C

Rev: 0

!age 1 o" #2 $le%troni% &ile'ame: 30100)32*+lsor./eet: s !artial Vol*

T/e %al%ulation o" t/e partially-"ille %ylinri%al portion o" a /oriontal vessel is straig/t-"orar an %an 6e one using t/eanalyti%al e+pressions note a6ove* T/e e9uation given 6y aplan (V

2 s/oul 6e very a%%urate sin%e it is ire%tly erive

"rom an e+a%t mat/emati%al moel presente in *R** .tanar Mat/emati%al Ta6les; 12t/ $*(1)5); p* 3))*

T/e partial volume o" /eas is open to ina%%ura%ies an /ile t/e analyti%al e9uations are suita6le "or estimating, t/emet/o usually use is t/e e met/o "or etermining t/e li9ui "ra%tion o" t/e entire /ea* &or t/is purpose, t/e DoolittlQn* $ng* /em* 21, p* 322-323 (1)2C e9uation is use:

VpartialH 0*000)3 /2(3r - /

/ere, Vpartial

H partial volume, gallons

/ H ept/ o" li9ui in 6ot/ /eas, in* r H insie raius o" t/e /oriontal /eas, in*

('ote t/at t/is is t/e same e9uation o""ere 6y aplan, a6ove, "or a is/e-only /ea* is e9uation "or an ellipsoial/ea, alt/oug/ o" t/e same "orm, is 12 in e+%ess o" t/e 6asi% Doolittle relations/ip*

Doolittle mae some simpli"ying assumptions /i%/ a""e%t t/e a%%ura%y o" t/e volume given 6y /is e9uation, 6ut t/ee9uation is satis"a%tory "or etermining t/e volume as a "ra%tion o" t/e entire /ea* T/is "ra%tion, %al%ulate 6y Doolittle@s"ormula, is given in t/e Ta6le liste a6ove an regresse in t/e a%%ompanying /art* T/e Ta6le or t/e resulting 3r orepolynomial e9uation,

e H -2 (/B3L 3 (/B2- 0*001> (/B L 0*0001

%an 6e use to arrive at a partial volume o" stanar is/e, torisp/eri%al (A.M$ &D, ellipsoial, an /emisp/eri%al/eas it/ an error o" less t/an 2 o" t/e entire /ea@s volume*

oni%al /eas@ volumes are e"ine 6y t/e e+a%t mat/emati%al e+pression "or a trun%ate %one:

V%H / (D2L D L 2 B 12

/ere, V%H total %oni%al volume, %u* "t*

/ H /eig/t o" t/e %one, "t H iameter o" t/e small en, "t

D H iameter o" t/e large en, "t/en a tan volume %annot 6e %al%ulate, or /en greater pre%ision is re9uire, %ali6ration may 6e ne%essary* T/is isone 6y raining (or "illing t/e tan an measuring t/e volume o" li9ui* T/e measurement may 6e mae 6y eig/ing, 6a %ali6rate "lui meter (i*e*, Mi%ro Motion oriolis "lometer, or 6y repeately "illing small measuring tans /i%/ /ave6een %ali6rate 6y eig/t* &rom t/e non "lui ensity at t/e measure temperature, t/e e9uivalent volume %an 6e9ui%ly %onverte "rom t/e measure "lui mass*


15/72

Art Montemayor Doolittle "7uation 3or Pariall+Filled Vessel HeadsMay 2#, 1))C

Rev: 0

!age 15 o" #2 $le%troni% &ile'ame: 30100)32*+lsor./eet: s !artial Vol*

T/e Doolittle relations/ip %an 6e applie to oriontal an Verti%al-oriente $llipsoial (an &D vessel /eas* oeveit is important to note that the H/D ratio that sets the fractional Coefficient, Ze, is measured differently in bothcases* Re"er to t/e a6ove illustrations o" $llipsois oriente /oriontally an verti%ally*

ForHori9ontal Vessel Heads.

n t/is %ase, note t/at t/e BD ratio represents t/e Ei9ui ept/ ivie 6y t/e Ma8or A+is (internal iameter o" t/e$llipsoial /eas*

For Verti1al Vessel Heads.

T/e BD ratio %orresponing to t/is orientation is t/e Ei9ui ept/ ivie 6y t/e!inorA+is, not t/e Ma8or A+is (internal

iameter o" t/e $llipsoial /eas* T/is means t/at t/e nsie Dept/ o" Dis/ (DD must 6e non* T/e DD is t/e ept/o" t/e /ea at its %enter an in%lues t/e insie %orner raius 6ut not t/e straig/t "lange or nominal t/i%ness o" t/e /ea*/ara%teristi% DD@s "or various types o" /eas are:

.tanar is/e /ea: ); p* 2#>

/ere, V H li9ui volume in t/e is/, gallons (e+%luing "lange se%tion H li9ui ept/ in t/e is/, in%/es E H raius o" t/e is/, in%/es (usually e9ual to t/e tan D, minus > in%/es

oriontal vesseliameter (D(ma8or a+is

minor a+is(D

oriontal Vessel eas@ orientation Verti%al Vessel eas@ orientation


16/72

Art Montemayor Regression o" Doolittle !artial Volume oe""i%ient

!age 1> o" #2

0*000 0*000000

0*050 0*00#250

0*100 0*02C000

0*150 0*0>0#50

0*200 0*10000

0*250 0*15>250

0*300 0*21>000

0*350 0*2C1#50

0*00 0*352000

0*50 0*25250

0*500 0*500000

0*550 0*5##50

0*>00 0*>C0000*>50 0*#1C250

0*#00 0*#C000

0*#50 0*C3#50

0*C00 0*C)>000

0*C50 0*)3)250

0*)00 0*)#2000

0*)50 0*))2#50

1*000 1*000000

Ze

3;Ze00 00*000000

0*200000

0*00000

0*>00000

0*C00000

1*000000

1*200000

3;-< %-( = (-% %'0*&*$%))/*/*"&$0- = ('$$%%RE $

Coe33i1ients 3or Partial Volu8es in "lli,soids #,

H5D Ze

3;Ze2M; !age 15


20/72

Art Montemayor $llips

!

* D*, in%/es Vol* Gallons

12 0*)C

1C 3*31

2 #*C3

30 15*30

3> 2>*

2 1*))

C >2*>#

5 C)*23

>0 122*1

>> 1>2*)2

#2 211*52

#C 2>C*)3

C 335*C)

)0 13*12

)> 501*3C

102 >01*3)

10C #13*CC

11 C3)*5)

120 )#)*2>

12> 1133*>1

132 1303*3)

13C 1C)*33

1 1>)2*1>

150 1)12*>1

15> 2151*31>2 20)*3

1>C 2>C#*0C

1# 2)C5*3)

1C0 330*))

1C> 3>>*>3

1)2 011*0

1)C 3)C*)5 $llipsoial ea nsie Diameter H $%* in%/es

20 C11*0)

210 52C*21 Volume o" .ingle $llipsoial ea H $$(('*$ Gallons H $0$'0>$

21> 5#11*03

222 >200*2)

22C >#1>*#3

23 #2>1*0#

20 #C3*0>

&t3

0 50 100 150 200 250 300

0*00

1000*00

2000*00

3000*00

000*00

5000*00

>000*00

#000*00

C000*00

)000*00

3;-< &'&&&0*)$() -%'///>%*/&$

RE &'///////)%

%.$ "lli,soidal Head Volu8e

Inside Dia8ete r4 in1hes

Volu8

e4Hallons

Re"eren%e:Trinity nustries, n%*ea Division'avasota, TW!rou%t .ervi%esatalog X #)>2M (1))>


21/72

Art Montemayor 2:1 $llipsoial easMay 21

R

!age 21 o" #2&ile'ame: 30100)

ors/eet: $llipsoial

In1hes $&&'& A,,ro-i8ate area 3or no99le atta1h8ent

#tart o3 Knu1kle Radius 88 %0*&

Inside De,th

Knu1kle Radius ; I'D'5>$'%> In1hes Dish Radius

Note. $$('/) In1hes

Veri3+ all di8ension $&>) 88 %/0 88

:ith 2endor dra:ins

$%* In1hes

(%&&'> 88

NOT".

"lli,soidal %.$ heads are 3abri1ated and 8easured usin the Internal Dia8eter ;ID< o3 the head'

Note that this 8easure8ent 1on2ention is o,,osite to that o3 the A#!" FD head'

An+ 1+lindri1al shell 3abri1ated to 3it these heads 8ust 1on3or8 to or 8at1h the ID di8ension'

Tanent Line

#traihtFlane;Varies0( -%'//0))()$>

RE &'////%/0>)/

A#!" FD H"AD VOL!"

Inside Dia8ete r4 in1hes

Volu8

e4Hallons



23/72

Art Montemayor A.M$ &lange an Dis/e easMay21, 2003

Rev: 0

!age 23 o" #2&ile'ame: 30100)32*+ls

ors/eet: A.M$ &D eas

All Di8ensions

Veri3+ all di8ension

:ith 2endor dra:ins

NOT".

A#!" FD heads are 3abri1ated and 8easured usin the Outside Dia8eter ;OD< o3 the head'

Note that this 8easure8ent 1on2ention is o,,osite to that o3 the "lli,soidal head'

An+ 1+lindri1al shell 3abri1ated to 3it these heads 8ust 1on3or8 to or 8at1h the OD di8ension'

'ot all all t/i%nesses are s/on* nterpolate "or appro+imate insie ept/ '0& $& *$& >$ $$>

&'0& %> $'*( >'>> %*J $( *$& >$ $$(

&'*( %> $' >'0& **& $* *$& > $$>

&')0 %> %'%0 >'*/ $/ *$& 0) $$/

&'( %* $')0 >'$ $& **& >> $%%

&'0& %* $')0 >')0 %J $( **& >> $%$

&'*( %* $' >')0 )$$ $* **& > $%$

&')0 %* %'%0 >'/> $/ **& 0) $%0

&'( (& $' >' $& )*% > $%>

&'0& (& $' >'$ (&J $( )*% > $%%

&'*( (& $' >'$ )*% $* )*% > $%%&')0 (& %'%0 0'&& $/ )*% 0) $%)

&'( (& %'&& 0'0* $& )*% 0$ $>$

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Art Montemayor A.M$ &lange an Dis/e easMay21, 2003

Rev: 0

!age 25 o" #2&ile'ame: 30100)32*+ls

ors/eet: A.M$ &D eas

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26/72

Art Montemayor emisp/eri%al urve &it.eptem6er 12

!age 2> o" #2$le%troni% &ile'ame: 30100)or./eet: emisp/eri%al u

1*00 0*2>2

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H"!I#PH"RICAL H"AD VOL!"

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27/72

Art Montemayor Dis/e urve &it.eptem6er 1

!age 2# o" #2$le%troni% &ile'ame: 30100

or./eet: Dis/e

1*00 0*053

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28/72

Art Montemayor &lange an Dis/e easMay 21, 2003

Rev: 0

!age 2C o" #2&ile'ame: 30100)32*+lsors/eet: Dis/e eas

All Di8ensions

Veri3+ all di8ension

:ith 2endor dra:ins

NOT".

F D heads are 3abri1ated and 8easured usin the Outside Dia8eter ;OD< o3 the head'

An+ 1+lindri1al shell 3abri1ated to 3it these heads 8ust 1on3or8 to or 8at1h the OD di8ension'

'ot all all t/i%nesses are s/on* nterpolate "or appro+imate insie ept/ '%0 $& *$& %/ $&

&'0& %> $'0& >'( %*J $( *$& ( $$$

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&'0& (& >'*( >'*( (&J $( )*% $$ $$

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$'%0 $)& (')0 (0'&& %&>J (% >($ /0 /

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$'%0 $& (')0 >$'0& %%J (% >0)% /0 $&0>$'*( $& >' >$')0 0)/$ >$ >0)% $%> $&*&

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JTJ ;88< JR$J;88J

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31/72

Art Montemayor ylinri%al Vessel Volume Relations/ipMay 2#, 1))C

Rev:1(0>B0>B01

!age 31 o" #2 $le%troni% &ile'ame: 30100)32*+lsor./eet: ylinri%al Tan Volume

Dia8'4 in' al'5in' Dia8'4 in' al'5in' Dia8'4 in' al'5in' Dia8'4 in' al'5in'

15*0 0*#>5 2C*0 2*>>> 52 )*1) )> 31*33

15*5 0*C1# 2C*5 2*#>2 53 )*551 )C 32*>53

1>*0 0*C#0 2)*0 2*C5) 5 )*)1 100 3*000

1>*5 0*)2> 2)*5 2*)5) 55 10*2C5 102 35*3#3

1#*0 0*)C3 30 3*0>0 5> 10*>>2 10 3>*##

1#*5 1*01 31 3*2># 5# 11*0# 10> 3C*202

1C*0 1*102 32 3*C2 5C 11*3C 10C 3)*>5#

1C*5 1*1> 33 3*#03 5) 11*C35 110 1*10

1)*0 1*22# 3 3*)30 >0 12*20 112 2*>)

1)*5 1*2)3 35 *1>5 >2 13*0#0 11 *1C>

20*0 1*3>0 3> *0> > 13*)2> 11> 5*#50

20*5 1*2) 3# *>55 >> 1*C10 11C #*31

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21*5 1*5#2 3) 5*1#1 #0 1>*>>0 122 50*>05

22*0 1*>> 0 5*0 #2 1#*>2> 12 52*2#C

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23*0 1*#)) 2 5*))C #> 1)*>3C 12C 55*#05

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2*0 1*)5C >*5C2 C0 21*#>0 132 5)*21

2*5 2*01 5 >*CC5 C2 22*C>1 13 >1*050

25*0 2*125 > #*1) C 23*))0 13> >2*CC>

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2>*5 2*3CC ) C*1>3 )0 2#*50 12 >C*55#2#*0 2*#) 50 C*500 )2 2C*### 1 #0*502

2#*5 2*5#1 51 C*C3 ) 30*02 1> #2*#

1C #*#3

ylinri%al Volumes o" Vessels --- e+presse as Gallons o" Ei9ui ontent per in%/ lengt/ o"yliner*

.our%e: /emi%al $ngineers@ an6oo; !erry /ilton; 5t/ $ition; p* >-C>


32/72

Art Montemayorune 0

!age 32 o" #2 $le%troni% &ile'ame: 30100or./eet: &ittings@ V

VOL!"TRIC CAPACIT6 FOR BTT"LD"D FITTIN#

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33/72

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!age 33 o" #2$le%troni% &ile'ame: 3010

or./eet: &ittings@

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34/72

Art Montemayorune 0

!age 3 o" #2 $le%troni% &ile'ame: 3010or./eet: &ittings@ V

H enter to en o" run

M H %enter to en o" 6ran%/

Pi,e Ca,s.

V H Volume

D H nsie iameter

$ H lengt/

t H all t/i%ness

Crosses.

V H Volume

D H nsie iameter

H enter to en o" run

M H %enter to en o" 6ran%/

Con1entri1 e11entri1 redu1ers.

V ; D%5>< ;" t D5$% 52,#01 51,)5C

1C 53,0)C 52,353

20 53,5C# 52,C1

22 5,1## 53,2)

2 5,C#C 5,12C

2> 55,#00 5,)#

2C 5>,35) 55,>10

30 30,53) 30,0#1 5#,0 5>,>53

32 32,31 31,C31 5C,5) 5#,C2

3 3,1#> 33,>)C 5),)0 5),1C5

>%

20 #>,#> #5,C25

22 ##,1#2 #>,253

2 32,031 31,5>1 ##,>3) #>,#23

2> 33,>1# 33,132 #C,C)) ##,)#2

2C #),5# #C,>50

30 3#,053 3>,50 C0,>3> #),#10

32 3C,)02 3C,3#5 C1,>2 C0,50

3 0,C0 0,22) C2,31 C1,25

3> 2,C>> 2,311 C3,2#> C2,3>5

>

22 125,1C> 123,C#

2 C5,13 C3,)C 125,>># 12,35C

2> C),35 CC,1>3 12>,>)3 125,3##

2C 12#,3 12>,031

30 )C,305 )#,0# 12C,0 12>,#3>32 103,0 101,#53 12),5>1 12C,25

3 10#,)5) 10>,>35 130,>2 12),151

3> 113,050 111,>)3 131,1) 130,113

3C 11C,31# 11>,)2# 133,521 132,20#

0 123,#>0 122,33# 13,#10 133,02

2 12),3#C 12#,)23 135,)>0 13,>>0

135,1#3 133,>C5 13C,#2 13#,32

> 11,1 13),>22 10,25> 13C,)5


40/72

Profiles of Torispherical Dished Heads

The /olume calculator assumes the head &roile to e a &erect elli&se, 0hich is correct orelli&soidal head ut only a&&ro2imate or a Toris&herical &roile. Toris&herical heads can

&roiles de&ending on the relationshi& et0een: 1 3nuckle radius, &herical 4adius and Di

T0o ty&ical Toris&herical &roiles are sho0n elo0 in Red, and the true elli&se or the sam

head height is sho0n in Blue. Treating a Toris&here as an elli&se or /olume calculation 0gi/e a slight under estimate o the /olume. The error 0ill de&end on the relationshi& et0

radius, &herical 4adius and Diameter used.


41/72

Art Montemayor Volume o" a !artially &ille Torisp/eri%al =ottom ea uly 2

!age 1 o" #2&ile'ame: 30100

or./eet: & D !artial V

V"RTICAL TANK BOTTO! TORI#PH"RICAL H"AD VOL!" CALCLATION

D %4$(> mm H >'&% in%/es

ron Raius %4$(> mm H >'&% in%/es

?nu%le Raius *'00M

?nu%le Raius $(/' mm H 0'0& in%/es

6 H /%)'% mm

a H //%'% mm

% H $4)*0'* mm

Y H &'>> raians

%)') Z

+ H $%(') mm H >') in%/es

H %>>') mm H /'*( in%/es

/ H + L (*'> mm H $>'0$ in%/es

Appro+* ea Volume H

appro+imate %al%ulation "or nu%le se%tion

H (*'$ L >$%'(

H )/'> litres H %$&'/$ 4. gals

Volu8e o3 ,artiall+ 3illed Toris,heri1al head.

Le2el in "nd dish.#e1tor Area Knu1kle Area Total Head Volu8e

77 7r7 7+7 7r7 litres

0 & & & & & //% & & &M

10 () () (/0 / & //% & / $M

20 )> )> 00* (* & //% & (* 0M30 $$$ $$$ *) & & //% & & $&M

0 $>) $>) ))/ $>% & //% & $>% $M

50 $> $> *) %%$ & //% & %%$ %M

>0 %%$ %%$ />* ($* & //% & ($* >&M

#0 %0 %>0 //% (* $( $4&&& >$ >%) 0>M

C0 %/0 %>0 //% (* 0& $4&%% $*& 0>* *M

)0 ((% %>0 //% (* ) $4&>0 %( **/ >M

100 (*'>0 %>0 //% (* $%> $4&*) >$% )/'> $&&M

'otes:

(1 .e%tor volume H

(2 ?nu%le volume H

(3 Torisp/eri%al (also %alle A.M$ &D /eas are esigne an "a6ri%ate in t/e 4.A on t/e 6asis o" using t/e

Tan nternal Diameter(3

Ri

ri

DB2 - ri

6 RiB (R

i- r

i

((Ri- r

i2- 62[

.in-1(a B Ri

Ri os Y - %

Ri- % - +

B > \ (3a2L 2 L B 3 \ + ((DB22L (DB2a L a2

Ei9ui eig/t7/7 (mm Volume (1 Volume (2

! B > \ 77 (3 \ 7r72L 772

! B 3 \ 7+7 (7r72 L 7r7 \ a L a2

outsideiameter as t/eir nominal iameter*

a

6

+

Y

Ri

ri

%

/

0 10 20 30 0 50 >0 #0 C0 )0 1000

20

0

>0

C0

100"(+ H - 0*3#>151C31+N3 L 1*53300#22+N2 - 0*0>>3>>021+

RO H 0*))))>C5#1

Verti1al Toris,heri1al Tank Head Volu8e

Le2el o3 Fill

Volu8e

o3Fill


42/72

Art Montemayor Verti%al Tan =ottom Torisp/eri%al ea Volume.ep

!age 2 o" #2&ile'am

or./eet: Verti%al &

*D* H >'& in%/es

H ?nu%le-Raius (D &'&* in%/es

" H is/-raius parameter ("D $

D H 5*0 in%/es

"D H C in%/es

= 0*C# raians 0*CC3>C3 0*>C0C5

a1 H )*##0> in%/es 1*0>200 0*50C#)2a2 H *53C in%/es

D1 H #C*>3C3

s H 5*5>55C

t H C*)0#5 C*)0#5

u(/ H 5*5C31)5

mits o" t/e $9uation

0*00 h )*## )*## h 1*22 1*22 h Top

/ H 15*353#) in / H 15*353#) in / H 2 in

V H 5C,20 %0%'/& Gallons V H 5,255 %(>') Gallons V H 102,1C3 >>%'(

os H .in H

A%os H Asin H

in3 H in3 H in3 H


43/72

Art Montemayor Determining Vessel Volumesune 15, 2003

Rev: 0

!age 3 o" #2&ile'ame: 30100)32*+ls

or./eet: Re"eren%e Arti%le

T/e "olloing arti%le appeare in 7/emi%al !ro%essing7 magaine on 'overm6er 1#, 2002; pp* >-50:

Co8,utin Fluid Tank Volu8es,dated e7uations allo: enineers to 1al1ulate the 3luid 2olu8es o3 8an+ tanks 7ui1kl+ and a11uratel+

By Dan Jones, Ph.D., P.E.

al%ulating "lui volume in a /oriontal or verti%al %ylinri%al tan or ellipti%al tan %an 6e %ompli%ate, epening

on "lui /eig/t an t/e s/ape o" t/e /eas (ens o" a /oriontal tan or t/e 6ottom o" a verti%al tan* $+a%t

e9uations no are availa6le "or several %ommonly en%ountere tan s/apes* T/ese e9uations allo rapi ana%%urate "lui-volume %al%ulations*

All volume e9uations give "lui volumes in %u6i% units "rom tan imensions in %onsistent linear units* All

varia6les e"ining tan s/apes re9uire "or tan volume %al%ulations are e"ine in t/e ]Varia6les an De"initions^

sie6ar* &ig* 1 an &ig* 2 grap/i%ally illustrate /oriontal tan varia6les, an &ig* 3 an &ig* grap/i%ally

illustrate verti%al tan varia6les*

$+a%t "lui volumes in ellipti%al /oriontal or verti%al tans %an 6e etermine 6y %al%ulating t/e "lui volumes o"

appropriate %ylinri%al /oriontal or verti%al tans using t/e e9uations es%ri6e a6ove, an t/en 6y a8usting

t/ose results using appropriate %orre%tion "ormulas*

Hori9ontal 1+lindri1al tanks&lui volume as a "un%tion o" "lui /eig/t %an 6e %al%ulate "or a /oriontal %ylinri%al tan it/ eit/er %oni%al,

ellipsoial, guppy, sp/eri%al or torisp/eri%al /eas /ere t/e "lui /eig/t, /, is measure "rom t/e tan 6ottom to

t/e "lui sur"a%e* A guppy /ea is a %oni%al /ea it/ its ape+ level it/ t/e top o" t/e %ylinri%al se%tion o" t/e

tan, as s/on in &ig* 1* A torisp/eri%al /ea is an Ameri%an .o%iety o" Me%/ani%al $ngineers (A.M$-type

/ea e"ine 6y a nu%le-raius parameter, , an a is/-raius parameter, ", as s/on in &ig* 2*

An ellipsoial /ea must 6e e+a%tly /al" o" an ellipsoi o" revolution; only a /emi ellipsoi is vali - no ]segment^

o" an ellipsoi ill or, as is true in t/e %ase o" a sp/eri%al /ea t/at %an 6e a sp/eri%al segment* &or a

&igure 1* !arameters "or oriontal ylinri%al Tans it/ oni%al, $llipsoial, Guppy or .p/eri%al eas

sp/eri%al /ea, _a_ I R, /ere R is t/e raius o" t/e %ylinri%al tan 6oy* &or %on%ave %oni%al, ellipsoial,

guppy, sp/eri%al or torisp/eri%al /eas, _a_ I EB2*


44/72


Rev: 0

!age o" #2&ile'ame: 30100)32*+ls


1. =ot/ /eas o" a tan must 6e ienti%al* A6ove iagram is "or e"inition o" parameters only*

2.

3.

4. &or %onve+ /ea ot/er t/an sp/eri%al, 0 I a I a , "or %on%ave /ea a I 0

5.

6. $llipsoial /ea must 6e e+a%tly /al" o" an ellipsoi o" revolution

7.

=ot/ /eas o" a /oriontal %ylinri%al tan must 6e ienti%al "or t/e e9uations to or; i*e*, i" one /ea is %oni%al,

t/e ot/er must 6e %oni%al it/ t/e same imensions* oever, t/e e9uations %an 6e %om6ine to %al%ulate t/e

"lui volume o" a /oriontal tan it/ /eas o" i""erent s/apes*

&or instan%e, i" a /oriontal %ylinri%al tan /as a %oni%al /ea on one en an an ellipsoial /ea on t/e ot/er

en, %al%ulate "lui volumes o" to tans, one it/ %oni%al /eas an t/e ot/er it/ ellipsoial /eas, an

average t/e results to get t/e esire "lui volume* T/e /eas o" a /oriontal tan %an 6e "lat (a H 0, %onve+

(a J 0 or %on%ave (a I 0*

T/e "olloing varia6les must 6e it/in t/e ranges state:

" J 0*5 "or torisp/eri%al /eas* D J 0*

Varia6les use in Volumetri% $9uations an t/eir De"initions

a T/is is t/e istan%e a /oriontal tan@s /eas e+ten 6eyon (aJ0 or into (aI0 its %ylinri%al

se%tion or t/e ept/ t/e 6ottom e+tens 6elo t/e %ylinri%al se%tion o" a verti%al tan* &or a/oriontal tan it/ "lat /eas or a verti%al tan it/ a " lat 6ottom, a H 0*

T/is is t/e %ross-se%tional area o" t/e "lui in a /oriontal tan@s %ylinri%al se%tion*

D T/is is t/e iameter o" t/e %ylinri%al se%tion o" a /oriontal or verti%al tan*

T/ese are t/e /eig/t an it/, respe%tively, o" t/e ellipse e"ining t/e %ross se%tion o" t/e 6oy

o" a /oriontal ellipti%al tan*

T/ese are t/e ma8or an minor a+es, respe%tively, o" t/e ellipse e"ining t/e %ross se%tion o" t/e

6oy o" a verti%al ellipti%al tan*

3 T/is is t/e is/-raius parameter "or tans it/ torisp/eri%al /eas or 6ottoms; "D is t/e is/ raius*

h T/is is t/e /eig/t o" "lui in a tan measure "rom t/e loest part o" t/e tan to t/e "lui sur"a%e*

k T/is is t/e nu%le-raius parameter "or tans it/ torisp/eri%al /eas or 6ottoms; D is t/e

nu%le raius*

L T/is is t/e lengt/ o" t/e %ylinri%al se%tion o" a /oriontal tan*

ylinri%al tu6e o" iameter D (D J 0, raius R (R J 0 an lengt/ E (E J 0

&or sp/eri%al /ea o" raius r, r J R an _a_ I R

E J 0 "or a J 0, E J 2_a_ "or a I 0

0 I / I D*

_a_ I R "or sp/eri%al /eas*_a_ I EB2 "or %on%ave ens*

0 I / I 2R "or all tans*

0 I I 0*5 "or torisp/eri%al /eas*

E J 0*

3

H

A

B


45/72


Rev: 0

!age 5 o" #2&ile'ame: 30100)32*+ls


R T/is is t/e raius o" t/e %ylinri%al se%tion o" a /oriontal o" verti%al tan*

r T/is is t/e raius o" a sp/eri%al /ea "or a /oriontal tan or a sp/eri%al 6ottom o" a verti%al tan*

T/is is t/e "lui volume, o" "lui ept/ /, in a /oriontal or verti%al %ylinri%al tan*

Hori9ontal tank e7uationsT/e "olloing are t/e spe%i"i% e9uations "or " lui volumes in /oriontal %ylinri%al tans it/ %oni%al, ellipsoial,guppy, sp/eri%al, an torisp/eri%al /eas (use raian angular measure "or all trigonometri% "un%tions an

DB2 H R J 0 "or all e9uations*

n t/e V" e9uation "or torisp/eri%al /eas, use L (- "or %onve+ (%on%ave /eas*

n t/e /oriontal tan e9uations, V" is t/e total volume o" "lui in t/e tan in %u6i% units %onsistent it/ t/e linear

units o" tan imension parameters, an A" is t/e %ross-se%tional area o" "lui in t/e %ylinri%al 6oy o" t/e tan

in s9uare units %onsistent it/ t/e linear units use "or R an /* T/e e9uation "or A" is given 6y:

Hori9ontal 1+lindri1al tank e-a8,lesTo e+amples %an 6e use to %/e% appli%ation o" t/e e9uations*

&in t/e volumes o" "lui, in gallons, in /oriontal %ylinri%al tans 10C in%/es Qin* in iameter it/ %yliner

lengt/s o" 15> in*, "or %oni%al, ellipsoial, guppy, sp/eri%al an ]stanar^ A.M$ torisp/eri%al (" H 1, H 0*0>

/eas, ea%/ /ea e+tening 6eyon t/e ens o" t/e %yliner 2 in* (e+%ept torisp/eri%al, "or "lui ept/s in t/e

tans o" 3> in* (e+ample 1 an C in* (e+ample 2* al%ulate "ive times "or ea%/ "lui ept/ - "or a %oni%al,

ellipsoial, guppy, sp/eri%al an torisp/eri%al /ea*

&or e+ample 1, t/e parameters are D H 10C in*, E H 15> in*, a H 2 in*, / H 3> in*, " H 1 an H 0*0>* T/e "lui

volumes are 2,01*1) gallon (gal "or %oni%al /eas, 2,3C0*)> gal "or ellipsoial /eas, 1,)31*#2 gal "or guppy

/eas, 2,303*)> gal "or sp/eri%al /eas an 2,02C*>3 gal "or torisp/eri%al /eas*

&or e+ample 2, t/e parameters are D H 10C in*, E H 15> in*, a H 2 in*, / H C in*, " H 1 an H 0*0>* T/e "lui

volumes are >,1C0*5 gal "or %oni%al /eas, #,103*5 gal "or ellipsoial /eas, 5,)5*11 gal "or guppy /eas,

>,)35*1> gal "or sp/eri%al /eas, an 5,)3)*)0 gal "or torisp/eri%al /eas*

&or torisp/eri%al /eas, ]a^ is not re9uire input; it %an 6e %al%ulate "rom ", an D* &or t/ese torisp/eri%al

/ea e+amples, t/e %al%ulate value is ]a^ H 1C*2CC in*

Verti1al 1+lindri1al tanksT/e "lui volume in a verti%al %ylinri%al tan it/ eit/er a %oni%al, ellipsoial, sp/eri%al or torisp/eri%al 6ottom %an

6e %al%ulate, /ere t/e "lui /eig/t, /, is measure "rom t/e %enter o" t/e 6ottom o" t/e tan to t/e sur"a%e o" t/e

"lui in t/e tan* .ee &ig* 3 an &ig* "or tan %on"igurations an imension parameters, /i%/ also are e"inein t/e ]Varia6les an De"initions^ sie6ar*

&igure 2* !arameters "or oriontal ylinri%al Tans it/ Torisp/eri%al eas

3


46/72


Rev: 0

!age > o" #2&ile'ame: 30100)32*+ls


A torisp/eri%al 6ottom is an A.M$-type 6ottom e"ine 6y a nu%le-raius "a%tor an a is/-raius "a%tor, as

s/on in &ig* * T/e nu%le raius t/en ill 6e D, an t/e is/ raius ill 6e "D* An ellipsoial 6ottom must

6ottom an R is t/e raius o" t/e %ylinri%al se%tion o" t/e tan*

T/e "olloing parameter ranges must 6e o6serve:

```` D J 0*

&igure 3* !arameters "or Verti%al ylinri%al Tans it/ oni%al, $llipsoial or .p/eri%al =ottoms

Verti1al tank e7uationsT/e spe%i"i% e9uations "or "lui volumes in verti%al %ylinri%al tans it/ %oni%al, ellipsoial, sp/eri%al an

torisp/eri%al 6ottoms are provie in t/e Verti%al Tan $9uations sie6ar (use raian angular measure "or all

trigonometri% "un%tions, an D J 0 "or all e9uations*

&igure * !arameters "or Verti%al ylinri%al Tans it/ Torisp/eri%al =ottoms

6e e+a%tly /al" o" an ellipsoi o" revolution* &or a sp/eri%al 6ottom, _a_ I R, /ere a is t/e ept/ o" t/e sp/eri%al

a J 0 "or all verti%al tans, a I R "or a sp/eri%al 6ottom*

" J 0*5 "or a torisp/eri%al 6ottom*

0 I I 0*5 "or a torisp/eri%al 6ottom*


47/72


Rev: 0

!age # o" #2&ile'ame: 30100)32*+ls


Verti1al 1+lindri1al tank e-a8,lesTo e+amples %an 6e use to %/e% appli%ation o" t/e e9uations "or verti%al %ylinri%al tans; "or ea%/ e+ample,

%al%ulate t/e "lui volumes "or %oni%al, ellipsoial, sp/eri%al an torisp/eri%al 6ottoms*

&or e+ample 1, D H 132 in*, a H 33 in*, / H 2 in*, " H 1, an H 0*0>* T/e "lui volumes are 250*># gal "or a

%oni%al 6ottom, #C3*3> gal "or an ellipsoial 6ottom, 5C3*>0 gal "or a sp/eri%al 6ottom an )0*0# gal "or a

torisp/eri%al 6ottom*

&or e+ample 2, D H 132 in*, a H 33 in*, / H >0 in*, " H 1, an H 0*0>* T/e "lui volumes are 2,251*1C gal "or a

%oni%al 6ottom, 2,)02*C3 gal "or an ellipsoial 6ottom, 2,>5C*> gal "or a sp/eri%al 6ottom an 3,03>*#> gal "or

a torisp/eri%al 6ottom*

&or a torisp/eri%al 6ottom, parameter 7a7 is not re9uire input, 6ut %an 6e %al%ulate "rom t/e values o" ", ,

an D* &or t/ese e+amples, t/e %al%ulate value is a H 22*353 in*

Hori9ontal and 2erti1al elli,ti1al tanksT/e %ross-se%tions o" tan 6oies o" /oriontal an verti%al tans it/ ellipti%al 6oies are ellipses* &or t/is

arti%le, a /oriontal ellipti%al tan must 6e one o" to possi6le %on"igurations, s/on in &ig* 5, /ere t/e ma8or

an minor a+es o" t/e ellipti%al %ross-se%tions are eit/er verti%al or /oriontal*

T/e /eas o" /oriontal ellipti%al tans an t/e 6ottoms o" verti%al ellipti%al tans may 6e any o" t/ose es%ri6e

a6ove "or t/e %orresponing %ylinri%al tans, it/ t/e assumption t/at t/e /eas an 6ottoms are 7e"orme7

proportionately to t/e e"ormation o" t/e %ylinri%al 6oy to "orm t/e ellipti%al 6oy*

n %ertain %ases su%/ as t/ose it/ torisp/eri%al /eas an 6ottoms an sp/eri%al /eas an 6ottoms, it is

ne%essary to istinguis/ /i%/ ellipti%al a+is e"ines t/e /ea or 6ottom s/ape an /i%/ a+is /as 6een

proportionately stret%/e or %ompresse "rom t/e %ylinri%al tan s/ape to "orm t/e ellipti%al tan s/ape;

t/ere"ore, t/is istin%tion ill 6e mae "or all %ases "or t/e sae o" %onsisten%y, not ne%essity*

To %al%ulate t/e "lui volume in a /oriontal ellipti%al tan it/ t/e ellipti%al 6oy oriente in one o" t/e to

orientations s/on in &ig* 5 - /ere t/e /ea parameters are e"ine in t/e verti%al plane t/roug/ t/e tan

e9uations "or /oriontal %ylinri%al tans it/ t/e appropriately s/ape /eas* Multiply t/e volume "oun 6y

&igure 5* ross-se%tions o" oriontal $llipti%al Tans

To %al%ulate t/e "lui volume in a /oriontal ellipti%al tan it/ t/e ellipti%al 6oy oriente in one o" t/e to

orientations s/on in &ig* 5 - /ere t/e /ea parameters are e"ine in t/e /oriontal plane t/roug/ t/e tan

%enterline (plane goes t/roug/ D - %al%ulate t/e volume o" a /oriontal %ylinri%al tan it/ D H D

using t/e

D

BDto get t/e ellipti%al tan "lui volume*


48/72


Rev: 0

!age C o" #2&ile'ame: 30100)32*+ls


"-a8,les 3or hori9ontal elli,ti1al tanks&in t/e "lui volumes (in gal* o" /oriontal ellipti%al tans it/ ellipsoial, sp/eri%al an torisp/eri%al /eas it/

/eas, " H 0*C an H 0*1 "or torisp/eri%al /eas, "lui /eig/t / H C in*, an /ea parameters o" ea%/ tane"ine (1 in a /oriontal plane t/roug/ t/e tan %enterline an (2 in a verti%al plane t/roug/ t/e tan %enterline*

&or e+ample 1, %al%ulate /oriontal %ylinri%al tan volumes it/ D H 120 in*, E H 15> in*, a H 25 in* "or ellipsoial

an sp/eri%al /eas, " H 0*C an H 0*1 "or torisp/eri%al /eas, an / H 5#*> in* (C in* + 120B100, an multiply

t/e volume "oun 6y 100B120* &or e+ample 2, %al%ulate /oriontal %ylinri%al tan volumes it/ D H 100 in*,

E H 15> in*, a H 25 in* "or ellipsoial an sp/eri%al /eas, " H 0*C an H 0*1 "or torisp/eri%al /eas, an / H C,

an multiply t/e volume "oun 6y 120B100* T/e results are summarie in t/e "olloing ta6le:

T/e values "or 7a7 in t/e a6ove torisp/eri%al /ea %ases are 2#*0>5 in* "or e+ample 1 an 22*55 in* "or e+ample 2*

e"ining t/e %ross-se%tion o" t/e tan 6oy*

To %al%ulate t/e "lui volume in a verti%al ellipti%al tan, /ere t/e 6ottom parameters are e"ine in t/e plane

To %al%ulate t/e "lui volume in a verti%al ellipti%al tan, /ere t/e 6ottom parameters are e"ine in t/e plane

volume*

"-a8,les 3or 2erti1al elli,ti1al tanks&in t/e "lui volumes (in gal* o" verti%al ellipti%al tans it/ %oni%al, sp/eri%al an torisp/eri%al 6ottoms it/ t/e

H 0*2 "or t/e torisp/eri%al 6ottom, "lui /eig/t / H 53 in* ea parameters o" ea%/ tan e"ine (1 in a plane

%al%ulate verti%al %ylinri%al tan volumes it/ D H )> in*, a H 3 in* ("or %oni%al an sp/eri%al 6ottoms, " H 0*)

an H 0*2 ("or t/e torisp/eri%al 6ottom, an / H 53 in*, an multiply t/e volume "oun 6y #2B)>* &or e+ample 2,

%al%ulate verti%al %ylinri%al tan volumes it/ D H #2 in*, a H 3 in* ("or %oni%al an sp/eri%al 6ottoms, " H 0*)

an H 0*2 ("or t/e torisp/eri%al 6ottom, an / H 53 in*, an multiply t/e volume "oun 6y )>B#2* T/e results are

summarie in t/e "olloing ta6le:

%enterline (plane goes t/roug/ D

- %al%ulate t/e volume o" a /oriontal %ylinri%al tan it/ D H D

an a "lui

/eig/t /@ H /(D

BD using t/e e9uations "or /oriontal %ylinri%al tans it/ t/e appropriately s/ape /eas*

Multiply t/e volume "oun 6y DBD

to get t/e esire ellipti%al tan "lui volume*

t/e "olloing measurements: DH 100 in*, D

H 120 in*, E H 15> in*, a H 25 in* "or ellipsoial an sp/eri%al

&or a verti%al ellipti%al tan, e"ine DAan D

=to 6e t/e ma8or an minor a+es, respe%tively, o" t/e ellipse

t/roug/ 6ot/ t/e tan %enterline an t/roug/ DA, use D H D

A* 4se t/e e9uations a6ove "or a verti%al %ylinri%al

tan it/ t/e appropriately s/ape 6ottom* Multiply t/e volume "oun 6y D=BD

Ato get t/e ellipti%al tan volume*

t/roug/ 6ot/ t/e tan %enterline an t/roug/ D=, use D H D

=* 4se t/e e9uations a6ove "or a verti%al %ylinri%al

tan it/ t/e appropriately s/ape 6ottom* Multiply t/e volume "oun 6y DABD

=to get t/e esire ellipti%al tan

"olloing measurements: DAH )> in*, D

=H #2 in*, a H 3 in* "or %oni%al an sp/eri%al 6ottoms, " H 0*) an

t/roug/ t/e tan %enterline an DAan (2 in a plane t/roug/ t/e tan %enterline an D=* &or e+ample 1,


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al%ulate values "or 7a7 in t/e torisp/eri%al-6ottom %ases are 25*>C in* an 22*55 in* "or e+amples 1 an 2,

respe%tively* !

oriontal Tan $9uations

Coni1al Heads

Vf=A f L+(2a R

2

3 )(K)for 0h


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"lli,soidal Heads

u,,+ Heads ;"11entri1 Cone

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Vessel_Volumes.xls