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TIE U N IV E R SIT Y OF 0KLAJ10?.rA |

GRADUATE COLLEGE

PIL.SSUIL DROP THROUGH BUBBLE CAPS

A THE: US SUB?' IT T !’D TO THE GRADUATE FACULTY

i n p a r t i a l f u l f i l l m e n t o f th e r e q u ir e m e n ts f o r th e d eg ree o f DOCTOR OF PHILOSOPJIY

BY J IM .IE LEE HUITT N orm an, Oklahoma 1950 UNIYEKS11Y OF OKLAHOMA l i b r a r y

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UMI Number: DP10028

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PRESSURE DROP THROUGH BU3I3LE CAPS

APPROVED BY

0ENERAL

THESIS COMMITTEE

3 4 4 6 12

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ACKNOWLEDGMENTS

The w r i t e r w i s h e s t o e x p r e s s h i s s i n c e r e a p p r e c i a t i o n to : D r . R. L . H u n t i n g t o n , D e p a r t m e n t o f C h e m ic a l E n g i ­ n e e r i n g , U n i v e r s i t y o f O klaho m a, f o r h i s a d v i s e a n d d i r e c t i o n of th is in v e s tig a tio n . D r. L . G. A l e x a n d e r , D r . F . C. F o w l e r , a n d P r o f e s s o r L . S . R e id f o r t h e i r h e l p f u l s u g g e s t i o n s d u r i n g t h i s i n v e s t i ga t i o n . J . J . F o x , M. S i l v e r g l e l t , L . R. B r o o k s , C. N. W i n d l e , J . H. L i l b u r n , S . L . F o r r e s t e r , a n d E . C. H e l d f o r a s s i s t a n c e i n c o n s t r u c t i o n and o p e r a t i o n o f t h e e q u i p m e n t . M a g n o lia P e t r o l e u m Company f o r s p o n s o r i n g t h i s p r o ­ j e c t u n d e r t h e M a g n o lia P e t r o l e u m Company F e l l o w s h i p i n Chem­ i c a l E n g i n e e r i n g , U n i v e r s i t y o f O k lah o m a. JIMMIE LEE IIUITT

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TABLE OF CONTENTS

Page LIST OF T A B L E S ..............................................................................................

V

LIST OF ILLUSTRATIONS...............................................................................

Vi

CHAPTER I.

INTRODUCTION AND ST ATE! TENT OF PROBLEM....................

I

II.

THEORY- AND EQUATIONS...........................................................

6

III.

DESCRIPTION OF VARIOUS PIECES OF APPARATUS . .

16

IV .

PROCEDURE OF COLLECTING EXPERIMENTAL DATA. . .

31

V.

EXPF.REMEUTAL DATA....................................................................

42

V I.

ANALYSIS OF THEORETICAL EQUATIONS AND EXPERIMENTAL RESULTS .......................................................

94

APPLICATION OF THEORETICAL EQUATIONS UNDER VARIOUS CONDITIONS .............................................

1 24

V II. V III.

CONCLUSIONS.........................................................................................130

LITERATURE CITED .........................................................................................

iv I ii Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.

131

L IS T OF TABLES

T a b le

1.

Page P h y s i c a l P r o p e r t i e s o f L i q u i d s U sed i n I n v e s t i g a t i o n ...............................................................................

43

2.

P r e s s u r e D rop f o r t h e G as T h r o u g h Dry S l o t s .

. .

45

3.

E f f e c t o f L i q u i d V i s c o s i t y on P r e s s u r e D r o p .

. .

47

4.

E f f e c t o f S u r f a o e T e n s i o n on P r e s s u r e Drop . . .

49

5.

TTinimum S l o t O p e n in g a n d P r e s s u r e t o O v e r­ come S u r f a c e T e n s i o n ...........................................................

51

L e n g t h o f S l o t O p e n in g f o r V a r i o u s Gas Flow H a t e s ...................................................................................................

55

O b s e rv e d S l o t O p e n in g f o r V a r i o u s G as F lo w R a t e s on 0 . 2 5 - I n c h W id th S l o t ......................................................

57

7.

P r e s s u r e D rop D a ta f o r a 0 . 1 1 - I n c h W id th S l o t .

.

58

8.

P r e s s u r e D ro p D a ta f o r a 0 . 2 5 - I n c h T'ri d t h S l o t .

.

63

9.

P r e s s u r e D rop D a ta f o r a 0 . 3 7 5 - I n c h W id th S l o t



72

C a l c u l a t e d and O b s e rv e d P r e s s u r e D rop3 T h r o u g h B u b b le C ap s U n d e r V a r i o u s C o n d i t i o n s • . . . .

80

P r e s s u r e D rop and L i q u i d H e i g h t on T r a y ....................

83

6A. 6B.

10. 11.

v

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L IS T OF ILLU STRA TIO N S

F ig u r e 1. 2.

Page D ia g ra m o f A p p a r a t u s f o r P r e s s u r e D rop T h ro u g h B u b b le Cao S l o t s ..................................................

17

View o f A p p a r a t u s f o r P r e s s u r e D rop T h ro u g h B u b b le Cap S l o t s ..............................................................

18

View o f A p p a r a t u s f o r S u r f a c e T e n s i o n E f f e c t on P r e s s u r e D r o p ..............................................................

21

4.

View o f O n e - F o o t ’’Column S e c t i o n ” ...........................

23

5.

View o f S q u a r e and Round T ype B u b b le C a p s .

6.

View o f O n e - F o o t ”Column S e c t i o n ” Show ing L iq u id H e ig h t I n d i c a t o r s and P r e s s u r e D roo M ano m eter ......................................................

3.

7.

. . .

View o f T h i r t y - I n c h ’’Column S e c t i o n ” and B l o w e r ......................................................................................

24

26 28

8.

D iag ram o f T h i r t y - I n c h T r a y S h o w in g Cap A r r a n g e ­ m ent and P o i n t s ’Vhere E q u i v a l e n t L i q u i d H e i g h t s ".'ere O b t a i n e d ........................................................................ 29

9.

P r e s s u r e D rop T h ro u g h Dry S l o t s ................................

10.

E f f e c t o f L i q u i d V i s c o s i t y on P r e s s u r e D ro p .

. .

98

11.

E f f e c t o f S u r f a c e T e n s i o n on P r e s s u r e D rop . . •

100

12.

Minimum S l o t O p e n in g f o r I n c i p i e n t V a p o r F lo w . .

102

13.

P r e s s u r e t o Overcome S u r f a c e T e n s i o n D u r in g I n c i p i e n t V a p o r F l o w ....................................................... 104

14.

K. V a l u e s o f V a r i o u s S l o t s

96

in C a lc u la tin g P re ssu re t o Overcome S u r f a c e T e n s i o n .........................................105 vi

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v ii F ig u r e

Page

15.

L e n g t h o f S l o t O p e r a t i n g f o r P a r t i a l l y Ooened S l o t s ........................................................................................................ 107

16.

P r e s s u r e Drop T h ro u g h A 'Vet S l o t ..........................................109

17.

C a l c u l a t e d and O b s e r v e d P r e s s u r e D rop T h r o u g h V a r i o u s C a p s .....................................................................................112

18.

C a l c u l a t e d a n d O b s e rv e d P r e s s u r e D rop on T h i r t y - I n c h T r a y ...........................................................................114

19.

'V a te r H e i g h t on T h i r t y - I n c h T r a y a t an A i r Flow R a te o f 0 .0 1 1 0 CFS p e r S l o t ....................................116

20.

'V a te r H e i g h t on T h i r t y - I n c h T r a y a t an A i r Flow R a te o f 0 .0 1 4 6 CFS p e r S l o t ....................................117

21.

C a l c u l a t e d and O b s e r v e d L e n g t h o f S l o t O p e r a t i n g ...............................................................................................119

22.

C a l c u l a t e d a n d O b s e r v e d P r e s s u r e D r o p ............................... 121

I

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PRESSURE DROP THROUGH BUBBLE GA i’S CHAPTER I INTRODUCTION MID STATEMENT OF PROBLEM I n t h e many i n d i v i d u a l o p e r a t i o n s w h ic h e m p loy f r a c ­ tio n a tio n , g le

t h e b u b b le t r a y i s one o f t h e m o s t i m p o r t a n t s i n ­

o ie c e s o f p r o c e s s e q u ip m e n t.

d istilla tio n

I t h as been e s tim a te d t h ^ t

e q u ip m e n t makes uo o v e r o n e - h a l f t h e i n v e s t m e n t

f o r r e f i n e r y proco33 f a c i l i t i e s ^ - .

The b u b b le t r a y r e o r e s e n t s

o n ly a f r a c t i o n o f t h i s in v e s tm e n t, b u t i t a s i z e a b l e a m o u n t.

s till

c o n stitu te s

Many p a p e r s h a v e b e e n w r i t t e n on t h e f a c ­

t o r s i n v o l v e d i n t h e d e s i g n o f b u b b l e t r a y s ^ - * 2 *3 *4 *3 *®»7 *Q»9 » 1 0 , 1 1 , 1 2 , a t t a c k i n g t h e p r o b le m w i t h d i f f e r e n t c o n s i d e r a t i o n s . P r o g r e s s h a s b e e n made i n d e r i v i n g e q u a t i o n s w h ic h can be useu in d e s ig n in g a t r a y ,

but d e sig n e rs s t i l l

re ly to a g ro at

e x t e n t upon e x p e r i e n c e . P r i o r t o ’Vorld ’Vur I I , m a j o r e m p h a s i s was p l a c e d on t h e d e s i g n o f c o lu m n s fro m t h e s t a n d p o i n t o f c a p a c i t y .

The

S o u d e r s a n d Brown® e q u a t i o n , W = c f d ^ d i - d 2)]l / 2 w h ere ’V as m ass v e l o c i t y , l b s . p e r s q . f t . p e r h r . d i= d e n s i ty o f l i q u i d , l b s . p e r ou. f t . 1

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d2 = d e n s i ty o f v a p o r, l b s . p e r c u . f t . C = a c o n s t a n t d e p e n d i n g o n p l a t e s p a c i n g and su rfa c e te n sio n i s one o f t h e b e s t c r i t e r i a o f f e r e d f o r c a l c u l a t i n g colum n d ia m e te rs.

Q u ite o f t e n l i t t l e

a t t e n t i o n vwas g i v e n t o t h e

n u m b er o f c a p s , a n d t h e t r a y w as l a i d o u t w i t h a s many c a p s a s s p a c in g and a r e a p e r m i t t e d .

To m e e t i n c r e a s e d p r o d u c t i o n

dem ands d u r i n g t h e w a r , c o lu m n s w e re l o a d e d beyond t h e d e s i g n maximum a s c a l c u l a t e d by t h e a b o v e e q u a t i o n .

Poor f r a c tio n ­

a t i o n r e s u l t e d , a n d i n v e s t i g a t i o n showed t h a t some o f t h e c a p s on t h e t r a y w e re n o t f u n c t i o n i n g p r o p e r l y .

I n some o f t h e

l a r g e r c o lu m n s t h e e f f i c i e n c y w as i n c r e a s e d by c l o s i n g p art

o f th e c a p s .

o ff

T h i s shows t h e n e c e s s i t y o f know ing more

a b o u t t h e m e c h a n i c s o f a b u b b le c a p .

K now ledge o f t h e p r e s ­

s u r e r e q u i r e d t o make a c a p p a s s v a p o r u n d e r v a r i o u s c o n d i ­ t i o n s and th e p r e s s u r e d ro p th ro u g h a c ap f u n c t i o n i n g p r o p e r ly a r e o f p rim a ry im p o rtan c e in d e s ig n in g a t r a y . T he i m p o r t a n c e o f t h e p r e s s u r e d r o p t h r o u g h t h e b u b b le ca?3

i s o f t e n n o t a g r e e d u p o n by d i f f e r e n t d e s i g n e r s .

P e rry ^ -3

s t a t e s t h a t f o r b o t h a t m o s p h e r i c and p r e s s u r e o p e r a t i o n , p r e s ­ su re d ro p s ov er p l a te s a re n o t a s e rio u s d e sig n l i m i t a t i o n , p r o v i d i n g t h a t t o l e r a n c e s f o r l i q u i d d e p t h and p e r c e n t o f 14 v a p o r r i s e r a n d s l o t a r e a a r e a l l o w e d . R h y s and M in ic h n o tic e d

i n t h e i r t e s t s t h a t when t h e v a >or d i s t r i b u t i o n on a

t r a y -was p o o r , t h e m e a s u r e d p r e s s u r e d r o p s w e re much h i g h e r th a n p r e d i c te d . 22

I n v e s t i g a t i o n s 1 , 3 *1 2 , 1 4 , 1 5 *I 5 *1 7 , 1 8 , 1 9 , 2 0 *2 i *

* o f f e r m eans o f p r e d i c t i n g t h e p r e s s u r e d r o p t h r o u g h e i t h e r

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]

3

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p a r t o r t h e w h o le b u b b l e c a p .

E m p iric a l e q u a tio n s a re s e t

| it |

f o r t h w ith l i m i t a t i o n s to t h e i r u s e .

No m e n t i o n i s made o f

t h e minimum p r e s s u r e d r o p r e q u i r e d t o make t h e c a p p a s s v a p o r .

j

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G r i s w o l d ^ 6 and R o g e r s a n d T h i e l e ^ 7 o f f e r e q u a t i o n s

i

j /i''* I j

1 i

f o r c a l c u l a t i n g t h e p r e s s u r e d r o p b a s e d on t h e h y p o t h e s i s t h e p r e s s u r e d r o p i s d e t e r m i n e d by t h e d i f f e r e n c e b e tw e e n t h e 23 l i q u i d l e v e l i n s i d e a n d o u t s i d e t h e c a p . S h e rw o o d sta te s th a t, a t b e st,

th e s e e q u a tio n s a r e o n ly a p p ro x im a tio n s .

The

e q u a t i o n s a r e v a l i d up t o t h e p o i n t a t w h ic h t h e f u l l h e i g h t ]

o f t h e s l o t s a r e o p e r a t i n g , b u t n o minimum p r e s s u r e d r o p was

j

in d ic a te d .

K i r s c h b a u m 24 o f f e r s a n e x c e l l e n t q u a l i t a t i v e d i s ­

c u s s i o n o f t h e p r e s s u r e d r o p b u t o f f e r s no m ean s o f c a l c u l a \

tio n .

He m e n t i o n s t h a t , a f t e r t h e s t a t i c f o r c e s an d t h e f r i c -

I I

t i o n f o r c e s h a v e b e e n o v e rc o m e , t h e r e s t i l l a r e t h e r e s i s t ­ a n c e s o f f e r e d by t h e c o h e s i o n o f t h e b u b b l e s i n fo a m an d t h e 12 s u r f a c e t e n s i o n t o be o v e rc o m e . C i c a l e s e , e t a l o f f e r th e m o s t c o m p l e t e m etho d o f c a l c u l a t i n g t h e p r e s s u r e d r o p b u t do n o t c o n s i d e r t h e minimum p r e s s u r e d r o p .

T h ere a r e a l s o equa­

t i o n s ^ 7 *^8 w h ic h a r e o f f e r e d t o c a l c u l a t e t h e p r e s s u r e d ro p ;

o f a s l o t f u l l y o p e r a t i n g by c o n s i d e r i n g i t a s a n o r i f i c e . H a rrin g to n e t a l

25

sta te

th e p r e s s u r e d ro p th ro u g h b u b b le c a p s

h a s become m ore i m p o r t a n t s i n c e t h e d i a m e t e r s o f t h e f r a c t i o n ­ a t i n g c o lu m n s h a v e b e en i n c r e a s e d , a n d t h e r e i s a n e e d f o r m ore r e s e a r c h t o be d o n e . In g e n e r a l, i t a p p ea rs t h a t p re v io u s in v e s tig a to r s

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4 have in c lu d e d th e p r e s s u r e d ro p f a c t o r i n s t u d i e s o f o t h e r p ro b lem s o f t r a y d e s i g n . w h ic h c o r r e l a t e a re of l i t t l e

E m p iric a l e q u a tio n s a re o ffe re d

th e d a ta o f a p a r t i c u l a r i n v e s t i g a t i o n b u t

v a l u e w hen a p p l i e d t o o t h e r c a s e s .

seem ed d e s i r a b l e

T hus, i t

t o a tta c - c t h e p r e s s u r e d ro p p ro b lem w ith

o n l y t h a t p r o b l e m i n m ind a n d t o maice t h e i n v e s t i g a t i o n c o n ­ s i d e r i n g o n l y t h e f u n d a m e n t a l v a r i a b l e s e n c o u n t e r e d when d e a l ­ i n g w i t h a b u b b le c a p , a l i q u i d ,

and a v a p o r .

S t a t e m e n t o f P r o b le m T he p u r p o s e o f t h i s

i n v e s t i g a t i o n w as t o a r r i v e a t a

m e th o d o f c a l c u l a t i n g t h e p r e s s u r e d r o p im posed on t h e v a p o r a s i t p a s s e s th ro u g h a b u b b le c a p .

In o rd e r t h a t th e r e s u l t ­

i n g m e th o d o f c a l c u l a t i o n m i g h t a p p l y g e n e r a l l y t o v a r i o u s l i q u i d s a n d g a s e s , i t w as n e c e s s a r y t o d e t e r m i n e t h e r e l a t i o n b e tw e e n t h e p r o p e r t i e s o f v a r i o u s l i q u i d s a n d g a s e s and t h e p re s su re dro p.

I t w as a l s o n e c e s s a r y t o d e t e r m i n e t h e r e l a ­

t i o n o f th e p h y s i c a l c h a r a c t e r i s t i c s o f th e cap i t s e l f to th e p re s su re drop. To n a r r o w t h e p r o b l e m i n t o t h e s c o p e o f t h i s s t u d y , th e c a p and n o t th e t r a y was s t u d i e d .

I t i s re a liz e d

th a t

t r a y h y d r a u lic s i s an im p o rta n t f a c t o r in tr a y d e s ig n , but it

i s f e l t t h a t an u n d e rs ta n d in g o f th e p r e s s u r e dro p th ro u g h

t h e c a o s w i l l a l s o h e l p s o l v e some o f t h e p r o b l e m s i n t r a y h y d ra u lic s. T h e p r o b l e m o f f e r e d many d i f f e r e n t a v e n u e s o f a p p r o a c h ,

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5 and t h e one c h o s e n i s t h o u g h t t o be o f v a l u e t o b o t h t h e e n g in e e r and s c i e n t i s t .

C e r t a i n a s s u m p t i o n s w e re m ade, b u t

a l l w ere made w i t h c a u t i o n , a n d i t

i s b e lie v e d t h e i r e f f e c t

d o e s n o t a l t e r t h e f i n a l r e s u l t beyond t h a t w h ic h w ou ld be c a u s e d by e x p e r i m e n t a l e r r o r s .

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|

CHAPTER I I

!

j

THEOHT AND EQUATIONS

t

| I

T he p r e s s u r e d r o p n e c e s s a r y t o c a u s e a v a p o r t o f l o w

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s i d e o f t h e c a p t o f a l l b elow t h e t o p o f t h e s l o t , i s d e p e n d ­ e n t upon t h e d e n s i t y o f t h e l i q u i d a n d t h e s x t e n t t o w h ic h th e s l o t i s open.

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10 w h ic h g i v e s t h e c e n t e r o f p r e s s u r e , L , e q u a l t o 2 / 3 L . fo re,

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t h e c a p f r o m t h e t o p o f t h e s l o t t o some d i s t a n c e L b e lo w t h e t o p o f t h e s l o t c a n be c a l c u l a t e d by APX =

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w h e re A?q = p r e s s u r e d r o p i n l o s . p e r s q . f t . c a u s e d by s l o t b e i n g o p e n e d L f e e t ' 1 = d e n s i t y o f l i q u i d on t r a y i n l b s . o e r c u . ft. L - l e n g t h o f s l o t open i n f e e t P r e s s u r e D rop Due t o S u r f a c e T e n s i o n T he n e x t p r e s s u r e t o be c o n s i d e r e d i s t h a t p r e s s u r e n e c e s s a r y t o c a u s e t h e v a p o r t o b r e a .t t h r o u g h t h e o p e n p o r ­ t i o n o f t h e s l o t w h ic h h a s l i q u i d o u t s i d e t h e c a p a g a i n s t t h e s l o t o p e n in g .

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w h e re h = h e i g h t o f l i q u i d r i s e i n f e e t c a u s e d by t h e su rfa ce te n s io n = d e n s ity of th e l i q u i d in l b s . p e r cu . f t . s = su rface te n s io n in l b s . of fo rc e per f t . g = g r a v ita tio n a l c o n sta n t r = r a d i u s o f t h e b u b b l e i n f e e t fo rm e d a t t h e slo t T h i s e x p r e s s i o n i s p o s s i b l e by a s s u m i n g t h e c o n t a c t a n g l e i s zero .

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11 and •width o f t h e o p e n s l o t , a n d t h e s u r f a c e t e n s i o n . t h i s a n a l y s i s and th e above e q u a t i o n , i t p re s s u re (h ? i) er.

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a n d o r e s s u r e n e c e s s a r y t o f o r c e t h e b u b b l e t h r o u g h a m embrane o r sm a ll c a p i l l a r y .

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a n e x p r e s s i o n becom es o o s s i b l e t o d e t e r m i n e t h e maximum T r e a ­ s u r e f o r o v e r c o m in g t h e s u r f a c e t e n s i o n e f f e c t . The e q u i v a l e n t r a d i u 3 may be c a l c u l a t e d _ e q u iv a le n t d ia m e te r - L W 2 ~ L+ W

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w h e re r = e q u i v a l e n t r a d i u s i n f e e t L = s l o t l e n g t h i n f e e t open to flo w o f v a p o r w = s l o t w id th i n f e e t O b s e r v a t i o n s d u r i n g t h i s i n v e s t i g a t i o n showed t h a t t h e b u b ­ b l e s co m in g f ro m a su b m e rg e d s l o t a p p r o a c h e d t h e d i m e n s i o n s o f t h e o p e n p o r t i o n o f t h e s l o t a t i n c i p i e n t f l o w , and t h a t t h e r a d i u s o f c u r v a t u r e o f t h e b u b b l e o f v a p o r w as l e s s a t th e to p

o f th e s l o t .

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12 L W g k

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l e n g t h o f s l o t i n f e e t o pen t o f l o w w id th o f s l o t in f e e t g r a v i t a t i o n a l c o n sta n t a c o n sta n t su rfa ce te n s io n of liq u id , lb s . of fo rce per f t .

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t h e s l o t s , a v e l o c i t y h a s t o be g i v e n t o t h e v a p o r w h ic h a g a i n n e c e s s i t a t e s a p r e s s u r e d r o p due t o t h e o r i f i c e o f th e s l o t s .

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q _ w

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10

13 C o n s i d e r i n g o n l y h e a t an d c o m p r e s s i o n e n e r g i e s , g i v e AS = J t d s - J p d7

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w h e re T = a b s o l u t e t e m p e r a t u r e s = e n tro p y Wf = w ork t o o v e rc o m e f r i c t i o n By r e w r i t i n g A(PV) i n E q u a t i o n 10 a s PdV + YdP a n d s u b s t i t u t i n g E q u a t i o n 11 and E q u a t i o n 12 i n t o E q u a t i o n 1 0 , t h e r e r e ­ su lts 13 S i n c e t h e r e i s no w ork d o n e , t h e t e r m w i s z e r o .

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w f r e f e r s t o t h e w o rk t o o v e rc o m e t h e f r i c t i o n o f f e r e d t o t h e f l o w o f t h e v a p o r t h r o u g h t h e s l o t w h ic h t e n d s t o s e r v e a s an o r i f i c e .

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t i o n s , E q u a t i o n 13 r e d u c e s t o 14 S i n c e t h e volum e o f a g a s v a r i e s a s t h e a b s o l u t e p r e s s u r e , an d t h e a b s o l u t e

p r e s s u r e s d i f f e r o n l y s l i g h t l y s i n c e AX i s

s m a l l , t h e t e r m V may be r e p l a c e d by t h e r e c i p r o c a l o f t h e v a p o r d e n s i t y and -c o n sid e re d c o n s t a n t f o r a cap a s th e change i n t e m p e r a t u r e b e tw e e n p o i n t s 1 and 2 i s s m a l l .

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14 m o s t a few i n c h e s )

and c o n s i d e r i n g t h e v a p o r d e n s i t y c o n s t a n t

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2g 3y l e t t i n g AP0 b e t h e p r e s s u r e d r o p b e tw e e n p o i n t s 1 and 2 , E q u a t i o n 15 r e d u c e s t o 16 By a s s u m i n g t h e

sq u a re o f th e a v e ra g e v e lo c it y e q u a ls th e

av erag e o f th e v e l o c i t i e s sq u a re d , th e r e r e s u l t s 17 w h e re AP0 = p r e s s u r e d r o p i n l b s . p e r s o . f t . due t o th e s lo t a c tin g a s an o r if ic e C s a c o n sta n t = d e n s ity of vapor in lb s . per cu. f t . pass­ in g th ro u g h th e s l o t Q, = volum e o f v a p o r i n c u . f t . p e r s e c . th ro u g h th e s l o t l G = v olum e o f v a p o r i n c u . f t . p e r s e c . th ro u g h th e cap L = le n g th of s l o t open in f e e t w = w id th of s l o t open in f e e t g = g r a v ita tio n a l c o n sta n t A = c r o s s s e c t i o n a l a r e a o f a n n u l u s b e tw e e n t h e r i s e r and c a p i n s q . f t . The v a p o r h a s e n t e r e d t h e r i s e r a n d p a s s e d t h r o u g h th e s l o t s .

F o r t h i s flo w o f v a p o r t o ta k e

p la c e , a p re ssu re

d r o p i s n e c e s s a r y , an d t h i 3 i s e q u a l t o t h e sum o f t h e i n d i ­ v id u a l p ressu re d ro p s. 17, th e re r e s u lts

By a d d i n g E q u a t i o n s 2 , 3 , 5 , 3 , a n d

th e t o t a l p r e s s u r e d ro p th ro u g h th e b u b b le

cap, A? = APr* ♦ A ? s «■ APq ♦* APj

A Po

R eproduced w ith perm ission o f the copyright owner. Further reproduction prohibited w itho ut perm ission.

18

15 or 0 .1 4 7 fvQ|

+

♦ 2 /3

2ks(L+W) Cev [ q 2 q| ♦ “ Sw f + 2g ~ J % 2' ^

.. • 19

I t i s w o r t h w h i l e t o n o t e t h a t no m e n t i o n o f v i s c o s i t y w as made i n t h e d e r i v a t i o n o f t h e p r e s s u r e d r o p e q u a t i o n s . I t i s b e l i e v e d t h e v i s c o s i t y o f t h e l i q u i d on t h e t r a y h a s no b e a r i n g on th e p r e s s u r e d ro p th ro u g h th e b u b b le c a p .

Ac­

t u a l l y , t h e v a p o r d o e s n o t f o r c e i t s way t h r o u g h t h e l i q u i d u n til i t

i s f r e e of th e s l o t s .

th e s l o t s , i t

A f t e r th e v ap o r h a s once l e f t

i s no l o n g e r u n d e r t h e f o r c e o f t h e v a p o r i n

th e cap in th e se n se t h a t i t i s r e s t r i c t e d

to d ire c tio n of

f l o w o r s i z e o f c h a n n e l i n w h ic h t o f l o w .

T here i s p o s s ib ly

a p r e s s u r e dro p e n c o u n tere d a s th e l i q u i d

i s b e in g fo rc e d

from th e c a p , b u t o nce th e cap i s o p e r a t i n g t h i s l i q u i d o n ly o ffers a sta tic

f o r c e due t o i t s h e i g h t .

The v i s c o s i t y o f t h e v a p o r i s o f m i n o r i m p o r t a n c e b e ­ c au se o f th e l e n g t h o f flo w o f th e v a p o r th r o u g h a r e s t r i c t e d c h a n n e l.

P o s s i b l y t h e g r e a t e s t e f f e c t w o u ld be i n t h e r i s e r ,

a n d s i n c e t h e r i s e r i n t h e c a p i s u s u a l l y o f t h e o r d e r o f one t o f o u r in c h e s h ig h , t h i s e f f e c t i s p ro b ab ly n e g l i g i b l e .

The

o t h e r p o s s i b i l i t y c o n c e rn in g th e e f f e c t o f v i s c o s i t y on th e p re s s u re d ro p i s in th e flo w o f v a p o r th ro u g h th e s l o t s .

If

th e flo w i s i n c i p i e n t ,

t h e p r e s s u r e d r o n due t o t h e o r i f i c e

e ffe c t is n e g lig ib le .

I f th e q u a n tity i s s u f f i c i e n t to r e ­

s u l t i n a c o n tin u o u s flo w o f v a p o r th ro u g h th e s l o t , th e R e y n o ld s n u m b er w o u ld be s u c h t h a t t h e d i s c h a r g e c o e f f i c i e n t w o u ld be n e a r l y c o n s t a n t .

R eproduced w ith perm ission o f the copyright owner. Further reproduction prohibited w itho ut perm ission.

CHAPTER I I I j i

DESCRIPTION OF VARIOUS PIECES OF APPARATUS

|

S in g le S lo t A p p a ratu s

j

j

D u r i n g t h i s i n v e s t i g a t i o n t h e r e w ere s e v e r a l s e p a r a t e

;

p i e c e s o f a p p a r a t u s e m p lo y ed f o r d i f f e r e n t p h a s e s o f t h e i n -

|

v e stig a tio n .

|

v a r i a b l e s on a s i n g l e s l o t .

j

The f i r s t a p p a r a t u s w as a s s e m b l e d t o s t u d y t h e A d iag ra m i s p re s e n te d a s F ig u re

1 a n d a p h o t o g r a p h o f t h e e q u ip m e n t i s i n F i g u r e E .

A 4 - in ch

by 4 - i n c h b y 3 l / 4 - i n c h s q u a r e b u b b l e c a p w as u s e d .

A se c tio n

i

|

o f two s l o t s w as re m o v e d , a n d t h e r e m a i n i n g s l o t s w e re c l o s e d .

| The b o tto m w as c l o s e d by s h e e t m e t a l , and t h r e e p i p e n i p p l e s | w e re b r a z e d i n t o t h e c a p . A 3 / 8 - i n c h p i p e i n t h e t o p s e r v e d I | a s a n i n l e t f o r th e g a s . A second p ip e n i p p l e i n th e to p |

s e r v e d a s a l e a d t o t h e s t a t i c m a n o m e te r a n d t h e l i q u i d - l e v e l

!

i n d ic a to r f o r th e l iq u i d in s id e th e c a p .

! I

p i e was i n t h e b o tto m o f t h e c a o a n d s e r v e d a s t h e s e c o n d l e a d

|

The open s e c t i o n c u t f r o m t h e s l o t s s e r v e d a s a m ea n s f o r

|

v a r y in g th e s l o t l e n g t h and w i d t h .

|

w i t h s o l d e r u n t i l t h e o p e n p o r t i o n was p e r p e n d i c u l a r t o t h e

|

to th e l i q u i d - l e v e l i n d ic a t o r f o r th e l i q u i d in s id e th e cap .

b o tto m o f t h e c a p .

j

T he t h i r d p i p e n i p -

The e d g e s w e re b u i l t up

T h i n s h e e t s o f c o p p e r w e re u s e d t o make 16

| | R eproduced w ith perm ission o f the copyright owner. Further reproduction prohibited w itho ut perm ission.

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.

A -tO L U M N

SECTION*

B-BUBBLE CAP C -PR E SSU R E DROP MANOM ETER D-LIQUID LEVEL INDICATOR FOR

HOLD DOWN BAR ^ G A S INLET LEADS TO LIQUID k ^ L E V E L INDICATOR V UH.AIUK u

LIQUID IN CA P E-LIQUD L E V E L INDICATOR LIQUID ON TRAY

LEAD TO LIQUID F -G A S LEVEL INDICATOR *E*

FOR

FLOW M E T E R S

-CXH

G

A PP A R A T U S

FO R

PR ESSU R E DROP

Jl

THROUGH

FI GURE

I

o

BUBBLE

CAP

SLOTS

View o f A o p a r a t u s f o r P r e s s u r e D ro p T h r o u g h B u b b le Cap S l o t s F ig u re 2

R eproduced w ith perm ission o f the copyright owner. Further reproduction prohibited w itho ut perm ission.

19

th e t o p and s i d e s o f th e s l o t .

T h e y w e re p l a c e d t o g i v e t h e

d e s i r e d l e n g t h and w i d t h a n d t h e n s o l d e r e d i n t o p l a c e . The c a p w as p l a c e d i n a "c o lu m n s e c t i o n " w h ic h w as one f o o t i n d i a m e t e r .

T he p i p e n i p p l e i n t h e b o t t o m o f t h e

c a p e x t e n d e d t h r o u g h a h o l e i n t h e b o t to m o f t h e " t r a y " . T h i s w as made t i g h t b y s o l d e r i n g .

A b a r w edged b e tw e e n t h e

t o p o f t h e fr a m e a n d t h e c a p s e r v e d t o h o l d t h e c a p s e c u r e l y . A p i p e t a p i n t h e b o t to m o f t h e " t r a y " s e r v e d a s a l e a d t o t h e l i q u i d - l e v e l i n d i c a t o r f o r t h e l i q u i d on t h e t r a y .

T h is

l i q u i d - l e v e l i n d i c a t o r a lo n g w ith th e l i q u i d - l e v e l i n d i c a t o r f o r t h e l i q u i d i n s i d e t h e c a p a n d t h e m a n o m e te r f o r t h e s t a t i c p r e s s u r e i n s i d e t h e c a p w e re on a s m a l l p a n e l b o a r d a t t a c h e d t o t h e f r a m e s u p p o r t i n g t h e c o lu m n s e c t i o n .

The c o n n e c t i o n s

b e tw e e n t h e p i p e n i p p l e s on t h e c a p a n d t h e s e i n d i c a t o r s c a n b e s t be s e e n by F i g u r e 1 . Two d r y g a s f l o w m e t e r s w e re c o n n e c t e d i n p a r a l l e l . T h ey s e r v e d t o m e t e r t h e g a s g o i n g t o t h e c a p .

The p u r p o s e

o f t h e tw o m e t e r s i n p a r a l l e l w as t o i n s u r e a d e q u a t e g a s f l o w w ith o u t e x c e e d in g th e m e te rin g c a p a c i ty o f th e m e te r s . A p p a r a t u s F o r S t u d y Of S u r f a c e T e n s i o n The a p p a r a t u s u s e d t o s t u d y t h e e f f e c t o f s u r f a c e t e n ­ s i o n on t h e p r e s s u r e d r o p c o n s i s t e d e s s e n t i a l l y o f a 2 - i n c h by 2 - i n c h by 3 - i n c h r e c t a n g u l a r box w i t h a s l o t i n one s i d e a n d tw o c o p p e r t u b e s .

A H a y f s d r a f t g a g e a n d a tw o t h o u s a n d

m i l l i l i t e r b e a k e r w e re t h e o t h e r e s s e n t i a l p i e c e s o f e q u i p -

R eproduced w ith perm ission o f the copyright owner. Further reproduction prohibited w itho ut perm ission.

{ I !

m ent t o make up t h e a p p a r a t u s . c a n be s e e n i n F i g u r e 3 .

j j

A p h o to g rap h o f t h i s a p p a r a tu s

The s n a i l box w as o f s h e o t m e t a l w i t h a 3 / 4 - i n c h by 2 - i n c h s l o t i n one s i d e .

O v e r t h i s s l o t w e re t h i n s h e e t s o f

3

I

c o p p e r g a s k e t m a t e r i a l spaced to g iv e th e d e s i r e d 3 l o t w id th and l e n g t h .

The c o p p e r g a s k e t s h e e t s w e re s o l d e r e d t o t h e

j

box an d made t i g h t a r o u n d t h e e d g e s .

I n t h e t o p o f t h e box

|

was a c o p p e r t u b i n g n i p p l e f o r t h e i n l e t o f a i r .

| i j

n e a r t h e b o t to m was a n o t h e r c o p p e r t u b i n g n i p p l e t o p r o v i d e

t

j

On one s i d e

a p a s s a g e way f o r t h e l i q u i d i n t o t h e box o t h e r t h a n t h r o u g h th e s l o t .

! j i i ! i I

The c o p p e r t u b i n g n i p p l e on t h e t o p o f t h e box was

t h i r d p o r t i o n o f t h e "Y* w as c o n n e c t e d t o a r u b b e r s u c t i o n

i

b u lb .

c o n n e c te d t o a g l a s s "Y" by a r u b b e r t u b e .

T he s e c o n d p o r t i o n

o f t h e "Y" was c o n n e c t e d t o t h e E a y f s d r a f t g a g e , and t h e

The H a y 's d r a f t g a g e w as c o n n e c t e d i n s u c h a m an n e r

to

s e r v e a s a s t a t i c m a n o m e te r w hose s c a l e was i n s u b - d i v i s i o n s of l/1 0 0 -in c h .

A s m a l l m e t a l 3 C a le w i t h s u b - d i v i s i o n s o f

l / 6 4 - i n c h w as p l a c e d a g a i n s t t h e box and a d j a c e n t t o t h e s l o t o p e n in g . sta n d .

T h e b e a k e r f o r t h e l i q u i d s a t on t h e b a s e o f a r i n g The box w as h e l d b y a clam p t o t h e r i n g s t a n d a n d

c o u ld be r a i s e d o r l o w e r e d i n t o t h e b e a k e r .

A l i g h t fo cu sed

on t h e s l o t o p e n i n g w as t h e r e m a i n i n g p i e c e o f e q u ip m e n t i n t h is p a rtic u la r a p p a ra tu s.

R eproduced with perm ission o f the copyright owner. F urther reproduction prohibited w itho ut perm ission.

21

View o f A p p a r a t u s f o r S u r f a c e T e n s i o n E f f e c t on P r e s s u r e D rop F ig u re 3 I R eproduced with perm ission o f the copyright owner. F urther reproduction prohibited w itho ut perm ission.

22

G l a s s Column S e c t i o n E m p lo y in g Two C aps The t h i r d a p p a r a t u s T.vas o ne t o c h e c k t h e c o n c l u s i o n r e a c h e d a f t e r t h e a n a l y s i s o f t h e e x p e r i m e n t a l d a t a on t h e s i n g l e s l o t and t h e t h e o r e t i c a l e q u a t i o n s .

A "c o lu m n s e c ­

t i o n " o n e - f o o t i n d i a m e t e r c o n s i s t e d o f a w ooden " t r a y " ,

two

b u b b le c a p s , l i q u i d dow ncom er, g l a s s t u b e f o r l i q u i d o v e r ­ f l o w , and a g l a s s s h e l l . e q u ip m e n t. u re 5.

F ig u re 4 i s a p h o to g rap h o f t h i s

The b u b b l e c a p s w ere tw o t y p e s a s shown i n F i g ­

The s q u a r e t y p e c a p w as a 4 - i n c h by 4 - i n c h by 3 1 / 4 -

i n c h c a p w i t h r e c t a n g u l a r s l o t s 3 / l o - i i i C h by 1 - i n c h . w e re e i g h t s s l o t s c lo s e d .

par s id e .

T here

On t h r e e s i d e s t h e s l o t s w ere

Two o f t h e s e c a p s w ere s p a c e d 1 l / 2 - i n c h e s a p a r t on

t h e wooden t r a y w i t h t h e o p e n s l o t s o f e a c h c a p o p p o s i t e t h o s e o f t h e o t h e r c a p and 90 c e g r e e s t o t h e d i r e c t i o n o f f l o w o f l i q u i d a c r o s s th e t r a y .

A 3 / 8 - i n c h p ip e n i p p l e s e rv e d a s a

g a s i n l e t t o e a c h c a p , and a l / 8 - i n c h p i p e n i p p l e s e r v e d a s n le a d

t o a m a n o m e te r. The o t h e r t y p e o f c a p was a r o u n d c a p w i t h i t s

d ia m e te r 3 7 /8 - in c h e s .

in sid e

I t s h e i g h t w as 2 3 / 4 - i n c ’n e 3 i n c l u d i n g

t h e l e g s w h ic h w e re 1 / 2 - i n c h a n d SDaced 1 2 0 d e g r e e s a p a r t . T h e r e w ere t h i r t y s l o t s w i t h a 3 / l 6 - i n c h w i d t h and a 1 - i n c h le n g th .

A 3 / 8 - in c h p ip e n i p p l e i n th e c e n t e r o f th e cap to p

s e rv e d a s a g a s i n l e t , and a l / 8- i n c h p ip e n i p p l e s e r v e d a s a l e a d t o a m a n o m e te r . w ays.

T h i s t y p e c a p was em oloyed i n two

T he f i r s t w as w i t h t h e s k i r t c l e a r a n c e , a n a t h e s e c o n d

w i t h o u t t h e s k i r t c l e a r a n c e by c u t t i n g t h e l e g s o f f s o t h e

R eproduced w ith perm ission o f the copyright owner. Further reproduction prohibited w itho ut perm ission.

t

23

i

j i! View o f O n e - F o o t "Column S e c t i o n " F ig u re 4

R eproduced w ith perm ission o f the copyright owner. Further reproduction prohibited w itho ut perm ission.

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.

I

25

j

j

b o t to m o f t h e s l o t s r e s t e d c n t h e t r a y .

I n e a c h c a s e tw o -

I

t h i r d s o f t h e s l o t s W9 r e c l o s e d , and t h e c a o s s p a c e d 1 l / 2 -

|

| i n c h e s b e tw e e n e d g e s w i t h t h e o p e n s l o t s o f one c a p f a c i n g | I t h o s e o f t h e o t h e r c a p a n d a t 90 d e g r e e s t o t h e d i r e c t i o n o f | | f l o w o f l i q u i d on t h e t r a y . j

)

The s h e l l o f t h e " c o lu m n s e c t i o n ^ w as a p y r e x g l a s s

i

s h e l l o n e - f o o t i n d i a m e t e r and 2 l / 2 - f e e t i n h e i g h t . tray ,

\ fa lse

c o n s i s t i n g o f a m e t a l c o n t a i n e r , and a s h e e t a e t a l down­

ed/ .3 r s a t on t h e w ooden t r a y .

T he c r o s s - s e c t i o n a l a r e a o f

t h e downcom er w as a p p r o x i m a t e l y t e n p e r c e n t o f t h e o l a t e a r e a , an a t h e a r e a u n d e r t h e d o w n s p o u t w as t h e sa m e. f o r t h e l i q u i d was a 2 - i n c h g l a s s t u b e . w e re

The o v e r f l o w

Four cooper tu b es

i l a c e d do tw e e n t h e c a o s w i t h t h e u p p e r e n d b e i n g f l u s h

w i t h th e w ooden " t r a y ” .

T h e y e x t e n d e d below t h e t r a y a n d

w a re c o n n e c t e d t o f o u r l i q u i d - l e v e l i n d i c a t o r s on t h e p a n e l b o a r d a s s e e n by F i g u r e 6 . v a le n t s ta tic C ap 3 .

T hese i n d i c a t o r s gave th e e q u i­

p r e s s u r e o f t h e l i q u i d on t h e t r a y b e tw e e n t h e

T he m a n o m e te r on t h e p a n e l b o a r d w as c o n n e c t e d t o t h e

l./3 - in c h n i p p l e s on th e c a o s . 7 / a t e r was s u p p l i e d f r o m a 1 2 0 0 - g a l l o n s t o r a g e t a n k by m eans o f a pump, a n d i t w as m e t e r e d b e f o r e d e l i v e r y t o t h e " tra y " .

A b a r r e l serv ed to c a tc h th e w a te r le a v in g th e t r a y ,

a n d a s e c o n d pump r e t u r n e d t h e w a t e r t o t h e s t o r a g e t a n k .

j

344612

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.

26

i

j

View o f

O n e - F o o t "Colum n S e c t i o n " S n o w in g L i q u i d E e i g i i t I n d i c a t o r s a n d P r e s s u r e D ro p M an o m eter F ig u re 6

R eproduced w ith perm ission o f the copyright owner. Further reproduction prohibited w itho ut perm ission.

\

; ;

27 T h i r t y - I n c h T r a y W ith T h i r t e e n C aps The f o u r t h a p p a r a t u s w as s i m i l a r i n p u r p o s e t o t h e t h i r d a p p a r a t u s d e s c r i b e d a b o v e , b u t i t was more e l a b o r a t e , a s shown by F i g u r e 7 .

I t w as a " c o lu m n s e c t i o n " t h i r t y - i n c h e s

i n d i a m e t e r , a n d t h e t r a y w as o n e - i n c h plyw ood c o a t e d w i t h w a terp ro o f v a r n is h .

T h e r e w e re t h i r t e e n b u b b l e c a p s o n t h e

t r a y , a r r a n g e d i n ro w s o f f o u r - f i v e - f o u r , 90 d e g r e e s t o t h e d i r e c t i o n o f flo w o f th e l i q u i d a c r o s s th e t r a y .

The b u b b le

c a p s w e re s p a c e d a t e q u i d i s t a n c e s a p a r t w i t h 6 - i n c h e s b e tw e e n c e n te rs.

F o u r s m a l l p i e c e s o f s h e e t m e t a l w e ld e d on t h e cap

s e r v e d t o s e c u r e t h e c a p s t o t h e t r a y by wood s c r e w s . rise rs fitte d

The

t i g h t l y i n t o t h e w ooden t r a y and e x t e n d e d 2 -

in c h e s above th e t r a y .

T e n p e r c e n t o f t h e t r a y was a l l o t e d

t o e a c h , t h e l i q u i d downcom er a n d t h e o v e r f l o w .

F o rty le n g th s

o f c o p p e r t u b i n g s p a c e d a t v a r i o u s p o i n t s on t h e t r a y s e r v e d a s l e a d s t o l i q u i d - l e v e l i n d i c a t o r s on t h e p a n e l b o a r d .

T h ey

w e re f l u s h w i t h t h e t r a y a n d e x t e n d e d down t h r o u g h t h e s e c t i o n b e lo w t h e t r a y .

T he a r r a n g e m e n t o n t h e t r a y i s shown i n F i g ­

u re 8 . T he s e c t i o n belo w t h e t r a y w as o n e - f o o t i n h e i g h t a n d se rv e d a s th e f a l s e

" t r a y " b e l o w , i n t h a t t h e a i r c o u l d be

f e d t o t h i s c h a m b e r w i t h t h e o n l y o u t l e t b e i n g up t h e v a p o r rise rs.

I n t h i s s e c t i o n w e re two t a p s ; one w as c l o s e d f o r

a t h e r m o m e t e r w e l l , a n d t h e o t h e r w as open f o r a m a n o m e te r. An a i r d u c t 7 - i n c h e s i n d i a m e t e r c o n n e c t e d t h i s c h a m b e r w i t h

R eproduced w ith perm ission o f the copyright owner. Further reproduction prohibited w itho ut perm ission.

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.

29

DIAGRAM OF 3 0 -INCH TRAY ARRANGEMENT AND POINTS LIQUID

HEIGHTS

WERE

WATER

SHOWING CAP WHERE EQUIVALENT

OBTAINED

FLOW

SECTIONS D ia g ra m o f T h i r t y - I n c h T r a y S h o w in g Cap A r r a n g e m e n t a n d P o i n t s Where E q u i v a l e n t L i q u i d H e i g h t s W ere O b t a i n e d F ig u re 8 R eproduced w ith perm ission o f the copyright owner. Further reproduction prohibited w itho ut perm ission.

30 a B u f f a l o F o r g e I n d u s t r i a l E x h a u s t F a n w h ic h w a s c a p a b l e o f w o rk in g a g a i n s t a 5 - In c h w a te r s t a t i c h e a d .

A maximum d e ­

l i v e r y o f 5000 c u b i c f e e t p e r m i n u t e o f a i r c o u l d be o b t a i n e d w ith t h i s f a n .

I n t h e a i r d u c t w e re two p i t o t t u b e s .

s t a t i c m a n o m e te r w a s a l s o o n t h e a i r d u c t . s a t on t h e l i q u i d dow ncom er t o t h e t r a y . in to th is fa ls e

A "fa lse

A tra y ”

The w a t e r w as f e d

t r a y f ro m a 2 - i n c h p i p e w h ic h w as c o n n e c t e d

to th e w a te r i n l e t f o r th e c o o lin g to w er o f th e U n i v e r s i ty o f Oklahoma po w er p l a n t . f l o w f ro m t h e t r a y .

A b a r r e l serv ed to c a tc h th e o v er­

A seco n d b a r r e l c o n n e c te d t o th e f i r s t

h a d a t r o u g h a n d V - n o t c h w e i r w h ic h s e r v e d a s a m eans o f d e te r m in in g t h e w a te r flo w r a t e . A p a n e l b o a r d w i t h t e n l i q u i d - l e v e l i n d i c a t o r s was m o u n ted on a m e t a l a d j u s t a b l e s t a n d .

T h is a llo w e d th e p a n el

b o a r d t o be l e v e l e d a n d a t t h e 3 ame h e i g h t a s t h e t r a y .

The

c o n n e c t i o n s t o t h e l i q u i d - l e v e l i n d i c a t o r s w e re r u b b e r t u b i n g a n d c o u l d be c o n n e c t e d t o a n y o f t h e c o p p e r t u b e s co m in g fro m th e t r a y .

T h is f a c i l i t a t e d

th e stu d y o f any p a r t i c u l a r p o r­

t i o n on t h e t r a y w i t h a minimum o f i n d i c a t o r s o n t h e p a n e l b o ard .

R eproduced with perm ission o f the copyright owner. F urther reproduction prohibited w itho ut perm ission.

CHAPTER TV

j

PROCEDURE OF COLLECTING EXPERIMENTAL DATA

| j

|

T e c h n iq u e I n O b t a i n i n g D a t a U s i n g S i n g l e S l o t A p p a r a t u s The a p p a r a t u s shown i n F i g u r e s 1 a n d 2 w as u se d t o

I c o l l e c t e x p e r i m e n t a l d a t a on a s i n g l e s l o t i n a b u b b le c a p . The s i z e o f t h e s l o t w as f i r s t d e c i d e d upon a n d t h e c o p p e r g a s k e t s t r i p s w e re a d j u s t e d t o g i v e t l i i s d e s i r e d o p e n i n g . A f t e r t h e s t r i p s w e re s o l d e r e d i n p l a c e , t h e c a p w as p l a c e d on t h e " t r a y " , a n d t h e n i p p l e e x t e n d i n g t h r o u g h t h e b o tto m o f t h e " t r a y " was s o l d e r e d t o p r e v e n t t h e t r a y fro m l e a k i n g . The 3 / 8 - i n c h n i p p l e on t h e t o p o f t h e c a p was c o n n e c t e d t o j t h e g a s m e t e r by m ean s o f a r u b b e r h o s e .

T he l / 4 - i n c h n i p p l e

I on t h e t o p o f t h e c a p was c o n n e c t e d t o a "Y" c o n n e c t i o n by i rubber tu b in g .

The "Y" c o n n e c t i o n i n t u r n w as c o n n e c t e d t o

; a m a n o m e te r a n d t o t h e t o p o f t h e l i q u i d - l e v e l i n d i c a t o r f o r 1 th e l i q u i d

in s id e th e cap.

The n i o p l e on t h e b o tto m o f t h e

I c a p a n d e x t e n d i n g t h r o u g h t h e t r a y w as c o n n e c t e d t o t h e b o tto m o f th e l i q u i d - l e v e l i n d i c a t o r f o r th e l i q u i d in s id e th e c a p . I The p i p e n i p p l e i n t h e b o t to m o f t h e t r a y a n d a d j a c e n t t o i t h e c a p was t h e n c o n n e c t e d t o t h e b o tto m o f t h e l i q u i d - l e v e l 3i

R eproduced w ith perm ission o f the copyright owner. Further reproduction prohibited w itho ut perm ission.

32

in d ic a to r fo r

th e l iq u id

j

on th e t r a y .

A llc o n n e c tio n s

j

w e re

i

t h e n c h e c k e d t o i n s u r e t h a t n o n e w as l e a k i n g .

! I

A s n a i l c a r p e n t e r * s l e v e l w as t h e n p l a c e d o n t h e t r a y , an d t h e b o l t s i n t h e l e g 3 o f t h e f r a m e w e re a d j u s t e d u n t i l t h e t r a y w as l e v e l .

The d i s t a n c e b e tw e e n t h e t o p o f t h e

s l o t an d t h e " t r a y " w as m e a s u r e d t o t h e n e a r e s t l / o 4 - i n c h

j

j by m eans o f a m e t a l s c a l e . T he d e s i r e d l i q u i d s e a l d e p t h | ! w as d e c i d e d u p o n , a n d t h e l i q u i d w as t h e n p o u r e d i n t o t h e

\

’’ co lu m n s e c t i o n ” .

A few m i l l i l i t e r s

I

o f t h e same l i q u i d w e re

i

! p o u r e d i n t o a g r a d u a t e d c y l i n d e r , an d t h e m e t a l s c a l e was I! I lo w ered i n t o t h i s l i q u i d . As e c o n d m e t a l s c a l e w as p l a c e d | I ' | a d j a c e n t t o th e f i r s t m e ta l s c a l e and g r a d u a l l y lo w e re d u n t i l j

]

i t to u c h e d th e l i q u i d .

i

?! r e a d .

T h e n t h e b o t t o m o f t h e m e n i s c u s was

The d i f f e r e n c e b e tw e e n t h e b o t t o m o f t h e m e n i s c u s a n d

j j

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! t h e o o i n t w h e re t h e s e c o n d m e t a l s c a l e t o u c h e d t h e l i q u i d j s e r v e d a s a c o r r e c t i o n t o be a p p l i e d t o t h e m e a s u r e m e n t o f : t h e d e p t h o f t h e l i q u i d on t h e t r a y .

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TABLE V I I I COfIT’ D PRESSURE DROP DATA FOR A 0 , 2 5 - INCH WIDTH SLOT .....................................LIQUID........................................................................................... GAS.................................................. Name

Seal

Temp. D e n s i t y

S u rfa c e T ension

Name

(Lb3, p e r ( F e e t ) ( ° F . ) Cu. F t . ) (D ynes p e r Cm.) 62.4 W a t e r 0 , 2 5 0 80 71.8 Propane 62.4 71 .8 0 . 2 5 0 80 62 .4 71.8 0 . 2 5 0 80 62 .4 71.8 0 . 2 5 0 80 Note:

Temp, D e n s i t y

Flow R a t e

( L b s . p e r (Cu. F t . p e r Se o . ) ( ° F . ) Cu. F t . ) 0.1067 88 0.00926 88 0.1067 0.0 14 0 0.1067 0.0188 88 0.1067 88 0.0246

Observed Pressure Drop {PSF) 17.9 19.0 19.5 20.3

S l o t d i m e n s i o n s w e r e 0 . 5 0 - i n o h by 0 . 2 5 - i n o h . M

72

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1 .0 0 1 .0 0 0 .9 3 8 0 .9 7 5 0 .9 6 3 1 .0 0 1 .0 0 0 .9 8 5 0 .9 8 5

1 3 .4 1 3 .4 1 3 .4 1 3 .4 1 3 .4 7 .1 5 7 .1 5 7 .1 5 7 .1 5

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0 . 0 0 21 0.014C 0 .0 1 6 £ 0.023*; 0.033C 0 .0 0 6 2 0 .0 1 7 4 0 . 0 2 6 1; 0.032S

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.

80 TABLE X DROPS THROUGH BUBBLE CAPS UNDER VARIOUS CONDITIONS . . U H . .......... « R a te ,1 p e r T ray ith )

Flow R a te (C u . F t . per Sec. per S lo t)

Temp. D e n s i t y O b s e r v e d ( ° F . ) (L b s. per P r e s s u r e Drop Cu. F t . ) ( PSF)

C a lc u la te d P ressure Drop (PSF)

F lo w R a t e (L b s. o e r Sq. F t . per Sec.

1 6 .2 1 7 .1 1 8 .0 1 9 .1 1 9 .7 1 4 .5 1 5 .7 1 7 .3 1 7 .6 1 3 .0

0 .6 7 8 1 .1 7 1 .4 9 1.88 2 .2 5 0 .5 8 5 1 .1 3 1 .7 5 1.88 2 .2 3

1 5 .7 1 6 .4 1 7 .1 1 7 .6 1 8 .0 1 8 .3 1 4 .5 1 5 .8 1 6 .5 1 6 .8 1 7 .2 1 7 .5

0 .4 0 8 0 .8 8 5 1 .2 6 1 .4 6 1 .5 7 1 .6 4 0 .6 4 5 1 .0 6 1 .3 3 1 .5 1 1 .6 4 1 .7 9

1 7 .9 1 9 .7 1 9 .9 2 0 .3 20.8 1 7 .0 1 8 .4 1 9 .1 1 9 .6

0 .5 1 3 1 .3 1 1 .3 9 1.66 1 .9 2 0.866 1 .4 2 1 .7 4 1 .8 9

TEST A 2.6 M 2.6 2.6 2.6 .5 4 .5 4 .5 4 .5 4 »54:

0 .0 0 3 8 6 0.0120 0 .0 1 9 1 0 .0 3 1 7 0 .0 4 1 5 0 .0 0 2 7 8 0 .0 1 0 6 0 .0 2 6 0 0 .0 3 0 5 0 .0 4 1 1

87 87 87 87 87 87 87 87 87 87

0 .0 7 0 5 0 .0 7 0 5 0 .0 7 0 5 0 .0 7 0 5 0 .0 7 0 5 0 .0 7 0 5 0 .0 7 0 5 0 .0 7 0 5 0 .0 7 0 5 0 .0 7 0 5

1 6 .4 1 7 .4 1 3 .5 1 9 .1 2 1 .4 1 4 .8 1 5 .9 1 7 .7 1 8 .4 1 9 .2

81 31 81 81 81 81 . 85 85 35 85 85 85

0 .0 7 1 5 0 .0 7 1 5 0 .0 7 1 5 0 .0 7 1 5 0 .0 7 1 5 0 .0 7 1 5 0 .0 7 1 1 0 .0 7 1 1 0 .0 7 1 1 0 .0 7 1 1 0 .0 7 1 1 0 .0 7 1 1

1 5 .7 1 6 .0 1 6 .6 1 7 .2 1 7 .9 1 8 .5 1 4 .5 1 5 .3 1 6 .1 1 6 .9 1 7 .6 1 8 .2

88 88 ■ :’»O 08 88 88 38 88 88

0 .0 7 0 5 0 .0 7 0 5 0 .0 7 0 5 0 .0 7 0 5 0 .0 7 0 5 0 .0 7 0 5 0 .0 7 0 5 0 .0 7 0 5 0 .0 7 0 5

1 7 .9 1 9 .7 20.0 2 0 .5 2 1 .3 1 7 .2 1 8 .3 1 9 .5 20.0

TEST B 2.0 2.0 2.0 2.0 2.0 2.0 .5 5 w55 . 55 .5 5 .5 5 .5 5

0 .0 0 1 2 9 0 .0 0 6 5 6 0 .0 1 3 5 0 .0 1 8 1 0 .0 2 1 5 0 .0 2 3 6 0 .0 0 1 1 3 0 .0 0 8 8 5 0 .0 1 4 8 0 .0 1 9 5 0 .0 2 3 1 0 .0 2 7 4

.

TEST C 3 .4 5 .4 5.-1 5 .4 3 .4 .1 5 .1 5 .1 5 .1 5

0 .0 0 2 1 5 0 .0 1 4 0 0 .0 1 6 6 0 .0 2 3 7 0 .0 3 3 0 0 .0 0 6 3 4 0 .0 1 7 4 0 .0 2 6 7 0 .0 3 2 5

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Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.

81 TABLE X COMT'D CALCULATED AKD OBSERVED PRESSURE DROPS THROUGH BUI .VJATER. Temp.

(°P.)

S u rfa c e T e n s io n D e n s ity Seal (D ynes p e r Cm.) ( L b s . p e r ( F e e t ) Cu. F t . )

F lo w R a te (G-P'vl p e r F t . T ray 7/1 d t p

F lo w R a te (C u . F t . p e r Sec. p er S lo t) TEST D

73 78 78 78 78

7 1 .4 7 1 .4 7 1 .4 7 1 .4 7 1 .4

6 2 .4 , 5 2 .4 6 2 .4 6 2 .4 6 2 .4

0-.233 0 .2 3 3 0 .2 3 3 0 .2 3 3 0 .2 3 3

1.00 1 .00 0 .9 8 8 0 .9 8 3 0 .9 7 6

9 .8 5 * .8 5 9 .8 5 " 9 .8 5 9 .8 5

0 .0 0 3 1 3 0 .0 1 2 4 0 .0 2 2 9 0 .0 3 1 0 0 .0 4 7 5 TEST E

.MEDIUM LUBE OIL. 77 77 77

3 4 .0 3 4 .0 3 4 .0

5 4 .9 5 4 .9 5 4 .9

0 .1 6 7 0 .1 6 7 0 .1 6 7

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0 .0 0 2 4 1 0 .0 0 7 6 3 0 .0 1 2 7

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.

81 TA3L2 X C01IT ’ D DROPS THROUGH BUB -.LK CAPS URD2 R VARIOUS CONDITIONS

ivj R a te 'It. p e r T ray .dtb.)

Flow R a te (C u. F t . per Sec. oer S lo t)

Temp. D e n s i t y O b s e r v e d (° F .) (L bs. p e r P r e s s u r e Cu. F t . ) D rop (PSF)

C a lc u la te d P ressu re D rop (PSF)

Flow R a t e (L b s. o er Sq. F t. per Sec.

1 5 .8 1 6 .9 1S.1 1 8 .9 21.0

0 .6 0 7 1.22 1 .6 3 1.86 1 .9 8

10.1 1 0 .9 1 1 .5

0 .6 3 1 1 .0 8 1 .5 8

TEST D >.85 >.85 (.8 5 ’ >.85 i.8 5

0 .0 0 3 1 3 0 .0 1 2 4 0 .0 2 2 9 0 .0 3 1 0 0 .0 4 7 5

88 88 88 88 88

0 .0 7 0 5 0 .0 7 0 5 0 .0 7 0 5 0 .0 7 0 5 0 .0 7 0 5

1 5 .9 1 6 .7 1 8 .0 1 9 .0 2 0 .8

TEST S .................. PROPAKE____

• mm mm mm

0 .0 0 2 4 1 0 .0 0 7 6 3 0 .0 1 2 7

78 78 78

0 .1 0 8 0 .1 0 8 0 .1 0 8

1 0 .4 11.2 1 1 .7

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.

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32 flo w r a t e i n g a l l o n s p e r m in u te .

T he M ass Flow R a t e o f A i r

i s e x p re s s e d in pounds o f a i r p e r second p e r sq u a re f o o t o f s l o t area a c tu a lly o p e ra tin g .

T h is i s a c a lc u la te d v a lu e ,

s i n c e t h e l e n g t h o f s l o t o p e r a t i n g w as c a l c u l a t e d . The g r a p h i c a l a n a l y s i s sh o w in g t h e c o m p a r is o n o f t h e o b s e r v e d an d c a l c u l a t e d p r e s s u r e d r o p s a r e p r e s e n t e d i n t h e fo llo w in g c h a p te r. T a b l e X I c o n t a i n s d a t a c o l l e c t e d on t h e t h i r t y - i n c h " c o lu m n " h a v i n g t h i r t e e n c a n s e m p l o y i n g a s y s t e m o f w a t e r and a i r .

The c a p s w ere o f t h e s q u a r e t y p e m e n t i o n e d p r e v i o u s ­

l y a n d w ere s p a c e d s i x i n c h e s f r o m c e n t e r t o c e n t e r on a t r i ­ a n g u la r p a tt e r n .

T he i n s i d e d i a m e t e r o f t h e r i s e r s w a s one

an d s e v » n - e i g h t h s i n c h e 3 , a n d t h e r i s e r s e x t e n d e d two i n c h e s above th e t r a y .

T e n p e r c e n t o f t h e t r a y wa 3 a l l o w e d f o r

t h e downcom er a n d t e n p e r c e n t f o r t h e o v e r f l o w .

The c l e a r ­

a n c e f o r t h e dow ncom er w as one i n c h , and t h e o v e r f l o w w e i r w as o n e and o n e - e i g h t h i n c h e s h i g h .

T he d i s t a n c e b e tw e e n t h e

dow ncom er a n d o v e r f l o w w e i r w as e i g h t e e n a n d o n e - h a l f i n c h e s . The w i d t h o f t h e o v e r f l o w w e i r a n d t h e downcom er w as t w e n t y t h r e e and o n e - f o u r t h i n c h e s . In th e t a b l e ,

th e a i r flo w r a t e

r e f e r s to each s l o t .

The t o t a l v o lu m e f l o w i n g w as a ssu m e d t o be d i v i d e d e q u a l l y among a l l t h e s l o t s .

The w a t e r f lo w r a t e was a r r i v e d a t by

d i v i d i n g t h e g a l l o n s p e r m i n u t e by t h e a v e r a g e w i d t h s o f t h e o v e rflo w w e ir and t r a y d i a m e t e r and e x p re s s e d a s g a l l o n s p e r

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33

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2.03

P-l O ra © a 0 X3 G a a d cr*C a a a ■ a P4 © 0 ra ra 43 © •G *5 . ufa O a x ©fa E C >» 43 a GPi ©£4 rH ag a> 0 d ra a 43 a g •H 0 a n d c a Pi a E > a
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x 8

10

12

14

DISTANCE ON TRAY FROM DOWNCOMER (INCHES) Y /a te r H e i g h t on T h i r t y - I n o h T r a y a t a n A i r F low H a te o f 0 , 0 1 1 0 CFS p e r S l o t F i g u r e 19

16

18

US

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a:

SYMBOL

WATER FLOW RATE GPM P E R FT. OF TRAY WIDTH

— o

----------------

LL

2 .7

26.1 3 7 .8

o— 117

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WATER HEIGHT ON 3 0 -INCH TRAY AIR FLOW RATE = 0 .0 1 4 6 CFS PER SUDT

DISTANCE

ON

TRAY

FROM

DOWNCOMER

(INCHES)

W a te r H e i g h t on T h i r t y - I n o h T r a y a t a n A i r Flow R a te o f 0 . b l 4 6 OFS p e r S l o t F i g u r e 20

113 e r a t i n g , w as c o m p a red w i t h e q u a t i o n s o f f e r e d by G r i s w o l d 10 and R o g ers and T h i e l e 1 7 .

G r i s w o ld g i v e s

h = 1 .8 1 t

2 /3

1 /3

24

w h e re h = s l o t o p e n i n g i n i n c h e s f o r r e c t a n g u l a r s l o t s V - g a s r a t e i n c u . f t . p e r m in . p e r in c h o f s l o t w id th * d e n s ity of th e gas z d e n s ity o f th e l iq u id R o g ers and T h ie le g iv e V s (0 .5 1 )(0 .0 7 8 )h

7 /4

25

w h ere V = v o lu m e o f a i r t h r o u g h one s l o t i n c u . f t . per sec. h = s l o t le n g th in in c h e s S h erw o o d ^ s t a t e s th e s e e q u a tio n s a re u s e f u l in o b ta in in g a p p ro x im ate v a lu e s o f th e s l o t o p e n in g . A t e s t w a s made on a 1 / 4 by 1 - i n c h s l o t u s i n g a i r and w a t e r .

D a ta o f t h i 3 t e s t w e re p r e s e n t e d i n T a b l e VT-B.

F i g u r e 21 show s t h e r e s u l t s o f c a l c u l a t i n g t h e l e n g t h o f t h e s l o t o p e r a t i n g b y t h e a b o v e t h r e e m e n t i o n e d e q u a t i o n s and t h e a c t u a l observ ed v a lu e s .

T he f u l l l e n g t h o f t h e s l o t w as o p e n

a t an o b se rv e d a i r r a t e o f 0 .0 5 8 c u b ic f e a t p e r s e c o n d .

G ris­

w o ld ’ s e q u a t io n gave r e s u l t s a b o u t t e n p e r c e n t lo w e r th a n t h e o b s e r v e d s l o t o p e n i n g s a t low f l o w r a t e s , a n d t h e f u l l s l o t w as open a t a flo w r a t e o f 0 .0 5 5 c u b ic f e e t o f a i r p e r second.

R o g e r s and T h i e l e ’ s e q u a t i o n e q u a t i o n g a v e r e s u l t s

a b o u t t e n p e r c e n t h i g h e r th a n th e o b se rv ed o p e n in g s a t th e h i g h e r flo w r a t e s , a n d t h e f u l l s l o t w a s o p e n a t a f l o w r a t e o f 0 .0 3 8 c u b ic f e e t p e r se co n d .

E q u a t i o n 22 w a s f o u r p e r c e n t

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.

CALCULATED AND OBSERVED LENGTH

OF

SLOT

OPERATING

OBSERVED EQUATION (2 2 ) I O

ROGERS AND THIELE

z

GRISWOLD

H O

_J

u.

o

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z

GAS:

_J

LIQUID: WATER

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20

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30

4 0 50

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C a l c u l a t e d and O b s e r v e d L e n g t h o f S l o t O p e r a t i n g F i g u r e 21

70

90

120 low a t t h e l o w e r f l o w r a t e s , and t h e s l o t w a s f u l l y o p e r a t i n g a t a c a l c u l a t e d flo w r a t e o f 0 .0 5 6 c u b ic f e e t o f a i r p e r s e c ­ ond. A c o m p a r is o n o f t h e o r e s s u r e d r o p s c a l c u l a t e d by E q u a ­ t i o n s 24 a n d 25 w i t h t h o s e c a l c u l a t e d by E q u a t i o n 23 and ob­ serv ed v a lu e s i s p re se n te d a s F ig u re 20.

A c co rd in g t o G r i s ­

wold^-0 a n d R o g e rs a n a T h i e l e ^ , t h e p r e s s u r e d r o p i s e q u a l t o th e s l o t o p e n in g p lu s t h e s t a t i c h ead o f l i q u i d above th e slo t.

A s e a l o f one i n c h w as u s e d

in th e t e s t ,

and t h i s s t a ­

t i c head w as added t o th e c a l c u l a t e d l e n g t h t o g iv e th e p r e s ­ sure d ro p s.

The r e s u l t s

p i c t u r e d by t h i s f i g u r e a r e s i m i l a r

to th o se o f F ig u re 19. R hys and M i n i c h

14

p ropose an e q u a tio n f o r th e p re s su re

d r o p when t h e p r e s s u r e d r o p t h r o u g h t h e s l o t d o e s n o t e x c e e d t h e s l o t l e n g t h w h ic h i s hq = 0 .2 9

[V 2 (>v H a l

1 /3 . . . . . . .

26

w h e re h s = s l o t p r e s s u r e d r o p , i n c h e s o f h o t l i q u i d on t h e t r a y V = s l o t v e lo c ity c a lc u la te d w ith th e f u l l a r e a o f th e s l o t o p e n in g , f e e t p e r second = d e n s i t y o f t h e v a p o r , po u n d s o e r c u b i c fo ot Hs = s l o t h e i g h t , i n c h e s S = s p e c i f i c g r a v i t y o f l i q u i d on th e t r a y The r e s u l t s o f t h i s e q u a t i o n a r e v e r y c l o s e t o t h o s e o f R o g e r s and T h i e l e a n d a r e o m i t t e d i n F i g u r e 2 0 . P r e s s u r e d r o o d a t a on c o m m e r c ia l u n i t s c o n t a i n i n g t h e n e c e s s a r y v a r i a b l e s t o c h e c k E q u a t i o n 23 a r e v e r y r a r e i n t h e

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.

121

CALCULATED AND OBSERVED P R E S S U R E DROP 1

O BSERV ED

2

EQUATION (2 3 )

3

ROGERS

AND THIELE

GRISWOLD

16

NOTE: GAS:

AIR

LIQUID:

I 2 GAS FLOW

WATER

SEA L:

1.0

SLOT-'

LO * 0 . 2 5

3 RATE

( C F S ) x 10

C a l c u l a t e d a n d O b s e r v e d P r e s s u r e D rop F i g u r e 22

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.

122 lite ra tu re .

One e a s e o f m e r i t i s by C a e a l e s e e t a l 1 2 .

T h is

s t u d y w as made on. a n i s o b u t a n e t o w e r w i t h p r e s s u r e d r o o v a l u e s g i v e n a t t h e t i m e t h e t o w e r w as f l o o d i n g and when t h e t o w e r w as n o rm a lly o p e r a t in g . T est

T ray

The f o l l o w i n g i s a summary:

C o n d itio n

AP A c r o s s T r a y (In c h e s o f Hot L iq u id ) R e p o r t e d E q u a t i o n 23

1

Top

F lo o d ed

1

B o tto m

2

Top

2

B o tto m

F lo o d e d

4 .0 1 4 .5 6

N orm al

4 .7 3

N orm al

5 .2 2

4 .1 2 4 .6 1 4 .6 0 5 .3 0

S u r f a c e t e n s i o n was n o t ta ic e n i n t o a c c o u n t by p r e v i o u s in v e stig a to rs

1 4

1 6

*

1 7

*

in c a lc u la tin g th e le n g th of th e s l o t .

No a t t e n t i o n w as g i v e n t o t h e minimum s l o t o p e n i n g f o r t h e v a p o r to p a ss th ro u g h th e s l o t s .

R o g e r s a n d T h i e l e * s ^ 7 com­

p a r i s o n o f t h e i r e x p e r i m e n t a l a n d c a l c u l a t e d r e s u l t s d o e s show t h e c a l c u l a t e d r e s u l t s a r c low a t v e r y low f l o w r a t e s an d men­ t i o n t h a t t h e s u r f a c e t e n s i o n a f f e c t s t h i s minimum o o e n i n g . As s t a t e d

p re v io u sly ,

t h e e f f e c t o f s u r f a c e t e n s i o n i s m o st

i m p o r t a n t a t t h e minimum f l o w , and t h i s i s t h o u g h t t o be t h e r e a s o n why t h e i r c a l c u l a t e d

r e s u l t s a r e lo w .

T h is e f f e c t i s

a l s o i m p o r t a n t i n d e t e r m i n i n g t h e minimum p r e s s u r e d r o o f o r 14 a c a p . Rhys a n d M i n i c h s t a t e t h a t t h e u se o f c a p s w i t h a r e l a t i v e h i g h p r e s s u r e d r o p i n s u r e s good d i s t r i b u t i o n o f v a ­ p o r on t h e t r a y .

T h u s i t becom es i m p o r t a n t t o d e t e r m i n e t h e

minimum p r e s s u r e d r o p n e c e s s a r y f o r a c a o t o p a s s v a p o r .

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.

The

ii |

123

minimum p r e s s u r e d r o p c a n be d e t e r m i n e d by

a p p ly in g

E q u a tio n

[

|

23 t o i n c i p i e n t v a p o r f l e w , fro m w h ic h w ou ld r e s u l t AT3- oa APfc ~ \L^

*

, / , p T ^ gtf(L » W ) .............................27 2 / 3 vj^L +

'■fhere A?m = minimum p r e s s u r e d r o p t h r o u g h t h e b u b b le cap in l b s . p e r sq . f t . = d e n s i t y o f l i q u i d ab o v e t h e b u b b l e c a p i n lb s . per cu. f t . S - liq u id se a l in fe e t L = l e n g t h o f s l o t o p e n in g i n f e e t o b ta in e d f ro m F i g u r e 12 K * c o n s t a n t fr o m F i g u r e 1 4 ® * su rface te n s io n in lb s . of fo rce p e r f t . = w id th o f s l o t i n f e e t

; j j j j ■ ! ; I !

’.v ith t h e r e s u l t s and e q u a t i o n s p r e s e n t e d i n t h i s

!

i

c h a p te r , i t i s th o u g h t t h a t a b e t t e r u n d e rs ta n d in g o f th e

|

p rin c ip le s

I

can

be

in v o lv e d i n th e p r e s s u r e d ro p th ro u g h b u b b le c a p s

h a d by

th o s e p e o p le w o rk in g w ith th e b u b b le c a p s .

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.

CHAPTER V I I APPLICATION OF THEORETICAL EQUATIONS UNDER VARIOUS CONDITIONS Alien c a l c u l a t i n g t h e p r e s s u r e d r o p t h r o u g h b u b b le c a p s t o b8 e x p e c t e d f o r a g i v e n c o n d i t i o n o f f l o w f o r t h e v a p o r and l i q u i d sid e r.

on t h e t r a y t h e r e a r e many p o i n t s t o c o n ­

From t h e r e s u l t s o f t h i s i n v e s t i g a t i o n , E q u a t i o n s 22

a n d 23 a n d F i g u r e s 12 a n d 14 a r e o f p r i m a r y i m p o r t a n c e , b u t o n l y t o t h e e x t e n t t o w h ic h t h e v a r i a b l e s i n t h e s e e q u a t i o n s a r e know n.

T h e s e e q u a t i o n s c a n n o t be a p p l i e d t o a w h o le c o l ­

umn i n t h e s e n s e t h a t a l l t h e c a p s * v ill h a v e t h e same p r e s s u r e d ro p .

To be r i g o r o u s , t h e e q u a t i o n s s h o u l d be a p p l i e d t o

each in d iv id u a l c a p , but o f co u rse t h i s i s n o t d e s ir a b le . The n e x t b e 3 t r e s u l t w o uld be t o a p p l y th em t o a l l t h e c a p s on a s i n g l e t r a y .

To be a p p l i e d t o a l l t h e c a p s on a t r a y ,

c e r t a i n p o i n t s h a v e t o be k e p t i n m ind when e v a l u a t i n g c e r ­ ta in v a ria b le s.

T he f o l l o w i n g d i s c u s s i o n t r e a t s e a c h t e r m

o f E q u a t i o n 23 s e p a r a t e l y a s t o w h a t p r e s s u r e d r o p t h a t t e r m refers. The p r e s s u r e d r o p , APS » due t o t h e s t a t i c h e i g h t o f l i q u i d a b o v e t h e s l o t s i s n o t t h e same f o r a l l t h e c a p s . 12 4

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.

12 5 T h i s p r e s s u r e d r o p i s i n f l u e n c e d by t h r e e f a c t o r s w h ic h c a n ­ n o t be c o n t r o l l e d ; n a m e ly , t h e h y d r a u l i c g r a d i e n t , a t i o n o f th e l i q u i d s i t y a s th e l i q u i d n e g lig ib le

th e a e r ­

i n c l u d i n g fo a m in g , and t h e change in d e n ­ tr a v e r s e s th e t r a y .

in m ost o p e r a t io n s .

The l a s t o f t h e s e i s

The h y d r a u l i c g r a d i e n t w o uld

h a v e t o be c o n s i d e r e d when a r r i v i n g a t a v a l u e f o r t h e s e a l i n E q u a tio n 23. The minimum s e a l w o uld be t h e d i f f e r e n c e b e tw e e n t h e t o p o f t h e s l o t a n d t h e h e i g h t o f t h e l i q u i d ab o v e t h e s l o t 31 a s i t c ro s s e s th e e x i t w e ir. One i n v e s t i g a t i o n show s t h i s i s n o t a lw a y s t h e c a s e , b u t a t n o rm a l f lo w r a t e s i t i s t h o u g h t t h e minimum h e i g h t o f l i q u i d w e ir.

on t h e t r a y w ould bo a t t h e e x i t

T he h e i g h t o f t h e l i q u i d a t t h e e x i t w e i r c a n be c a l ­

c u l a t e d f r o m t h e w e i r f o r m u l a k n o w in g t h e l i q u i d f l o w r a t e s and ;« e ir w id th .

R hys a n d M inich'* 4 , D a v ie s '* , and Good a t a l °

o f f e r m e th o d s o f c a l c u l a t i n g t h e l i q u i d g r a d i e n t .

From t h i s

t h e a v e r a g e h e i g h t o f t h e l i q u i d o n t h e t r a y c a n be o b t a i n e d and th e a v e ra g e s e a l c a l c u l a t e d .

It

a g e s e a l be u s e d i n E q u a t i o n 2 3 .

I f t h e r e i s a f o a m in g t e n ­

dency o f th e l i q u i d , to th e s e a l .

i s reconaended t h i s a v e r ­

t h i s c o r r e c t i o n a l s o h a 3 t o be a p p l i e d

S o u d a r s e t a l 1 9 , H o l b r o o k a n d Baker**'1', and

S h erw o o d a n d Je n n y '* 0 o f f e r a d i s c u s s i o n o f t h i s p r o b l e m a n d i t s e f f e c t on t h e l i q u i d h e i g h t .

T h is c o r r e c t i o n sh o u ld a l s o

be a p p l i e d t o t h e a v e r a g e s e a l . T he a e r a t i o n e f f e c t i s g r e a t e s t a t h i g h v a p o r r a t e s ,

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.

126 and q u i t e o f t e n t h e e q u i v a l e n t l i q u i d h e i g h t u n d e r s t a t i c c o n d i t i o n s on t h e t r a y i s e q u i v a l e n t t o o n l y a f r a c t i o n o f th e a c tu a l h e ig h t o f th e a e ra te d l i q u i d .

I f th e d e n s ity o f

t h e l i q u i d be t a k e n a t s t a t i c c o n d i t i o n s , t h e d e n s i t y m i s t be m u l t i p l i e d by a n a e r a t i o n f a c t o r .

Kemp and P y l e & o f f e r

a m eans o f e s t i m a t i n g t h e s e f a c t o r s and t h e h y d r a u l i c g r a ­ d i e n t s e n c o u n t e r e d on b u b b l e c a p t r a y s .

Thus w ith th e s e

p o i n t s i n mind t h e p r e s s u r e d r o p due t o t h e l i q u i d

s e a l can

be c a l c u l a t e d . The p r e s s u r e d r o p , A P q, c a u s e d by t h e s t a t i c h e a d o f l i q u i d w h ic h i s d iffic u lty

j u s t o p p o s ite th e s l o t sh o u ld o f f e r l i t t l e

in c a lc u la tio n .

For th e a v e ra g e p r e s s u r e drop

due t o t h i s p a r t i c u l a r f a c t o r , t h e flo w o f v a p o r h a s t o be a ssu m e d s p l i t e q u a l l y among a l l c a p s .

T he l e n g t h o f t h e s l o t

o p e r a t i n g c a n be c a l c u l a t e d u s i n g E q u a t i o n 2 2 .

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h a s t o be g r e a t e r t h a n t h e minimum l e n g t h o f s l o t o p e n i n g i n t e r p o l a t e d f r o m F i g u r e 12 b e f o r e v a p o r c a n f l o w t h r o u g h t h e slo t.

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Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.

I 127

v a p o r '."Jill p a s s t h r o u g h t h e s k i r t c l e a r a n c e .

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123 tity

o f v a p o r t o c a u s e t h e s l o t t o be f u l l y o p e n e d , and t h e

w i d t h and a c t u a l o p e r a t i n g l e n g t h o f t h e " s k i r t s l o t " f o r t h e v a p o r i n e x c e s s o f t h a t r e q u i r e d f o r t h e s l o t t o be f u l l y opened.

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129 t h a t p o r tio n o f th e s t a t i c head in e x c e ss o f th e p re s s u re d rop o f a cap flo w in g v a p o r. not o ffse t,

I f t h e e x c e s s s t a t i c h e a d w ere

t h e t o w e r w o u ld become f l o o d e d .

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g r a d i e n t i s known, t h e s e a l s a b o v e t h e c a o s c a n be d e t e r m i n e d . T hen th e v a r io u s q u a n t i t i e s o f v a p o r g o in g to each cap can be d e t e r m i n e d by re m e c io e r in g t h a t t h e p r e s s u r e c r o p s h a v e t o be e q u a l . sin c e

T h i s w o u ld n e c e s s i t a t e a t r i a l and e r r o r s o l u t i o n

t h e a c t u a l o p e r a t i n g l e n g t h s o f s l o t s w ou ld h a v e t o be

c a l c u l a t e d by E q u a t i o n 2 2 , a n d t h e p r e s s u r e d r o p due t o t h e s l o t o p e n i n g e f f e c t w o uld h a v e t o be c o n s i d e r e d . p e rim en ta l d a ta a re not a tt a i n a b le

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Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.

CHAPTER V I I I

CONCLUSIONS The c o n c l u s i o n s w h ic h a r e t h e r e s u l t s o f t h i s i n v e s ­ tig a tio n are: 1.

T h e r e i s a minimum l e n g t h o f 3 l o t o p e n i n g b e lo w w h ic h t h e v a p o r w i l l n o t p a s s t h r o u g h t h e s l o t i n t o a l i q u i d h a v in g a f i n i t e

2.

surface te n s io n .

The l e n g t h o f t h e minimum s l o t o p e n i n g i s a f u n c t i o n o f t h e s l o t w i d t h and t h e s u r f a c e t e n ­ sio n of th e l i q u i d .

3.

T here i s a p r e s s u r e drop th ro u g h th e s l o t s cau sed by t h e s u r f a c e t e n s i o n o f t h e l i q u i d .

4.

The e q u a t i o n s p r e s e n t e d a r e o f v a l u e i n c a l c u ­ l a t i n g th e p r e s s u r e d ro o th ro u g h b u b b le c a p s .

5.

The e q u a t i o n s p r e s e n t e d c a n b e u s e d i n a n a l y z ­ i n g p r o b l e m s o f m al f u n c t i o n i n g b u b b le c a p s a n d tra y s .

130 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.

LITERATURE CITED 1.

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2 9 .9 .

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*A s e r i e s o f a r t i c l e s on H y d r o c a r b o n A b s o r p t i o n a n d F r a c t i o n ­ a t i o n P r o c e s s D e s i g n M e th o d s b e g i n n i n g i n May, 1 9 4 7 . 131 with permission of the copyright owner. Further reproduction prohibited without permission.

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B ik e r m a n , J . J . , S u r f a c e C h e m i s t r y f o r I n d u s t r i a l Re­ s e a r c h , A cadem ic P r e s s I n c . , New Y o r k ( 1 9 4 8 ) .

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!

133

j

4 5 , 435 (1 9 4 9 ).

j

!

30.

P e r s o n a l c o m m u n ic a tio n w i t h B r . E m i l J . 3 u r c i k , U n i v e r ­ s i t y o f O k lahom a, Norm an, O klah om a.

I

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M c C a r th y , E . L . , M. C h. E . T h e s i s i n C h e m ic a l E n g i n e e r ­ i n g . U n i v e r s i t y o f Oklahoma ( 1 9 4 9 ) .

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D a v i e s , J . A . , I n d u s t r i a l and E n g i n e e r i n g C h e m i s t r y . 3 9 , 7 7 4 ( 1 9 4 7 ^ ----------------------- ------------- -----------------

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E d m i s t e r , 77. C . , P e t r o l e u m E n g i n e e r . 2 0 , 193 ( 1 9 4 8 ) .

i I

i

UNIVFPFITY OF OKLAHOMA Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.