Pressure drop through bubble caps

394 91 7MB

English Pages 151

Report DMCA / Copyright

DOWNLOAD FILE

Polecaj historie

Pressure drop through bubble caps

Citation preview

INFORMATION TO U S E R S

This manuscript has been reproduced from the microfilm master. UMI films the text directly from the original or copy submitted. Thus, some thesis and dissertation copies are in typewriter face, while others may be from any type of computer printer.

T he quality of this reproduction is dependent upon the quality of the cop y submitted. Broken or indistinct print, colored or poor quality illustrations and photographs, print bleedthrough, substandard margins, and improper alignment can adversely affect reproduction.

In the unlikely event that the author did not send UMI a complete manuscript and there are missing pages, these will be noted.

Also, if unauthorized

copyright material had to be removed, a note will indicate the deletion.

Oversize

materials (e.g.,

maps,

drawings,

charts) are reproduced by

sectioning the original, beginning at the upper left-hand corner and continuing from left to right in equal sections with small overlaps.

ProQuest Information and Learning 300 North Zeeb Road. Ann Arbor, Ml 48106-1346 USA 800-521-0600

R eproduced w ith perm ission o f the copyright owner. Further reproduction prohibited w ith o u t perm ission.

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

NOTE TO USERS

This reproduction is the best copy available.

IJM I

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.

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

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

UMI Number: DP10028

UMI UMI Microform DP10028 Copyright 2004 by ProQuest Information and Learning Company. All rights reserved. This microform edition is protected against unauthorized copying under Title 17, United States Code.

ProQuest Information and Learning Company 300 North Zeeb Road P.O. Box 1346 Ann Arbor, Ml 48106-1346

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

PRESSURE DROP THROUGH BU3I3LE CAPS

APPROVED BY

0ENERAL

THESIS COMMITTEE

3 4 4 6 12

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

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

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

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

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

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

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

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

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

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

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

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

R eproduced w ith perm ission o f the copyright owner. F urther reproduction prohibited w ith o u t perm ission.

]

3

|

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

|

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

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

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 ,

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

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 .

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

|

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

j

t h r o u g h t h e subm erged s l o t s o f a b u b b l e c a p i s made up o f

;

b o t h s t a t i c a n d d y nam ic c o m p o n e n ts .

|

a t r a y i n a f r a c t i o n a t o r , i t r i s e s t o t h e t r a y ab o v e w h e re i t

A f te r th e vapor le a v e s

p a s s e s th r o u g h t h e v a p o r r i s e r and i n t o th e b u b b le c a p .

T here

|

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

j

e n t e r i n g th e r i s e r , flo w th r o u g h th e r i s e r , e x p a n sio n o f th e

i

j

v a p o r l e a v i n g t h e r i s e r a n d e n t e r i n g t h e b u b b le c a p , a n d t h e

I i

r e v e r s a l o f t h e d i r e c t i o n o f f l o w i n t h e b u b b le c a p .

!

t o flo w r e v e r s a l .

T hese

l o s s e s w i l l be r e f e r r e d t o h e r e a f t e r a s t h e p r e s s u r e d r o p due

B e f o r e t h e v a p o r c a n r e a c h t h e sub m erged s l o t ,

th e

sta tic

h e a d o f l i q u i d a b o v e t h e t o p o f t h e s l o t m u s t be o v e r ­

come.

T h is i s u s u a lly r e f e r r e d

th is

to a s th e liq u id

s e a l , and

p r e s s u r e d r o p i s t h a t t o o v e rc o m e t h e l i q u i d s e a l .

A fte r

t h i s l i q u i d s e a l e f f e c t h a s b e e n o v e rc o m e , t h e s l o t s m u s t : | ;

h a v e a " f r e e " p a s s a g e way f o r t h e v a p o r t o o a s s t h r o u g h .

i s a n o t h e r s t a t i c l i q u i d h e a d , and i s r e f e r r e d t o a s t h e p r e s ­ su re d ro p f o r th e s l o t o p e n in g .

i i

T h is

A s l o t c a n be c o n s i d e r e d t o

6

i

i

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

I

| f !

7

h a v e a " f r e e " p a s s a g e way i f t h e l i q u i d l e v e l i n s i d e t h e b u b b l e c a p i s b elow t h e t o p o f t h e s l o t .

Once t h e l i q u i d

le v e l

!

|

in s id e th e cap i s

b e lo w t h e t o p o f t h e s l o t , t h e v a p o r w i l l

i

■ be i n c o n t a c t w i t h t h e l i q u i d o u t s i d e t h e c a p i n t h e " o p e n !

j

p o rtio n " of th e s l o t .

I

s l o t , t h e r e i s a n a d d i t i o n a l p r e s s u r e n e c e s s a r y t o o v e rc o m e

I

t h e s u r f a c e t e n s i o n a c t i n g a g a i n s t th e b u b b le s l e a v i n g th e

i

o u ts id e o f th e s l o t .

F o r t h i s v a p o r t o brea-c aw ay f r o m t h e

F i n a l l y , t o g e t a n a d e q u a t e am o u n t o f

!

v a p o r t h r o u g h 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

; |i

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 .

I

P r e s s u r e D rop Due t o Flow R e v e r s a l

j

|

The f i r s t p r e s s u r e d r o p t o be c o n s i d e r e d i s t h a t d u e

I

j

t o flo w r e v e r s a l .

|

v a p o r d e n s i t y , an d t h e d i m e n s i o n s o f t h e c a p .

!

t h i s p r e s s u r e d ro p w i l l v a ry w ith each ty p e o f cap d e p e n d in g

i I

uoon th e h e ig h t and d ia m e te r o f th e r i s e r ,

O b v io u sly ,

t h e h e i g h t an d

d i a m e t e r o f t h e c a p , and t h e d e v i c e u s e d t o h o l d t h e c a o on th e t r a y .

;

I t i s a f u n c tio n o f th e v a p o r v e l o c i t y ,

Due t o t h e n u m e ro u s t y p e s o f c a p s and m e th o d s o f

s e c u r i n g t h e c a p on t h e t r a y , no a t t e m p t w a s made t o d e r i v e an e q u a tio n f o r c a l c u l a t i n g t h i s p re s s u re d ro p ,

’" h e n e m p lo y ­

i n g b u b b l e c a p s i n w h ic h t h e a r e a o f t h e r i s e r ,

th e c le a ra n c e

a r e a a t th e to p o f th e r i s e r , and th e a r e a o f th e a n n u la r s p a c e b e tw e e n t h e c a p and r i s e r a r e e q u a l , R o b i n s o n a n d G i l l ­ ila n d ^

s u g g e s t a n e q u a t i o n b y D a u p h in e 7 and S c h n e i d e r 20 ob­

t a i n e d fro m d a t a o n a i r .

I f a g a s d e n s i ty term i s

p laced i n

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

8 t h e e q u a tio n and th e c o n s t a n t ch an g ed , t h e r e r e s u l t s Pv Qc APr = 0 . 1 4 7 ----w h e re APr

=

p r e s s u r e d r o p due t o t h e f lo w r e v e r s a l in l b s . p er sq. f t . = d e n sity of vapor in lb s . per cu. f t . Qc =f l o w r a t e o f v a p o r i n c u . f t . p e r s e c . p e r cap D = d ia m e te r o f r i s e r in f e e t

P r e 3 3 u r e D ro p Due t o L i q u i d S e a l The l i q u i d s e a l w h i c h i s n e c e s s a r y f o r f r a c t i o n a t i o n i s t h e n e x t f o r c e t o be o v e rc o m e by t h e v a p o r .

T h is s t a t i c

h e i g h t o f l i q u i d h a s t o be overcom e by t h e v a p o r w h ic h p u s h e s th e l i q u i d o u t of th e cap u n t i l th e liq u id i s a t uhe t o p o f t h e s l o t s .

l e v e l i n th e cap

S in c e t h i s i s a s t a t i c f o r c e ,

it

may be c a l c u l a t e d fro m t h e d e n s i t y o f t h e l i q u i d on t h e t r a y and t h e d e p t h o f t h e l i q u i d , s e a l by means, o f t h e e q u a t i o n , A P g = ?1

s

. . .

......................................3

w h e re APS = p r e s s u r e d r o p d u e t o t h e l i q u i d s e a l i n lb s . per sq . f t . = 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 . p e r c u . ft. S = d e p th o f s e a l in f e e t P r e s s u r e D rop Due t o S l o t O p e n in g A t t h i s p o i n t , t h e v a p o r i s i n t h e c ap and t h e l i q u i d l e v e l i n th e cap i s a t t h e to p o f th e s l o t s . p re s s u re i s n e c e ssa ry to

An a d d i t i o n a l

pu3h t h e l e v e l o f t h e l i q u i d

in sid e

t h e c a p belo w t h e t o o o f t h e s l o t s b e f o r e t h e s l o t s h a v e a n " o p e n i n g ’*.

T h i s p r e s s u r e , w h ic h c a u s e s t h e l e v e l on t h e i n ­

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

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.

T he e x t e n t t o w h ic h t h e s l o t m u st o o e n b e ­

f o re v apor e sc a p e s th e cap i s a f u n c tio n of th e s u rfa c e te n ­ s i o n o f t h e l i q u i d and w i d t h o f t h e s l o t . s i o n e f f e c t w i l l be d i s c u s s e d l a t e r .

The s u r f a c e t e n ­

The f o l l o w i n g o a r a g r a p h

d e a ls s o le ly w ith th e p re s s u re n e c e s s a r y to cau se th e l iq u i d l e v e l i n t h e c a p t o f a l l a d i s t a n c e , L , below t h e t o p o f t h e slo t. C o n s i d e r a s l o t VT f e e t i n w i d t h and L f e e t i n l e n g t h su b m e rg ed i n a l i q u i d h a v i n g a d e n s i t y o f

lb s.

per cu. f t .

a s shown by t h e f o l l o w i n g d i a g r a m :

$ defTs/Jy

^ 9

S in c e th e s t a t i c

5

-W

A L

'

I

p r e s s u re a lo n g th e L a x is v a r i e s , a d e t e r ­

m in a tio n o f th e c e n te r o f p re s s u re i s n e c e s s a r y .

By t h i s

c e n te r o f p r e s s u r e i s m eant t h a t th e s t a t i c p r e s s u r e a t th e p a r t i c u l a r n o in t a p o lie d a lo n g th e L a x i s i s e q u a l to th e su m m atio n o f t h e v a r y i n g s t a t i c p r e s s u r e s a l o n g t h e L a x i s fro m t h e t o p o f t h e s l o t t o t h e l i q u i d l e v e l i n s i d e t h e c a p . T h i s c a n be d e t e r m i n e d f ro m t h e e q u a t i o n 2 6 , ijS jL " A

dt

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

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,

T h ere­

th e o re s s u re n e c e s s a ry to lo w er th e l i q u i d l e v e l in s id e

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 =

5

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 .

The f o r e s o p p o s i n g t h e breaicing -aw & y p r o c e s s

o f th e v apo r b u b b les i s th e s u rfa c e te n s io n o f th e l i q u i d . I f t h e s l o t be c o n s i d e r e d a n a l o g o u s t o a c a p i l l a r y t u b e 2 7 , t h e s t a t i c p r e s s u r e due t o t h e s u r f a c e t e n s i o n a g a i n s t t h e b u b b le o f v a p o r i s h

1

=



gr

..............................................................................................................................

6

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 .

The r a d i u s o f c u r v a t u r e i s d e p e n d e n t upon t h e l e n g t h

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

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.

From

c a n be s e e n t h a t t h e

becom es l e s s a s t h e a c t i v e l e n g t h becom es g r e a t ­

B ik e rm a n ^ ? s t a t e s t h a t B ech h o ld ^® c o n c l u d e d t h e r e was

a re la tio n sh ip

b e tw e e n t h e s u r f a c e t e n s i o n ,

b u b b le r a d i u s ,

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 .

F o r t h e maximum p r e s s u r e ,

t h e b u b b le r a ­

d i u s i s t h e r a d i u s o f t h e o p e n i n g t h r o u g h w h ic h t h e g a s w as fo rced .

I f r i n E q u a t i o n 6 be t a k e n a s t h e e q u i v a l e n t r a d i u s ,

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

by

.................................. 7

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 .

T h is c u r v a t u r e i s d e p e n d e n t upon v t L,

a n d 7T.

T h e r e f o r e a c o n s t a n t , k , may be i n s e r t e d

in E q u a tio n 6.

S u b s t i t u t i n g E q u a tio n 7 f o r r in E q u a tio n 6 g iv e s AP

- a c y ( L » T y ) ..................................................... a “ gLW

w h e re AP-g = maximum p r e s s u r e d r o p i n l b s . p e r s q . f t . due t o t h e s u r f a c e t e n s i o n e f f e c t

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

12 L W g k

= = = = v =

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 .

P r e s s u r e D rop Due t o O r i f i c e E f f e c t F in a lly ,

t o o b t a i n a n a d e q u a t e am ount o f v a p o r t h r o u g h

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 .

To a r r i v e a t t h i s

e ffect

p r e s s u r e d ro p , an e n e rg y

b a l a n c e n a y be w r i t t e n . C o n s id e r a s th e sy ste m th e v a p o r g o in g th ro u g h th e s l o t and a s t h e s u r r o u n d i n g s t n o s e t h i n g s o p p o s i n g t h i s f l o w o t h e r t h a n t h e l i q u i d , on t h e t r a y and t h e s u r f a c e t e n s i o n . L e t p o i n t 1 be i n t h e a n n u l u s b e tw e e n t h e r i s e r a n d c a p a n d p o i n t 2 be i n t h e s l o t .

3y a n e n e r g y b a l a n c e on a pound

+ q - w * E g + ? 2 ^ 2 + X2 + 2g * * ’ 9 w h e re E P 7 X U g q w

= = = = = » = -

i n t e r n a l energy a b so lu te p re s su re v o lu m e d i s t a n c e a b o v e some a r b i t r a r y d a tu m p l a n e v e lo c ity of vapor g r a v ita tio n a l c o n sta n t h e a t t r a n s f e r r e d fro m s u r r o u n d i n g s w ork d o n e on s u r r o u n d i n g s by s y s te m

C o l l e c t i n g l i k e t e r m s and r e p l a c i n g t h e d i f f e r e n c e o f l i k e te rm s by A q u a n t i t i e s r e s u l t i n 4 E + A ( F 7 ) + AX + ^ 2 ___ ^ 1 . 2g

q _ w

R eproduced with perm ission o f the copyright owner. Further reproduction prohibited w ith o u t perm ission.

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

11

and q = J t d s - wf

12

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 .

The t e r m

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 .

T h is t e r n i s u s u a lly n o t r e ta in e d a s a sep ­

a r a t e q u a n t i t y , b u t a c o n s t a n t , C, i s p l a c e d i n t h e e q u a t i o n t o t a k e c a r e o f t h e f r i c t i o n e f f e c t on t h e p r e s s u r e d r o p a n d i s c a lle d th e d isc h a rg e c o e f f i c i e n t .

T*fith t h e s e c o n s i d e r a ­

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 .

T h u s , by

n e g l e c t i n g t h e h e a d o f v a p o r o f AX f e e t i n h e i g h t ( a t t h e

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

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

f o r a s i n g l e c a p , E q u a t i o n 14 may be i n t e g r a t e d t o g i v e

=c

e v (u f - u i)

15

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

!

! 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 .

T h is c o r r e c t i o n h a v in g




tO

05

to

to

tO

to

o

o

o

o

o•

CO

»— I

o

to cm o

cm

CM

CM

tO

C1

• « 1—1

04

o

o•

CO CO

o•

o•

02

• >ti» co

to

» CO 1—t

05

o• o

CM

m

to

tO

to o•

to o*

to

om

o

05

05

CO

CO

to o t— 4 o» o

to

cm

s*

CO

« SJ*

CM • si*

CO

CO

CO

CO

CO

CO

to

• CO .c o

CO

CO • to to

CO • to to

CO • to to

co • to to

r-t

r-t

D-

C» C5 r-t

!>•

CO

05

CM

CO CO

CO CO

CO CO

o-

o

o

r- t

D•

r-l

CM

r—I

05

00





• St*

05

r-l

CO



o

• ■st*

o

CM

o o

• ■st*

05

to CM o

o o

to

to

05

O

to •

to 05

CO

r-t

to r-t

05

to

r—f •

1—1

CO



• to S 3 o > --** S3 E • M O • -H 33 e O • 0a1 o O • © * •« -JJ. © H E i a > © © o Q M • C© © c -l t3: • M M O > t-3

to

CO

© • 43 • o lO C43 © si* X to CQ si* o • u o o © O 4-1 O

C

te­ at

1—1 •

r-t •

r-t

• to to

• to to

• to to

to to

to

05 r-t

tO co

to

to

to

CO

CO

to CO

to

CO

o> to

CM

CO

05

CO

CO

05

(O

• to to

Q (-3 0

*-3

tn >>

43 ©

o o 01 ft

>

Q , C'N©HHtO • * • • • • • • • • • • • • ♦ * • • • • • • • • • • C Ot O C Ol O l O tOf M C -C H D O- O J C O O l r H O a c O ^ ^ W c O r f l O t D C - C O O C O O r - t W II •—II r-4 —4 r»-1 *—4 ri— r-4 rr-1 i—I r-4 >4 f—I( rH r—4 ri— r— lI r “4 r-I i— 4 H l t r*lJ r-4 l rH r—iI t— It r lI r-41» —I t—I i—

r

9 9 9 9 9 9



• • •

d— • >> © * 43 QiP •H

01

9 9

OJO ~ — •

TENSION

d © £-i

d © Q

© o

O CO

tO C»

oooooooooooooooooooooooooo » « » « » • • • • • • • • • • • • • • • • * • * ■ * c ooooooooooooooooooooooooo

tHc-c-C'-c-tNc-C'-c-c-c-tHC-c^cotoeotoeoeotototOtoeoto

©

©

3 : Q

CO

d r>» © • 43 C U ^ •H P«4

m

iH

N tD W M n C D H lO O M flO » W O C O > < -ltO rl< D O « C O < O N (I] O O H rlW W tO O rlrlW N W ^ O O rlH O J C in O O H M N

o

01

S' H Hi

(O

© O lO W >H tD O «O rlC O C D O >C O O H tO O ^'O H O >C ;C O M r1

r-» • E

-H

Hi

oooooooooooooooocooooooooo oooooooooooooooooooooooooo

r—

o

Q

0>0>0»0>0»0»0»0>Cft0i0>0>C3>0i0>0>0>0>0>0»Cft0»0»O0»CJ

(0 t0 » 0 iD (0 < 0 l0 iD iD (D (0 (D i0 (D i0 iD < 0 < 0 l0 i0 i0 (0 i0 O i0 < 0

o. «| e fr C 0 c 0 c 0 c 0 « r - 4 0 0 0 0 0 0 0 0 r ' - £ > c 0 t 0 t 0 t 0 c 0 0 ; > t - ! ^ r ~ o o 1 0 l0 » c i0 0 » 0 l© 0 c i> 0 > 0 > c i0 > 0 > 0 > c 5 © 0 l© © 0 l0 ic 9 0 l0 4 0 >

d

OF SURFACE EFFECT

a

• 0) +3 . o d -P © «Pmcn 2 •u o d© r-4 O a P=»-r

OH PRESSURE

DROP


c>oooooooooooo

■si' -^4*

9

d 0 • © -a d

W

W

K

W

•CO

cuin f— •1 • • 0 4•

CUCUCUCUCUCUc^OCNC'-tNr-lr-l.-lrH o o o o CO t o CO CO f—f t—1 f—t f—f o o o o • • • • o o o o 1—1 O r-l O CU o CU 'U* « i—1 c* 04 o o •

p p 04 o o •

p^ c* 04 o o •

c P~ 04 o o •

o r-i 04 o o •

c

o

o

o

o

o

o

o

o

CM co EO O •

O t o »n pP O CO O r -i r -l • * •

CO r-i CO O •

CO *■*in O •

CO CO r -i CO ^ CM c o o o O r -i r -i o * • • •

O

O

O

o

o

CM

P - 0 4 CM

o

CM

r r

O O O H r I H r-i r-f t o t o t o tO tO r-i o r - t I—i r— t r—i CC CO CO CD r-i r-t r-i r-i H P P- to p- P P p p e - d» p 04 a» 04 o o O o o o o • • • • • • * • ■ * * • • • • o o o o o o o o

O o

rr

M > O

£ o o

CQ




s p CO co i=3 S a . a "Tf co •s j* O 00 f t r-l CO CQ ft CQ OC rl CI2CO -Si* O O r l H W K H o o o o o o o • Pi o o o o o o ? O ©© . . . . . . O O O O O O O O ft o o o o o o ft Pi — tD O i O t O t O tO tO CO CO CO CO 00 >s ffl • •CO ft ft P s}*-sj* -s^ ■sj*-a* sj* t n i n i n i n i n t n in •rl tn tn tn in tn in i n i n m t n o t n in • t=4 o o o o o o o o o o o o o n ft 01 • • • • • • • ooooooo © ft f t o o o o o o o ft U '-*’ ft ps,{CP Cl Cl Oi CQCO eo t o eo c o co co eo 6 CD 00 CO CO CD CO 00 O |C 0 CO CO CO CO CO ffi

in

►40 o

ft

CD CO CD CO co ao CO CO CO CO

oo ao

, f t IN C- OIN C» IN ffl so sO so so to so ffl r—l r-i *—t r-l r—l r—l ft ffl • ffl ffl ffl ffl O O O O

ft •ft ffl 60X1 r-t •rl © «rl

►41-3 O

o o

o o o o o o in in tn tn m tn

g

02 02 02 02 02 02 02 •

»









r

O QOQOO mtnininintn 02 02 02 02 02 02 •





*





OOOOOOO

oooooo

ft £•

-P

© M e r-l

•H C rl ►4 f t O

ft ©

6 0 f t r-l • r l C "H

Q tJO

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

0.0833 71 0.0833 72 0.0833 72

u o o M £

1 r-i r—l •

I # t o sO C - CO CO CP r-i r— l r— l t—i r-l r-l r—l

O «1 ^

Medium Lube Oil

Q

CQ o S3 M

CM e - CV2

«

©

E-* o i-3

O r - l ■ 3 ftfel'*** tO tO lO CO CP Pi 03 O CQ • • • • • • ® tn p t l i l o i - i w t o ^ i n

0.0551 0.0551 0.0551

© Pi

79 79 78

■ft ®

5.56 6.50 7,39

60

©

ffl ft

2 * ffl O 43 0.43 rl 1 ft 5 •H • 5ft 1ft tft J ffl ooo 00 G ffl • o• o• o• © ft 3 « pJ O • '—' H Cl COCmCm S oPm CmCMCM © w 0 t* 1 © 1ra r4 aa rH a • o 2 to o o • 43 tH W G • 2d O £K > •rl O ffl oa f*k G Cl © 03 © o«o• o• < t* ft &-* ^ © ft5 ffl COCOCO O © Cm c V i G O (4 >: « M Q Q CO ■ —' w « >» © p? ft,43• COCOCO 43 Oj •rl CO o • fa Ml*• m3•*r' WtsOst>-COtOCOSOCOcOCaCOlOe' o o o H w n flo o H H w n jo oooooooooooooo oooooooooooooo

WMWWWNWrlrlrlrlrliJJW r— l i— I i—i(— I r— l «— I i— I (—Ir— l r— l r-l r— l * I r-l CmCmC'CmD-CmC'CmCmC-CmCmOCN oooocccocooooo oooooooooooooo

C C C C O C > O O g O i® tD G 2 ) > >

C'-C-C'-C'-CSCOCOCmcmo C-C'-C'-o

72

«o C- • • • • • • • • • • • CM50 m o to o CMo H rHH rH rH rH rHrH |H rH

m

0 4

*cI © f tft © *-« -—• f— f t p s . I CO - 2* C >

8 52 9 35

61

w « CO • ©o• r— •l CO • s— •1 tft Cft o 02 COtl* tft rH rH r-l r— 1r—l r—l (— i 50

tj*

>C >rl r) 3 fafalCU r-l'U, a)CUl>.i-ICOCUtOOinintn JH CO O CQI •













# * * # # •

o ta h o - t f io C ' Q S o ^ ' - J O J ' ^ ' o i ^

io o c d d

-



O *£> •



# •

»o h w

05 ffi Q -— H H H r H W W N H r l H H H H f l O O C B H r l H £ >

MOON^c D

IfllSO lO rtn h h h n w m

U

O fa ©

43

G

fa

o r—J

fa E-4

>3

O

CO

05

sM

Q

fa

ffi

3

ffi

O Ht— H

E -t

® CU •

S

1




fa

0 > 0 tO 0 t® C 3 i0 > O O O O O O O O O O

O JcO C 3C O C O C O C O C O C O C 30sC »a>0>00>C J>C »a>0»

ffi

vT &J Q

•rl

03



ffi

M H CO





rH rH H rH rH rH rH rH rH rH rH rH rH rH rH rH rH rH rH to f f i t O f f i f f i f f i f f i f f i f f i f f i f f i f f i f f i f f i f f i f f i f f i f f i f f i f f i

ffi

+3

O 3 G 3 C 3 O > C 0 C 0 C 0 C C C 0 C 0 C '- C - C ~ C ''C ^ e - C - t> C ^

Q J

Q H H



H



• • • • • • • • •

OOOOOO

o o o o o o

G

•r-t c

o

a» cu co to a* co CU CO ^ CU CN to O O r—tCU CU CO

©

u

a

m

N i— 1

* -3 0

o

>

fa

rH rH r-l #— 4 t r-4 r— t r-4 i— IO O O O O O O O O O OOOOOOOOOOOOOOOOOOO lNC-C'-C>-!>C'-tNC-C^e-C'-D-t>!>-OC»C--C-efa OOOOOOOOOOOOOOOOOOO G o o o o o o o o o o o o o o o o o o o

ffi • 0 .4 3

•H

fa

H M M

CO CM • o r-4 O 43 ffi Nt>COO»?OO^i, lGC>-CO«OC-«OOc'3'^, I>CDr-l w c ^ t o o o w w o o ^ f f i t o ^ o co o ito in f a CO O O r 4 « ? 5 t O ^ O H H W t O O O O H H W r t • u o o o o o o o o o o o o o o o o o o o G ffi • • • • • • • • • • ♦ • • • • • • • a o G. o o o o o o o o o o o o o o o o o o o

*

fa

CUCUCUCUCUCUCUCUCUCUCUCUCUCUCUCUCUCUCU o o o o o o c-C'-ssc-oe-CNo-C'-C'-C'-c^D-oe^e^oc-C'- c- cs d»e» c- d» -C - O -0c^c^D-e-c-oe'-c^D'C'-c-c-c-e-c^C'-c-o-c^ O D

fa

falc OO

E -i

.— f c3

ffi

C O ffi £ ffi

O r-4 r-i r—l r—l r-4 r-i CU CU CU CO CO CO CO CO CO

loO X C JD Q O C O C O Q O C O C O C O C O C O C O C O C D O C O C O C D

43

ffi

tow w ototo cocococococncootooootortiotocoeoeo 5oCOjCOCOCO®,,a4''tf'*li,U, 'i, '»t, ®®®COCOCO r l r i r i H r l r l r l H r l r i H H r f O O O O

O O

• • © • • • • • • • • » • » • • • • • « fa o o o o o o o o o o o o o o o o o o o

I r-i

o o > 3 *4 r-l © C5

O O r-4 I—( r—i 03 03 03 03 03 co

co co

ao

co

CO

CO

CO

c o c o

CO

c o

r-4 .—1 1—I r—l r-4 r-4 «





O O O O

I r-l

o o

>3*4 r-l © o

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



«

O O



64 n

©

LO o

o

>

© C X fa l W f f l O ^ H H W O c s W W o O ^ O ©

00 OCOj . . © 02 tifal © © O J ^ t O O O M C O Q ff lO iO ^ W tD i—I r - t i H r—I 4—I 02 ® Q —- « W H H H H W W W

W rltO W f i H l O ^

'

u

X!

O O O H W C O W N r t H

W

K

W

W

W

H

U

c fa ©

-P ©

> O

6

© © O D.

o

o

o

o

o

o

o

o

o

o

o

o

o

o

o

o

fa

© • in N O O o w w ^ ^ o o o o o o o & p © 0 t0 © < 0 © ® © © 0 0 © 0 © 0 ©

p •H

K

C-4

CD

'—

ra c ©

00

r-1 lO

fa CQ E* O

• o

-p © HMDHCJPW©^COCO«COCOO© f a CO OW CO© OHtOO>SO^O ©OlO • ^ ^ ‘ OO.PtDCOCO'^O.P.PCOCD'tf'M4 • *■< o o o o o o o o o o o o o o o o

Q

05

fP

a

HO O W H W lO O

CM i n CO CM rP IS S S tO

©

© G

©

o

1

© a

•H

G

t j t CO CO

O I CO CO CO CO 00 00

o

>

CQ

G K O

©

I rH

43



tC G rH •rl 3 -rl

hR o o

O rH © t o O

o o to to 03 Ol © • o o

s Oto tO rH rH © • O o

to to to to cs to rH • o

e* D» s to tO o rH rH rH rH O o O O • • • • • • • • o o o OOOOO

J© ©

r3r4 O

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

67 © tf tf © 5-1 > 3 ape, to• in• u © Ol co o> © CQ U I ra © q — £> U O PU

!SI

« •o p © C Q 05 • 5-4 o ©© r-l O CX fs< 5h-—>> © • P ap •H P=4 • © c cc • .O 0 © o 1-30 *• • • a fe e o © E h —**

©

p (S

Eh O

►J C O

B !-< a

hI*-* o

Y*--H

M 1 in

02•

00 < c• « • • • • • • • • • • •

• •

© e ©



55



r-4 M O

O

M M

>

*-s C5 O

P=, rn


©o>o©c>oo>0)©o>o>c>cs©Oio>o>c»



a Q

a

©

o

»— r - e-

tftf-tf-tftf.tf.tftftf'tf'tf'tfrtftftf'tftf'tf'ttl-tf

CO CO

COCOOOCOOOCDCOCOOOCOCDCOGOCOCDCOCOCOCOCO

c o CO CO CO

a a a a a a a C '- C - C ^ O t'O O Q O Q C O O co co o o co co o o co eo '.o to to to to o aaaaaa

co co o o ■



o o

p

JCJ © CsCX3 rH •H 55 -H rOtJO

CO CO CO CO CO CO CO

O O O O O O O ^ H r lH r lr lr lN O J W K W N •













#























o o o o o o o o o o o o o o o o o o o o p © 60£> r-l •H © -H s z

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



-© CD

©U

> 14

© ©

. f t ps , t O 1 0 t f O col • • •

CQ





c o CO • •

© CJ fc» CM-tp i n tO IN CO CD O 03 ® Q-— H H r H r l H H r H

in co COCQ o O C O r-l o c» cq CQ 0> to • • • . • . . . • • • • O r-l r-l COtji in in in c - 00 COo>

"3 CQ O

r— 1 r-l r-l r-l

5.25 6.14 6,86 7.29 8.16

68

i— 1 r-l

JO *-i

Q

zz O

5i

in

O o w M H >

CM •

a cc

pH


-w cu cO r4 r4 iO cO r4 c> r-i

Medium ^be Oil

© 40

0.00123 0.00730 0.0124 0.0164 0.0252

O F4

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

69 3 Q.|xJtOo ti ai oc/i|03O3CO'U*o3Oio„ CT

H .J

r-t O o r-

n

O O O r l r l H W

O

O

O

H

W

W

«

O

O

r

l N

W

I

O

O OJ

COtOCOCOCQEOCOCOSOtQEOCOCO

i a

01

43 •H a a

©

a

a.

G

© £-• rl © © Cl

© e ©

© • a .4 3 o» o> o» o> 03 03 03 03 03 03 03 03 03 03 • • • • © • • ♦ • • • • • • •© D - IS O- O' O- O E>t> C- c- OO-O-O-O-O-C'-O-O-O'O'C'O'O© © >> Q ■ —• SH-" © • CU*3 X? xi* xt4 x f xj« xj* x jl • Sh • *«*• ■*• s *• xj ^ > o COa a a a a „—, O' l> o o- a a a a a a +3 to to tOtOCDCDCDCOCDc © (— I rH ooooo © « • rH»rH• o« • • c• o• # o o c o -rH— u +© 3 © 0 0 0

• rH • © • © • CO •

ao OrH a c- rH a a C Ctt*to tf toa o cua xjt coa xi4xtf j*toa tO cucuX #O ' cuO ' a cu rH x rH cuo c o rH rH cuo o o o OrH o o o c o o o• o• o• o• o• o• o* Q • • • • • « o oo c c c oc c ooooc

8 8

•• • • • • • • • • • • • • • • • • « Q M O O’ M rJ•

© cj ©

• rHlOto r— 1a aCs^ o • o CUto O S-a t> cuto o- rHO OS *3 ©x* WC o o rHrHrH Eh COorHrHft! * t» • o• o*o• o• o«o• o• o«o• 3 ©o o o o o o o o o o O Cu

0

X O X i-H b mI o oa• o o w M < M a > o rH CO < 6-. < < E-* O a* O O a

-© lU> © X ?o rH Eh >> *> -H © © © « • a a ©

0

v_» ► 4 CD X 5 rH

cu

4 4

o

• • • • • • • • • • • < o• • • • • • • • • • • • • • •

3=

OCOOOOOCOQOQOO

aocooocococDaococoocooroffl I O £ C J O SO CO CO

^COCOCOSOCOOC^C^D-C'C'OO C O C O C O C D C D C O t O t O t O t O t O t o a a

COOCOOHHrlHHHWN «

























OOOOOOOOOOOOOO

u

© 43 ©

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

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

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

•a o © Ph —-* > G ft Jx2© in © CO© to

ti ra o co cs Hi»cocoocoo»©o2©o©Hi*o»©ftCD© © 03 14 p^| • • • • • • • • • • • • • • # • • • 33 h i— 1#— 1i— 1I— 1f— 1i— I i— I i— I(— | ft ft rH o ft 03 O O — r © © © C ' C O C O O f t C M C M e O c O © © D ' C O O O O »

© 43 as cs s o r— t ft • © c o • • • • « • » • • • • • • • •

K

Eh ft M Jr

K o

X

Z M 1 © cs © « O

M


i— 1t— 1r— I I— I f— i i— (

t!> O rl

© cm o - O ' o> cm f t -. P ■— -(4 ■ © • ft 43 h£ H* ■M* ■M* ■«*Hi* ** - M* xi* •M* Hi* ft Hi* • • • • • • • • m • • • •

>» 43 ft • • ra G CO • cm o © Q ft o ft e ©

or—4 o(—4 of—4 or-1 or—Ior —1

'

© S © z G O ft © G

e'CsO'CsO'O'O'O'rsO'C'COcooocococo

CO 00 © CO CO 00

CM CM CM CM CM CM CM CM 02 02 CM CM CM O (to 40 tO tO tO «o tO tO

©©©

©

• © © © © © © © © ft © «o to to © © tO ©o - ©O ' ©IS ■O' cs IS 0 " c s O ' c s c r IS «>• C» O ' CO© © to t o « CS O ' o o o o o CO © © © © © D - 0 " O ' 431© © © © © © Ifi to o sO O C O W lO O W tO lD O H O rH ^ W ^ •o o 43 © r—1 > W ( J l 0 2 r - l l f l M J > l O H W N O ' t , > - l i n ft OT o O O i —I f t C M O O O O f t C M O O . —I f t C MC M o ooooooooooooooooo •u « G ©o o o o o o o o o o o o o o o o o o O o

to

Hi*Hi* ^ ^4 ^4

• • CM CM tO c O

© © © © © © O ' O ' O ' O ' O ' IS o o o o o o © © © © © © CM CM 02 02 CM CM • • • • • •

o o o o o o u

©

© 43

03

C3

43 j£

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

73

-© © ©

w ■ a CXfcl

CO totoo 02to 01 °5P CO tototoCO o CO CO rH CO CO CT> • • • • • • • i • • • • • ©a © © a — o H 02CO -a* - a t toto P - CO CO f— I r— I »— I i— 1r— I i— I X> U

too 02to rH CO to CO 02CO to CO o to lO 02rH• to • • • • • * • • • • a tO p > CO CO o»o >CVI 02to-at toto

• CO >—1 '—1 tO lO CO co rH CO t o ca C5> rH cvi 43 © rH-at o -a4o rH -!» tt*

CM t o cu o to to o to CO lO O 02 o IN rH CVI CO o to o P- 02 CO o -at o> o o o rH rH 02 02 O o O r l to 02 o• o• o• o o o o o O rH rH8 o • • • • • • 8 ooooo ooooo oo

>

U

n

r l rH i—I r-I r t r—I

OP h

© 43

a 03



o

fo

CQ

O o



? o

rH

U

a o

© °-

O

o

a

o

o

O tO

rH 02 N O O O H H N

O

o



to w



o

o

o



o



o o o o o o o

9

o

Ph

c-1 O CQ < C O C5 •

«£T

Q §2

O o

a a

O S M 1

lO IN

to # o < 33 O C « H

43

•H



©

• •







• a

a o E-

f c H

55

a

r-» P-.

9 9 9

• 9

9

9

o o o

o

o

o

o

H

W

W

H

aa

o •H to

W

t O

^

t O

^

W

a ©

t > p - t o t n - a * c o - a « i o w t n - a < co

cococococococococococcco

©

©

o u

o c CM

a a

cx

• a o

SH

CU CU 0 2 CM CVI CV2 CU CV2 CV2 Cvi 02 CVI 02 © o 02• 02 CU CU CU CU CU CU CU CU C2 a p» I N N I N C ' - t N N t N P - t N N © a>.

E-|

o Eh < o Q a «-l Po PC a CQ Q C Q • rr • 43 r> C O • •rl to Q © M a S3 © P, o> Q

O

o Iqcococococococococdcooo



9

9

.—

a a a



9

cu

©

9

9

o

• • •



C OCD C O P» P- P- P- P- P- P- p- p- p- Po o o o o c o o o o o oo o o 1f— 1 r— 1r— I rH rH rH rH r-H 1H H r— rH rH rH i— • • 8 8 8 8 • • • • • • • • o o o o o o o o o o o oo o o

r-{ r~i r— t r-f r-t

a xi

t-Q O

n



• • •

© CO CO CO CO 00 Pho o o o o o o o •

• 0 -4 3

9

9

9 9

O O O O O O O O O r H r H r H

COCOC3COCDCOCDCCOOCOC3C3

© ©

exfrJ O COj tO CM O CS CO CO UtQ.t| • • • • • • “ I S C O OS OS r l r l ©Q

O

fa

U

XJ u

CO

CO

oi

© a -p] cs cs c- c» is cs

•rl

© a

©

O

O« O« O• O« O• O* OOOOOO

>» •P

Q

M

u



0 0 o t o C - r- l r-l r l CM O W OS rO O O r - l rH r l CM

a © O fa

fa O 2

• o

-P 0 f a CO

r— I

O

6 -t

r l rH rH r l CM CM

to o cs Os• •>#• CO o• • o• tO• rH• • • • • • > 43 •H © c © P

rH H O Oo CO tO W 05 to to st*C OrHC- r—1 © lO cu CO N

N N

N N

N N

N N

N N

CN IN CN I N CN I N

31.0

E* O P CO

© 43 C P5

O M O ® »o

rH ©

U

©

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

78

• •

© > m © a J3 O

0.0033



« • •

f-i cs a a

c n M to oo o co to co m o co|c- n c ' t O ' ^ i n w o > n H N {•4 p^j • • • • • • • • • • * C •—-tOasosOr-lCUtOtOtOtNaO

rH < tj*CO IO to to » — 1to CO o cucuas CO• to• cu •to• o• • • • •CN• • • »• CO o rH cuCO CO to LOto IN 1rH rH rH rH 1I— rH rH rH f—

* r-l - © -p C-4-S CNI Nt NI NCNl NCNl NCNt NCN ooooooooooo •rl ©Ph r-H rH r-H i—I rH r —I r—I rH rH rH rH © C O • G ® rO 55 o o o o o o o o o o o n •JO ,r— • o. •| (JfflOOSOOOOOOi e oPh1C O C O C O C O C D C O C O O O O O © ■ — e* j© c g £ a CJ a. 'o __, (X. g • c •H s O

• • • • • c • © • « EH • © • or* • c< • Pi • 3 • CC • • >» • 43 • •H © Q G M o o C‘ a M

u as

c.

a

© d > O — H —© • P.-P • ©

Ph

OOOOOOOOOOO



• • • • « • • • • •

OSCSCSOSOSGSCSCSOSCOOSCSCSCO

CD

g

as cs,

o

sh

Ph

OOOOOOOOOOOOOO

#









*

















CO 6 0 CO CO CO CO CO CO CO CO CO CO CO CO

or- o o o o w c s o o o

aoaococDaocococDcocccocococo



O 3 xjt -2 • 4 6 2 .4

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

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

Reproduced with permission o f the copyright owner. Further reproduction prohibited without permission.

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

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

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

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

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.

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

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

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

33

d

O

S •< rj-* r-M » fa p fa fa p co cc K & fa

0

d 0 a 43 0

© C O

fa d 0 a 43 0

© 00

so h i n io 1010 to--tin h > ooooooooooo WWWWWWWCUWWH

CiCiO lO tO ldlO a'-O aid ooooooooooo MWKWNWWWWNW

< d G»0 0 0 »tfaC*lOaCd 0 a OOOOOOOOO t I I 43 • • • • • • • • • I O 02 CJ WNNWMWW © C O

Pi © A § d P H Wt0^lO(0>tDQ OW r— I* — 1 +3 fa

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

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
» ©C -t • ©©©© o fa mo fa d fa fa >j • • © •O C Q •43 m ram ©fa Pi P i © a a •a a © co a c OlOO •e* fa # co a 10 • • 43 o • cc 0 0 C O fa o• g • ? • . ow pi-4 • 3 • ?-4 o • < D • 04 O • rH • • r4 • H o• • C • o O • • to • • • C O • • 0. 0 fa Pi d OQ 0 P i a Q© ra Pi ©d © u ©Pi ra ra © OH d Ehd ra © Pi 4* ©43 >. ©ra Pi ©3 cc©d P|43 O©fa 4343 O SC O© a d Pi Oa >) fa U 43 43 fad 5-1fa r© ©a o d e c S h © aoiH ©©©d -o4 3 o >a H ©© c u u (4 P faE-iQ (© a ©©©©0 Pi U Pi P ©434343raa a a a a c; CJ= a

CD

x

z

UJ -J $

5

a UJ

i l—

A-

■a —

X

_=n

CL.

WATER FLOW RATE GPM PER FT. OF TRAY WIDTH

SYMBOL — o

- 3 .6 -7.9 -14.2 2 4 .3 3 5 .6

— x — A D

0



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

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

a:

SYMBOL

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

— o

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

LL

2 .7

26.1 3 7 .8

o— 117

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

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

NOTE: o

z

GAS:

_J

LIQUID: WATER

z

SEAL:

1.0"

SLOT*.

1 ,0 x 0 .2 5

UJ

UJ CL

o

2

3

4

5

6 7 8 910

GAS FLOW

RATE

15

20

AIR

30

4 0 50

(CFS) x 10*

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 .

T h is le n g th

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.

I f t h i s le n g th i s l e s s th an t h a t o b ta in e d u s in g F ig u re

1 2 , th e s l o t w i l l o p e r a te o n ly i n t e r m i t t e n t l y a s th e p r e s s u r e below t h e c a p b u i l d s u p .

I f th e le n g th c a lc u la te d

t h e minimum, t h i s l e n g t h i s u sed i n E q u a t i o n 2 3 .

i s above I f th e c a l ­

c u la te d le n g th o f th e s l o t o p e ra tin g i s above th e a c t u a l le n g th ,

t h e a c t u a l l e n g t h s h o u ld be u s e d i f t h e r e i s no s k i r t

c le a ra n c e f o r th e cap.

I f th e re i s a s k i r t c le a ra n c e f o r th e

c a p , E q u a t i o n 22 w i l l a l s o s e r v e t o d e t e r m i n e t h e f l o w o f v a p o r n e c e s s a r y f o r th e f u l l s l o t to o p e r a t e .

The e x c e s s

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 .

T h is s k i r t

j

j

c l e a r a n c e c a n be b r o k e n up i n t o " s k i r t s l o t s " h a v i n g w i d t h s e q u a l to th e w id th o f a s l o t p lu s tw e e n t h e s l o t s .

' ha w i d t h o f t h e n e t a l b e­

T h e n E q u a t i o n 22 c a n be u s e d t o d e t e r m i n e

j j i

th e l e n g t h o f th e s k i r t c l e a r a n c e o p e r a t i n g by u s in g t h e w id th m e n t i o n e d a b o v e and t h e e x c e s s o f v a p o r a b o v e t h a t r e q u i r e d f o r th e f u l l s l o t to be o p e n ed .

;

j

I n a l l c a s e s when d e a l i n g

j !

w ith th e d e n s ity o f th e l i q u i d , p r e v i o u s l y s h o u l d be a p p l i e d

th e a e r a t i o n f a c t o r d is c u s s e d

j i j

to th e d e n s i t y .

t

I n d e t e r m i n i n g t h e p r e s s u r e d r o o , A P s , c a u s e d by t h e j s u r f a c e t e n s i o n , t h e c a l c u l a t i o n c a n be made r e a d i l y a f t e r

j

th e le n g t h i s d e te r m in e d .

T he w i d t h o f t h e s l o t and t h e s u r -

i |

fa c e te n s io n of th e l i q u i d

a t t h a t p a r t i c u l a r te m p e r a tu re have

]

t o be know n.

T h i s e f f e c t i s r a t h e r s m a l l , an d o n c e t h e s l o t

i s f u l ly o p e ra tin g , i t

i s assu m ed t o be z e r o a s m e n t i o n e d i n

a p rev io u s d is c u s s io n o f t h i s e f f e c t . The p r e s s u r e d r o p , APOJ due t o t h e o r i f i c e o f f e r s no oroblem . o n c e t h e

effe ct

le n g th of th e s l o t o p e ra tin g i s

i i j i

d e te rm in e d .

A g a i n t h e flo w o f v a o o r i s a ssu m e d t o be e q u a l l y

d i s t r i b u t e d among a l l c a p s c a l c u l a t i o n i s m ad e .

a n d a l l c a p s f l o w i n g when t h i s " I f th e can h a s a s k i r t c le a r a n c e th a t

i s p a s s i n g v a p o r , t h i s p r e s s u r e d ro p w i l l have t o be s e o a r a t e d i n t o tw o c a l c u l a t i o n s .

The

a m ou nt

i j

o f v a p o r flo w in g th ro u g h

t h e s l o t and f r o m t h e " s k i r t s l o t " h a v e t o be d e t e r m i n e d a s m en tio n ed a b o v e .

i

j i

se p a ra te ly ,

j j j

f o r t h a t quan-

j

T h e s e two q u a n t i t i e s a r e t r e a t e d

i

u s in g th e a c t u a l le n g th

and

w id th o f th e s l o t

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

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.

T h e s e two c a l c u l a t e d v a l u e s when a d d e d w i l l g i v e t h e

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 e f f e c t . The p r e s s u r e d r o p , A P r» c a u s e d b y t h e e x p a n s i o n , c o n ­ t r a c t i o n , and flo w r e v e r s a l o f th e v a p o r i n th e r i s e r and cap o f f e r s l i t t l e

d iffic u lty .

j

The v a r i o u s a r e a s t h e f l o w i s

d i r e c t e d t h r o u g h h a v e t o be c o n s i d e r e d i n d e t e r m i n i n g t h e f a c t o r s c a u sin g th e g r e a t e s t r e s t r i c t i o n to flo w .

The e q u a ­

t i o n o f f e r e d i n t h i s w o rk i s f o r t h e s e v a r i o u s a r e a s b e i n g e q u a l.

If

t h e s e v a r i o u s f l o w a r e a s a r e n o t e q u a l , D avies^-

o f f e r s t h e b e s t m eth o d o f c a l c u l a t i n g t h i s p r e s s u r e d r o p . D u r i n g t h e c o u r s e o f t h i s s t u d y on 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 l e c a p s , c e r t a i n t h e o r i e s w e re fo rm e d fro m tim e to tim e .

The f o l l o v j i n g p a r a g r a p h i s n o t s u b s t a n t i a t e d by

e x p e rim e n tal d a ta , b u t i t

i s th o u g h t i t m e r its c o n s id e r a tio n .

I t i s b e lie v e d th e p r e s s u r e d ro p s th ro u g h a l l th e cap s on a s i n g l e t r a y a r e e q u a l , b u t t h e v a r i o u s i n d i v i d u a l p o r ­ t i o n s o f t h e p r e s s u r e d r o p may v a r y f r o m c a o t o c a p . e x a m p le , i f t h e s t a t i c

For

head above one c ap i s g r e a t e r th a n a

j i

s o a s t o make t h e

j

T h is i s tru e even i f

j

s e c o n d c a p , t h e v a p o r w i l l be d i s t r i b u t e d

!

p r e s s u r e d r o p t h e same f o r b o t h c a p s .

a c ap i s n o t flo w in g v a p o r o r i s even p e r m i t t i n g th e l i q u i d

! i

t o flo w th ro u g h th e cap t o t h e t r a y b e lo w .

In th e l a t t e r

]

c a s e t h e f r i c t i o n c a u s e d by t h e l i q u i d f l o w w o u ld consume

!

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

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 .

E q u a t i o n s 22 and 23 and F i g u r e 12 c a n be o f g r e a t h e lo In a n a ly z in g a s i t u a t i o n of t h i s ty p e .

I f th e l i q u i d

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

S in c e ex­

th e q u a n t i t a t i v e v a lu e o f

t h e s e e q u a t i o n s i n a n a l y z i n g t h i s p r o b l e m c a n n o t be d e t e r ­ m in e d . ta tiv e

H o w e v e r, t h e e q u a t i o n s p r e s e n t a v e r y u s e f u l q u a l i ­ s o l u t i o n to th e p ro b lem .

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.

D a v ie s, I . A ., P e tro le u m R e f in e r . 2 9 .8 .9 8 (1 9 5 0 ): 121 ( 1 9 5 0 ) . --------------------------------

2 9 .9 .

2.

S t r a n g , L . C . , T r a n s a c t i o n s o f A m e ric a n I n s t i t u t e o f C h e m ic a l E n g i n e e r s , 1 2 , 1 6 6 . ( 1 9 5 4 ) .

3.

K i r k b r i d e , C. G . , P e t r o l e u m R e f i n e r . 2 3 , 321 ( 1 9 4 4 ) .

4.

B o l l e s , W. L . , P e t r o l e u m R e f i n e r , 2 5 , 513 ( 1 9 4 6 ) .

5.

M a y e r , N . , P e t r o l e u m R e f i n e r . 2 5 , 653 ( 1 9 4 6 ) .

6.

S o u d e r s , M . , J r . , a n d B row n, G. G . , 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 . 2 6 , 98 ( 1 9 3 4 ) .

7 . * E d m i s t e r , '7. C . , P e t r o l e u m E n g i n e e r . 1 8 ( 1 9 4 7 ) . 8.

P e a v y , C. C . , and B a k e r , E . M . , I n d u s t r i a l a n d E n g i n e e r ­ i n g C h e m i s t r y . 2 9 , 1056 (193777""

9.

G ood, A . J . , H u t c h i n s o n , M. H . , and R o u s s e a u , Trr. C . , I n d u s t r l a l an d E n g i n e e r i n g C h e m i s t r y . 3 4 , 1 4 4 5 ( 1 9 4 2 7 7

10.

S h e rw o o d , T . X . , a n d J e n n y , F . J . , I n d u s t r i a l and Eng­ i n e e r i n g C h e m i s t r y . 2 7 , 265 ( 1 9 3 5 ) .

11.

H o l b r o o k , G. E . , and B a k e r , E . M . , 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 0 , 1063 (193 4)

12.

C i c a l e s e , J . J . , D a v is , J . A ., H a r r in g to n , P . J . , H oughl a n a , G. S . , H u t c h i n s o n , A . J . L . , and ’Y a l s h , T . J . , P e t r o l e u m R e f i n e r . 2 6 , 495 ( 1 9 4 7 ) .

13.

P e r r y , J . E . , C h e m ic a l E n g in e e rs * H andbook, Second E d i t i o n , p p . 1 4 5 4 - 1 4 3 6 7 M c G r a w -H ill, Hew Y o r k , ( 1 9 4 1 ) .

*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.

132

14.

R h y s , C. 0 . , J r . , and M i n i c n , K. L . , " F r a c t i o n s t o r T r a y P e r f o r m a n c e and D e s i g n " , A T e c h n i c a l P a p e r p r e s e n t e d a t t h e L o s A n g e l e s R e g i o n a l M e e t i n g o f t h e A m e ric a n I n s t i t u t e o f C h e m ic a l E n g i n e e r s , M arch 6 - 9 , 1 9 4 9 ,

15.

R o b i n s o n , C. S . , a n d G i l l i l a n d , S . C . , T he E l e m e n t s o f F r a c t i o n a l D i s t i l l a t i o n , T h i r d E d i t i o n , M c G r a w - H ill, New Y o rk ( 1 9 3 9 ) .

15.

G r i s w o l d , J . , S c . D. 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 , I I . I . T . (1S31)".

17.

R o g e r s , M. C . , a n d T h i e l e , E . TJ . , I n d u s t r i a l a n d E n g i ­ n e e r i n g C h e m i s t r y . 2 6 , 524 ( 1 9 3 4 ) .

18.

Souders, M ., Jr., Huntington, R. L., Cornell, H. G., and Emert, F. L., Industrial and Engineering Chem­ istry, 30, 86 (1938H

19.

M a y e r, N . , S . It. 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 , Id. I . T . ------------(3.938) . :

20

.

S c h n e i d e r , 3 . M. 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 , K. I . T . ( 1 9 3 8 ) . -------------------------------------------------------------------

21

.

DauDhineC S c . D. 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 , M. I . T . (1939).

22

.

C a r e y , S c . D. 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 . M. I . T . (1 9 2 9 1 :

23.

S h e rw o o d , T . K . , A b s o r p t i o n a n d E x t r a c t i o n , F i r s t E d i t i o n , M c G r a w -H ill, New Y o rk ( 1 9 5 7 ) .

24.

K ir s c h b a u m , E . , D i s t i l l a t i o n and R e c t i f i c a t i o n , C h e m ic a l P u b l i s h i n g C o . , New Y o rk ( 1 9 4 8 ) .

25.

H a r r i n g t o n , P . J . , B r a g g , B. L . , a n d R h y s , C. 0 . , J r . , P e t r o l e u m R e f i n e r . 2 4 , 502 ( 1 9 4 5 ) .

26.

B u r i n g t o n , R. S . , H andbook o f M a t h e m a t i c a l T a b l e s a n d F o r m u l a s , H andbook P u b l i s h e r s , I n c . , S a n d u s k y , O h io , (19 47) .

27.

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 ) .

28.

B e c h h o l d , H . Z . , P h y s l k . Chem. , 5 4 , 3 2 8 ( 1 9 0 3 ) .

29.

Kemp, H. S . , and P y l e , C . , C h e m ic a l E n g i n e e r i n g P r o g r e s s ,

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

!

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

31.

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 ) .

32.

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 ^ ----------------------- ------------- -----------------

33.

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.