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Calibration of orifice meters at low Reynolds numbers Swain, Frederick Clifford 1966

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CALIBRATION OF ORIFICE METERS AT LOW REYNOLDS NUMBERS  by FREDERICK CLIFFORD SWAIN D i p l o m a , R o y a l M i l i t a r y C o l l e g e o f Canada, B. A. Sc.,  U n i v e r s i t y of Toronto,  I960  1961  A THESIS SUBMITTED IN PARTIAL FULFILMENT OF the r e q u i r e m e n t s f o r the degree o f MASTER OF APPLIED SCIENCE i n t h e Department o f CHEMICAL ENGINEERING  We a c c e p t t h i s t h e s i s as c o n f o r m i n g t o t h e r e q u i r e d standard-  THE UNIVERSITY OF BRITISH COLUMBIA January,  1966  ii  ABSTRACT  Seventeen square-edged o r i f i c e plates were c a l i b r a t e d t o study tiie e f f e c t o f varying throat length, both i n the absence and i n the presence o f geometr i c a l s i m i l a r i t y , on the c o e f f i c i e n t of discharge from 2 0 to 1 0 , 0 0 0 . 1  :  f o r pipe Reynolds numbers  The experiments involved the use of h y d r a u l i c a l l y smooth  pipe i n t e s t l i n e s o f 1 - inch, l o 5 - inch and 2 - inch nominal I.D., corner pressure 0.6. ;  taps and Beta r a t i o s ( o r i f i c e diameter^iipe diameter) of 0.2, O.U and •  S i x of the plates were b u i l t using design c r i t e r i a recommended by the A.S.H.E. i n " F l u i d Meters" ( l ) , and with Beta r a t i o s s p e c i f i e d a t 0 U» o  Each  test l i n e was used with two p l a t e s , which were i d e n t i c a l except f o r a v a r i a t i o n i n throat length within the range of the given design recommendations. A comparison o f discharge c o e f f i c i e n t s as a function of pipe Reynolds number indicated the followingt ( 1 ) Reynolds numbers 30 - 3 , 0 0 0 .  Consistent differences of 2-6% were observed i n the c a l i b r a t i o n curves due t o the v a r i a t i o n i n throat longth allowed by " F l u i d Meters".' ( 1 ) . (2)  Reynolds number 3,000 - 1 0 , 0 0 0 . Geometry appeared to be much l e s s important, as a l l c a l i b r a t i o n  curves tended to coincide. Two further p l a t e s , f o r the 1.5 - inch pipe only, were b u i l t using the A.S.M.E. "Power Test Code" ( 2 ) as a design reference.  They were designed to  have respectively the minimum and maximum throat length allowable under the code.  The r e s u l t s , when p l o t t e d , indicated that i n a pipe Reynolds number  range of h0 - 1 , 5 0 0 , plates b u i l t i d e n t i c a l l y except f o r small' differences i n throat length, s t i l l gave d i s t i n g u i 6 h a b l y d i f f e r e n t c a l i b r a t i o n curves.  iii  The remaining nine plates were divided into three groups of three plates each, encompassing the three pipe, diameters and three Beta r a t i o s . A l l plates within a group were geometrically s i m i l a r .  The r e s u l t s , f o r  pipe Reynolds numbers from 20 to 2,000, indicated that a t o t a l s p e c i f i c a t i o n of o r i f i c e shape gave consistent c a l i b r a t i o n curves with no apparent a b s o l ute size e f f e c t s . Thus, both " F l u i d Meters" *and the "Power Test Code" recommended design c r i t e r i a f o r standard o r i f i c e plates which do not completely take into account the e f f e c t ' o f geometry on the c o e f f i c i e n t of discharge a t low Reynolds numbers. are too l a r g e .  In p a r t i c u l a r , the tolerances allowed on throat length  TABLE OF CONTENTS  INTRODUCTION  1  EXPERIMENTAL  A 8  Apparatus V i s c o s i t y and D e n s i t y Measurements  2h  Experimental  25"  Procedure  THEORY  27  RESULTS AND DISCUSSION  33  NOMENCLATURE  U7  LITERATURE CITED  5*1  APPENDIX 1 - RESULTS  1-1  A Sample C a l c u l a t i o n  1-1  Tabulation o f Calculated Results  1-3  APPENDIX 2 - DATA Tabulation o f the Experimental  ". Data  APPENDIX 3 - ERROR ANALSSSS Tabulation o f the S t a t i s t i c a l Results APPENDIX U - CALIBRATIONS  2-1 2-2 3-1 3-2 U-l  C a l i b r a t i o n o f Thermocouples and Thermometers ....U-UO C a l i b r a t i o n o f tonometer F l u i d s  U-l6  LIST OF TABLES  Page Dimensions  o f G.S.  Orifice Series  and  A s s o c i a t e d Equipment Dimensions  lU  o f S t a n d a r d , Sharp and S p e c i a l  O r i f i c e S e r i e s and A s s o c i a t e d Equipment  15  ) Comparison  o f A c t u a l and T h e b r i t i c a l l y Maximum  E n t r y Lengths f o r Laminar and T u r b u l e n t F l o w s  19  D e s c r i p t i o n o f Manometers  20  R e s u l t s - O r i f i c e type 1.0  inch Standard  1-3  R e s u l t s - O r i f i c e type 1.5  inch Standard  1-5  R e s u l t s - O r i f i c e type 2.0  i n c h Standard  1-6  R e s u l t s - O r i f i c e type 1.0  i n c h Sharp  1-8  R e s u l t s - O r i f i c e type 1.5  i n c h Sharp  1-10  R e s u l t s - O r i f i c e type 2.0  i n c h Sharp  1-11  Beta - 0.2  1-13  R e s u l t s - O r i f i c e t y p e G.S.  Beta - O.U  1-16  Results - O r i f i c e  Beta - 0.6  1-21  Results - O r i f i c e  type G.S.  type G.S.  R e s u l t s - O r i f i c e type S p e c i a l 15  1-28  R e s u l t s - O r i f i c e t y p e S p e c i a l 30  1-29  Data - O r i f i c e type S t a n d a r d 1.0  inch  2-2  Data - O r i f i c e type S t a n d a r d 1.5  inch  2-3  Data - O r i f i c e  inch  2-5  type S t a n d a r d 2.0  Data - O r i f i c e type Sharp 1.0  inch  2-6  Data - O r i f i c e t y p e Sharp 1.5  inch  2-8  Data - O r i f i c e type Sharp 2.0  inch  2-9  Data - O r i f i c e type G.S.  B e t a - 0.2  2-11  Data - O r i f i c e  Beta - O.U  2-lU  type G.S.  Table 2-9  Data - O r i f i c e type 0. S. Beta  2-10  Data - O r i f i c e type S p e c i a l  15  2- 11  Data - O r i f i c e type S p e c i a l  30  3- 1  95% c o n f i d e n c e i n t e r v a l f o r K and Ren, type 1.0  3-2  n  3-3  95*  3-h  3-5  Orifice  i n c h Stand.?rd  95't c o n f i d e n c e i n t e r v a l f c r K and" Ren, type 1.0  Orifice  i n c h Standard  c o n f i d e n c e i n t e r v a l f o r K and Ren,  type 2.0  Orifice  i n c h Standard  95% c o n f i d e n c e i n t e r v a l f o r K and R e , type 1.5  Orifice  i n c h Sharp  95% c o n f i d e n c e i n t e r v a l f o r K and K e n , O r i f i c e type 1.5  ,3-6  i n c h Sharp  95^ c o n f i d e n c e i n t e r v a l f o r K and Re-n, O r i f i c e type 2.0  3-7  i n c h Sharp  95% c o n f i d e n c e i n t e r v a l f o r K and Ren, type G. S. Beta =0.2  3-8  =0.6  '  Orifice  i  95$ -confidence i n t e r v a l f o r K and Re-p* O r i f i c e ' type G. S. Beta = O.U  3-9  95% c o n f i d e n c e i n t e r v a l f o r K and R e , n  type G. S. Beta = 3-10  95$  0.6  confidence i n t e r v a l  f o r K and Rep,  Orifice  95% c o n f i d e n c e i n t e r v a l f o r K and Ren,  Orifice  type S p e c i a l 3-11  Orifice  type S p e c i a l  15  30  vi  Table' Ii-1 '  Page Data f o r t h e c a l i b r a t i o n o f t h e r m o c o u p l e s  h-2  1,2,3,14,5, and thermometer 1 . it-2  C a l i b r a t i o n d a t a f o r t h e thermometers 2 and 3  U-3  h-3  C a l i b r a t i o n data f o r carbon t e t r a c h l o r i d e  h-9  h-h  C a l i b r a t i o n d a t a f o r benzene  U-9  i  V  viii  LIST OF FIGURES  Figure 1  Page  R  C a l i b r a t i o n r e s u l t s - Ambrosius and S p i n k (10) 2 - i n c h and 3 - i n c h p i p e  2  3  C a l i b r a t i o n r e s u l t s - T h r a s h e r and B i n d e r (16) 1 - i n c h pipe,,  3  5*  C a l i b r a t i o n r e s u l t s - Galloway (Iii) 1»5  - i n c h and 2 - i n c h p i p e s  6  h  Schematic drawing o f the a p p a r a t u s  9  J>  Summary o f o r i f i c e p l a t e  6  Schematic drawing o f the t e s t s e c t i o n  17  7  1" M u l t i - p l a t e  21  8  1" O r i f i c e f l a n g e assembly  9  Schematic drawing o f an o r i f i c e p l a t e f o r the meter  design c r i t e r i a  flow straightener  ' 12  assembly  22  equation derivation 10  C a l i b r a t i o n r e s u l t s - S t a n d a r d and Sharp plates  11  orifice 3U  1 - inch test line  C a l i b r a t i o n r e s u l t s - S t a n d a r d and Sharp o r i f i c e lo$  12  27  plates 35  - inch test line  C a l i b r a t i o n r e s u l t s - S t a n d a r d and Sharp o r i f i c e  plates 36  2.0 - i n c h t e s t l i n e 13  C a l i b r a t i o n r e s u l t s - S t a n d a r d and Sharp o r i f i c e 1.0, 1.5  lli  and 2.0 - i n c h t e s t l i n e s  C a l i b r a t i o n r e s u l t s - S p e c i a l 15" and S p e c i a l o r i f i c e plates  plates 37  30 39  IX Figure 15  Page.  1.0, 16  o  0 - inch test l i n e s Beta -  0  U0 O.U  l o 5 and 2 » 0 inch test l i n e s  C a l i b r a t i o n r e s u l t s - G.S., loO,  18  l o ' 5 and 2  0  C a l i b r a t i o n results - G.S , loO,  17  Beta - 0 2  C a l i b r a t i o n r e s u l t s - G.S.,  1*1  Beta - 0 » 6  l o 5 and 2 o 0 - inch t e s t l i n e s  i\Z  C a l i b r a t i o n r e s u l t s - Standard, Sharp, U3  G.S., Galloway and A.S.M.E. U-l  Calibration of thermocouple 1  k-2  C a l i b r a t i o n of thermocouple 2  U-3  C a l i b r a t i o n of thermocouple 3  ^-6  U-l*  C a l i b r a t i o n of thermocouple U  ^"^  U-5  C a l i b r a t i o n of thermocouple 5  ^-8  U-6  C a l i b r a t i o n of thermometer  #1  h-11  U-7  C a l i b r a t i o n of thermometer  #2  k-l  U-8  C a l i b r a t i o n of thermometer  #3  U-9  C a l i b r a t i o n of carbon tetrachloride  U-10  ..Calibration of benzene  k-U 1  2  ^-13 U-lU U-l>  A 0 K N OV.' LK I1GE ME W T  T am  indebted  t o Dr. Norman E p s t e i n f o r h i s h e l p  and  encouragement d u r i n p the c o u r s e o f t h i s p r o j e c t . The  a s s i s t a n c e o f H r . R. Muelchen, Mr. J . Zorn  Hr. J . Baronowski i s a p p r e c i a t e d  3nd  f o r t h e i r s J v i c c and p r o f i c i e n c y  i n b u i l d i n g the r e q u i r e d equipment. I  a l s o wish t o thank the N a t i o n a l Research C o u n c i l  Canada f o r the f i n a n c i a l a s s i s t a n c e r e c e i v e d , and Department o f C h e m i c a l E n g i n e e r i n g support.  of  the  o f II.:i.C. f o r a d d i t i o n a l  INTRODUCTION Over the p a s t f i f t y y e a r s , a g r e a t d e a l o f r e s e a r c h has been concerned with the t h i n plate  o r i f i c e meter.  The c h a r a c t e r i s t i c s  o f the c a l i b r a t i o n  c u r v e s have been e x p l o r e d by many workers (5, 9, 1 0 , 16, 17) o v e r a v e r y wide range o f Reynolds Numbers.  H e r e a f t e r , Reynolds numbers based on i n s i d e  p i p e d i a m e t e r w i l l be a b b r e v i a t e d Ren  w h i l e t h o s e based on t h e o r i f i c e  d i a m e t e r w i l l be a b b r e v i a t e d Red. I t i s w e l l known t h a t a t h i g h Reynolds numbers, w h i c h i n t h i s s t u d y means Reynolds numbers based e i t h e r on p i p e d i a m e t e r o r o r i f i c e d i a m e t e r g r e a t e r than 10,000, the c o e f f i c i e n t o f d i s charge i s v e r y n e a r l y independent o f b o t h t h e Reynolds number and t h e d i a meter r a t i o B e t a .  However, a t a l o w Reynolds number (Rep o r Re^ l e s s than  1 0 , 0 0 0 ) , t h e c o e f f i c i e n t o f d i s c h a r g e appears t o be a f u n c t i o n o f Rep o r Re^, Beta and a "shape f a c t o r  (6).  I t i s t h e e f f e c t o f t h e shape f a c t o r on  the c o e f f i c i e n t o f d i s c h a r g e i n t h e l o w Reynolds number range w h i c h i s t h e primary concern o f t h i s s t u d y . A r e v i e w by I v e r s e n (6) i n 195li attempted t o s t a n d a r d i z e d i s c h a r g e c o e f f i c i e n t s o v e r t h i s range by compering t h e r e s u l t s o f s i x t e e n i n v e s b i g a t o r s who c a l i b r a t e d between lj and £0,000.  o r i f i c e p l a t e s at. Reynolds numbers (Rep o r Re^) However, the two d i f f e r e n t Reynolds numbers used by  d i f f e r e n t a u t h o r s , and t h e v a r i a b i l i t y o f p r e s s u r e t a p l o c a t i o n and o r i f i c e p l a t e d e s i g n , made a d i r e c t comparison o f most o f t h e s e data u n e n l i g h t e n i n g . The l a r g e s t s o u r c e o f r e a s o n a b l y comparable d a t a was t h a t i n w h i c h t h e e x p e r i m e n t e r s used c o r n e r p r e s s u r e t a p s .  These d a t a were r e c a l c u l a t e d  a c o n s i s t e n t d i s c h a r g e e q u a t i o n and Rep, and p l o t t e d from h t o 10,000.  using  f o r Reynolds numbers  :  U n f o r t u n a t e l y , d e v i a t i o n s from t h e mean c u r v e s i n c r e a s e d  from C.5% a t Rep =» 10,000 t o between 5> and 10;? a t Rep = h.  I v e r s e n concluded  t l i a f ' t h e e s s e n t i a l r e q u i r e m e n t f o r the s p e c i f i c a t i o n o f s t a n d a r d c o e f f i c i e n t s f o r o r i f i c e s i n the l o w Reynolds number range appears t o be a complete  2 s p e c i f i c s t a n d a r d i z a t i o n o f t h e o r i f i c e shape, n o t m e r e l y upper l i m i t s t o the s i z e o f t h r o a t w i d t h and o f p l a t e t h i c k n e s s " . The American S o c i e t y o f M e c h a n i c a l E n g i n e e r s has p u b l i s h e d (1, 2) s t a n d a r d d i s c h a r g e c o e f f i c i e n t d a t a f o r c o m m e r c i a l p i p e , 1.5 i n c h e s and l a r g e r , c o v e r i n g a range o f Ren  from  1,000 t o 10,000,000.  l i c a t i o n s i n c l u d e data f o r c o r n e r , f l a n g e , v e n a - c o n t r a e t a t a p s f o r Beta from  0.1 t o 0.75*  The  and p i p e  I.D. pubpressure  F o r such data t o be a c c u r a t e , s t a n d a r d  o r i f i c e meters must be b u i l t a c c o r d i n g t o d e s i g n s p e c i f i c a t i o n s a l s o found i n (1, 2).  T t i s o f i n t e r e s t t o o r i f i c e meter u s e r s t o f u l l y  understand  the i m p l i c a t i o n s o f u s i n g b o t h s t a n d a r d c a l i b r a t i o n data and s t a n d a r d c r i t e r i a a t low Reynolds numbers.  design  T h e i r use i m p l i e s t h a t v a r i a t i o n o f  o r i f i c e meter shape w i t h i n the upper and l o w e r l i m i t s a l l o w e d by the d e s i g n has no measurable e f f e c t on the d i s c h a r g e c o e f f i c i e n t . been amply . j u s t i f i e d f o r Reynolds numbers g r e a t e r than However, f o r Reynolds numbers s m a l l e r than  This a s s u m p t i o n has  10,000 (5, 6, '3,  10,000, e v i d e n c e  o f an e f f e c t o f  geometry on the c o e f f i c i e n t o f d i s c h a r g e has been shown (10, 16, Ambrosius and S p i n k from h0 t o  10,000  (10)  ll).  reported discharge c o e f f i c i e n t data f o r  and Beta below  0.75, u s i n g  9, l h ) .  Re  d  f l a n g e p r e s s u r e t a p s . The  o r i f i c e p l a t e s were o f s t a n d a r d A.S.K.E. d e s i g n , w i t h a v a r i e t y o f o r i f i c e t h r o a t l e n g t h s and p l a t e t h i c k n e s s e s , and were i n s t a l l e d i n 2 - i n c h , 3 - i n c h and U - i n c h nominal  T.D.  commercial p i p e .  C o e f f i c i e n t s of d i s -  charge when compared a t e q u a l Betas f o r t h e t h r e e p i p e s i z e s , d i d not correspond.  T h i s may  be seen f o r the 2 - i n c h and 3 - i n c h p i p e s i n F i g . l ,  t a k e n from the o r i g i n a l p a p e r .  Figure l j  CALIBRATION RESULTS - AMBROSIUS AND SPINK ( l O ) 2 - inch and 3 - inch pipe  Each pipe size appears to give a separate set of c a l i b r a t i o n curves  The  0  authors suggested that the lack of geometric s i m i l a r i t y due to the use of commercial pipe, the v a r i a t i o n i n o r i f i c e shapes and the use of flange taps caused the c a l i b r a t i o n curves to vary appreciably with pipe diameter for any given Beta  0  A more s p e c i f i c geometry e f f e c t was ( 1 6 ) , who  observed by Thrasher and Binder  studied the e f f e c t of o r i f i c e throat length on the c o e f f i c i e n t of  discharge using Betas of  0 „ 2 , 0 5 " and 0 7 and a Re o  o  d  range o f  2,800 - 80,00  Their work indicated that i f the o r i f i c e throat length was kept smaller than l/Uo  of the inside pipe diameter, no e f f e c t oFthe pipe diameter would be  observed,.  A l s o , discharge c o e f f i c i e n t s increased with o r i f i c e throat lengths,  the greatest increase occurring a t the l a r g e s t Beta and the smallest Reynolds number.  The  preceding  generalizations were based on graphs obtained from  the o r i g i n a l paper and recorded i n F i g . 2 „ Galloway (Xlt) designed and b u i l t two o r i f i c e meters i n accordance the design recomnendations contained i n ( 1 ) , for use i n l $ a  nominal I.D. copper water pipe.  with  and 2 - inch  A l l dimension r a t i o s between the two meters  were approximately equal, except f o r the plate thickness to inside pipe diameter r a t i o .  In c a l i b r a t i n g these two p l a t e s , Galloway found that the  two curves of discharge c o e f f i c i e n t as a function of Rerj were coincident over a range of Ren from 8 0 0 to 3 0 , 0 0 0 .  Below 8 0 0 , however, two  separate  curves were observed, with consistent differences i n discharge c o e f f i c i e n t between the two plates of 2-3%°  The pertinent part o f Galloway's data,  obtained from h i s PhJD. t h e s i s , i s recorded i n F i g  e  3»  Galloway concluded  that the two curves resulted from the geometric d i s s i m i l a r i t y of these  two  o r i f i c e plates« The present i n v e s t i g a t i o n was conceived as an attempt to extend the general usefulness of standard o r i f i c e plates to Ren of 1 0 0 , and to gain  5  0620  Z  A 3«0O2Cf  UJ  . • 0  • 9»00i0"  t  0 S*Q003  •ft  *  (ft  al Jt  • 10 *  4  REYNOLD'S  #  •  •  35  c  06K)  g  0 6 0 0  B  *•  t  ^5  u  , »-I  *  •  <5  5  * o> • >• I  53  N'JMBER-Nnio'  6  6.5  7  3  C TH. RN for platea w i t h b « U r a i l * af  0.620  C  «  • •  D g  •  •  •  Ii  •  **  * * » •* m «0 « •  in o aeo o  t  ;  o S «0060" « S •OWO^i a S •0 0 2 0 | • S '0010' o S •0003'''  ; -  z  •  o  cc t  ,  5  1 Q600 45  3.5 REYNOLD'S  o  4  C TL RN far plate, with b . U rati* . f " J  '  •  NUMBER-NxlO'  if)  •0  •  0.630  •  9  z  UJ  0  0  * 0  A  •  S-0.060  ;«  5-QO40"  i  X  a 4  0  **• • ft* •fl  -  f a -li—*  *4 IA m «*  Ul  0620  UJ  t  A 9-0.020*  cc <  #•  •V S - 0 . 0 1 0 '  X  a SrOOOS' 0610  45  o o  35  6  65  7  73  8  05  9  8  o  REYNOLO'S NUMBER-NxlO"  4  C Ta. U N for platea with W U rati* . f »,T  F i g u r e 2:  CALIBRATION RESULTS - THRASHER AND BINDER (16) 1 - i n c h pipe F o r Reynold's r e a d Reynolds  F i g u r e 3:  CALIBRATION RESULTS - GALLOWAY 1.5 and 2 - i n c h p i p e  (lU)  7 some understanding of the e f f e c t of geometry on the c o e f f i c i e n t of discharge a t low Reynolds numbers.  This was accomplished by designing and  calibrating  standard A.S.M.E. o r i f i c e plates arid observing the e f f e c t on the discharge c o e f f i c i e n t due to geometry d i f f e r e n c e s .  These differences could then be  eliminated between o r i f i c e plates i f they were b u i l t with exacting geometrical similarity.  /  8 EXPERIMENTAL  I  Apparatus  l  See F i g . k  a) General The purpose of the experimental apparatus was to c i r c u l a t e water or a solution o f polyethylene-glycol and water (known hereafter as PEG), a t a cpnstant hydrostatic head, and constant temperature, through a t e s t s e c t i o n . The solution was then returned to a supply tank f o r r e c y c l e . The apparatus consists e s s e n t i a l l y of three flow loops connected i n parallel.  Loop 1 includes the primary c e n t r i f u g a l pump and the heat ex-  changer » A globe valve, situated a t p o s i t i o n 11 i n F i g . Ii, controls to a major degree the pump discharge pressure, which i n t u r n , controls the rate at which f l u i d i s pumped into t h e constant head tanko  Loop 2 returns over-  flow f l u i d from the constant head tank to the main supply tank by means of a small gear pump and an overflow tank.  Loop 3 supplies f l u i d to the t e s t  section and the weighing station (see F i g . U), flow being controlled by valve 21.  At the completion of a run, f l u i d c o l l e c t e d i n the weighing tank  i s pumped to the main supply tank. b) Pumps A Peerless, Model B c e n t r i f u g a l pump supplied the primary motive power for the flow loops.  Its design capacity was 150 U.S. gallons per minute  against a 70 foot head.  I t was run by a 7 l/2 H.P.  3-phase constant speed  A.C. e l e c t r i c motor. A second c e n t r i f u g a l pump, Leraco Model FL 1 l/k> emptied the weighing tank a f t e r each experimental run.  I t was driven by a 1/2 H.P. single phase  A.C. e l e c t r i c motor,, A small gear pump, a Worthington Model 11F169B, emptied the overflow tank.  This pump, which was powered by a l/k H.P. single phase A.C. e l e c t r i c  9  FIGURE li:  SCHEMATIC DRAWING OF APPARATUS  Key to Figure U . (1) Multi-plate flow straightener 1 - inch l i n e (2) Multi-plate flow straightener 2 - inch l i n e (3) Multi-plate flow straightener  1.5  - inch l i n e  (U) Control valve 1 - inch l i n e (5) Control valve 2 - inch l i n e (6) Control valve, 1.5  - inch l i n e  (7) O r i f i c e assembly 1 - inch l i n e (8) O r i f i c e assembly 2 - inch l i n e (9) O r i f i c e assembly 1.5 inch l i n e (10) Constant head tank (11) Control valve i n heat exchanger loop (12) Heat exchanger (13) Primary pump  1  (lli) Overflow tank (15) Secondary pump to empty overflow tank (16) Check valve (17) Supply tank - 100 Imperial  gallons  (18) Secondary pump to empty weighing tank (19) Beam balance scales (20) Weighing tank (21) Control valve (22) Thermocouple 5 (23) Thermocouple U on the heat exchanger loop and thermocouple 6 on the c o n t r o l board  s  11 motor, ran continuously. c) Heat  Exchanger  Temperature c o n t r o l was provided by c i r c u l a t i n g c o o l i n g water through a single-pass she11-and-tube heat exchanger mounted above the primary pump outlet. d) Tankageo A 100 I m p e r i a l g a l l o n g l a s s - l i n e d supply tank, a 50 U.S. aluminum constant head tank, a 50 U.S. 50 U.S.  gallon  g a l l o n aluminum overflow tank and a  g a l l o n s t e e l weighing b a r r e l were used i n the experimental apparatus  0  The s t e e l b a r r e l was tygon-coated i n s i d e p r i o r to use, to ensure a noncorrodatle surfaces. The other tanks were chemically i n e r t to the experimental fluid*. e) P i p i n g Both 2-inch and 3-inch nominal diameter Type L copper water pipe was used throughout the main flow loops of the apparatus.  The t e s t s e c t i o n ,  which w i l l be described i n greater d e t a i l subsequently, contained 1 - i n c h , 1 1/2  - i n c h and 2 - i n c h Type L copper water pipe.  A l l j o i n t s were soldered^  A g l a s s window, i n s t a l l e d by a previous worker ( l U ) , ensured t h a t no undesi r a b l e entrained a i r passed through the t e s t s e c t i o n during a run.  Venting  was allowed f o r a t the top of the heat exchanger l o o p , and i n each o r i f i c e flange i n the t e s t s e c t i o n . f) Design of O r i f i c e P l a t e s Seventeen o r i f i c e p l a t e s were designed and b u i l t t o c a r r y out the experimental program.  Design c r i t e r i a f o r the Standard, Sharp and S p e c i a l  p l a t e s can be found i n " F l u i d Meters" ( l ) , and i n "Flow Measurement, Power Test Code" (2).  This information i s summarized i n F i g . 5 along w i t h design  information f o r the g e o m e t r i c a l l y s i m i l a r (abbreviated G.S.) s e r i e s and the s l i t w i d t h , t , f o r the corner pressure t a p s s  o r i f i c e meter D  Specific  12  A-S-M-E- — FLUID METERS t  2  /  '45'  t < D/30, (D-d)/8, d/8 2  If  D d  2  > D/30, (D-d)/8,  d/8,  Downstream Edge Is Bevelled At A 45° Angle Until t, £ D/30, (D-d)/8, d/8  \ STANDARD  t  SHARP  POWER  A-S-M-E45'  TEST  CODE  For D < 3 OOID< t, < 0 02D t = 3/3 2" ± 1/32" 2  b  SPECIAL GEOMETRICALLY 45  SIMILAR  t, = 1/ I 6 D t, »  I/32D  G S CORNER /  /  /  TAPS  /  U= /  PRESSURE  0 02 D  /  FIGURE 5:  SUMMARY OF ORIFICE PLATE DESIGN CRITERIA  dimensions  f o r e a c h o r i f i c e p l a t e a r e c o n t a i n e d i n T a b l e s 1 and  S i x p l a t e s , t h r e e each o f t h e " S t a n d a r d " and "Sharp" c o n s t r u c t e d o f l/8 - i n c h b r a s s p l a t e . r e f e r e n c e t o (1),  2.  t y p e s , were  They were designed w i t h  the more i m p o r t a n t geometric s p e c i f i c a t i o n s o f  which are contained i n F i g . 5 Two f u r t h e r p l a t e s , S p e c i a l 15 and S p e c i a l 30 were d e s i g n e d w i t h r e f e r e n c e t o (2).  l/8 - i n c h b r a s s p l a t e was a g a i n u s e d ; F i g . 5 (b) i  s p e c i f i e s t h e i r geometry. The f i n a l n i n e p l a t e s , t h e "G.S" s e r i e s , were machined 2 3A  inch brass bar stock.  Design c r i t e r i a were based on the  r e q u i r e m e n t s o f r e f e r e n c e 1 and g e o m e t r i c by F i g .  5  s i m i l a r i t y , as i l l u s t r a t e d  (c).  P r e s s u r e drop was measured i n the o r i f i c e taps.  from  A schematic drawing  flange by c o r n e r  o f t h e i r d e s i g n i s shown i n F i g . 5(d).  TABLE 1 DIMENSIONS OF G. S. ORIFICE SERIES AND ASSOCIATED EQUIPMENT O r i f i c e Type  G. S. Beta " 0.2  G. S. Beta 0 0.1*  G. S. Beta = 0.6  1.0232  1.0232  1.0232  1.5058  1.5058  1.5058  1.9851  1.9851  1.9851  0.2032  8.1*079  0.6131*  0.3012  0,6027  0.9011  0.3969  0.79UU  1.1912  0.198  0.399  0.599  0.200  0.399  0.598  0.200  0.1*00  0.600  O r i f i c e throat length ti, in. Design throat length  0.0339  0.0300  0.0339  0.01*72  0,01*39  0.01*71  0.0586  0,0595  O.O602  0.0320  0.0320  0.0320  .0.01*71 0,01*71  0.01*71  0.0620  0,0670  0.0620  Ratio  0.03U2  0.0293  O.033I  0.031U  0.0292  0.0339  0.0295  0.0299  0,0303  0.061*1*  0.061*1*  0.061*1*  0.0932  0.0933  0.0939  0.1257  0.1253  0.1272  0.061*0  0.061*0  0.061*0  0.091*1  0.091A  0.091*1  0.121*0  0.121*0  0.121*0  0.0630  O.O63O  0.0630  0.0619  0.0619  0.0619  0.0621*  0.0633  0.061*0  Width o f s l i t , t , in. Design width of s l i t  0.0201*5  0.0201*5  0,0201*!:  0,0301  0.0301  0.0301  0.0397  0.0397  0.0397  0.0201*  0.0201*  0.0201*  0>0301 0,0301  0,0301  C 9,0397  0.0397  0,0397  Ratio t /T)  0.020  0.020  0.020  0.020  0.020  0.020  0,020  0.020  Inside diameter of pipe D, i n . O r i f i c e diameter d, i n . Beta d/D  (1/32)D i n . ti/TJ  O r i f i c e plate thickness t2, i n Design plate thickness  (1A6)D i n .  . Ratio t2/D  s  0.02D i n . s  0.020  '  Entrance length, L^, i n . Ratio Li/D  85.13 83.2  85.13 83.2  85.13 83.2  88.56 58.8  38.56 $.8  58.56 8.8  39.87 U5.3  89.87 1*5.3  89.87 1*5.3  E x i t length, Ratio L2/D  39.56 32.96  39.56 32.96  39.56 32.96  li8.75 31.6  *8.75 31.6  0.75 (1.6  1*8.75 29.6  1*8.75 2l*.6  U8.75 21*.6  L2, i n .  TABLE 2 DIMENSIONS OF STANDARD, SHARP AND SPECIAL ORIFICE SERIES AND ASSOCIATED EQUIPMENT Orifice Type  Standard  Beta = o.U  Sharp  Beta '=> o.H  Special Beta O . U  Inside diameter of pipe D, in. Orifice diameter d, in. Beta d/D  1.0232  lo5058  1.9851  L 0 2 3 2  1.5058  1»9851  1.5058  1.5058  0.U09  0.616  0.795  O.Jill  0.613  0.793  0o605  0.603  o.Uoo  0.U03  o.Uoo  OoUOl  O0I1O7  0.U02  0.U02  0.U01  Orifice throat length ti, in. Ratio t i / b Recommended Maximum, i n . Recommended Minimum, i n .  0.0268  0.0U8I  0.0587  0.0  0.0  OoO  0.0166  0.0299  0.0262  0.0320  0.0296  OoO  0.0  0o03U2  0.0502  O0O662  0.0 0.0  Orifice plate thickness t2, in. Design plate thickness, i n . Ratio t2/D  0.121  0.125  0.12U  0.12U  0.120  0.127  0.12U0  0.125 0.119  0.125 0.0795  0.125 0o0619  0.125 0.121  0.125 0.0798  0.125  0.125  0.125  0.06U5  0 0823  O0O810  0.0301  0.0397  0 . 0 2 0 U  0.0301  0.0397  0.0301  0.0301  0 . 0 3 9 7  0.020U  0.0301  0,.0397  0..0301  0.0301  0.02  0.02  0.02  0.02  0.02  Width of s l i t tg, in. Design width of s l i t , i n . 0.02D i n . Ratio t /D  0.0  OoO  0.0110  O0O230 0.0301  0 o 0 l 5 l  0.020L(  0.020U  0 . 0 3 0 1  0  0.122  0.02  0.02  Entrance length, L]_, i n .  88.56  88.56  88.56  88.56  38.56  88.56  880 5 6  88.56  Ratio Li/D  58.8  58.8  58.8 •  58.8  58.8  58.8  5808  58.8  Exit Length, I/?, in  1.8.75  U8.75  U8.75  U8.75  1.8.75  U8.75  U8o75  U8.75  Ratio 1^/4)  31.6  3106  3106  31.6  3106  31.6  31.6  31.6  s  0.02  16 g) Test Section  See F i g , 6  The t e s t section consists of three p a r a l l e l horizontal t e s t l i n e s made from 1 - inch, 1 l/2 - inch and 2 - inch copper water pipe. l i n e s contained  Each of the test  the following components$  (1) Globe valve (2) Multi-plate flow straightener (3) Calming section (U) O r i f i c e flange assembly (5)  E x i t section  (6) Thermocouple well In working out the design f o r the t e s t section, there was as to the positioning of the multiplate flow straighteners,  some question  Sprenkle  (7)  recommended i n s t a l l i n g them approximately eight pipe diameters upstream of the o r i f i c e plates for turbulent flow.  Galloway (Hi) concluded that h i s  discharge c o e f f i c i e n t c a l i b r a t i o n curves had the l e a s t scatter at 8 l/2 diameters upstreamo v i r t u a l l y impossible to each other.  Unfortunately,  due  to t e c h n i c a l d i f f i c u l t i e s , i t was  to b u i l d the flow straighteners geometrically s i m i l a r  Hence, there was  no guarantee that the v e l o c i t y p r o f i l e s  produced at the o r i f i c e plates would be i d e n t i c a l f o r d i f f e r e n t sized pipes. Therefore, i t was  decided to i n s t a l l the flow straighteners immediately  following the globe valves i n each l i n e .  I t was  reasoned that the flow  p r o f i l e s would then, i n a l l p r o b a b i l i t y , be f u l l y developed i n traversing the calming section. E m p i r i c a l l y , the s i t u a t i o n i s as follows:  For laminar flow, assuming  a f l a t v e l o c i t y p r o f i l e at the entrance, the following equation (8,  13)  predicts the approximate length of s t r a i g h t pipe required to produce a f u l l y developed v e l o c i t y p r o f i l e  X /b t  -  0,05  Bej)  (  I  N  17  F I G U R E 6 i • SCHEMATIC DRAWING  OF THE T E S T  SECTION  Key to Figure  6.  (1) Control valve. (2)  Multi-plate flow straightener.  (3)  Orifice  flange vents.  (k) Pressure l i n e t o manometers. (5) O r i f i c e assemblyo (6)  Thermocouple f o r 1 - inch l i n e .  (7)  Thermocouple f o r 2 - inch l i n e .  (8)  Thermocouple f o r 1 l / 2 - inch l i n e .  19 In turbulent flow, an entrance length of from I4O to 5 0 pipe diameters i s considered s u f f i c i e n t to produce a f u l l y developed turbulent velocity-  p r o f i l e ( 3 ) o A comparison o f the t h e o r e t i c a l requirements with the actual entrance lengths i s supplied i n Table 3 . TABLE 3  Comparison o f A c t u a l and T h e o r e t i c a l l y Maximum Entry Lengths f o r Laminar and Turbulent Flows  Nominal Pipe Size in„  1 2  " •  X D Actual  D  eq. 1 Ren - 2 1 0 0  83o2 W o 3  X D turbulent Re > 2 1 0 0  - I t  D  U0  105  - 105 • 105  -  50  IiO - SO  ho  -  50  ...  Obviously, f o r Reynolds numbers greater than 2 1 0 0 , assuming turbulent flow, there i s s u f f i c i e n t entrance length a v a i l a b l e .  However, f o r Reynolds  numbers close to but l e s s than 2 1 0 0 , not even the one - inch pipe provides s u f f i c i e n t entrance length f o r a complete p r o f i l e development. According to Sprenkle (7), however, the multi-plate flow straights ner produces a w e l l rounded v e l o c i t y p r o f i l e immediately downstream. I t i s therefore reasonable t o assume that this rounded rather than f l a t s t a r t i n g p r o f i l e should r a d i c a l l y shorten the entrance length necessary f o r a f u l l y developed v e l o c i t y p r o f i l e . A minimum o f 2$ pipe diameters was recommended by the A.S.M.E. report on F l u i d Meters (2), t h i s requirement.  f o r the e x i t s e c t i o n .  A l l ttoee flow l i n e s s a t i s f i e d  20 Working drawings o f t h e m u l t i - p l a t e f l o w s t r a i g h t e n e r and the o r i f i c e f l a n g e a s s e m b l y f o r the 1 - i n c h t e s t l i n e may be found F i g s . 7 and 8. i n reference  respectively i n  Drawings f o r the 1 . 5 and 2 - i n c h t e s t l i n e s a r e c o n t a i n e d  (lli).  h) P r e s s u r e Measurement Differential  p r e s s u r e s were measured u s i n g one o r '>iore o f f o u r  U-tube manometers.  A d e s c r i p t i o n c f each f o l l o w s i n Table h.  TABLE h .-  1  DESCRIPTION OF THE HAKOl-IB'fSPS  No.  Liquid  Type I'-tube  '•I  2  • U-tube i n v e r t e d  3  U-tube u o r i p h t i • U-tube i n v e r t e d  •h  The nanometers wpre connected O.D. copper t u b i n g . a cathetometer  iie r c u r y  uprirht  7? cm.  150 cm.  Air c  Length  ciu  C6H6  52 cm.  150  cm.  t o t h e o r i f i c e f l a n g e s b y 3/°' - i n c h  P r e s s u r e head d i f f e r e n c e s were measured by means o f  t o 0 . 0 0 5 i n c h e s f o r the f i r s t 130 r u n s .  For the remaining  r u n s , d i f f e r e n t i a l heads w jre measured t o ' 0 . 0 5 cm. w i t h o u t s p e c i a l _ v i e w i n g f  equipment. i ) Temperature Measurement - See F i g . h and F i g . 5. Temperature was measured u s i n g s i x c o p p e r - c o n s t a n t a n and t h r e e r e s e a r c h q u a l i t y thermometers.  thermocouples  The s i x thermocouples and  thermometer #1 were c a l i b r a t e d a g a i n s t P l a t i n u m R e s i s t a n c e Thermometer #l693l!i.  The' o t h e r two thermometers were c a l i b r a t e d u s i n g thermometer  i'l as a s t a n d a r d .  A Leeds and Northrup // 8662 o r t a b l e P r e c i s i o n p  P o t e n t i o m e t e r , w i t h e x t e r n a l S t a n d a r d Weston C e l l ' % l l 6 6 k i j , was usedtipto  FASTEN PLATES TOGETHER WITH 4 - 1/16" BRASS OR COPPER RODS SOLDER RODS TO PLATES SOFT  I.D.  PIPE  1.025 IN.  CROSS-SECTIONAL AREA FREE AREA OF P L A T E  SOLDER  37n/4(.l20) RATIO  FREE  2  =  0.8252 IN.  2  0.4184 IN  AREA  TO  2  PIPE  AREA  = .4184/.8252 . = .5070  COPPER  WATER  PIPE  RUBBER  GASKET  DRILL 37 HOLES 0 120 DIAMETER ON 17/128" SQUARE PITCH USE # 31 ASA TWIST DRILL  1/8"  5/16 DRILL 6 HOLES EQUALLY SPACED  LOCATING SCALE:-  FULL. I  1/16" DRILL 4 HOLES  PLATE  PLATE  MATERIAL  BRASS  SCALE : - F U L L .  REQUIRED  FIGUR'S  7:  BEVEL INLET SIDE OF EACH HOLE AS SHOWN  •2  l"  MULTIPLATE  FLOW  SECTION MATERIAL  BRASS  HOLE SCALE:-  REQUIRED  STRAIGHTENER  THROUGH  ASSEMBLY  NONE  ro M  — t,  J_i_  1/4"SECTION  1  —1 MSECTION B-B  -I 1/4" -  r SCALE:-  A-B  ORIFICE PLATE Fill I MATERIAL:- -BRASS  DRILL AND T A P 6 HOLES FOR 1/4X2 CAP SCREWS  SECTION  DRILL AND TAP 1/4 NPT  A-A  FIGURE 8: l" ORIFICE ASSEMBLY SCALE:- FULL MATERIAL :- BRASS I REQUIRED  IN)  23 measure thermocouple E.M.F.  This was the same equipment used o r i g i n a l l y to  c a l i b r a t e the temperature measuring equipmento Thermocouples 1, 2 and 3 indicated f l u i d temperatures a t the o r i f i c e meters o Thermocouples k and 5 measured, respectively, the heat exchanger loop and the upstream header temperatures. Thermocouple # 6 and thermometer # 1 measured the temperature a t the control boardo  The remaining thermometers, § 2 and #3, were used res-  p e c t i v e l y i n the density and v i s c o s i t y measurements o f the f l u i d samples removed during a r u n  0  Temperature control was maintained i n the flow loop by two methods. One method was to compare the E.M.F. of thermocouple 6 with the E.M.F. of one of thermocouples 1, 2 or 3, depending on which t e s t l i n e was being used, on a Scalarap galvanometer.  Temperature could be maintained within 0 5°F» o  using t h i s method, as long as room temperature fluctuations remained s m a l l  0  However, due to large temperature variations during some days i n the summer, the above method could not always be used«  In this case, the  cooling water rate was set a t a reasonable l e v e l and the f l u i d temperature was allowed to vary slowly with room temperature.  This method also gave  good r e s u l t s , as the temperature change f o r any one run was always small. A non-weighted average of from 3 to 7 E.M.F. readings over a run was accepted as the correct temperature measurement by both methods. j) Weighing. A platform scale, with a capacity of $00 pounds, was used f o r a l l the c a l i b r a t i o n runs.  This scale was l a s t calibrated by Galloway (lk) i n 1963,  and found to be accurate to i 2 oz. over i t s entire range.  2h  II  V i s c o s i t y and Density Measurements The f i r s t 130  runs were c a r r i e d out using tap water as the t e s t f l u i d .  Densities and v i s c o s i t i e s were obtained from reference (18),  assuming the  p h y s i c a l properties of tap water were very nearly those o f d i s t i l l e d water,, For  the remaining runs, o n e - l i t r e samples of the test f l u i d were removed  from the experimental apparatus a t the beginning and at the end of each day's experimental runs. Approximately l £ 0 ml. was set aside f o r v i s c o s i t y measurements.  The remainder was used i n the density determination.  a) V i s c o s i t y The kinematic v i s c o s i t y measurements of the samples were c a r r i e d out by means of two Cannon - Fenske p r e c i s i o n viscometers, C-8 and C-3. Normally, four duplicate readings were taken f o r each sample' over a temperature range o f 70 - 80°F  o  To obtain the v i s c o s i t y of the f l u i d f o r a s p e c i f i c experimental run, the  following procedure was adhered t o .  (1) , The viscosity.was plotted as a function of temperature f o r each of the two samples on arithmetic graph paper. (2)  Two l i n e s which appeared to best f i t the data were drawn through the  two sets of p o i n t s . (3)  This graph was entered with the average temperature recorded a t the  o r i f i c e f o r the s p e c i f i e d run and the run number. (U) A double i n t e r p o l a t i o n vjas used t o obtain the correct v i s c o s i t y based on the run number and the average temperature. b) Density  !  A Cenco #167!?2-C precision hydrometer was used to measure the density of the PEG s o l u t i o n .  I t s accuracy was checked against a Westphal Balance  and found to be correct within 0.3$.  The density measurements were taken  and plotted i n the same manner as described previously f o r v i s c o s i t y . .1  However, f l u i d d e n s i t y a t the o r i f i c e  (/^ ) and i n the manometer  o b t a i n e d i n s l i g h t l y d i f f e r e n t ways.  D e n s i t y i n the f l o w l o o p g r a d u a l l y  i n c r e a s e d d u r i n g the day due t o w a t e r e v a p o r a t i o n . by i n t e r p o l a t i o n .  (f^ ) 0  were  Hence |/0)was o b t a i n e d  However, e v a p o r a t i o n was n o t p o s s i b l e i n the manometers.  T h e r e f o r e the d e n s i t i e s o f t h e t e s t f l u i d i n the manometer were o b t a i n e d u s i n g o n l y the morning sample.  The manometers were f l u s h e d o u t and r e f i l l e d  each w o r k i n g day. I t s h o u l d be noted t h a t i n the g i v e n open s y s t e m , c o n c e n t r a t i o n o f t h e e x p e r i m e n t a l s o l u t i o n was always t a k i n g p l a c e due t o the e v a p o r a t i o n o f water.  Thus, b o t h the v i s c o s i t y and d e n s i t y o f the c i r c u l a t i n g t e s t  i n c r e a s e d d u r i n g a day's r u n s . n e t mere than 0.7% Ill  Ths f o l l o w i n g procedure  w a t e r o r PEG.  Spot checks i n d i c a t e d t h e i n c r e a s e t o be  f o r v i s c o s i t y and 0.1;? f o r the d e n s i t y .  E x p e r i m e n t a l Procedure  was i n i t i a l l y  fluid  Jee F i g . h. was c a r r i e d o u t on s t a r t - u p .  The s u p p l y  tank  f i l l e d w i t h a p p r o x i m a t e l y 100 I m p e r i a l g a l l o n s o f e i t h e r T h i s a u t o m a t i c a l l y primed t h e Peerless-; pump.  v a l v e s i n the t e s t s e c t i o n were opened.  A l l v e n t s and  A f t e r s w i t c h i n g on the p r i m a r y  pump, v a l v e 21 was f u l l y opened and v a l v e H  was p a r t i a l l y c l o s e d .  h e a t exchanger was a d j u s t e d as d e s c r i b e d p r e v i o u s l y .  The  Test f l u i d was pumped  i n t o the c o n s t a n t head t a n k , and flowed o u t through b o t h the test s e c t i o n and  the o v e r f l o w l i n e i n t o the w e i g h i n g  tank and o v e r f l o w t a n k , r e s p e c t i v e l y .  These t a n k s were emptied as r e q u i r e d i n t o the s u p p l y t a n k .  U s u a l l y , one-  h a l f hour was r e q u i r e d t o remove most o f the e n t r a i n e d a i r from the system. T h i s was c o n s i d e r e d t o be a l m o s t complete when a i r was no l o n g e r i n e v i d e n c e upon v e n t i n g the t e s t s e c t i o n ,  the p r i m a r y pump was then s h u t down and any  r e m a i n i n g a i r a l l o w e d t o c o a l e s c e f o r a p p r o x i m a t e l y 1$ - 30  minutes.  The pr.mp was then s t a r t e d a ^ a i n and the l i n e s once more v e n t e d .  T  'sually,  26 a small additional amount of a i r bubbled from the test section vents. The system was then deemed ready for an experimental run. The steps taken to complete an experimental run were as follows. (1) Valve 11 was adjusted to supply adequate liquid to maintain a constant hydraulic head during the experimental run. (2) The test section was checked to ensure that liquid was flowing through the correct test l i n e . (3) Flow into the weighing tank was adjusted by valve 21. . (U) The platform scale was set somewhat in excess of the tare weight, and a stopwatch was activated when the lever arm passed through the zero point.  The same procedure was used at the end of a run.  (5) The manometers, thermocouples and thermometer were read as often as practicable during a run. (6) The weighing tank contents were returned to the supply tank at the completion of a run.  THEORY D e r i v a t i o n o f the O r i f i c e P l a t e M e t e r E q u a t i o n Assumption  ft  =• c o n s t a n t  T  ru  0  OL_l o  1  F i g . 9 Schematic Drawing o f an O r i f i c e P l a t e f o r the Meter E q u a t i o n  Derivation  Mechanical Energy 3alance f o r Steady S t a t e :  _2  IH 2<* c jR  Pl  =2 TJ  P'  2<A gc  Iwf  P?  2  V  P  1  z  R e - a r r a n g i n g e q u a t i o n 2, _2 Uz  -  2o< gc  gc  2  Let Cv  (  ? x  P'  ?)  P*  z  -Pi  Now  6  • 17  a  TT  d'  Al  -  Iwf  Ibf  Iwf  28  -4^  by d e f i n i t i o n  (7)  From equation 6, 2  _2  7,  and from equation _2 U,  (8)  _2 - U  (9)  0  Combining  equations  3> U, 8 and 9,  x3 -1  -  c*c",  and  c<2  i  2g  1/2  (Pl  c  -P ) 2  (10)  f u n c t i o n s o f Reynolds number  a r e  i  the e f f e c t s o f which are i n c l u d e d i n  C  v  , a modified  coefficient of velocity. Then 2g  1  (Pl  c  2 1/  -P ) 2  (11)  />'  Now, by re-arranging equation 11^  1 - C  2 c  £  4  I  |2g ( P l c  ft'  P2)  (12)  29 or C  v  C  jl-  c  ,3*  J2g  (Pl-P2)/^  c  /  (13)  'c That i s ,  U  c  "  C  (lh)  2 g (P -P ) c  1  2  where  Mow W  -  M  o  /  -  J  2 g  c  /  / (PI-PS)  (  1  6  )  Define  K  -  C/ J/  -  K  ( 1 7  )  Then W  A  Q  J2g  c  f>  (Pj-Pg)  (  l  8  )  Equations 16 and 18 are the same as equations 98 and 99 respectively i n F l u i d Meters ( l ) . To obtain working equations the following substitutions were made.  For a two-liquid v e r t i c a l manometer,  across the o r i f i c e plate i n l b F / f t . ^  P i - P2 i s the pressure drop  30  Then P  1UL x ( 2 . 5 U )  l - ?2  2 H  (  I D  n  I)  or  P  -P  X  *{\ft -p  - 2.0U818  2  0  c  |)  (19)  where H  - difference i n l e v e l s o f the o r i f i c e manometer, cm.  A  • cross-sectional area of o r i f i c e , f t .  Q  -  TT  / d  -0.005U52 d  v2  2  ',f t .  2  d  • diameter o f o r i f i c e , inches  K  • discharge c o e f f i c i e n t , v e l o c i t y of approach factor included, dimensionless  w  - mass flow rate, l b ^/sec.  D  - diameter of t e s t l i n e , inches  f>  - density of f l u i d a t o r i f i c e , l b yi/ft.  - 62.U287 /O p n  - density o f f l u i d a t o r i f i c e , gm./ciru^ m  density of manometer f l u i d , gm./cm.^  31  - density of test f l u i d i n manometer, gm./cm.^ - discharge coefficient, velocity of approach factor not included, dimensionless. The substitution of the above conversions into equation (19) gives W  •  K A  J 2 (32ol7UO) (62.U287 jo  0  ) (2.0H818 H ( | £ , - / g  Re-arranging equation 2 0 , K  183.3U6  -  d  2  w  J8227O8708 H ^ d ^ O  -/g  |)  and from equation 17, C  -  K  \l  - Q  H  The Reynolds number based i n pipe diameter i s given by, ReD  "  UW TT  where  u  0  -  D  U  Q  absolute viscosity  |)  32  \)  0  - kinematic viscosity, centistokes  The working equation, based on the experimental units, then becomes Re  D  -  h  -  22,737  w  1  2  •  W  H88.16  or Ren  (2^)  The corresponding orifice Reynolds number i s Red  - 22,737  w  A l l calculations for C, K, ReD in an I.B.M. 70U0 electronic computer. '  (  2  5  )  and Red were carried out  33 RESULTS AND DISCUSSION Discharge coefficients, both with and without the velocity of approach factor included, and Reynolds number based on both pipe and orifice diameter, were calculated for each run by an I.B.M. TOkO Computer and may be found i n Appendix H o  The original data, which were used i n the above calculations,  may be found i n Appendix IIIo  Discharge coefficient K was plotted as a  function of Reynolds number, Rey). The results i n this form, were easily compared with standard A.S.M.E. orifice plate calibration data available i n references (1) and (2), as well as with Galloway's (lk) data,, Figures 10, 11 and 12 compare discharge coefficient calibration curves for the minimum and approximately maximum values of t  x  allowed by the  A.S.M.E. - Fluid Meters (1) orifice plate design, for each of the three pipe diameters studied,, It i s obvious that a difference i n calibration curves of from 2 to 6% exists between each of the two plates at a given pipe diameter, Rerj between 100 and 1000. The calibration curves of the three Sharp and the three Standard orifice plates are compared i n Fig. 13.  The curves for the three Sharp  plates are nearly co-incident. Since these three plates are also very nearly geometrically similar, except for the t2/D ratio, one can conclude that the effect of the t2>fo ratio on the calibration curves i s small. On the other hand, the Standard plates are dissimilar i n both the tiA> t^^) ratios.  a n  d  Since the spread of the three Standard calibration curves i s  about the same as the spread for the Sharp plates, i t appears that the t^/fo ratio does not affect the discharge coefficient to a significantly larger degree than does the t2/D ratio. However, scrutiny of Table 2 indicates a correlation between the t\/D ratio and the three Standard calibration curves. For instance, considering the three Standard orifice  IA  i  1  1  o ° oo  .72  o  SHARP  .69  '  BETA  10"  SYMBOL  o  0-4  10"  STANDARD  o  .70  SIZE  ORIFICE  o  o  .71  i i i i i  0-4  o  .68  o  .67  8 Q  o  d  .66  oo  o o  «58  .65 .64  ©o  .63 .62  Re D J_J  4  6  8  10  2  4  6  L  8  10 2 FIGURE 10: ' CALIBRATION RESULTS - STANDARD AND SHARP ORIFICE PLATES  4  6 8  1-INCH TEST LINE  10  i .72  r i  o  i  rr~r  ORIFICE  .71  1  BETA  SIZE  STANDARD  1-5"  0-4  SHARP  1-5"  0-4  i i i  SYMBOL  O, -  Q  .70  .69 .68 .67 .66  .65  .64  CD .63  .62  Re J  4  I  I I I  6 8  J_ 10  2  j  D  i  4  i  6  i  i i i  8  JL 10  2  _l  4  FIGURE 11 - CALIBRATION RESULTS - STANDARD AND SHARP ORIFICE PIATES 1„5 INCH TEST LINE  I I 1_L  6 8  10 VA  i r  CD  .72  Q)  .71  ORIFICE  SIZE  BETA  STANDARD  2 0 "  0-4  2  0-4  SHARP  Q>  .70  o  69  TT  0"  SYMBOL  o  CD  o o o  .68  0 o  .67  o  .66  .65 .64 .63  ©  .62  Re J  4  I  w  D  l__L_L  6 8 FIGURE 12:  J  10  2  4  6  I  I  8  O  «©*t I  L  10  2  O,  I  4  ©© I  l l l l  6 8  CALIBRATION RESULTS - STANDARD AND SHARP ORIFICE PLATES - 2„0 INCH TEST LINE  10 CN  1—I  4  6  FIGURE 1 3 i  8  IO  2  2  4  6  8  10  3  2  4  I  6  I  I I  8  1 0 ^  CALIBRATION RESULTS - STANDARD AND SHARP ORIFICE PLATES 1 . 0 , 1.5 AND 2 . 0 INCH TEST LINES - J  plates, the highest calibration curve i n terras of K was obtained in the 1<>5 - inch test l i n e .  This corresponded to the highest t]_/TJ ratio of  the three Standard plates. corresponding results.  The 2 - inch and 1 - inch test lines gave  There was no similar pattern for the t2A^ ratioo  Therefore, there does in fact appear to be an effect of t^/D regardless of the effect of t 2 / D . The results plotted on F i g . Hi represent calibration curves based on design recommendations of the A.S.M.E. - Power Test Code ( 2 ) .  Special  15 and Special 30, the two orifice plates involved, have respectively the minimum and maximum values of t i recommended i n ( 2 ) .  Both plates.were  built for the 1.5 - inch test line only. It i s interesting that even under the more rigorous specifications of reference (2) for tj_, geometry effects on the discharge coefficient, although smaller than those between the sharp and standard plates, are s t i l l observable. Figures 15, 16 and 17 contain the calibration curves of the nine plates designated G.S. 0.U and 0 6 . o  The G.S. series includes diameter ratios of 0.2,  The three plates included i n each diameter ratio were  geometrically similar.  Figures 15and 16 , with Betas of  pectively, yielded single curves. Fig. 17, had a much larger data spread.  0 2 and 0 U reso  o  however, with a Beta of 0.6,  Since experimentally, accurate data were  d i f f i c u l t to gather for the /2>0.'6.^pai&fees due to the small clocking time <9  l  for the fixed throughput of fluid required to f i l l the weigh tank, and the relatively small manometer differentials, a larger spread i n the data was to be expected  0  A comparison of some of the results of this study for the 1»5 - i n c h pipe with data from Galloway's calibration curves, and with standard A.S.M.E. calibration data, i s recorded i n F i g . 18. For Re^ between 100  i  i — r r ~ r  73 .72 .71  r~~i—i i i i ORIFICE  O  8  °i 8 ° 8 e 8  O  1 — i — i — I  i  SIZE  S P E C I A L 15  1-5"  SPECIAL  1-5"  30  r  BETA  SYMBOL  0-4 0-4  - o  O  .70  o  .69  9.  .68  9 ) .67  .66  .65  .64  .63  Re i  6  8  10  2  4  l  6  i  _L  i i  8  10  2  4  FIGURE l k : 3ALIBRATI0N RESULTS - SPECIAL l£ AND SFECIAL 30 ORIFICE PLATES  J  1  I  1  8  I 10 U> NO  i  i  i i  a 72 SIZE  ORIFICE *  71  o70  BETA  G S  IO"  0-2  G S  1-5"  0-2  G S -  2 0 "  0-2  . SYMBOL  W O  o ,68 ,67 66  3  65  ,64  0  63  „62  Re, j 10  4 FIGURE  i 6  1$:  i i i  8  J  10^  CALIBRATION  2  RESULTS - G . S . ,  I  4 BETA -  L  6 0.2,  8  10°  1.0, 1.5 AND 2.0  2 INCH  4 TEST  LINES  g"  1  i—i—r  I—TT  i  SIZE  BETA  G S  IO"  0-4  GS-  1-5"  0-4  ORIFICE  2  G S  3  SYMBOL  3  0 4  0"  r  O  ©  o  3  o  s Re  3, D  _L  4  6  8  FIGURE 16:  10  2  _i_  4  C A L I B R A T I O N RESULTS - G . S . ,  6 BETA  8 - O.U,  2  10 1.0,  1.5  4  6  AND 2.0 I N C H T E S T L I N E S  8  10  1 r  i—i—i  r  .85 SIZE  ORIFICE .84 .83  GS-  10"  0-6  G S  15"  0  2 0 "  G S-  SYMBOL  BETA  O  6  0-6  .82 .81 .80  o  .79  0  o  .78  .77  .76  .75  o G  L  Re J  4  6  8  10  2  D  _L  L  4  6  FIGURE 17: CALIBRATION RESULTS - G.S., BETA  8 0.6,  10  2  J  4  I  I  6  1.0, 1.5 AND 2.0 INCH TEST LINES  I  8  10 •pro  1 .72  I  IV I  3  ORIFICE .71  SYMBOL  STANDARD SHARP  . 7 0 \-  €  S P E C I A L 15  3  SPECIAL3C .69  G S  O  4  GALLOWAY  e  ASME  .68 .67  SIZE  1-5"  BETA  0 4  .66 .65 .641 .63 .62U  Re J 6  8  FIGURE 18:  10  2  4  I 6  L 8  J  1  0  CALIBRATION RESULTS - STANDARD, SHARP, G.S.,  2  4  GALLOWAY AND A.S.M.E,  I  I  I  8  I  10  and 1,000, a l l data f a l l between the Sharp and Standard c a l i b r a t i o n curves. Between Her> o f 1,000 and 10,000, the same generalization applies with two exceptions.  F i r s t l y , the curves which were separate and d i s t i n c t a t a  Reynolds number o f 1,000, gradually merged by Reynolds number o f 10,000. Secondly, the A.S.M.E. standard c a l i b r a t i o n data curve plotted lower than the Sharp plate c a l i b r a t i o n cui've between Ren of 1,000 and 10,000. This difference appears to increase s l i g h t l y a t lower Reynolds numbers, and might indicate a s l i g h t u n r e l i a b i l i t y of the standard A.S.M.E. discharge c o e f f i c i e n t s over t h i s range. A.S .M.E.  The apparent u n r e l i a b i l i t y o f the standard  data may be connected with the shape o f the o r i f i c e plates used i n  the o r i g i n a l study by Marchetti (15), who b u i l t h i s plates with a 30° bevel rather than a 1*5° bevel as was used i n t h i s study.  Both bevel angles are  acceptable under A.S.M.E. standards (2). Considering the e f f e c t of other small geometry changes observed from the discharge c o e f f i c i e n t data i n the o low Reynolds number region, i t seems possible that the 15  difference i n  the angle of downstream bevel could cause the discharge c o e f f i c i e n t s given i n reference (1)  f o r corner taps to be lower than those found i n both this  study and Galloway's work. A.S.M.E. design c r i t e r i a allow a range of o r i f i c e plate thickness o f l/l6 - l/& inch and an o r i f i c e throat length, depending on the reference used, of e i t h e r ( i ) t i between 0.01D and 0.02D (2) or ( i i )  (1)  less than  f o r inside pipe diameter up to 3 inches.  Similar  design c r i t e r i a are available f o r pipe sizes greater than 3 inches.  It is  the implication o f the design codes that v a r i a t i o n of geometry within the l i m i t s s p e c i f i e d should have no discernible e f f e c t on the discharge coefficient.  Results presented here have shown this implication to be  untenable,  i n g e n e r a l , f o r p i p e Reynolds numbers l e s s than 10,000.  T h r a s h e r (16)  and C a l l o w a y  (11;)  geometry on c a l i b r a t i o n c u r v e s .  have shown the e f f e c t o f o r i f i c e  Both suggested t h a t more s p e c i f i c  orifice  p l a t e c r i t e r i a were needed. The  G.S.  s e r i e s was  designed  F l u i d Meters ( l ) d e s i g n s t a n d a r d s geometric s i m i l a r i t y .  The aim was  to s t a y w i t h i n the A.S.M.A. w i t h i n the o v e r - r i d i n g c r i t e r i o n to a r r i v e a t d e s i g n c r i t e r i a  p l a t e s w h i c h c o u l d be used w i t h c o n f i d e n c e as Rep  o f 100.  designed for  The  Beta w i l l be The  for orifice  and w i t h o u t c a l i b r a t i o n as  low  r e s u l t s i n d i c a t e 'that t h i s i s p o s s i b l e f o r p l a t e s  s i m i l a r t o the 0.3.  p l a t e s designed  of  s e r i e s w i t h the use o f c o r n e r t a p s .  u s i n g the same g e o m e t r i c a l shape as the G.S.  That i s , series,  the o n l y p a r a m e t e r .  preceding  r e s u l t s i n d i c a t e a s t r o n g e f f e c t of o r i f i c e geometry,  p r i m a r i l y o r i f i c e t h r o a t l e n g t h , on the c o e f f i c i e n t of d i s c h a r g e Reynolds numbers f r o m 100  t o 10,000.  O r i f i c e . ' t h r e a t l e n g t h can a l s o be  d i s c u s s e d w i t h re Terence t o o t h e r workers i n the f i e l d . Johansen's ( 9 )  Sharp type and  Iversen  (6) p l o t t e d  Tuve .and S p r e n k l e s (£) S t a n d a r d type 1  p l a t e r e s u l t s , along w i t h o t h e r s , f o r comparative purposes. s c r u t i n y o f the c u r v e s  f o r pipe  orifice  Careful  i n d i c a t e s t h a t Johansen's p l a t e s have s l i g h t l y  d i s c h a r g e c o e f f i c i e n t s f o r the same Reynolds number and  3eta.  lower  Thrasher  (16)  too observed a t r e n d of i n c r e a s e d d i s c h a r g e c o e f f i c i e n t w i t h t h r o a t l e n g t h , as was  observed a l s o i n the p r e s e n t s t u d y .  c a r r i e d out by Grace and Lapple  A more;extreme comparison  ( 1 7 ) , whose c a l i b r a t i o n s o f Sharp and  S t a n d a r d (t]_ = d) p l a t e s f u r t h e r c o n f i r m e d  was' Thick  that, d i s c h a r g e c o e f f i c i e n t i n -  creased w i t h t h r o a t l e n g t h . F u r t h e r l i g h t i s thrown on the p r e s e n t r e s u l t s by c o n s i d e r i n g the "Standard Short.Tube" d i s c u s s e d i n P e r r y f u l l , the d i s c h a r g e c o e f f i c i e n t i s about 0.82.  For a S h o r t Tube r u n n i n g However, when a s h o r t tube  1*6 i s running f r e e , the value of the c o e f f i c i e n t i s about 0.62.  The  liquid  i n a tube "running f r e e " separates at the upstream sharp edge and does not touch the w a l l s o  A tube running f u l l , on the other hand, has l i t t l e or no  separation upstream, and the whole v e s s e l i s f i l l e d with f l u i d .  Since there  i s less contraction with a " f u l l " tube, the c o e f f i c i e n t of discharge i s larger.  Comparison of the data from the Sharp and Standard s e r i e s shows a  s i m i l a r increase of discharge c o e f f i c i e n t .  The Sharp plates tend, t o a c t  l i k e standard short tubes•"running f r e e " , whereas the Standard and Special plates a c t l i k e tubes "running  full".  An explanation f o r this behaviour arises from speculation as to the exact point a t which flow separation takes place. aration can only occur a t the knife edge.  For a sharp p l a t e , sep-  However, f o r the Standard and  Special p l a t e s , separation i s possible at both the upstream and downstream ends of the o r i f i c e t h r o a t .  I t seems plausible that a t low Reynolds numbers,  separation would occur a t the downstream edge, while higher Reynolds numbers would s h i f t the point of separation t o the upstream edge due to the increased fluid inertia.  Hence, a t the downstream pressure  tap f o r a Sharp p l a t e ,  contraction w i l l be equal to or greater than that allowed by a Standard or Special p l a t e .  Therefore discharge c o e f f i c i e n t s f o r Sharp plates should  be l e s s than (low Ren), or a t the most equal to (high Ren) those obtained for o r i f i c e plates with f i n i t e throat length. to this p a t t e r n .  The a c t u a l results conformed  U7 NOMENCLATURE  A  • constant i n resistance thermometer equation, ( ° C . ) - 1  Ao  - o r i f i c e cross-sectional area, f t . 2  Al  » upstream pipe inside cross-sectional area  A2  « downstream pipe inside cross-sectional area  Ap  • pipe inside cross-sectional area, i n  B  - constant i n resistance thermometer equation, (°C.)~2  Beta  • r a t i o , d/D dimensionless  C  •» c o e f f i c i e n t of discharge, v e l o c i t y of approach term not included,  2 0  JJ_*J£L  dimensionless  C  c  • c o e f f i c i e n t of contraction,  dimensionless  C  v  • c o e f f i c i e n t o f v e l o c i t y , dimensionless  C  v  - c o e f f i c i e n t of v e l o c i t y including  the e f f e c t of  , and cX  dimensionless d  • o r i f i c e diameter, i n .  D  - pipe inside diameter, i n .  g g  • l o c a l acceleration due to g r a v i t y , f t . / s e c . ^ c  - g r a v i t a t i o n a l constant, (lbM) ( f t . y ( l b j ' )  (sec.)2  H  • pressure drop across the o r i f i c e , cm. of l i q u i d  I.D.  - inside diameter, i n . or f t .  K  • discharge c o e f f i c i e n t , v e l o c i t y of approach factor  Iwf  - internal f r i c t i o n a l dissipation (lb.p-ft.)/lb  Li  » length o f unobstructed pipe upstream of the o r i f i c e , i n .  L2  • length of unobstructed pipe downstream of the o r i f i c e , i n .  Pj.  « pressure sensed by upstream pressure tap, l b . p / f t .  P2  • pressure sensed by downstream.pressure tap, l b . p / f t .  included  2  U8 P l - ?2 • p r e s s u r e drop a c r o s s o r i f i c e  P'  lb.p-ft. l b .  M  PEG  • s o l u t i o n o f p o l y e t h y l e n e g l y c o l (E9000) and w a t e r  Re  » Reynolds number f o r f l o w t h r o u g h c i r c u l a r  passage  - U',.'/n'^(diameter), d i m e n s i o n l e s s REd o r Re  = Reynolds number based on o r i f i c e d i a m e t e r and f l u i d  d  c o n d i t i o n s a t the o r i f i c e RED o r Re  • Reynolds numbers based on pipe I.D. and f l u i d  n  c o n d i t i o n s a t the o r i f i c e Ro  = r e s i s t a n c e o f the p l a t i n u m r e s i s t a n c e thermometer •  Rt  OOC.,  a  ohms  " r e s i s t a n c e of t h e platinum r e s i s t a n c e  thermometer  a t t o C . , ohms ti  - t i m e , see's.  t]_  • o r i f i c e throat length, i n .  t  » o r i f i c e plate thickness, i n .  2  t^  • w i d t h o f p r e s s u r e measuring s l i t , i n .  T  - t e m p e r a t u r e , °F. o r °C.  T sl  ™ temperature o f thermocouple 1  ^cs2  " temperature o f thermocouple 2 - r e f e r r e d t o t h e  C  resistance Tcs3  " temperature o f thermocouple 3 - r e f e r r e d t o the resistance  T k c s  c s  £  thermometer  - temperature o f thermocouple I4 - r e f e r r e d t o the resistance  T  thermometer  thermometer  - temperature o f thermocouple 5 - r e f e r r e d t o the resistance  thermometer  t  U9  Tmsl  • temperature of thermometer 1 - referred to the resistance thermometer  ^ms2  * temperature of. thermometer 2 - referred to the resistance thermometer  Tms3  a  temperature of thermometer 3 - referred to the resistance thermometer  T^i  = temperature read by thermometer 1  1^2  ° temperature read by thermometer 2  T3  • temperature read by thermometer 3  U^  o bulk average upstream velocity, ft./sec,  u*2  » bulk average downstream velocity, ft./sec.  U  - bulk average velocity at the orifice, ft./sec.  m  0  W  = mass flow rate, l b . /sec.  W  - weight of working f l u i d , l b .  X  = actual upstream length of unobstructed pipe i n test  a  section, i n . X  • length of unobstructed pipe i n test section,  t  i n . predicted by equation 1 Ul  =• absolute viscosity, (lbH)/(ft.) (sec.)  U  - absolute viscosity of fluid at the o r i f i c e .  Q  50  Greek Symbols  f> tl  or V  0  = d e n s i t y , lbw/ft.3 = kinematic  v i s c o s i t y o f f l u i d a t o r i f i c e , C.S.  FC o r ^ .  = d e n s i t y o f manometer f l u i d , gin./cm.3  PBO o r  = d e n s i t y o f t e s t f l u i d i n manometer l e g s , gm./cm.3  PO o r p /3  o  = density oftest fluid a t o r i f i c e , • r a t i o , d/D  dimensionless  gm./cm.3  51 LITERATURE CITED  1.  A.S.M.E. "Fluid Meters" - Their Theory and Application" Report of the A.S.M.E. Research Committee on Fluid Meters, 5th ed., New York, 1959•  2. '  Supplement to A.S.M.E. Power Test Codes, Part 5, Chapter U, • "Flow Measurement", New York, 1959.  3.  Prandtl, L. and 0. G. Tietjens,  Applied Hydro and Aero Mechanics,  Dover Publications Inc., New York, 1957. U.  Perry, J„ H  D  edo, Chemical Engineers' Handbook, McGraw-flill Book  Company, I n c , New York, 1950© 5«-  Tuve, G.L. and R. E. Sprenkle, "Orifice Discharge Coefficients for Viscous Liquids",  6.  Iversen, H. W.,  Instruments, 6, 201 (1933)°  Orifice Coefficients for Reynolds Numbers from k to  50,000. Trans. A.S.M.E., 18, 359 (1956). 7.  Sprenkle, R.E. and N. S. Courtright, "Straighteneing Vanes for Flow Measurements", Mech. Eng., 80, 71 (1958).  8.  McCabe, W.L. and J . C. Smith, Unit Operations in Chemical Engineering, McGraw-Hill Company, Inc., New York, 1956, p 103.  9.  Johansen, F.C., "Flow through Pipe Orifices at Low Reynolds Numbers", Reports and Memoranda No. 1252 of the Aeronautical Research Committee, London, England, June 1929.  10.  "Ambrosius, E.E. and L.K. Spink, "Coefficients of Discharge of SharpEdged Concentric Orifices i n Commercial 2-In., 3-In. and U-In. Pipes for Low Reynolds Numbers", Trans A.S.M.E., 69, 805 (19U7).  11.  L i n d e n , f l . R. and 0. F. Othmer, " A i r Flow Through S m a l l O r i f i c e s i n t h e V i s c o u s Region",-Trans  12.  A.3.M.E., 71, 765  (19h9)•  Kowalke, 0.. L., "Manner o f L i q u i d Flow Through a P i p e - L i n e O r i f i c e " , 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 , 30, F e b r u a r y , 217.(1938).  13.  R o t h f u s , R. R., and R. S. P r e n g l e , • " L a m i n a r - t u r b u l e n t i n smooth p i p e s " , I n d . Eng. Chem., hh  U'.  Transition  1683 (1952).  f  G a l l o w a y , L. R., and W. E p s t e i n , Ph.D. T h e s i s , U n i v e r s i t y o f B r i t i s h C o l u m b i a , December, 1963.  IS.  M a r d h e t t i , M., " I b o c c a g l i E I Diaframmi N o r m a l i z z a t l I.S.A.", L ' E n e r g i a E l e t t r i c a , 13, 7^9, A p r i l ,  16.  (1935).  T h r a s h e r , L. V., 3nd R. C. H i n d e r , "Small O r i f i c e M e t e r s " , I n s t r u m e n t s and A u t o m a t i o n , 27, November 1R10 (195M.  17.  G r a c e , H. P., and C. i\  Lapple, "Discharge C o e f f i c i e n t s o f Small  Diameter O r i f i c e s and Flow N o z z l e s " , T r a n s . A.C.M.E. 73, 639 (1951).  18.  Handbook o f C h e m i s t r y and P h y s i c s , F o r t y - S e c o n d E d i t i o n ,  Chemical  Rubber Company, 1960-1?6l.  19.  P r . r r a t t , L. G., P r o b a b i l i t y and E x p e r i m e n t a l E r r o r s ir. S c i e n c e . John W i l e y and Sons (1961), C h a p t e r 3«  20.  Ratkowsky, D. A., " E s t i m a t i o n o f Random E r r o r i n a D e r i v e d Q u a n t i t y " , The J o u r n a l o f C h e m i c a l E n g i n e e r i n g E d u c a t i o n , 3, 3, Decamber, (1965).  I-l  APPENDIX 1 - RESULTS  A Sample C a l c u l a t i o n  S i n c e a n e l e c t r o n i c computer was u s e d f o r a l l c o m p u t a t i o n s , a sample c a l c u l a t i o n w i l l be p r e s e n t e d t o i n d i c a t e t h e method used* Tables 1-11  RUN  i n c l u s i v e c o n t a i n the r e s u l t s in t a b u l a r f o r m .  321  •  Wa  -  230  ti  «  636.U s e c .  />o  -  1.03576  gm./c.c.  pho  -  1.03551  gm./c.c.  lb.  1.58687U  Pc  gm./c.c.  H  13.96  cm.  Vo  22.11  cm / s e c .  W  W /ti s  d  0.60267 i n .  D  1.5058 i n .  C o e f f i c i e n t o f D i s c h a r g e - r e f e r to e q u a t i o n s K  >  -  I83.3U6 x W  I83.3U6 x 230/636ok  21 and 22.  (26)  1-2  C  ll  -  -  K  -  0.70118  v  f 0.60267 )  I 1.5o58 /  h  (27)  Reynolds number - refer to equations 24 and- 2-5  Rep  -  22,737 W D  -  (28)  Vo/f  -  22,737 x 230/636.U 1.5058 x 22.11 x 1.03576  -  238.2953  ;  ;  !  Re  d  -  -  22,737 x 230/636.U .$60267 x 22.11 x lo03576  /  595.3925  1  (29)  P  [ I  TABLE  ,  j  RESULTS ;  RUN NO.  K.  j  ! | i f \  I  4  TYPE 6 2 0  2  143 505 506 506 506 5 0 7 '  REd  1.0  INCH  "  6  0.7 2 0 8 7 0.72116 0.72645 0.72472 0.71284 0.67352 0.71440 0.70952 0.71245 0.70525 0.70330 "  RED  "  STANDARD  °« ^ ______ 0.61248 0.61958 """6.61162 0.61971 0.61174 0.6214 6 0^134 7 0.62171 0.61372 0.62131 0.61332 0.62372 0.61570__ "0.62371 "0.61569' 0.62670 0.61865 0.6 2 8 2 1 0 ._62 0 1 4 0.6300 7 0.62197 0.63374 0.62560 0.63906 0.63085 0.67911 6 . 6 7 0 38" 0.70911 0.70000 0^0995 0.70082 0771067 6.70154 0.70357 0.69453 0.71381 0.70463 0.71717"" " " 0770795 0.71985 0.71060  13 8 139 140 141 1  „  C '  j _105 f~ 106" \ 107 | 10 8 \ 109 | 110 j 111 4 112 113 114 115 116 117 118 i 131 ] 132 | 133 i 134 | 135 j"~~136 | 137  |  L"  ;  ,  ORIFICE  ! f [' |  -._  '  [ f  1-1  0 .71161 6.71189 0.71711 0.71540' 0.70 3 6 7 0.66486 0.70 5 2 1 _ 6770040 0.70329 0.69618 0.69426""'"  17870.59 16409.~13 ' 14850.35 13 74Q.3 4 12921.98 11862.65 ___10812.85 """9914.63 8857.76 78 3 5.8 5__ 6823.5 5 5906.14 5448.68 5108". 94 532.89 513.61 514.20 479.84 442.44 401.55" 378.13  7144.39 6560.13" 5936.95 5h 93«_18_ 5166.01 4742.51 4322.81 3963.72" 3541.20 3 1 3 2 .j65_ 2121.95 .2361.19 _2JLT8• 30_ 2042748 213.04 205_^3J_ 205.57 191.83 , 176.88 166753" 151.17  JL9jL_  3  9  3  273.98 211.55 179.71 117774 60.49 523 .31 5 2 3 7 31 544.41 544.41 735.46""  11 JL JL 109.53 . 84.58 71.85 41,OT 24.18 4  !  20  3  ?_^ L 2  209.21 217.65 217.65 294763"  \  T A B L E 1-1  »  I  (CONTINUED)  l-U  I  1 r  i  1 1 f  i i  REd  RED  RUN NO.  •K  C  507 508 508 509 509 510 510 511 511 512 513  0.69969 0.68854 0.69546 0.67706 0.68214 0.66744 0.67159 0.66373 0.66802 0.66119 0.65742 \0.65289  0.69070 0.67969 0.68652 0.66836 0.67337 0.65886 0.66296 0.65520 0.65943 0.65269 0.64897 0.64450  735.46 1069.75 1069.75 • 1457.30 1457.30 1868.09 1868.09 2153.88 2153.88 2484.79 2807.02 3152.25  294.03 427.67 427.67 582.60 582.60 746.83 746.83 861.09 861.09 993.38 , 1122.20 1260.22  0.64859  0*64026  3465.72  1385.54  514 515  t  i  TABLE  |  i  !  |  I  |  j  ! |.  i  1-5  RESULTS  i  1 I  1-2  RUN NO,  O R I F I C E TYPE 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 151 152 153  154  155 156 157 "158" 159 160 161 162 522  REd  C  K 1.5 I N C H  0.62085 0.62124 0.62191 0.62223 0.62355 0.62494 0.62657 ,0.62642 0.62667 0.62723 0.62958 0.59021 0.62826 0.63190 0.63191, 0.63644 0.64260 0.66205 0.70805' 0.70990 0.71284 0.71529 0.71857 0.72178 0.72444 "0.72845 0.72879 0.73028 0.72926 0.71748 0.71756 0.71433  RED  STANDARD  0.61208 0.61246 0.61312 0.61343 0.61474 0.61611 0.61771 0.61757 • 0.61782 0.61837 0.62068 0.58187 0.61938 0.62297 0.62298 0.62745 0.63352 0.65270 0.69804 0.69986 0.70277 , 0.70518 0.70841 0.71157 ' 0.71420 0.71815 0.71849 0.71996 0.71896 0.70734 0.70742 0.70423  24475.65 22863.66 21252.59 19866.99 17531.19 15535.87 13671.72 12264.85 11142.61 9940.64 9015.34 9261.79 9051.35 7876.09 7313.32 6303.64 5121.76 3481.27 789.43 739.79 681.21 639.78 577.55 503.33 439.36 380.53 334.35 272.55 194.23 126.15 638.24 638.24  10018.14 9358.34 8698.91 8131.77 7175.70 6359.00 5595.98 5020.13 4560.79 4068.81 3690.07 3790.95 3704.82 3223.77 2993.42 2580.15 2096.39 1424.92 • 323.12 302.80 278.83 261.87 236.40 206.02 179.84 155.76 136.85 111.56' 79.50 51.64 261.24 261.24  i  i j ! 1 | j ;  j  | j l  i  TABLE  1-3  1-6 •  RESULTS j  RUN NO. ORIFICE 123 124 125 126 127 128 129 130 144 145 146 147 148 149 150 151 152 153 154 155 5 1 6 *" 517 517 518 518 519 519 520 119 120 121 122  K  C  STANDARD TYPE 2.0 INCH 0.62077 0.61274 0.61406 0.62211 0 .61554 0.62360 0.66456 0.65596 0.62403 0.61596 0.61871 0.62681 , 0.62889. . 0.62076 0.63736 0.62912 0.68444 0.69340 0.69689 0.68788 0.70142' 0.69234 0.70513 0.69601 0.70869 0.69953 0.43668 0.43103 0.71484 0.70560 0.72101 . 0.71168 0.72113 0.71180 0.72377 0.71441 . 0.84451 0.83358 0.58198 0.57445 0.68967 0.68075 0.68422 0.67537 0.67877 0.66999 0.66727 0.67601 . 0.6718 8 0.66319 0.66271 0.65414 0.66957 0.66091 0.65710 0.64860 • . • 0.61720 0.60922 0.61908 0.61107 0.61622. 0.60825 0.62045 0.61243  REd  19133.92 16532.48 14313.22 13165.24 11113.59 9821.69 8523.60 6195.34 972.91 880.63 788.40 709.75 642.69 355.81 497.95 431.30 399.75 339.98 240.16 98.24 791.16 1274.16 1274.16 1655.82 1655.82 2266.27 2266.27 • 2753.32 29017.75 27418.22 25298.8 1 23024.33  RED  7660.89 6619.32 5730.77 5271.13 4449.69 3932.43 . 3412.70 2480.51  i ;  •;  3 82 9. .5 59 4 35  !j  315.66 2 7 28 54 7. .1 32 142.46  i ij  1 92 9. .6 38 7 17  !j  160.05 19 36 6. .1 12 6  i j i  39.33 316.77 510.15 510.15 662.96 662.96 907.38 907.38 1102.38 11618.21 , 10977.78 10129.21  1  i |  9218.54  I  !  TABLE  1-3  (CONTINUED)  i-7  ; i  !  j j  REd  RED  0.7009*6  7 1 4 . 1 6  292.31  i  0 . 7 0 4 8 0  0 . 6 9 4 8 4  7 1 4 . 1 6  292.31  !  0 . 7 0 0 7 2  0 . 6 9 0 8 2  9 8 0 . 0 0  401.12  524  0 . 6 9 6 4 5  0 . 6 8 6 6 1  9 8 0 . 0 0  401.12  525  0 . 6 9 5 5 6  0.68573  1434.92  587.33  525  0 . 6 8 3 6 0  0 . 6 7 3 9 3  1434.92  587.33  526  0 . 6 7 5 6 1  0 . 6 6 6 0 6  1795.61  7 3 4 . 9 6  526  0 . 6 7 6 8 0  0 . 6 6 7 2 4  1795.61  734.96  527  0 . 6 6 8 7 9  0 . 6 5 9 3 4  2172.42  8 8 9 . 2 0  528  0 . 6 6 4 0 3  0 . 6 5 4 6 4  2 5 4 7 . 2 3  1042.61  528  0 . 6 6 8 1 2  0 . 6 5 8 6 7  2 5 4 7 . 2 3  1042.61  1  529  , 0 . 6 5 9 7 1  0 . 6 5 0 3 8  2 9 2 3 . 3 0  1196.54  :  529  0 . 6 6 6 0 6  0 . 6 5 6 6 4  2 9 2 3 . 3 0  1196.54  530  0 . 6 5 6 3 7  0 . 6 4 7 0 9  3 2 1 0 . 5 9  1314.13  1  530  0 . 6 6 0 1 6  0 . 6 5 0 8 3  3 2 1 0 . 5 9  1314.13  !  K  C  523  0 . 7 1 1 0 1  523 524  RUN NOo  i  :  TABLE RUN NO. "520' 521  1-3  (CONTINUED) REd  . 0.66072 0.67054  "275*3732"" 1653.41  0.65217 0.66187  TABLE  1-8 RED 1102.38 662.00  1-4  RESULTS RE  RUN NO. ORIFICE,TYPE 16 17 18 19 20 21 22 23 24 _ „ 26 65 66 67 68 69 2 5  76"  71 72 163 164 165 "166"  1.0  0.63052 0.62033 0.61947 0.62015 "6'. 62 076" 0.62017 _0_.62487_ 6 o62811 0.62851 0.62968 0.62678" 0.62853 0.59776 0.62607 0.62937 0.63387 ~ 0 . 6 3 6 9 9~ 0.64364 0.63788 0 .67497 0.67445 _0.67618_ 0". 6 7 8 3 6  INCH  RED  SHARP  0.62227 .61222 .61137 .61204 o 61264" .61206 • 616_70_ .61990 .62029 .62144 V61859" .62031 .58994 .61788 .62114 .62558 .62866" .63522 .62954 .66614 .66563 .66734 .66949"  16936.86 16731.18 15413.04 1_5770.70 "1474 2."5 5" 15155.87 13768.09 12351.68 11454.73 _10382.54_ 9228.73 7270.82 6748.87 5906.86 5171.94 4938.78 "43 Ol". 39" 2855.88 1856.59 500.15 459.91 _427.JL5_ 383.33  6799.91 6717.33 6188.11 _6331.71_ 5918.92 6084.86 5527.69 4959.02 4598.91 _4168.44 3705." 2'6~ 2919.13 2709.57 2371.52 2076.46 1982.85 "1726.95" 1146.59 745.39 200.80 184.65 171.50 153.90  TABLE  !  i J j  ! !  j !  i  \  1 |  167 168 169 170 • 172 173 174 537 537 538 "• 5 3 8 539 539 540 541 541 542 542 543 543 544 545 546 547 548  0.68306 0.68867 0.68878 0.69662 0.69987 0.71566 0.72070 0.67865 0.67695 0.66971 0.66738 0.66258 0.65949 0.65637 0.66200 0.65343 0.65950 0.65130 0.65605 0.64896 0.65121 0.65039 0.64659 0.64680 0.64608 0.64486  ,  0.67413 0.67966 0.67978 0.68 7 5 1 0.69071 0.70630 0.71128 0.66978 0.66809 0.66095 0.65865 0.65392 0.65086 0.64779 0.65335 0.64488 0.65088 0.64278 0.64747 0.64047 0.64270, 0.64189 0.63813 0.63834 0.63763 0.63643  1-4 ( C O N T I N U E D ) 333.47 272.10 242.89 214.93 169.75 140.42 75.23 361.86 361.86 585.96 585.96 830.73 830.73 1076.46 1076.46 1370.13 1370.13 1627.06 1627.06 1897.44 1897.44 - 2122.90 2442.51 2729.45 3079.60 3442.51  1-9 133.88 109.24  j !  97.52 86.29 68.15 56.38 30.20 145.28 145.28 . 235.26 235.26 333.53 333.53 432.18 432.18 550.09 550.09 6 5 3.24 • 653.24 761.79 761.79 852.31 980.63 1095.83 1236.41 1382.12  j ;  • ! i  I  ;  j J | j 1  TABLE  1-5  1-10  RESULTS RUN NO.  i i V  t  j  i r  [  \  I  !  j  ?  ORIFICE 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 184 185 . 186 187 188 ,189 190 191 192 193 194  C  K. TYPE  1.5 I N C H  0*63002 0.62241 0.62483 0o62433 . 0.61715 0.62355 0.62453 0c62525 0.62565 0.62253 0o62469 0.62614 0.62823 0.62836 0.62868 0.62902 0.62729 0.63171 0.63666 0.64608 0.64784 0.66881 0.67528 0.67038 0.67006 0.67526 0.67828 0.68264. 0.68582 0.69029 0.68938 0.69881  REd  RED  SHARP  0.62129 0.61378 0.61617 0.61568 0.60860 0.61491 0.61588 0.61658 0.61698 0.61390 0.61603 0.61746 0.61952 0.61965 0.61996 0.62030 0.61859 0.62295 0.62783 0.63712 0.63886 0.65954 0.66592 0.66108 0.66078 0.66590 0.66887 0.67318 0.67631 0.68072 0.67982 0.68912  24070.00 23310.43 21960.13 20820.31 19019.91 17491.17 15474.76 14042.96 12673.94 12591.53 12376.08 11670.46 11264.74 10416.85 9449.70 8962.40 8179.23 7222.65 6050.00 4369.63 2643.86 764.94 600.73 695.90 669.51 550.69 478.38 423.80 383.44 335.31 298.51 239.84  9804.79 9495.39 8945.35 8481.05 7747.66 7124.94 6303.56 5720.33 5162.66 5129.09 5041.33 4753.90 4588.63 4243.25 3849.29 3650.79 3331.77 2942.11 2464.44 1779.95 1076.96 311.59 244.70 283.47 272.72 224.32 194.86 172.63 156.19 136.59 121.60 97.70  ! ; i  ! j j I j j 1 | ! ! | | i  I  I  I j I 1 { \ \ | | i | j | f__ j 1 |  TABLE RUN NO.  K  195 557 557 558 558 "559" 559 560 560 561 561 ""'562 562 5 63 563 564 564 565 565  0.70666 0 c6 72 3 9 0.66723 0.66947 0.66400 0.66549' " 0.66131 , 0.6 5 6 00 0.65834 . 0.65369 0.65777 0.65198 0.65191 0.6 5 1 5 7 0.65485 0.64981 0.65482 •0~o'65 2 0 3 0.65537  C  REd  0o69687 p ._66_3 0 7 0.65798 0.66019 • 0.65480 ""6.65626 0.65215 0.64691 0.64922 0.64462 0.64866 0.64294 " 0.64288 0_.64 2_54 0.64577 0.64080 • 0.64574 'o'.64299~ 0.64629  .  TABLE  140.40 §J32JL? 7 632.27 937.81 937.81 1192.34 1192.34 1602.23 1602.23 1832.61 1832.61 2~108~.74 2108.74 2417.08 2417.08 2823.35 2823.3 5 ~3d8'l.99 3081.99  57.19 257.55 257.55 382.01 382.01 48 5.69 485.69 65 2.66 652.66 746.50 ...J ' 8~5 8"798 858.98 984.58 984.58 1150.08 1150.08 1255.43 1255.43 4 6  !  ' OR I F I C E""T Y P E " "2". 0 ~ I N C H 73 74" 75 76 77"  0 .6165 7 0.61710 0.61695 0.61605 0.61884 :  ~  S HA RP  0 .6084 7 6.60899 0.60885 0.60796 "0.61071 '  t i ! \ i ! i  j  ,'  i  '  •  ;  RESULTS NO.  ;  5 0  1-6  ;  ;  •  i  RED  |  j I ^  \  i_n  1-5' ( C O N T I N U E D )  !  "  i  !  3 0 9 4 4.8 3 28390.81 26945.65 24677.14 \ """2243274'8'  0  11411.53" 10830.65 9918.84 9Q16Y6T  1  TABLE  1-6  (CONTINUED)  1-12  i  :  (  1  j1 r  [  c •  K  RUN NOo  REd  RED  .  •  78  0 . 6 1 6 0 3  0 . 6 0 7 9 3  19827.95  7969.73  79  0 . 6 2 0 3 5  0 . 6 1 2 2 0  17034.42  6 8 4 6 . 8 9  80  0 . 6 1 9 9 7  0 . 6 1 1 8 2  14540.36  5844.42  81  0 . 6 2 0 6 4  0 . 6 1 2 4 9  13400.24  82  0 . 6 2 1 8 2  0 . 6 1 3 6 5  11714.69  83  0 . 6 2 2 3 9  0.61421  10460.65  84  0 . 6 2 0 7 4  .  •  0.61258  5386.15 '  4708.66  8 3 2 3 . 8 3  3345.72  85  0 . 6 2 8 1 0  0 . 6 1 9 8 5  6 2 2 5 . 0 3  2502.12  86  0 . 6 3 5 7 6  0 . 6 2 7 4 1  4 9 9 5 . 2 1  2007.80  172  0 . 6 5 7 1 4  0 . 6 4 8 5 1  1065.29  4 2 8 . 1 9  0 . 6 5 9 0 1  0 . 6 5 0 3 6  1002.63  4 0 3 . 0 0  0 . 6 5 1 0 4  8 7 3 . 0 0  350.90  0 . 6 5 2 2 9  8 3 0 . 8 5  333.95  7 1 6 . 1 7  287.86  173  .  •  4 2 0 4 . 6 0  | 1  175  0 . 6 6 0 9 7 0 . 6 6 4 2 3  |  176 177  0 . 6 6 6 2 1  0 . 6 5 7 4 6  6 0 7 . 1 0  244.02  178  0 . 6 7 2 6 8  0 . 6 6 3 8 4  511.62  2 0 5 . 6 4  179  0 . 6 7 5 9 7  0 . 6 6 7 0 9  4 4 5 . 6 0  179.11  180  0 . 6 7 8 1 0  0 . 6 6 9 1 9  4 1 2 . 7 5  165.90  181  0 . 6 8 4 6 2  0.67563  342.11  137.51  *  182  0 . 6 8 1 6 2  0 . 6 7 2 6 6  2 4 2 . 0 8  9 7 . 3 0  j  183  0 . 6 8 3 3 3  0 . 6 7 4 5 5  163.67  65.78  549  0 . 6 6 6 0 2  0 . 6 5 7 2 7  6 8 4 . 4 0  275.09  550  0 . 6 5 8 9 6  0 . 6 5 0 3 1  9 9 5 . 7 1  400.22  550  0 . 6 5 5 0 1  0 . 6 4 6 4 1  995.71  400.22  j  549  0 . 6 5 7 8 7  0 . 6 4 9 2 2  6 8 4 . 4 0  275.09  j  551  0.65608  0 . 6 4 7 4 6  1290.80  518.83  !  551  0 . 6 5 2 6 1  0 . 6 4 4 0 4  1290.80  518.83  I  552  0 . 6 5 1 8 3  0 . 6 4 3 2 7  1565.40  629.20  I  552  0 . 6 4 9 9 1  0 . 6 4 1 3 7  1565.40  6 2 9 . 2 0  553  0 . 6 4 6 5 4  0 . 6 3 8 0 5  1978.86  7 9 5 . 3 9  0.64788  0 . 6 3 9 3 7  1775.05  7 1 3 . 4 7  555  0 . 6 4 6 1 0  0 . 6 3 7 6 1  2 2 7 4 . 5 9  914.26  556  0 . 6 4 5 9 0  0 . 6 3 7 4 1  2 5 0 6 . 8 1  1007.60  174  j j  \  I ii  |  1  1 •  .  554  ,  0 . 6 5 9 7 1 •  0 . 6 5 5 5 1  •  ' j  | 1  T A B L E 1-7  1-13  RESULTS RUN NO. ORIFICE  ~ K-  TYPE  "~  G.S.  ""  C™  "  "  "REd  RED  BETA=0.2  __2 26 0.72378 0 . 7 2 3 22 227 ' 0.71729 " 0.71674~ 228 0.71652 0.71597 229 0.71 5 1 7 0.71462 230 0.7T341 6.71286 231 0.70676 0.70621 _232_ 0.70076 0.70021 "233 0.72605 6772548™ 384 0.70136 0.70082 385 °jJH* °_2 0.71347 386 6.71574 0.71518 396 0.71665 0.71609 __397 0.70344 0.70289 398 6".69750" " 0.69695 399 0.68900 0.68847 400 0.674 80 0_._6_7428 401 0.66534 0.66482 402 • 0.65586 0.65535 403 • 0.65258 0.65207 404 0.65411 0.65361 405 0.65212 0.65162 40 6 0_. 6 4 9 1 5 0o6 4 8 6 5 407 0.64643 , 0.64593 408 0.64213 0.64163 _409 0 . 6 2 6 9 5J 0.62646 410 ~ 0 . 6 2 5 8 1 "* 0.62532 ,411 0.62413 0.62365 211 0. 71 33 4 0. 7 1 2 7 7 212 0.71426 0.Y1369 213 0.71598 0.71541 _214 0.J1624 0.71566 215 6.71753 " 0771695  _309.06 283.91 258.32 2_3J7o_82 213.93 183.98 150.29 "118.73 693.29 486.18 292.46 360.60 585.89 ~(>Si"o52 797.41 891.30 987.07 1101.00 1206.72 "l374.~07 1536.46 1695.16 1823.78 1989.61 2131.20 2266.35 2387.62 ^AtP* 403.25 383.91 372.54 35"i'.'0 2  •  "  .61.36 56.37~ 51.29 47.22 42.48 36.53 29.84 23757" 137.65 96.53 58.07 71.60 116.32 \3b*S0 158.32 176.96 195.98 218.60 239.59 272.Y1  305.05 336.56 362.10 395.03 42 3_.14 449.97" 474.05 85.11 80.66 76.79 71» 10 721 5 1  j f  TABLE  1-7 ( C O N T I N U E D )  f  t jI 8 1 1  J1  j ij if a *  1 1  1i ' I I • i ;  1 ?  1  .  RUN _N0. 216 217 218 219 220 221 222 223 224 393 394 421 422 423 424 425 425 426 427 . 428 429 430 431 432 433 434 435 436 387 388 389 390 391 392 196 197  K 0,71610 0,71818 0,71689 0,71584 0,71518 0.71364 0,71163 0,70905 0,70094 0,70819 0,70347 . 0,70492 0,69094. 0,67601 0,66781 0,64692 0,66264 0,65579 0,64510 0,64974 0,63482 0,67960 0,64365 0.63809 0.63542 0.63210 0 . 6 2 9 0 1 .. 0.62625 0.65988 0.66237 0.67054 0.67596 0.68354 0.70003 0.70083 0.70286  C 0.71553 0.71761 ' 0.71632 0.71527 0.71460 0.71307 0,71106 0.70848 0.70038 0.70762 0.70291 0.70435 0.69039 0 .67547 0.66728 0.64640 0.66211 0.65527 0.64459 0.64922 0.63432 0.67905 0.64314 0.63758 0.63492 0.63159 0.62850 0.62575 0.65935 0.66184 0.67000 0.67542 0.68299 0.69947 0.70027 0.70230  V  REd 3 2 9 . 19 292.81 260.16 234.17 209.19 180.70 163.51 144.85 118.79 468.92 611.44 505.24 732.56 933.14 1051,17 1148.15 1176,06 1307,30 1619,99 1482.91 1688.08 1795.25 1952.48 2174.37 2318.45 2585.45 2852.28 3096.45 1206.69 1092.23 972.18 870.95 752.04 501.44 546.14 524.01  ;  1-iU RED 65.84 58.57 52.04 46.84 41.84 36.14 32.70 28.97 23.76 93.79 122.30 101.05 146.52 186,64 210.25 229.65 235.23 261.48 324,02 296.60 337.64 359.07 390.52 434.90 463.72 517.12 570.49 619.33 241.23 218.35 194.35 174.12 150.34 100.24 109.18 104.76  i  : ;  :  i  ; ; • j ! j ! j !  : I j I  [  TABLE RUN  l 1  !  1 1  \  1  K  N0 . 198 199 200 201 202 • 203 204 205 206 207 208 209 210 412 413 414 415 415 416 417 418 419 420  ' C  ^ •  1-7  0.70349 0o70638 0o70756 0.70992 0,71197 0.79539 0.71346 0.71429 0.71312 0.71345 0.70992 0,70086 • 0.68997 0.69015 0.67471 0.66292 0.64331 0.65418 0.64715 0.64289 0.63812 0.63596 0.63311 •  REd  ; 0.70293 0.70582 0,.70700 0.70936 0.71140 0.79475 0.71289 0.71372 0.71255 0.71288 0.70935 0.70030 0.68941 0.68960 0.67417 0.66239 0.64280 0.65366 0.64664 0.64237 0.63761 • 0.63545 0.63261  1-15  (CONTINUED) RED  , 494.63 463.33 432.71 402.69 357.42 321.99 249.39 320.88 228.20 201.40 172.45 • 137.86 89.55 689.82 928.13 1129.73 1319.19 1341.48 1512.90 1667.22 1847.13 2009.08 2137.98  98.88 92.63 86.51 80.50 71.45 64.37 49.86 64.15 45.62 40.26 34.48 27.56 17.90 137.90 185.55 225.85 263.72 268.18 ' 302.45 333.30 369.27 401.64 427.41  T A B L E 1.-8  1-16  RESULTS REd  RUN NO* URTF'IC'E T Y P E 278 "279" 280 _28_1_ 282 283 284 "28 5 " 286 _2_8J_ 288 289 _290 3 3 5~ 336 _3 3_7_ 3 38 339 340 "341" 342 _343_ 4 52 453 454 455" 456 _4_5_7_ 458 459 460 461  6.S.  Oo 7 1 3 9 4 _ "bo 7 1 6 7 0 Oo 7 1 8 0 4 Oo 7_189 7_ 0 . 72078 Oo 7 2 2 7 8 Oo _ "oV 7 2 1 3 5 Oo 7 1 8 5 3 Oo 7p_O_O_0_ Oo 7 1 9 6 6 Oo 6 9 4 3 4 Oo 6 7 8 5 8 "Oo 6 9 9 4 2 " Oo 7 0 1 5 8 Oo 7 0 4 2 6 ,70696 ,71006 ,71358 77175 6™ ,71967 ,71416 Oo 9 7 8 4 6 Oo 6 8 7 6 8 Oo 6 8 2 9 9 "oV 6 9 1 8 0 " 67630 Oo 672_9 3_ Oo 66472 "Oo 66068 Oo 66202 0. 7 4 7 5 8" 7  2  2  8  6  RED  BEfA=0.4 0o70487 0 . 70 7 5 9 " Oo 7 0 8 9 2 _0Wj0983_ 0.71162 0.71360 0.71367 " 0 * 71 2 1 8 " 0o70940 0.69111 0.71051 0o68551 0.66996 V. 6 9 0 5 3" 0.69266 0o69532 0.69798 0o70104 0o70452 "0o70844" 0.71053 0.70509 0.96603 0.67894 jO. 67432 6.68 3 0 1 " 0.66771 0.66438 0.65627 0.65229 0.65361_ "0 • 7 3 8 0 9  510.80 " 4 6 7 o 6 5" 432.32 396.62 349o56 291*59 252o51 ""213.38" 184.17 1 3 6 . 19 127o28 104.90 62.83_ "832.21 796.34 715.90 654.73 577.21 5 02.81_ "45"l«29 372.30 297.58 1012.11 940.29 1170.87 93T.¥0~ 1379.75 1520.09 1905.70 2176.82 2472.26 ""32 0 3 . 33*  203.62 "l8*6~.42" 172.33 158.10 139.34 116.23  19°  966  8'5. 06" 73.41 54.29 50.74 41.82 _25.05 33T.74* 317.44 285.37 260.99 230»09 200o43 "l79o89" 148.41 118o62 403.45 374.82 466.J4 "371.20" 550.00 605.94 759.65 867.73 985.50 1.2 76.79 2"  TABLE  RUN NO.  !  I  j j  i  | '  ] \ j  I  '  462 463 496 496 497 4 9 7  498 498 499 500 500 500 501 502 503 504 303 304 305  306 307 308 309 310 311 312 313 314 315 316 318 319 320 321 322 ""323""  K 0o67843 0.65051 0.71040 0.70358 0.68889 0.68653 0.67508 0.68312 0.66927 0.67195 0.66187 0.66669 0.66345 0.66399 0.65530 0.64984 0.70322 0.70541 0.70705 0.71078 0.71468 0.71844 0.71905 0.72188 0.72431 0.72376 • 0.72274 0.71514 0.69006 ""6.6937 5 0.69789 0.70185 0.70616 0.71232 0.71728 """"" "'677198 3  1-8  C 0.66981 0.64225 0.70137 0.69464 0.68014 0.67780 0.66650 0.67444 0.66077 0.66341 0.65346 0.65821 0.65502 . 0.65556 0.64698 0.64158 0.69414 0.69630 0.69792 0.70160 0.70545 0.70917. 0.70976 0.71255 0.71496 0.71441 0.71340 . 0.70590 • 0.68115 0.68479 0.68888 0.69279 0 .69704 0.70 312 0.70802 0.71054 ;  (CONTINUED)  RE d 3236.59 3506.91 528.95 528.95 1049.96 1049.96 1458.86 1458.86 1669.02 1669.02 2146.14 2146.14 2166.24 2394.86 2666.39 2920.06 751.92 707.81 650.71 591.52 516.56 448.64 399.01 327.04 279.46 247.57 193.77 127.54 1105.42 996.31 903.03 799.28 .657.94 595.39 523.43 414.89  i  •  \  1-17  RED  ;  t  1290.18 / 1397.93 210.85 210.85 418.54 418.54 581.53 581.53 : 665.31 665.31 855.50 85 5.50 863.51 954.64 1062.88 : 1164.00 300.94 283.29 260.44 236.74 206.74 179.56 159.70 130.89 111.85 99.09 77.55 51.05 '442.42 398.75 361.42 319.90 26 3.33 238.30 209.49 166.05  i I | j ' ""I ! J | ! •i i  i  i  F  TABLE  t; i  \ |,  J  '1 '1  •>  I.  J i i i  f  1 .t  ?  \  i f i  1 " i  i  J  i  |  s f  1 1 1 I tI f.  i  it  >] ,t  i r  RUN NO. 324 325 326 327 320 321 322 323 324 325 347 347 348 348 349 349 350 350 351 352 353 354 355 356 357 358 437 438 439 440 441 442 443 444 445 479  •  K  C  0.72441 0.72046 0 .68844 0.69279 0.70405 0.71036 0.71520 0.71756 0.72577 0.74440 0.69440 0*72841 0o72257 0.70866 0.71570 0.70581 0.71000 0.70207 0.70473 0.70039 0.69559 0.69598 0.69342 0.69132 0.68956 0.68979 0.96660 0.95361 0.94671 0.94056 0.93743 0.93401 0.93618 0.93526 0.78782 0.71429  0.71506 0.71116 0.67955 0.68384 0.69496 0.70119 0.70597 0.70830 0.71640 0.73479 0.68544 0.71900 0.71324 0.69951 0.70646 0.69670 0 .70083 0.69301 0.69563 0.69135 0.68660 0.68700 0.68446 0.68239 0.68065 0.68088 0.95412 0.94130 0.93449' 0.92842 0.92533 0.92195 0.92409 0.92319 0.77765 0.70506  1-8  1-18  (CONTINUED) REd 322.06 166.29 1105.94 1027.76 657.94 595.39 523.33 414.89 322.06 166.29 159.59 159.59 350.28 350.28 486.70 486.70 599.37 599.37 704.03 819.12 885.49 939.17 986.39 1027.40 1080.36 1103.49 1005.13 1450.37 1713.92 2081.17 2362.95 2750.67 2579.03 2983.54 2855.22 614.11  .  '  ;  RED 128.90 66.55 442.63 411.34 263.33 238,30 209.45 166.05 128.90 66.55 63.87 6 3.87 140.19 140.19 194.79 194.79 239.89 239.89 281.77 327.84 354.40 375.89 394.78 411.20 43 2 . 3 9 441.65 402.29  58 80 6 5 .. 49 97 832.95 945.73 1100.91 1032.21 1194.11 1142.75 245.79  t L  i  1  ! |  j ; :  ; j j  1  TABLE  !'  :  1-8  — RUN NO,  ij t  ! i  ). ;  i  479 480 480 481 481 482 483 483 484 484 485 485 486 486 487 487 291 292 293 294 295 296 297 298 299 300 301 302 327 —• 7 " 328 328 329 329 330 3 30 3 2  K 0,70530 0,69571 0,69203 0,68680 0.68497 0,67682 0.66847 0.68104 0.66487 0.67191 0.65941 . 0,66124 0.65726 0.66105 0.65303 0.65863 0.59829 0.69770 0.69970 0.70559 0.70882 0.71417 0.71546 0.71919 0.72195 0.72368 0.72529 0.74560 0.72650 0 . 7 2 3 7 1 " "" 0.71957 0.70878 0.72150 0.71077 0.71460 0.70471 "  C 0.69619 0.68673 0.68310 0.67793 0.67613 0.66808 0.65984 0.67224 0.65628 • 0.66324 0.65090 0.65270 0.64877 0.65252 0.64460 0.65012 0.59057 0.68869 0.69067 0.69649 0.69967 0.70495 0.70623 0.70991 0.71264 0.71435 0.71593 0.73597 ' 0.71713 0.71437 0.71028' 0.69963 0.71219 0.70160 0.70538 0.69561  (CONTINUED) REd  614.11 956.14 956.14 1240.47 1240.47 1451.76 1756.44 1756.44 1990.83 1990.83 2365.10 2365.10 2686.18 2686.18 2910.15 2910.15 839.70 921.38 828.93 704.39 630.47 562.34 508.82 450.16 372.12 301.33 239.30 175.33 196.67 196.65 479.67 479.67 358.69 358.69 597.20 597.19  1-19 RED 245.79 382.68 382.68 496.48 496.48 581.04 702.98 702.98 796.80 796.80 946.59 946.59 1075.10 1075.10 1164.74 1164.74 336.02 368.70 331.71 281.87 252.29 225.03 203.61 180.14 148.91 120.58 95.76 70.16 78.70 78.69 191.95 191.95 143.53 143.53 238.98 238.98  ; '  '  !  i \ \ !  ! ' : i !1 ;  TABLE  RUN NO.  1  '  331 331 3 32 332 334 334 344 344 345 :• 345 346 346 447 446 448 449 450 451 488 288 289 289 490 490 491 491 492 492 493 493 494 494 495 495  K  0.70964 0.69957 0.70423 0.69557 . 0.69469 0.6849 5 0.93140 0.91743 0.92150 0.91676 0.78451 0.74688 0.92768 0.94977 0.91965 0.91449 0.91221 0.90931 0.69753 0.68742 0.70406 0.69305 0.69617 0.68973 0.67719 0.67406 0.67203 0.66835 0.66577 0.67375 0.66011 0.65789 0.65833 0.66216  1-8  (CONTINUED)  c 0..7004*8 0 .69054 0..69514 0..68659 0,.68573 0..67611 0..91938 0..90559 0..90960 0..90493 Oi,77438 Oi.73725 0«.91571 0..93751 0..90778 Oi.90269 0..90044 Oi.89758 Oi.68853 0«.67855 Oi.69497 Oi.68411 Oi.68719 0..68083 0..66845 0..66536 Oi.66335 Oi 65973 Oi.65718 0..66506 0<.65159 Oi.64940 0<,64984 Oi.65362  REd  1  715..13 715..13 796..33 796..33 1010..86 1010..86 447..50 447..50 622i.56 622..56 797.,10 797..10 1688,.34 1171,.90 2033i.71 2223i.48 2589i• 40 2854..70 658..75 658..75 679..02 679..02 940i.16 940..16 145li.99 1451.• 99 1666..83 1666,.83 1987.,65 1987.,65 2287i,08 2287.,08 ' 2571.,94 2571.• 94  1-20 RED  I 286 .17 286 .17 318 .67 318 .67 404 .51 404 .51 179 .07 179 .07 249 .13 249 .13 318 .97 318 .97 . 675 .62 468 .95 813 .82 889 . 76 1036 .19 1142 .35 263 .61 263..61 271 .72 271,.72 376 .22 376,.22 581,.04 581,.04 667,• 01 667,• 01 795,• 39 795,.39 915 .21 915,•2.1 1029,.21 1029,.21  ! I  1 i  ! j'  ; i  ! ; ! ! j j  ;  1  i  ! ; ]  TABLE  1-21  1-9  RESULTS K  RUN NO. ORIFICE ; !  i 1  I  i  I I  } !  235 236 ' 237 238 239 240 241 242 . 243 *4 245 246 247 248 377 378 379 380 381 382 383 602 603 604 605 606 607 608 2t  6  0  9  610 611 612  TYPE .  C G.S.  0.81264 0.81750 0.81570 0.80851 0.80517 0.81387 0.81614 0.81693 0.81565 0.81858 0.81029 0.79140 0.81497 0.81682 0.78104 0.79917 0.81588 0.80980 0.81278 0.80722 0.80534 0.80778 0.81167 0.79400 0.78087 0.77322 0.76785 0.75881 0.75469 0.78178 0.77041 0.81098  v  BETA»0.6 0.75835 0.76288 . 0.76121 0.75450 0.75138 0*75950 ' 0.76162 0.76235 0.76116 0.76390 .0.75615 0.73853 0.76052 0.76225 0.72886 0.74578 0.76138 0.75570 • 0.75848 0.75329 . 0.75154 0.75382 0.75 7 4 4 : 0.74095 ' 0.72870' 0.72156 0.71655' 0.70812 0.70427 0.72956 0.71894 6.75680 '  REd  «  7 9 5 i,45 755«,84 6 9 4 ,,65 6 0 7 .,07 5 2 0 .,84 479«,70 4 1 0 ,,63 3 6 6 ,• 2 5 3 2 2 ,.12 2 6 1 ,.44 2 1 0 ,.72 1 4 9 ,• 4 2 4 5 8 ,.49 5 2 5 ,.28 2 3 7 ,.94 4 1 1 .00 5 1 4 ,.03 . 6 4 4 .18 7 2 9 .78 8 3 1 .59 9 0 1 .75 5 2 0 .49 1 0 5 6 .82 1 4 6 9 .88 1 8 6 8 .42 2213" ."97 2 4 2 6 .79 2 8 5 9 .21 3 0 0 2 .15 . 1 8 4 5 .77 2 2 4 4 .26 7 1 6 ."8"4  RED  *  476.85 453.11 416.43 363.93 312.23 287.57 246.16 219.56 193.10 156.73 • 126.32 89.57 274.86 314.89 142.64 246.39 308.15 386.17 437.49 498.52 540.58 312.02 633.54 881.16 1120.07 1327.22 1454.81 1714.03 1799.72 1106.50 1345.38 429.73  | j j  TABLE  j'  !  1-9  (CONTINUED) . REd  C  RUN NO.  K  613 614 657 658 658 659 659 660 660 661 661 662 662 663 663 664 664 665 665 666 666 667 667 668 668 669 669 670 670 263 264 265 266 267 268 269  0.79774 0.79919 0.69832 0.81305 . 0.81290 0.80424 0.80471 . 0.80240 0.79679 0.81740 0.81746 \ 0.81418 0.81568 0.81440 0.81108 . 0.80903 0.81057 0.80812 0.80861 0.80489 0.80211 0.80281 0.79304 0.79399 0.79507 0.82579 0.79538 0.81881 0.80777 0.81015 0.81203 0.81352 0.81395 • 0.81916 • 0.81927 0.82261  • 122 RED  •  •  •  v  0.74444 0.74580 . 0.65166 0.75873 0.75860 0.75051 0.75095 0.74879 0.74356 ; 0.76279 0.76284 0.75978, 0.76118 0.75999 0.75690 0.75498 0.75642 0.75413 0.75459 0.75112 0.74853 0.74918 0.74006 0.74094 0.74196 0.77062 0.74224 /. . 0.76411 ' 0.75381 0.75642 0.75817 0.75956 0.75996 0.76483 0*76494 < 0.76805 s  1  1  1301.48 1258.76 . 146.74 324.50 324.50 223.12 223.12 193.51 193.51 406.57 406.57 474.50 474.50 581.14 581.14 760.04 760.04 757.15 757.15 888.02 888.02 958.51 958.51 . 1014.38 1014.38 144.39 144.39 189.57 189.57 978.47 920.45 867.69 793.79 728.58 654.57 616.93  I  780 .21 754 .60 87 .96 194 .53 194 .53 • 133.75 133 .75 116,,00 . 116,• 00 243 .73 i 243 .73 284 .45 . 284 .45 348 .38 1 348 .38 455 .62 455 .62 453,.90 453 .90 532 .35 532 .35 574 .61 574 .61 608 .10 j 608 .10 i 86 .56 ! 86 .56 113 .64 '! 113 .64 585 .54 550 .82 519 .25 475 .03 436 .00 . 391,.71 369 .19 1  1-9 ( C O N T I N U E D )  TABLE |  !  |  | I  REd  C  K  RUN  1-23 RED  NO.  270 271 272 273 . 274 275 276 371 372 373 374 375 376 636 637 638 639 " 640 641 642 643 644 699 699 700 • 700 701 701 702 702 703 703 704 704 70 5 705"""  x  0.82550 0.82652 0.82740 0.82761 0.82714 0.81616 0.82551 0.79936 0.80518 0.81789 • 0.81749 0.81461 0.81283 0.81439 0.81289 0.80562 0.79980 0.79344 0.78679 0.78450 0.77755 0.80074 0.80980• ' 0.79290 0.83938 0.80521 0.82864 0.82058 0.82260 0.82682 0.82324 0.82115 0.82066 0.82046 0.81585 0.81349 x  0.77075 0.77170 0.77253 0.77272 0.77229 0.76203 . 0.77076 0.74634 0.75178 , 0.76365 0.76327 0.76058 0.75892 0.76038 0.75898 0.75219 0.74676 0.74082 0.73461 0.73247 0.72598 0.74763 0.75609 0.74031 . 0.78371 0.75181 , 0.77369 0.76616 0.76805 0.77198 , 0.76864 0.76669 0.76623 ' 0.76605 0.76174 . 0.75954 ;  \ !  570.24 516.78 465.57 399.35 363.06 310.06 262.79 264.77 393.26 530.04 694.17 789.12 925.12 694.21 939.81 1244.45 1458.13 1686.63 1852.85 2067.98 2234.86 1371.66 • 150.45 150.45 183.52 183.52 261.26 261.26 401.63 401.63 528.94 528.94 591.59 591.59 703.20 703.20  341.25 309.25 278.61 238.98 217.27 185.55 157.26 158.44 235.34 317.19 415.41 472.23 553.62 415.44 562.41 744.71 872.58 1009.32 1108.80 1237.54  ! • ! j : ; i ! j j j j ! 1 .1  1337.40 820.84 90.03 90.03 109.82 109.82  i j j  156.34 156.34 240.35 240.35 316.53 316.53 354.03 354.03 420.81 420.81  j !  L j  I  TABLE  1-9  (CONTINUED)  1-21*  {.  i .  1 •  :  i  i i [  RUN NO. 706 706 249 250 251 252 253 254 255 256 257 258 259 260 261 262 359 - 359 360 360 361 361 363 363 . 366 366 367 367 368 368 369 370 578 578 579 579  K 0.81705 0.81184 0.81829 0.82045 . 0.87115 0.82062 0.82247 0.82451 0.81370 0.82340 0.83027 \ 0.82495 0.81084 0.81422 0.81861 0.7790 2 0.81410 0.82799 0.82451 0.82356 0.81963 0.81920 0.8185 7 0.81944 0.81729 0.81145 0.82509 0.81386 0.81797 0.81251 0.81305 0.79211 1.07401 1.15465 1.06722 1,14944  ,  \ '  •  v  C  REd  0.76286 0.75799 0.76340 0.76541 0.81271 0.76558 0.76730 0.76920 0.75911 0.76817 0.77458 0.76961 ' 0.75645 0.75960 0.76370 0.72676 0.75949 0.77245 0.76920 0.76832 0.76465 0.76425 0.76366 0.76447 0.76247 0.75702 0.76974 0.75927 / 0.76310 , 0.75800 0.75851 0.73897 1.00196 1.07720 0o99563 1.07234  8 1 5 .48 8 1 5 .48 7 9 0 .78 7 8 3 .64 7 2 0 .81 6 7 8 .25 6 5 9 .32 6 3 2 .24 5 8 4 .31 5 7 2 .58 5 1 8 ,.79 4 7 0 .81 4 0 3 .64 3 0 0 .12 2 2 4 .19 94 .36 2 9 2 .24 2 9 2 .24 3 9 5 .50 3 9 5 .50 5 4 1 .28 5 4 1 .28 8 3 8 .32 838 .32 8 1 2 .77 8 1 2 .77 9 4 6 .60 9 4 6 ,.60 5 7 0 .41 5 7 0 .41 4 6 2 .13 \ 2 9 8 .06 6 9 6 .75 . 6 9 6 .75 9 1 4 ,.66 9 1 4 ..66  .  RED  488.01 488.01 474.53 470.24 432.53 407.00 395.64 379.39 350.63 343.59 311.31 282.52 242.21 180.09 134.53 56.62 175.37 175.37 237.33 237.33 324.81 324.81 503.05 503.05 487.72 487.72 568.03 568.03 342.29 342.29 277.31 178.86 418.10 418.10 548.86 548.86  .  T A B L E 1-9 RUN NO.  i  580 580 581 581 582 582 583 583 584 584 585 ' 585 586 586 587 587 588 588 589 589 590 590 591 591 592 592 615 616 617 , 618 619 620 621 671 671 672  K  c  1.05007 1.11011 1.03642 1.09301 1.02306 1.07882. 1.02144 1.02144 '1.07783 1.15260 . 1.07791 \ 1.13981 1.05738 1.11272 1.04966 1.09720 1.05283 1.08743 1.03728 1.09437 1.02967 1.08750 1.04821 1.11026 1.06753 1.12516 0.80546 > 0.81472 0.79906 0.79811 0.78803 0.79216 0.85034 , 0.86647 0.80937 ; 0.83760  0 .97963 1.. 0 3 5 6 4 0 .96690 1 .01969 0 .95443 1 .00645 0 .95292 0 .95292 1 .00635 1 .07615 1 .00642 1 .06421 0 .98725 1.. 0 3 8 9 2 0 .98004 1 .02443 0 .98300 1 .01531, 0 .96849 1 .02179 0 ,96138 1 .01537 0 .97869 1 .03663 0 .99673 1.. 0 5 0 5 4 , 0.. 7 5 1 4 3 0 , 7 6 0 0 7 /• 0,. 7 4 5 4 5 ' 0., 7 4 4 5 7 0,. 7 3 5 1 7 0., 7 3 9 0 3 . 0.. 7 9 3 3 0 0., 8 0 8 3 5 0.,75508 Oi• 7 8 1 4 2  N  (CONTINUED) REd 1256.91 1256.91 1535.11 1535.11 1787.14 1787.14 1886.25 1886.25 665.98 665.98 1082.36 1082.36 1438.28 1438.28 1699.67 1699.67 1949.02 , 1949.02 2119.11 2119.11 2300.42 2300.42 1618.57 1618.57 1058.55 1058.55 778.62 1083.77 1327.06 1573.45 1777.80 410.71  .  V  537.89 230.83 230.83 335.48  RED 754.23 754.23 921.18 921.18 1072.41 1072.41 1131.88 1131.88 398.54 398.54 647.71 647.71 860.70 860.70 1017.12 '1017.12 1166.34 1166.34 1268.13 1268.13 1376.63 1376.63 968.59 968.59 633.47 633.47 467.22 650.34 796.33 944.18 1066.81 246.45 322.77 138.51 138.51 201.31  •  •  TABLE  RUN NO. 580 580 581 581 582 582 583 583 584 584 585 585 586 586 587 587 588 588 589 589 590 590 591 591 592 592 615 616 617 618 619 620 621 671 671 672  (CONTINUED)  •  ,  1-26  REd  C  K  1.05007 1. 11011 1.03642 1.09301 .1.02306 1.07882 1.02144 1.02144 1.07783 1.15260 1.07791 \, 1 . 1 3 9 8 1 1.05738 1.11272 1.04966 1.09720 1.05283 1.08743 1.03728 1.09437 1.02967 1.08750 1.04821 1.11026 1.06753 1.12516 0.80546 0.81472 0.79906 0.79811 0.78803 0.79216 0.85034 0.86647 0.80937 0.83760  1-9  0.97963 1.03564 0.96690 1.01969 0.95443 1.00645 0.95292 0.95292 1.00635 1.07615 '1.00642 1.06421 0.98725 1.03892 V 0.98004 1.02443 0.98300 1.01531 0.96849 1.02179 • 0.96138 1.01537 0.97869 1.03663 0.99673 1.05054 0.75143 • 0.76007 ' 0.74545 0.74457 0.73517 0.73903 0.79330 0.80835 0.75508 0.78142  :  1  -  1256. 91 1256. 91 1 5 3 5 . 11 1 5 3 5 . 11 1 7 8 7 . 14 1 7 8 7 , 14 1 8 8 6 . 25 1 8 8 6 . 25 6 6 5 . 98 6 6 5 . 98 1 0 8 2 . 36 1 0 8 2 ..36 1 4 3 8 . 28 1 4 3 8 , 28 1 6 9 9 . 67 1699. 67 1949, 02 1 9 4 9 ,.02 2 1 1 9 . 11 2 1 1 9 , 11 2 3 0 0 , 42 2 3 0 0 ,.42 1 6 1 8 . 57 1 6 1 8 ..57 1 0 5 8 ..55 1 0 5 8 . 55 7 7 8 , 62 1 0 8 3 . 77 1327, 06 1 5 7 3 . 45 1 7 7 7 . 80 410. 71 5 3 7 . 89 2 3 0 . 83 2 3 0 . 83 3 3 5 . 48  I  RED  .  7 5 4 .,23 7 5 4 ,,23 9 2 1 ,,18 9 2 1 ,,18 1072 .41 1 0 7 2 ,. 4 1 1 1 3 1 ,.88 1131 .88 3 9 8 ,. 5 4 3 9 8 ,. 5 4 6 4 7 ,. 7 1 6 4 7 ,. 7 1 8 6 0 ,• 70 8 6 0 ,, 7 0 1 0 1 7 ,, 1 2 1017 .12 1166 .34 1166 .34 1268 .13 1 2 6 8 ,. 1 3 1376 .63 1 3 7 6 ,. 6 3 968 .59 9 6 8 ,. 5 9 6 3 3 ,, 4 7 633 .47 4 6 7 ,, 2 2 6 5 0 ,, 3 4 7 9 6 ,. 3 3 9 4 4 ,.18 1 0 6 6 ,. s i 2 4 6 ,.45 3 2 2 ,,77 1 3 8 ,. 5 1 1 3 8 ., 5 1 2 0 1 ,.31  ,  |  i  i  | -j |  .  j  f !  I  |  TABLE RUN NO.  K  672 673 673 674 674 675 675 676 677 677 678  0.82307 0.83937 0.83293 0.82676 0.82522 0.84605 0.83310 0.82930 0.80634 0.82638 0.82966 -  1-9 ( C O N T I N U E D )  C  0.7678*6 0.78306 0.77706 0.77130' 0.76986 ; 0.78930 0.77721 0.77367 0.75225 . 0.77094 0.77400  1-27  REd  RED  335.48 390.84 390.84 417.46 417.46 501.68 501.68 516.78 585.78 585.78 657.07  201.31 234.53 234.53 250.51 250.51 301.04 301.04 310.11 351.51 351.51 394.29  ! ; i  i  1  TABLE  J'  I  RESULTS K  RUN NO. ORIFICE 622 623 .624 625 626 627 628 629 630 631 632 633 634 635 687 687 688 ' 688 689 689 690 , 691 692 692 693 693 694 694 695 696 696 697  TYPE  c  • . REd  . '  RED  S P E C I A L 15  0,70271 0.67113 0.69327 0.68742 0.68393 0,67216 0.66851 0.66401 0.66104 0.65852 0.65817 0.65713 0.65864 0.68355 0.73112 0.71479 . 0.71569 0.71717 0.70720• 0.70360 0.69210 0.68498 0 . 6 7 5 5 2 v, 0.67822 0.68000 0.68233 0.70733 0.70154' 0.69590 0.70486 0.7002 7 "" 0 . 7 1 0 6 1 x  1-26  1-10  0.69349 0.66233 0.68418 0.67840 0.67496 0.66335 0.65974 0.65530 0.65237' 0.64989 0.64953 0.64852 0.65000 0.67458 0.72153 . 0.70542 0.70630 0.70777 0.69792 0.69437 0.68302 0.67599 0.66666 0.66933.' 0.67108 0.67338 0.69806 0.69234 0.68678 0.69561 0.69109 0.70129  V  6 6 3 ..83 1 5 8 1 .,29 6 5 0 .,27 8 6 0 ..92 1 0 7 7 ,,13 1 3 6 8 ,.60 1 6 5 5 ,.47 1 9 9 0 ,.84 2 2 6 9 ,,90 2 5 8 9 ,,79 2 8 9 9 ,.36 2 9 2 9 ,.81 3 0 3 6 ,.88 1 0 2 5 ,.32 149,.87 1 4 9 ,.87 2 3 2 ,.52 2 3 2 ,.52 4 2 5 ,.12 4 2 5 ,.12 6 4 7 ,.13 8 2 6 ,.78 1 0 1 1 ,.26 1 0 1 1 ,.26 9 9 6 ,.74 9 9 6 ,.74 3 4 2 ,.02 3 4 2 ,.02 5 2 8 ,.88 4 1 7 ,,87 4 1 7 ,.87 3 0 4 ,.37  266.71 635.33 261.27 345.90 432.77 549.88 665.13 799.88 912.00 1040.52 1164.91 1177.14 1220.16 411.95 60.22 60.22 93.42 93.42 170.81 170.81 260.00 332.19 406.30 406.30 400.47 400.47 137.42 137.42 212.49 167.89 167.89 122.29  ! i ! ! 1  | ! !  TABLE  !  RUN NO.  K  C  697  0.71120  0.70187 TABLE  1-10  (CONTINUED) REd  1  1  -  2  9  RED  304.37  122.29  RE  RED  1-11  RESULTS. K  RUN NO. ORIFICE  TYPE  C  '  S P E C I A L 30 •  1 |  1 j  !  I 1  1! \ ! | j  "645 6^6 647 648 ' 649 650 651 652 653 654 655 656 "79 6  6  7  9  680 680 681 681 681. 682 682 683 684  0.70685 0.69628 0.68713 0.67637 . 0.66948 0.66508 0.65996 0.65730 0.65763 • 0.71599 • 0.67818 0.68694 0.71365 0.71054 \ 0.71634 0.71879 0.71548 0.71505 0.71330 0.69890 0.71350 0.69991 0.72389  0.69770 0.68726 0.67823 0.66762 0.66081, 0.65647 0.65141 0.64878 0.64911 0.70672 0.66940 . 0.67804 0.70441 0.70134 i 0.70706 ; 0 . 7 0 9 4 9 .' 0.70622 0.70579 0.70406 • 0.68985 0.70426 ' 0.69084 0.71451  ;  !  679.08 937.97 1201.92 1438.19 1807.33 2149.35 2549.32 2851.29 3198.12 368.64 1375.46 1215.86 129.50 129.50 299.95 299.95 428.84 428.84 428.84 717.55 717.55 688.49 246.73  271.98 375.67 ' 481.39 576.02 723.87 860.86 1021.05 1141.99 1280.90 147.65 550.90 486.97 51.87 51.87 120.14 120.14 171.76 171.76 171.76 287.39 287.39 275.75 98.82  ! ;  ] I i  j l 1  1 1 j \  ..  TABLE RUN NO.  K  C  684  0.72170 0.71954 0.71945 0.62820 0.72351  0.71235 0.71022 0.71013 0.62007 0.71414  685 686 686  1-11  (CONTINUED) REd  246.73 192.75 192.75 114.36 114.36  „,  1-30 RED 98.82 77.20 77.20 45.80 45.80  ! i I  2-1 APPENDIX 2  - DATA  TABLE 2-1  2-2 [  DATA RUN NO.  WS  ORIFICE TYPE 105 106 107 108 109 110 111 112 113 | 114 { 115 116 117 118 131 i 132  I I  3  3  134 135 136 137 138 139 140 141 142 143 505 506 506 506 507  380.00 375.00 265.00 270.00 286.00 300.00 245.00  TI  1216.0 1313.0 1027.9 1127.8 .1267.0 1438.0 1286.4 2"30V00 • 1 3 2 6 . 6 1421.8 220.00 1575.6 215.00 1584.6 188.00 1644.0 169.00 175.00 1912.0 1375.2 117.00 733.2 235.00 240.00 783.5 788.1 240.00 782.1 220.00 991.4 255.00 1114.0 255.00 1108.4 232.00 1314.6 233.00 181.00 • 1165.9 1308.2 175.00 1207.4 137.00 93.00 1251.0 1727.2 66.00 1165.2 190.00 1165.2 190.00 967.8 163.00 967,8 163.00 749.4 170.00  PBO  PO  STANDARD  j PC  1.0 INCH  0.997478 0.997926 0.997882 0.997442 0.997394 0.997860 0.997895 0.997701 0.997915 0.997701 0.997981 0.997655 0.997597 0.997992 0.997926 0". 9 9 7 5 8 5 0.997538 0.997915 0.997886 0.997490 0.997871 0.997454 0.997882 0.997430 0.997369 0.997538 0.997442 0.997246 1.041800 1.042260 1.042220 1.041810 1.041740 1.041980 1.041920 1.041700 1.041620 1.041700 1.041600 1.041410 1.041560 1 .041450 1.041550 1.041420 1.041520 1.041420 1.042950 1.042700 1.042920 ' "1.042500 1.042950 1.042720 1.042920 1.042730 1.030930 1.031130 1.030930 1.031130 1.030920 1.030950 1.030920 1.030950 1.031030 1.030930  H  u  i  !  1 1  i'  1 .5901 1 .5898 1 .5895 1 .5919 1 .5919 1 .5915 1 .5911 1 .5910 1 .5906 1 .5902 1 .5900 1 .5898 1 .5893 1 .5884 1 .5940 1 .5937 1 .5932 1 .5926 1 .5921 1 .5909 1 .5893 1 .5910 1 .5907 1 .5918 1 .5913 1 .5921 1 .5919 1 .5945 0 .0000 1 .5931 0 • 0000 1 .5931  0.974 62.590 0.969 52.450 0.967 42.740 0.970 36.520 0.973 32.440 27.760 0.980 22.970 0.981 0.974 19.040 0.973 15.030 11.640 0.97C 8.750 0.969 6.495 0.969 5.069 0.936 3.884 0.928 51.860 32.090 47.280 31 .820 46.660 31.600 40*660 31.280 33.040 31.020 25.970 30.420 21.620 29.540 15.410 30.420 11.820 30.240 8.640 33.700 6.250 33.650 . 2 . 7 7 0 ,3 3". 6 50 0 . 8 2 0 ,'33.670 13.090 16.800 7.250 16.800 14.070 16.680; 7.830 16.680 26.200 16.630 i  TABLE 2 - 1  i RUN ; NO. 507 508 , 508 509 509 "5 16" 510 511 511 512 513 514 515  WS  TI  170.00 200.00 200.00 230.00 230.00 275.00 275.00 300.00 300.00 285.00 300.00 300.00\ 300.00  749.4 610.2 610.2 519.8 519.8 485.8 485.8 461.9 . 461.9 381.3 356.4 317.8 289.9  PO  (CONTINUED)  PBO  1 .030930 1 .030890 1 .030890 1 .030880 1 .030880 ! ."030880 l .030880 1.030850 1 .030850 1 .030820 1 .030800 1 .030800 1 .030790  I .031030 1 .030990 1 .030990 1 .030950 ' 1 .030950 f . 0 3 0920 1 .030920 1 .030990 1 .030990 1 .031050 1 .031130 1 .031220 1 .031220  PC  0.0000 0.0000 13.5416 0.0000 13.5412 "6 . 0 0 0 0 13.5408 0.0000 13.5409 13.5413 13.5416 13.5419 13.5420  2-3 H  14.430 31.110 2.513 58.630 4.760 98.780 8.040 131.480 10.697 14.460 18.550 23.660 28.800  I i  u  16.630' 16.520 16.520i 16.370! 16.3701 1673 40" 16.340-' 16.260 16.260 16.220; 16.170; 16.150i 16.100' ;  1  TABLE 2 - 2  LRUN  DATA WS  TI  PO  PBO  NO. ORIFICE  TYPE  87 3_60j.00_ 88 385.00 89 390.00 90 _ 3 6 0 . 0 0 "91" 3 9 0 . 0 0 " 92 400.00 93 365.00 94 340.00 95 375.00 96 335.00 97 325.00  STANDARD  1.5  PC  H  U  INCH  5 5 6 . 8 , 0.997952 0.997970 634.5 0.997992 0.997992 690.4 0.998004 0.997701 684.2 0_.9979 70_ 0 . 9 9 7 8 0 2 "8 3174" "6.998067 0.99"784~8 950.6 0.998172 0.997893 978.8 0.998224 0.997882 1019,4 0.998203 0.997893 1231.4 0.998244 0.997860 1230.6_ 0 . 9 9 8 2 6 5 0.997792 131674 "07998 2 65"' "6 • 997800  1.5939 51.630 1.5941 45.400 1.5919 39.390 1_.5927_ _34j_100_ 1 . 5 9 31 26.970 1.5935 21.590 1.5934 _L6^870_ 13.500 1 . 5935 11.250 1 . 5932 1 . 5927 _8_.980_ 1 • 5928" 7 .T30  0.976 .981, .983 .979| "."98 9"; !  .001! .008! .005 .0.10 .012  76'i 2  i 1 I  TABLE 2-2 (CONTINUED)  2-U  I I  ! RUN L  N 0  WS  PO  PBO  PC  H  «  320.00 165.00 315.00 300.00 275,00 340.00 193.00 290.50 330.00 345.00 350.00 350.00 315.25 355.00 275.00 245.00 290.00 195.00 140.00 248.00 248.00 235.00 235.00 310.00 310.00 285.00 285.00 335.00 335.00 320.00 528 310.00 528 310.00 1529 340.00 529 340.00 530 330.00 "530 330.00 ! 98 j 99 fTOO 101 (102 1103 104 151 152 153 154 "155" 156 157 158 159 160 161 162 522 522 523 523 "524~ 524 525 1 525 526 526 "527 L  TI  '  U  Ii !  1283.4 0.,998120 0". ,997770 1 .5925 "679.9 0.,998078 o,,997724 1 .5921 1546.8 0,,997747 o.,997561 1 .5908 1564.2 0.,997882 0.,997608 1 .5912 1659.2 0. 997904 0.,997597 1 .5911 2 524". 8 "6","997882 0<,"997573 1 .5909 2114.0 0«,997882 0,,997514 1 .5904 1.042700 1,,042680 1 .5916 390.5 474.6 1.,042800 1.,042720 1 .5916 540.8 1. 042780 1.,042700 1 .5908 585.2 1. 042820 1.,042700 1 .5905 648.8 i . 042890 i~.,"042826 f .5903 i.042960 l.,042850 1 .5902 674.6 872.6• I..043020 l i ,042900 1 .5903 780.0 I. 043000 l . ,042980 1 .5902 792.8 l . 043050 l . ,043060 1 .5902 1148.6 I. 043160 • l .,043170 1 .5903 , 1082.0 I. 043250 . l ,043240 1 .5902 1191.9 I. 043380 i<,043340 1 .5901 798.4 I. 031890 l . .031950 1 .5951 798.4 I. 031890 l . ,031950 0 .0000 694.2 l , ,031650 i i .031960 1 .5949 694.2 I.,031650 l , .031960 0 .0000 6"71.4 I,.031500 i i .031980 1 .5946 671.4 l . 031500 0 .0000 i i ,031980 430.6 i i 1 .5943 031220 ,031880 I. l . 031220 430.6 l . ,031880 0 .0000 405.5 I. 031210 l . .031850 0 .0000 405.5 I. 031210 i . ,031850 13 .5433 323.5 "1. 031090 l . .031800 0 .0000 268.8 I. 031010 i i .031800 0 .0000 268.8 l . 031010 i i ,031800 13 .5429 259.8 I. 030900 l . .031770 0 .0000 259.8 I. 030900 l . ,031770 13 .5423 227.6 I. 031020 l . 031730 0 .0000 227.6 l . 031020 I- 031730 13 .5420  8 .512 7 .121 4 .968 4..403 3 .242 2., 100 0<.910 54 ,600 47«,450 39 .670 34 .650 27i. 950 20 .790 15 .640 H i , 620 8 .920 5..930 3 .030 1<.330 9.. 130 5 .028 11 .050 6 .135 21 ."180 11.,690 44.,200 24i,940 39.,790 3., 270 58.,210 80..280 6.,540 104,,750 8..475 129.,900 10.,590  0.995! 0.991 0.956 j 0.969 j 0.972 ! 0.972 i 0.969 1 33.340 ' 33.250 ,' 33.130 j 33.070 i 33".040 : 32.840 | 32.750 i 32.770 i 32.690 j 32.760 ! 32.810 • 32.920 | 17.400 I 17.4001 16.950 16.950 1 1~6.850 16.850 16.500 i 16.500 i 16.460 1 16.460 1 16.290 ! 16.200 j 16.200 1 16.020! 16.020 ;16.160 | 16.1601  TABLE  2-3 j j  DATA RUN ; NO, i  ORIFICE  WS  TI  .  PO  PC  H  U  I i i  TYPE  STANDARD  2.0  INCH  330.6 0., 9 9 8 0 3 5 3 3 0 .,00 3 9 1 . 1 3 6 0 .,00 b,'9978T5" 375, 00 445.5 0,, 9 9 7 7 2 4 370, 00 484.0 0, 9 9 7 7 1 8 375, 00 590.6 0, 9 9 7 7 0 1 732.6 4 0 0 ,,00 0, 9 9 7 6 5 5 3 6 0 ,,00 763.2 0,, 9 9 7 6 3 2 3 5 0 , 00. 809.3 0~,9975*95" 4 0 0 ,,00 1 0 9 8 . 6 • 0,9 9 7 5 7 3 3 1 5 . 00 980.0 o. 9 9 7 5 6 1 2 8 5 , 00 1020.6 0, 9 9 7 5 7 3 2 9 8 ,,00 1468.2 0,, 9 9 7 5 7 3 3 3 5 , 00 •1. 0 4 2 3 8 0 292.2 3 3 5 , 40 322.8 1, 0 4 2 4 0 0 375. 00 404,4 1. 0 4 2 3 5 0 389.2 1, 0 4 2 3 5 0 1 147 3 2 5 , 00 4 3 7 , 8 1. 0 4 2 3 0 0 . 3 3 0 , 0 0 { 778.8 149 3 2 5 . 00 1. 0 4 2 3 0 0 2 9 0 , 00 1. 0 4 2 3 5 0 495.0 150 3 0 5 , 00™ 151 5 9 6 . 2 " " T . "042450" 776.4 1. 0 4 2 1 6 0 360. 00 152 3 4 5 . 00 1. 0 4 2 3 0 0 865.5 153 2 4 5 , 00 1. 0 4 2 3 6 0 154 865.2 1, 0 4 2 9 2 0 120. 00 992.5 155 586.8 1. 0 3 0 8 1 0 2 7 0 , 00 516 415.2 " 51 7" 3 0 5 . o b " r . 030800" 3 0 5 . 00 1. 0 3 0 8 0 0 517 415.2 1. 0 3 0 8 1 0 375.0 I 518 3 6 0 . 00 1. 0 3 0 8 1 0 3 6 0 , 00 375.0 277.4 1. 0 3 0 8 4 0 1 519 3 6 5 . 00 3 6 5 . 00 1. 0 3 0 8 4 0 519 277.4 ^ 5 2 0 " 3 5 0 . bo " 2 1 9 T l " . 1.0 3 0 8 1 0 " 119 | 120 121 122 123 124 125 "126" 127 128 129 130 144 145 146  PBO  1.5953 0.998110 1 .5947 6.99'8029 1.5943 0.997992 0.997926 1.5941 1.5937 0.997915 0.997849 1 .5931 1.5927 0.997792 0.997692 1.5921 1.5907 0.997514 1.5907 0.997550 1 .5902 0.997490 1.5902 0.997490 1.5897 1.042620 1.5895 1.041890 1 .5894 1.042100 1.5889 1.042000 1.042000 1.5889 1 .5886 1.041900 1.5889 1.041900 f". 0 4 1 9 2 0 1 . 5 8 8 2 1 .5894 1.041960 1.5887 1.041960 1.5887 1.042000 1.5896 1.042180 1.031220 0.0000 17031300™ 1 . 5 9 2 5 1.031300 0.0000 1.5928 1.031380 1 .031380 0.0000 0.0000 1.031400 1.031400 13.5416 f. 031450" 0.0000  4 4 .,930 38 .020 32,,110 26., 130 18,,020 13.,280 9.,870 7 ,312 5.,890 4,,550 3.,414 - 1.,756 4 9 .• 0 8 0 39,,870 3 1 ,,370 2 5 ., 190 20.,320 16.,410 12.,060 9..05*0" 7.,420 5,,450 2,,020 0<.774 4,,287 2 0 .,400 11. 280 35. 680 19, 660 37. 950 3. 0 6 5 56. 900  0.986 0.962 0.954 0.952 0.951 0.947 0.945 0.942 0.939 0.939 0.939. 0.939 32.340 32.380 32.280 32.290 32.190 32.190 32.290 32 ."550 31 . 8 4 0 32.180 32.360 33.760 16.140, 16.000 16.000 16.090 16.090 16.110' 16. no! 16.100  TABLE ; RUN : NO.  WS  \ 520 \ 521  350.00 210.00  TI 219.1 217.6  PO  !  PC 13.5417 0.0000  U  H 4.640 19.950  16.100 16.200  2-4 • •  WS  RUN NO.  16 17 18  \ 1  1  !  9  20 21 22 23 24 25 26  1  r~65~ [ 66 f  67 68 69 70 71  !  1  f  I < 163 | 164 I 165 166 167 7  i  2  TI  TYPE  SHARP  295.00 280.25 275.00 275.00 255.00 280.00 250.00 230.00 210.00 200.00 160.00 240.00 205.00 260.00 210.00 170.00 130.00 100.00 90.00 265.00 290.00 248.00 258.00 250.00  1019.5 1008.7 1071.5 1049.6 1064.4 113679 1119.9 1145.9 1130.7 1176.2 1052.0 1663.8 1684.3 2264.0 2046.3 1927.1 1717.1 194979 2786.4 858.0 1020.4 938.5 1087.0 1208.0  ORIFICE  i  1.031450 1.031560  TABLE  2-6  (CONTINUED)  PBO  1.030810 1.030910  I J  2-3  PBO  PO 1.0  PC  H  U  INCH  0.997442 0.997369 0.997394 0.997271 0.997146 0.997146 0.997120 0.997146 0.997120 0.997221 0.997992 0 ."99*8244 0.998162 0.998224 0.998405 0.998078 0.997948  07998120 0.997837 1.042680 1.042750 1.042960 1.042920 1.043110  0.997585 0.997970 0.997992 0.997678 0.997418 0.997246 0.997196 0.997171 0.997146 0.997120 0.997171 0.997345 0.998345 0.998424 0.998244 0.998305 0.998224 0.998203 0.998141 1.042390 1.042580 1.042780 1.042860 1.043000  1.5909 1.5941 1.5943 1.5917 1.5897 1.5884 1.5800 1.5765 1.5765 1.5745 1.5780 1.5891 1.5975 1.5982 1.5979 1.5971 1.5964 1.5962 1.5956 1.5874 1.5878 1.5880 1.5882 1.5883  51.048 48.400 41.400 43.223 36.183 38.383 31.507 25.360 21.685 18.170 14.573 12.792 9.945 8 .063 6.371 4.649 3.395 1.526 0.617 52.860 44.810 38.530 30.880 23.150  0.948 0.921 0.924 0.922 0.902 0.902 0.900 0.902 0.900 0.909 0.914 1.100 1.000 1.078 1. 100 0.991 0.976 0.996 0.96 5 32.780 32.800 32.83032.860; 32.930  TABLE 2-4 (CONTINUED)  Z -!{ 1  —  f  RUN : NO. | • [ |  WS  168 210.00 169 180.00 170 180.00 172 132.00 173 230.00 85.00 Pi 7 4 537 89.00 537 89.00 122.00 538 122.00 538 539 179.00 539 179.00 199.00 540 199.00 540 541 244.00 541 244.CO 542 245.00 542 " 2 4 5 . 0 0 543 293.00 293.00 543 544 295.00 545 303.00 546 285.00 "547 280.00 548 275.00 t  • TI 1243.4 1191.6 1356.5 1306.2 2718.2 1877.8 756.4 756.4 649.7 649.7 676.3 676.3 . 583.7 583.7 567.7 567.7 479.4 479.4 494.9 494.9 446.7 398.3 335.0 292.6 , 257.9  PO 1.043250 1.043420 1.043410 1.042700 1.042900 1.042980 1.031400 1.031400 1.031250 1.031250 1.031210 1.031210 1.031180 .1.031180 1.031100 1.031100 1.031120 1.031120 1.031070 1.031070 1.031010 1.031060 1.031050 1.031020 1.030980  PBO  PC  1 .5883 i.043150 1 .5884 1.043280 1.043180 1 .5878 1.042500 1 .5858 1 . 0 4 2 5 9 0 ' 1. 5 8 5 8 1.042590 1 .5852 1.031320 1 .5926 1.031320 0 .0000 1.031270 1 .5939 1.031270 0 .0000 1.031800 1 .5915 1."0 3" 18 00 0 . 0 0 0 0 1.031220 0 .0000 1 . 0 3 1 2 2 0 13 . 5 4 0 0 0 .0000 1.031100 1 . 0 3 1 1 0 0 13 . 5 3 9 5 0 .0000 1.031110 f . 0 3 ' l l T 0 - y -. 5 3 9 1 1.031080 0 .0000 1 . 0 3 1 0 8 0 13 . 5 3 9 0 1 . 0 3 0 9 8 0 13 . 5 3 8 4 1 . 0 3 1 1 0 0 13 . 5 3 9 0 1 . 0 3 1 2 1 0 13 . 5 3 9 8 1.03X280 "13". 5 4 0 1 1 . 0 3 1 3 1 0 13 . 5 4 0 2 3  H 15.170 12.130 9. 160 5.280 3.540 1 .000 7.450 4.075 19.440 10.680 39.660 21.716 36.400 2.950 58.390 4.725 83.080 6.750 112.320 9.195 11.470 15.400 19.240 .24.400 30.420  U 32.930 32.990 32.750 31.600 31.980 .31.9~30~ 17.450 17.450 17.200 17.200 17.100 17.100 17.000 17.000 16.840 16.840 16.860 16 . 8 6 0 16.750 16.750' 16.700 •16.720; 16.730 16.680, 16.630,  TABLE 2 - 5 DATA RUN ; NO.  WS  sORIFICE  TYPE  290.00 315.00 325.00 I 270.00 i 1 Zfl 2 8 0 . 0 0 250.00 | 42 i 4 3 _ 245.00 250.00. | 44 235.00 45 | 46 290.00 265.00 47 285.00 48 49 290.00 225.00 50 51 265.00 235.00 t 52 240.00 1 53 225.00 ' 54 55 200.00 190.00 "56 57 129.00 184 375.00 185 385.00 186 360.00 187 310.00 188 365.00 |. 1 8 9 415.00 395.00 190 191 345.00 ! 192 335.00 193 250.00 f 194 205.00 ! |  f  I 1  37 38 39 40  Ti  SHARP  PBO  PO  1 .5  PC  H  INCH  488.4 0 . 997196 560.7 0 . "997 0 6 9 612.0 o . 997105 538.1 o. 997069 613.6 0 . 997018 595.7 0 . 997018 652.5 0 . 997146 724.0 0 . 997296 747.8 0 . 997369 941 . 8 0 . 997221 890.5 o. 997044 1008.7 O i 997120 1065.8 0. 997095 879.8 o. 997271 1131.7 o. 997369 1062.8 0. 997320 1189.3 0. 997320 1283.9 0. 997146 1346.6 0. 997271 1775.5 0 . "997246 1977.7 0. 997320 539.8 1. 042900 7 0 7 . 0 • 1 .0 4 2 9 0 0 562.4 1. 043040 512.4 1. 042850 735.8 i". 0 4 2 8 2 0 964.6 1. 042780 1038.6 1. 042790 1045.4 1. 042270 1. 042440 1146.0 952.6 1. 042520 969.4 Ii 042540  U  .  i •  0.997146_ 1.5765 0T997345 1 .5891 1.5888 0.997296 1.5888 0.997296 1.5882 0.997246 1.5882 0.997246 0.997394 1.5895 1.5902 0.997490 1.5904 0.997514 0.997538 1 .5906 0.997345 1.5891 0.997271 1 .5886 0.997538 1.5906 0.997724 1.5921 1.5902 0.997490 1.5919 0.997701 0.997538 1.5906 0.997724 1.5921 0.997724 1.5921 1.5874 0.997120 1.5889 0.997320 1.5890 1.043120 1.5888 1.043090 1.5889 1.043090 1.5891 1.043190 1.5891 1.043170 1.5887 1.043080 1.5886 1.043080 1.5877 1.042900 1.5872 1.042760 1 .5901 1.043460 1.5863 1.042780  44..376 39< . 8 5 5 3 5 .,352 31.,615 2 6 .,782 2 2 .,187 1 7 .,670 1 4 ,, 8 9 4  0.917 0.896 0.899 0.896 0.892 0.892 0.902 0.914 0.921 1 2 - ,313 0.909 1 1 ., 9 4 0 0.894 11.,102 0.90C 9 ,, 9 6 8 0.898 9 ,, 1 5 6 0.913 8 ., 0 6 5 0.921 6,,774 0.911 6,,018 0.911 5 ., 0 5 0 • 0.902 3<, 7 4 8 0.912 2. 650 0.91C 1 ,, 3 4 5 0.911 0,, 4 9 6 32.28C 5 4 ., 7 0 0 32.22C 3 2 ,, 9 8 0 32.69C 4 6 ,,220 41., 330 32.12C 32.02C 2 7 ., 360 31.97C 2 0 ,, 4 1 0 31.90C 1 5 ,. 7 5 0 30.61C 1 1 ., 7 7 0 9 ,• 1 2 0 3 1 . 0 0 0 31.26C 7,, 3 4 0 31.35C 4 ,665  i  TABLE  RUN '• NO,  WS  195 557 ! 557 558 1 558 f559" | 559 [_560 I 560 1 561 I 561 562~ 562 ! 563  135,00 165.00 165,00 230.00 230.00 275.00 275.00 305.00 305.00 370.00 370.00 295,00 295.00 300.00 300.00 300.00 300.00 30b'i»00 300.00  i  5  6  3  564 564 565 565  TI  PO  (CONTINUED)  PBO  PC  2-9 : H  U  1088.4 562.8 562.8 530.5 530.5 498.6 498.6 410.5 410.5 438.1 438.1 303.3 303.3 268.8 268.8 230.0 • 230.0 211,3 211.3  1.042570 1.031080 1.031080 1.031060 1.031060 " l . 031086" 1,031080 1.031120 1.031120 1 .031050 1.031050 1.031070 1.031070 1.031090 1.031090 1.031100 1.031100 1.031080 1.031080  I !  1.042450 1.031400 1.031400 1.031420 1.031420  1 , 6" 3~142"6" 1.031420 1,031450 1.031450 1.031480 1.031480 1.031510 1.031510 1.031520 1.031520 1.031590 1.031590 1.031640 1.031640  1.5857 1 .5916 0.0000 1 .5915 0.0000  l".  5915 0.0000 0.0000 13.5401 0.0000 13.5402 0.0000 13.5406 0.0000 13.5408 0.0000 13.5411 0.0000 13.5411  1.570 9. 500 5.240 20.960 11.570 34.330 18.878 34.810 2.850 45.310 3.690 60*380 4.980 79.620 6 . 500 109.350 8. 880 128.630 10.500  WS  ORTF ICE"T Y P E 73 74 75 76 "77"  265.00 350.00 385.00 385.00 390V00 "  TI  SHARP 254.8 361.8 424.4 465.6 '5 0 9 . 7  '  PO  6•997926  1  / / PBO  PC  H  j | U  J i  2.0-INCH 0.997792 0.997915 0.997821 0.997759  31.410 16.670 16.670 16.620, 16.620 16.630 16.630 16.670 16.670 16.570 16.570 16.580 16.580' 16.600 16.600 16.610 16.610 16.560 16.560,  2-6  DATA  ' RUN NO.  |  i  TABLE  ] !  2-5  j i  0.998035 0.997948 0.997815 0.997918 6.997666 "  1.5947 1.5940 1.5928 1.5937 1 .5916  48. 41. 36. 30. 26.  190 650 712 550 000  0.960 0.973 0.9610.957; 0.974  TABLE RUN [NO^  WS  78 ' 3 8 0 o 0 0 j 79 3 8 5 . 0 0 | 80 3 9 0 . 0 0 385.00 81 370.00 \ 82 " 370.00 f"83 | 84 3 6 0 . 0 0 | 85 2 6 0 . 0 0 86 280.00 320.00 172 173 3 2 0 . 0 0 fl'74 3 6 5 . 0 0 175 360.00 390.00 : 176 ] 177 3 5 0 . 0 0 178 345.00 179 320.00 240.00 "180 181 350.00 2 I 182 7 5 . 0 0 t 183 2 5 5 . 0 0 | 549 2 6 0 . 0 0 295.00 [550 295.00 550 549 260.00 551 355.00 355.00 i ! 552 3 5 0 . 0 0 552 350.00 '"553 310.00 •554 300.00 ! 555 350.00 1556 350.00  1  1  5  [  5  1  TI  PO  2-6  (CONTINUED)  PBO  PC  2-10 H  U  ; '  554.4 646.2 763,8 825,2 911,8 10 2 3 . 2 " 1270.6 1229.6 1650.2 267,0 283.4 351,3 376.8 473.4 501.0 589.8 627.9 526.1 908.6 1002.2 1366.2 636.4 496.0 496.0 636.4 462.4 462.4 373.9 373.9 261.8 2 82.6 256.2 232.3  0". 9 9 78 26 0 ,998045 0.993193 0.997826 0,998183 0.997826 0.997735 0.998130 0.998067 0.997804 6."99 8 0 4 5 0 . 9 9 7 6 4 4 0.997904 0.997618 0.997886 0.997618 0.997886 0.997644 1.041780 1.041570 1.041600 1.041840 1.041920 1,041600 1.041570 1.041920 1.041580 1.041950 1.041980 1.041670 1.041900 1.041700 1.041910 1.041700 1.041750 1.041510 1 .041760 1.041670 1.041610 1.041530 1.041930 1.041610 1.031380 1.030910 1.030930 - 1.031320 1.030930 1.031320 1.031380 1.030910 1.030900 1.031300 1.030900 1.031300 1.030970 1.031400 1 .030970 1.031400 1.031000 1.031420 1.030980 1.031420 1.031010 1.031370 1.031040 1.031390  1.5930 1.5930 1 .5930 1.5922 1.5927 1 .5914 1.5911 1 .5911 1.5913 1.5860 1.5862 1.5850 1.5848 1.5847 1.5850 1.5852 1.5851 1.5852 1.5848 1.5842 1.5840 1.5922 1.5918 0.0000< 0.0000 1.5917 0.0000 1 .5917 0.0000 0.0000 0.0000 0.0000 0.0000  2 1 ., 0 1 0 1 5 , • 730 1 1 .• 510 9 .• 6 0 0 7 . • 230 5 .742 3 .546 ' 1 .929 1« . 2 1 2 5 9 .. 150 5 2 . , 190 4 4 • 160 3 7 . • 210 27< • 4 0 0 1 9 ., 5 8 0 1 3 ,, 4 6 0 10 • 120 8 ., 0 6 0 5 ., 6 4 0 2. 890 1. 330 6 ., 5 6 0 1 4 ., 2 1 0 7 , ,'816™ . 3 ., 6 5 6 2 3 . 890 1 3 . 120 3 5 . 995 19. 670 3 1 . 800 2 5 . 450 4 2 . 380 5 1 . 570  0.987 1.003 1.002 0.994 0.989 ; 0.987 0.972 0.970 0.970  ' ' :  ! j j ' ;  30.780 i 30.810' 32.550 31.450 i 31.460 i 31.470; 31.270 | 31.280 j 30.240 30.800 ! 31.010 31.190; 16.500 | 16.510' 1 6 . 510 j 16.500! 16.440! 16.440: 16.530! 16.530 16.540! 16.530; ;  16.600 I 16.610;  TABLE 2-7 DATA RUN NO*  WS  :0 RTF ICE TYPE  rr G.S.  "  PO  PBO  PC  H  BETA=0.2  148*00 1611.6 1.042190 lOOoOO" 1187.6 1.042200 100.00 1294,9 1.042360 101.00 1427,8 1.042300 114,00 1791.4 1.042350 80»00 1472,9 1.042320 72o00 1622.6 1.042400 65.00 "1856V0 1.042440' 797.8 1.028550 72.00 853.8 1 .028600 54.00 1786.0 68.00 1.028650 1 396 87.00 1709.4 1.029760 397 • 87.00 1054.2 1.029730 941.8 r.~0295 50' 398 90.00 807.9 1.029430 399 89.00 893.3 1.029480 400 110.00 1077.2 146.00 1.029350 I | 402 158.00 1045.8 1.029360 870.8 1.029360 [40 3 144.00 ""194V00"~T034Y5"~~T."0293T0 404 205.00 977.6 1.029330 J 405 834.2 1 .029340 406 193.00 ! 407 248.00 997.0 1.029340 802.8 1.029350 408 218.00 409 194.00 667.4 1 .029360 410 " 2 26.00" 730.1 1 .029410 821.8 268.00 1.029420 1 411 897.5 1 .042300 ! 211 168.00 n 212 160.00 902.9 1.042260 .213 186.00 1107.8 1.042190 801.5 1.042100 ! 214 130.00 '8 7i."4 1.042070 ~21"5~ 133.06 ! 226 1 -227 1 228 229 230 231 232 ! "233 i 384 j 385 3  8  6  4 0 1  i  j  ;  r  !  U  1.5899 1.042270 1.5882 1.042030 1.5878 1.041990 1 .041970 1.5874 1.5871 1.041920 1.041850 1.5866 1.5862 1.041870 "i"."6'4"l'890" 1.5860 1.028350 1.5877 1 .5872 1.028370 1.028400 1.5871 1.030580 0.0000 1.030310 0.0000 f.'030620 0.0000 1.030060 0.0000 1.030000 0.0000 1.029870 0.0000 1.029860 0.0000 1.029830 13.5413 1.629840 13.5411 1.029840 13.5411 1.029850 13.5410 1.029890 13.5412 1.029910 13.5412 1.029930 13.5411 170299 50 13.5409 1.029910 13.5408 1.042510 1 .5901 1.042410 1.5898 1.5897 1.042360 1.5897 1.042220 1.042170 1.5895  67.660 58.070 48.980 41.280 33.590 24.950 16.950 9. 840 69.040 32.740 11.810 11.400 31.120 42.460 57.830 75.330 93.900 120.070 11.960 15.310 19.260 23.660 27.580 33.310 40*040 45.570 50.850 59.900 53.570 47.870 44.630 39.390  31.910 31.850 32.100 31.940 31.940 31.700 31.700 31.670 14,165 14.155! 14.165 15.340 15.310 15.110 15.020 15.020 14.930 14.920 14,900 "14.W6 14o840 14.840 14.830 14.840 14.830 14.850 14.850 31.860 31.830 31.680L-  31.540 31.500  TABLE 2-7 (CONTINUED) RUN NO.  WS  145.00 217 103.00 '218 100.00 1219 188.00 • 220 95.00 [221 " 94.00 (222 103.00 (223 95.00 224 86.00 393 227.00 394 125.00 f421 ~ "92.00 422 200.00 U23 154.00 | 424 216.00 425 187.00 425 187.00 426" 304.00 427 194.00 J428 197.00 1429 225.00 430 310.00 1431 195.00 f432 " "2 03.00 433 244.00 ) 434 245.00 ; 43~5 250.00 [436 250.00 1 196 235.00 !'197~"2 5 5 . 0 0 ™ i 198 240.00 [199 200.00 i 200 215.00 ;201 190.00 202 180.00 "203 "155.00" 216  • TI  PO  PBO  1017.3 1.042000 l ' . 042110 813.0 1.041910. 1.042090 890.4 1.041880 1.042020 1865.2 1.041800 1.042000 1056.5 1.041770 1.041860 1208.6 1.041760 1.041810 1440.0 1.041800 1.041890 1494.0 1.042160 1.042150 1647.6 1.042140 1.042170 2540.8 1.028850 1.028450 1081.2 1.028790 1.028460 '8 77".7 T . 0 2 9 7 3 0 " lV0*30140~ 1324.8 1.029630 1.030070 805.4 1.029570 1.030000 1008.6 1.029480 1.029930 801.6 1.029450 1.029900 782.6 1 .029450 1.029900 1141.4 1.029480 T . 029840 589.8 1.029430 1.029790 653.4 1 .029440 1.029740 657.8 1.029400 1.029670 852.2 1.029400 1.029630 495.6 1.029320 1.029510 "~463'„6""" "Y. 029310 1.029500" 508.3 1.029690 1.029570 466.4 1.029420 1.029560 431.4 1 .029410 1.029580 397.9 1.029400 1.029550 743.8 1.041960 1.042160 842.5" "1". 0419 70 17642160 837.9 1.042010 1.042410 744.7 1.042030 1.042360 854.5 1.042060 1.042410 • 809.1 1 .042130 1.042440 861.4 1.042200 1.042340 818".8 T . 042500 , f . 340"  PC  H  1.5890 34. 520 1 .5887 27. 130 1 .5888 21. 390 1.5885 17. 290 1.5878 13. 800 1.5877 10. 370 1.5898 8. 788 7. 001 1.5895 1.5893 4. 829 1.5858 13. 780 1.5858 23. 390 0.0000 10. 350 0.0000 22. 350 0.0000 37. 460 0.0000 48. 160 0.0000 60. 900 0.0000 60. 900 0.0000 77. "250 0.0000 121. 770 0.0000 100. 860 0.0000 136. 000 13.5363 11. 050 13.5390 14. 410 13.5387 18. 160 13.5389 22. 000 13.5388 26. 630 13.5386 32. 730 13.5382 38. 810 1.5895 58. 700 1.5894 - -53-"570 1.5902 47. 840 1.5902 41. 710 1.5902 36. 490 1.5901 31. 580 1.5900 24. 860 1.5901 16. 340  u  I  31.370 ' 31.350 1 31.280 1 31.190 ; 31.150 i 31. 190 : 31.700 31.800 ; 31.830 ' 13.980 i 13.875 15.210 ! 15.110 i 15.025 1 14.940 i 14.900 i 14.900 ' 147940 : 14.890 j 14.910 1 14.860 j 14.860 I 14.780! 14.~77~6 1 15.180 ; 14.900 i 14.900 i 14.880 ' 31.810.: 31 ."'76TT; 31.840' 31.870 i 31.9701 32.060 1 32.140| 32.310 j  TABLE ( [RUN .NO.  (CONTINUED)  2-13 1  WS  155,00 150,00 115,00 103,00 97,00 77,00 80,00 260,00 1388 2 3 5 , 0 0 [389 185,00 236,00 !390 3 9 1 """"159","00 392 157,00 156,00 412 413 190.00 414 220,00 415 270.00 ,415 270.00 ;416 270.00 |417 293.00 i418 305.00 419 275,00 420 290.00 ;204 j205 42 06 ,;207 .1208 •209 '210 [387  2-7  TI  PO  PBO  PC  H  _ 1058,4 794.8 857,6 870.3 962,0 957,0 1530,6 834,4 839,0 • 742,3 1058.8 825,5 1219,0 838.4 764,6 724.4 762,0 749.3 . '663.4 654,6 614.2 508,8 504.2  . U  | !  1 ,042250 1 .042380 1 ,042290 1 .042240 1 .042310 1.042230 1 ,042340 1 .042150 1 .042300 1 .041860 T • 0 4 2 3 30" " 1 . 0 4 1 8 30 1.042380 1 .041800 1 .028850 1 .028350 1 .028890 1 .024420 1 .028910. 1.028450 1 .028950 1 .028380 1 ."0290 20 i 7'6 2 8 3 8 0 1.029080 l .028460 1 .029590 I .030030 1 .029510 i .030050 1 .029540 I.030050 1 .029360 I .030060 1Vo 2 9 3 6 0 " i .03 0 0 6 0 1 .029590 I.030070 1 .029570 •i .030080 1.029600 I .. 00 33 00 10 39 00 1 .029610 I 1 .029620 I.030190  1.5900 1.5898 1.5895 1.5891 1.5885 1 .5882 1.5878 1.5869 1.5865 1.5864 1 .5859 1.5856 1.5859 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000  12 . 160 20 . 1 5 0 10 .210 7 .950 5 .832 3 . 812" 1 .661 63 . 9 2 0 ' 50 . 9 3 0 39 . 6 4 0 31 . 2 2 0 22 . 8 1 0 9 .720 11 .290 21 . 0 7 0 32 . 6 0 0 47 . 130 47 . 130 61 . 4 3 0 75 . 2 9 0 94 . 0 5 0 112 . 1 8 0 128 . 1 7 0  32.280 ' 32.330 32.300 i 32.300 32.140 ! 32.080 • 32.080 14.380 ' 14.280 ' 14.275 14.250 i 147260 : 14.300 i 15.010 : 14.900 i 14.960 • 14.950 1 14."950 I 14.970 i 14.940 ! 14.960; 14.970 14.970! !  I ;  T A B L E 2-8 "  ~~  2-lk  — —  •  DATA WS  "RON NO.  TT ''  PO  . PBO  PC  H  -  G.S.  BETA=0.4•  •  '  . ! u  ;  1  i  :  j  |  ORTFTCE TYPE 278 "279" 280 281 282 283 284 T "28 5 i 2 8 6 1 i1 2 8 7 i 288 289 290 i 335 336 L 337 338 339 340 341 342 343 452 453 454 -"45 5 456 457 \ 458 i 459 460 461  j  '}  1.5918 730.7 1.045710 252.00 1.045490 1.5916 1 1 9 2 . 1 T."045 3 8 0 ~~ T . 0 4 5 6 3 0 "3 7 5 . 0 0 843.5 1 .045500 1 .5916 245.00 1.045290 1 .5903 1127.5 301.00 1 .045160 1.045140 1.5897 972.8' 1.045030 1.044930 230.00 1.5893 1669,5 330.00 1 .045060 1.044970 1 .5889 1054.2 1.044870 1.045070 182.00 1.5887 1.044730 "160.00 T 0 9 5 ' . y ~ 1 . 0 4 4 9 8 0 949.8 1.5890 1.044780 1.045000 121.00 1.5885 1829.2 1.044480 1.044780 170.00 1.5876 1494.4 1.044250 130.00 1.044690 1.5871 2122.6 1.044000 152.00 1.044610 1.5871 2458.4 1.043980 1.044480 105.00 1 .5886 643.5 1.036220 1.036350 225.00 1.5885 660.7 1.036250 1.036380 215.00 1.5883 1037.5 1.036220 1.036380 310.00 1.5881 901.4 1.036180 245.00 1.036350 682.4 1.036340 1.5880 1.036480 165.00 1.5879 830.8 1.036300 175.00 1.036540 • 8 3 0 . 4 1.036590" 1." 03 64 0 0 " 1 ."5878 157.00 1.5876 959.6 1.036400 150.00 1.036570 1.5877 1115.4 1.036500 140.00 1.036720 579.8 1.029870 0.0000 160.00 1.029070 0.0000 l.:030170 168.00 624.0 1.029780 541.5 1.030060 0.0000 180.00 1.029680 0.0000 1. 0 2 9 6 8 0 1.029880 230.00 • 870.0 566.5 1.029870 0.0000 1.029550 220.00 531.8 1.029930 0.0000 231.00 1.029710 416.5 1.029880 0.0000 220.00 1.029400 441.6 1.029880 0.0000 265.00 1.029310 380.2 • 1.029360 1.029810 13.5426 260.00 265.4 235.00 1 . 0 2 9 3 30 " 1 . 0 2 9 6 7 6 " 1 3 . 5 4 2 1  60< .340 49< ,830 4 2 .,320 3 5 ., 720 27. 9 0 0 19.,410 14. 8 1 0 10< ,"650 8.,160 4<,578 3., 8 0 0 2.,768 1.,031 64.,""450 55.,490 46 <,440 38.,150 29..940 22< , 500 "17.,"93 0™ 12., 190 7,,980 11.,080 21 .330 32..970 20 ,'3 30 45 ,910 58..000 87..930 114., 8 9 0 12.» 230 16 ,080  i  36.000 .35.870 35.830. 35.900 36.080 36.160 36.470 367520 36.900 36.410! 36.470 36.430 36.280 2'2.~600" 21.980 22.450 22.330 22.530 22.530 22.530, 22.580 22.680 14.770 15.500 15.370 157370 15.240 15.470 15.010 14.93014.980 14.97Q  TABLE  2-8  2-15  (CONTINUED)  1  WS  RUN NO,_  TI  •  PO  PBO  PC  335.1 1.029740 13.5419 300*00 1.029340 462 2 8 3 . 6 1 . 0 2 9 7 2 0 13*5419 1 . 0 2 9 3 1 0 463 275*00 7 9 3 . 5 0.0000 1.030680 |496 122*00 1.030100 1 .5929 793.5 1.030680 1 .030100 i496 122*00 1*5927 561.4 1.030620 170*00 1497 1.030010 561".4™ 1 . 0 3 0 0 1 0 f4"97" " T 7 0 . 0 0 lT6'3"062(f 0 . 0 0 0 0 0.0000 5 3 1 . 0 1.030610 1 . 0 3 0 0 1 0 223*00 j'498 1 3.5407 5 3 1 . 0 1 . 0 3 0 6 1 0 f 498 2 2 3 * 0 0 1 .030010 0 .0000 1 . 0 3 0 5 9 0 3 0 5 * 0 0 6 3 5 . 2 1 . 0 3 0 0 0 0 [ 499 1 3 .5405 1.030590 305*00 635*2 1.030000 500 331.0 1.030580 0.0000 1.030030 [ 500 2 0 5 . 0 0 2 0 5 * 0 0 , 3 3l7o""" f.*030030" lV'0305"80~ 1 3 . 5 4 0 0 f500 385.7 1 . 0 3 1 7 0 0 13.5483 265*00 1.031000 {501 393.8 1.031580 13.5480 300*00 1.031030 j 502 296.8 250*00 1.031500 13.5477 1.030970 1503 327.2 1 .030900 1.031420 13.5471 300*00 I 504 1.5862 1.043610 482*2 350*00 1 .043810 [303 1.5866 "557.4" 1 .043820 |3*04 ~ 3 8 0 * 0 0 r."'043880" 1.5864 596*9 1.043830 305 375.00 1.043980 682.9 1.5860 1.043800 1.043980 390*00 5 306 1.5858 1 .043990 732,0 1.044100 I 307 365.00 1.5856 400*00 923.0 1.044200 1.044930 1 308 1.5849 723,4 279.00 1.043900 1.044280 1 309 916.8" [310 " 2 9 0 * 0 0 " 1 . 0 4 4 3 70' 1.0*4 3 95 0~ 1 . 5 8 4 7 1.5844 2 0 8 . 0 0 7 6 8 , 6 1.044000 1.044430 J 311 1.5839 1223.5 1 .044980 1.044470 | 312 2 9 3 . 0 0 1.5834 1046,4 1.043900 195.00 1.044400 j 313 1.5831 1.044050 300.00 2452.0 1.044500 ; 314 1.5876 583.0 1.035660 1.036120 1 315 400.00 1.5874 610.4 1.035680 380.00 1.036210" t"316 1.5872 1.035620 284*50 1 .036210 j 318 504.2 744.8 1.5871 1.035580 365.00 1 .035900 i 319 699.8 1.5869 1.035510 1 .035800 r320 280.00 1.5869 636.4 1.035510 321 230.00 1.035760 1 .5869 1070,6 • 1 . 0 3 5 7 5 0 1.035480 322 340.00 1 .5869 ~ 1 7 0 3 5 2 30 " 3 2 3 "225.00'"" -""899 ."2 T. 0 3 5 6 5 0 " -  H  19.960 25.470 6.640 11.940 49.280 27.060 53.820 4.330 71.580 • 5.850 121.800 9. 8 9 0 12.270 15.060 18.900 22.780 58.260 51.050 43.170 35.320 26.650 19.960 15.770 10.530 7. 6 6 0 6 .024 3 .654 1.610 53.540 43.620 35.420 26.430 17.410 13.960 10.630 6.550  U  1 1  14*980 : 14.975 • 15*730 • 15.730 ; 15.610 15.610 : 15.580 15.580' 15.570, 1 5 . 5 7 0 .' 15.620 15.620: 17.150' 17.200: 17.080 16.980; 34.890J 3 4."810 34.890: 34.890' 34.880| 34.900 34.920 1  1  :  3 47940" 34.980; 34.9401 34.740, 34.650 22.600! "22 7 7 5 0 ' 22.750, 22.330i 22.150, 22.110L 22.100! 21 ."9 7 Oj  I I  1  TABLE  [RUN  2-8  (CONTINUED)  I  ?-sXA'  1  WS  TI  215o00  1106*4  1 .035640  1.035120  1 .5869  3. 900  21*980  115o00  1146.7  1*035640  1.035140  1.5870  1 .050  21.970.  290.00  436.4  1*035590  1.035180  1.5869  50.500  21.890  255o00  413.5  1*035560  1.035180  1.5872  42.930  21.860  1 320  280o00  699.8  1*035800  1.035510  0.8739  59.760  22.150 j  \32l  230o00  636*4  1*035760  0.8739  47.890  22.110 •  '.322  340o00  1070.8  1*035750  1.035480  0.8738  36.460  22.100  [323 ! 324  225o00 215*00  899.2 1106.4  1.035650 1*035640  1.035230 1.035120  0.8733  325  115.00  1146.7  1.035640  1.035140  22.460 13.230 3*350  21.970 ' 21.980 21.970 ;  ! 347  lOloOO  1049.3  PO  PBO  PC  H  U  NOo  i 324 j325' |32<T"  j 327  "T.035510 "  0.8731 0.8731 0.8719  ii  3.520  21.970  " 1.5847  0.950  21.970  4.615  21.880 i  1.035020  1.5844 0.8716  1.035770  1.034980  1.5841  768.2  1.035770  1 .034980  0.8714  31.480  21.920 j 21*920  732.3  1.035830  1.035010  1.5839  14.150  21.990 i  265*00  732.3  1.035830  l". 0 3 5 0 i d  0.8714  48.550  21.990|  351  265*00  620.0  1.035930  1.035000  1-352  270*00 235*00  543*4 437,7  1*035990 • 1.036010 •  1.035090 1.035100  506*0 507.6  1.036130  1.035190  1.5834  1.036150  1.035130 1.035160 1.035280'  1.035110 1.035720 " T . 0 3 5 7 2 0 " "~ T . 0 3 " 5 l T d  l"347 |348  ""101.00  "104973"  174*00  1.035700  1.035020  |348  174o00  827*0 8 27.0  1.035700  349  i  225*00  768.2  : 349  225*00  350  265*00  "3 50 "  1 353 ;354  290*00  355  305*00  •  356  280*00  448.2  1.036150  ! 357  315*00  478.4  1.036210  . 1.5837 1.5838  16.130 9.  '  120  20.040  21.880 |  22.110 j  27.420 32.470  22.090! 22.080 j  36.970 40.950  22.220!  1.5832 1*5829  44.560  22".  49.750  22.190!  52.100  22.2401  1.5836  22.180: 140 !  358  290*00  430.2  1.036280  1.035360  1.5830 1.5832  437  224*00  538.4  1.029410  1 .030250  0 . 0 0 0 0  5.410  438  250*00  417.4  1.029390  1.030230  0 . 0 0 0 0  11.520  15.135'  439  320*00  454.4  320*00  3 77.0  1,030230 1.030080  0 . 0 0 0 0  440 441  1.029320 1.029230  16.160 23.790  15.060: 14.""950":  315*00  327.3  1 .029210  1.030080  0.0000  442  330.00  298,4  1.029040  1.029830  0.0000  30.790 40.970  14.7401  443  320*00 265.00  308,4  444  1.029060 1.028960  1 .029810 1 .029890  0.0000 0.0000  35.900 47.350  14.750; 14.630-  445  280.00  245.6  1.029880  0.0000  61.200  14.640i  479  190.00  681.0  17631130  1. 5 9 57  2 2 2 . 6  •  1.028970  l"T03'06~80  0.0000  8 . 120"  15.170,  14.930'  16.*63b1  ! 2-17 [  TABLE 2 - 8 (CONTINUED) \ RUN [NO.  WS  TI  PBO  PO  190o00  6 8 1 . 0  1.030680  1.031130  625.8 625.8  1.030720 1.030720  4 7 5 . 7  |! 4 8 0  2 7 3 , 0 0  I  480  2 7 3 . 0 0  |  481  2 6 5 , 0 0  1  481  2 6 5 , 0 0  1.5945  35.080  16.440  0 . 0 0 0 0  19.280  16,440  .0.0000  27.280  16.510-  1.030830  0 . 0 0 0 0  2 9 0 , 0 0  367.2  1.030590  1,030830  282,4 282,4  1.030480 1.030480  250,00,  485  300,00.  3 00,00  288.3  288,3"  4 0 . 6 9 0  16.460  13.5420  3.230  16.460'  1.030800  0 . 0 0 0 0  51.690  16,280.  1.030800  13.5416  1.030350  1.030700  0 . 0 0 0 0  1."0303 50  i"7o3'b'7'oo  '  1.030340  13.5411  -  !  4.170  7 2 . 6 2 0  16,280 16.110  0 . 0 0 0 0  9 4 . 1 7 0  5.950  i~6","iTo  1.030730  13.5409  7.670  16.100'  109.890  16.100  300,00  254.0 2 5 4 , 0  1.030340  1.030730  3 2 5 , 0 0  256.4 256,4 283.9  1.030250  1.030620  0 . 0 0 0 0  1.030250  1.030620  13.5405  1,044060  1.043870  1  289,0  1.044050  1.043810  1.5880  52.870  312.0  1.044080  1.043760  1.5875  . 4 2 . 5 6 0  35.510' 35.720'  3 0 0 , 0 0  3 2 5 , 0 0 3 1 0 , 0 0 3 4 5 , 0 0 3 3 5 , 0 0  .5884  8.900  6 0 «  110  1  15.950 15.950' 35.650 35".  520  424,9  1.044150  1.043760  1.5873  30.590  3 7 0 , 0 0  448.2  1.044250  1  1.5869  2 4 . 5 3 0  35.890.'  2 9 6  3 5 0 , 0 0  4 7 6 , 3  1.044180  1.043790  1,5867  19.160  35.820'  1.044150  1.043820  1.5867  15.580  35.760.  '1.044140  1.043900  1,5863  11.970  1  294  \  295  I |  1.030940  1.030590  2 5 0 , 0 0  292"  16.700  1.030570  3 6 7 . 2  484  293  16.700  11.580  2 9 0 , 0 0  484  |  2 0 . 9 4 0  0 . 0 0 0 0  1". 0 3 0 9 0 0 '  483  291  1.5952  1.031070 1.030940  i  .  1.031070  1.030610  483  487  1  1 6 . 6 3 0  1.030570  1  I 487  f  4.560  4 7 5 . 7  2 7 5 o 00"  486  U .  0.0000  ~420",0"  } 482"  ;  i  H  l  1479  r485" ,j 486  PC  390,00  297  3 5 0 , 0 0  f29'8"  2 7 5 , 0 0  j  2 0 0 , 0 0  299  1 3  00  r"3oi  2 9 0 , 0 0 3 0 5 , 0 0  302  3 3 2 , 0 0  327  140,00  "'327  1.044140  414.9  1  '  .043880  1.5861  35.520:  3.369  35.800  7 4 2 . 7  1.044190  1.043770  1,5860  975,8  1.044300  1.043620  1.5852  1460,0  1.044250  1.043480  1,5846  1 .689  35.550  868.5  1.036230  1.035990  0.8735  3.000  22.640  6.890  2 2~. 6"4"0"  1703  1.036300  1.036020  175 79" 1.5876  1.036300  1.036020  0.8733  350 18.690  1.036360  1.036080  1.5876  2.950  1.036080  0.8733  10.300  1.036100  1.5875  I  328  2 5 0 . 0 0  \  329  2 3 0 . 0 0  !  329  2 3 0 . 0 0  :  330  3 7 5 . 0 0  636.4 786.4 786.4 7 7 7 . 0  1.036360 •  "3 7 5 " . 0 0 " " "~ ~ 7 7 7 , 0 " " " T .  1.036350  5990  5.276  1.036320  328  6  357 0 0" 35.510'  8.080  1 4 0 . 0 0 ~ ~ " 8 6 8 " . 5" 2 5 0 . 0 0 636.4  i  '"'330  527.3 """47074""  .043630  0 3 6 3 6 0 " ' "" " 1 • 6 3 6 1 0 0  8  '"  678733  5.  8.  190 "28Y520~  22.620  2 2 . 6 2 0 2 2 . 5 2 0 22.52022.320| 2 2 " . 3 20"  TABLE 2-8 :RUN ,NO. j331 |331 "3 32 332 J3 34. ^"34 344 344 345 345 346 i 346 ,'447 ! 446 448 449 450 451 488 '2 88  f  2 8 9  289 [490 | 490 |491 J 491 '  4  9  2  [ 492 [493 !"49T j 494 |494 5495 1 495  WS  TI  PO  493.6 280.00 1.036250 493.6 280.00 1.036250 544.4 345.00 1.036310 544.4 345.00 1.036310 396.1 315.00 1.036250 396.1 315.00 1.036250 604.2 225.00 1.036950 604.2 1.036950 225.00 536.4 280.00 1.037130 536.4 280.00 1.037130 357.2 1.037260 240.00 1.037260 240.00 , 357.2 325.00 365.0 1.028990 485.4 300.00 1.028990 .317.0 1.028990 340.00 307.0 1.028990 . 360.00 274.6 375.00 1 .028990 259.4 390.00 1.028980 630.0 236.00 1.030160 630.0 236.00 1.030160 634.5 245.00 1.030160 634.5 245.00 1.030160 611.4 325.00 1.030130 611.4 325.00 1.030130 389.3 1.030110 320.00 3 8 9 . 3 320.00 1.030110 333.4 315.00 1.030110 333.4 315.00 1.030110 289.2 325.00 1.030100 28'9.2 " 1 ."030100 325.66 365.00 283.0 1 .030070 283.0 365.00 1.030070 2~5"5 . 1 370.00 1 .030080 255.1 370.00 1 .030080  PBO  (CONTINUED) PC  1 .5873 .1.036190 0 .8733 1.036190 1.036210 1 .5873 1.036210 0 .8734 1 .5874 1.036410 1.036410 o". 8 7 3 6 1 .5877 1.036600 1.036600 0 .8741' 1 .5877 1.036580 1.036580 0 .8739 1 .5876 1.036620 f . 0 3 6 6 2 0 " 6". 8 7 4 0 1.029850 0 .0000 1.029850 0 .0000 1.029820 0 .0000 1.029870 0 .0000 1.029830 0 .0000 1 . 0 2 9 8 30" 0 . 0 0 0 0 1.030570 1 .5927 1.030570 0 .0000 1.030570 1 .5923 1.030570 0 .0000 1 .5928 1.030660 l.~63~b660 0". 0 0 0 0 1 .030770 1 .5935 1.030770 0 .0000 1.030810 1 .5938 1.030810 0 .0000 1.030850 0 .0000 1 T 6 3 0 8 50"""13". 5 4 1 6 1.030800 0 .0000 1 . 0 3 0 8 0 0 13 . 5 4 1 5 0 .0000 1.030670 1 . 0 3 0 6 7 0 13 . 5 4 1 4  u  H  ! i  21.910 ' 11. 480 21.910 t 3 9 .,970 14. 5 5 0 21.980 1 ,470 21.980 ! 50. 23. 5 5 0 _ 21.730 • 21.730" 8 2 . "ooo 22.970 2. 8 7 0 22.970 : 10. 0 3 0 7 6 0 2 3.140 i 5. 7 2 0 2 3 . 1 4 0 '• 19. 170 2 3 .260 13. ,"220 ""23T260 49. 14.670 j 8.,920 4., 100 1 4 . 6 7 0 | 13., 170 1 4 . 6 7 0 , 15.,920 14.670 21. 700 14.670 14.650. 26. 470 5.,110' 1 5 . 8 0 0 ! 15.800 2. 870 15.800 : 5.,333 15.800 i 3. 0 0 0 15.710 1 10.,330 15•710 j 5."740 15.730] 26. 080 14.,370 15.730! 15.750. 34. 970 15.750" 19. 310 27. 530 15.710: 15.710! 2.,215 15.670! 36. 890 15.670! 3.,060 15.670i 46. 910 3. 820 15.670J1  ;  !  !  !  /  TABLE 2 - 9  2-19  1  i  DATA | RUN [ NO. 1  iORIFICE  j  WS  TI  PO  ' PBO  PC  U  ! i  TYPE  G.S.  i  BETA=0.6  1.044390 1 .5930 355.00 430.1 1.044350 335.00 433.4 1 ."044280 1.044380 1.5925 237 330.00 470.5 1.044000 1.044200 1 .5920 | 238 400.00 655.0 1.043920 1.044090 1.5916 { 239 390.00 746.9 1.043870 1.044030 1.5912 240 305.00. 645.6 1.043630 1.044070 1.5906 280.00 688.2 1.043700 1.043990 1.5903 |2 4 2 2 6 5700* 7 2874 "T.043680 i~. 04 3890 1 .5902 S 243 230.00 718.0 1.043680 1.043810 1.5900 1 244 252.00 964.6 1.043710 1.043700 1.5896 i 245 197.00 930.0 1.043760 1.043790 1.5900 246 140.00 932.9.. .1.043710 1.043780 1.5901 245.00 531.6 1.043710 1.043980 1.5902 {"248"""296700* 549.4 1.043700 1.043770 1.5903 377 180.00 1152.8 1.037320' 1.037210 1.5877 190.00 699.0 1.037450 1.037240 1.5874 13378 7 9 245.00 716.6 1.037660 1.037310 .1.5873 1 380 275.00 641.6 1.037600 1.037350 1.5896 ! 381 330.00 681 . 1 1.037520 1.037380 1.5866 | 382 " "2 80". 00* "'"5 05.8" 17637670 T7637450 1.5864 ! 383 285.00 473.8 1.037620 1.037540 1.5864 ] 602 240.00 941.2 1.031790 1.032090 1.5918 | 603 210.00 409.4 1.031680 1.032110 1 .5916 604 245.00 344.0 1 .031700. 1.032090 1.5916 I 605 300.00 330.6 1.031690 1.032080 0.0000 "3 37.3" 1. 031670 ~f. 0326"80 0.0000 r"606 "3 60". 0 0 | 607 300.00 256.0 1.031610 1.032080 0.0000 ! 608 340.00 245.7 1.031640 1.032070 0.0000 i 609 330.00 228.2 1.031590 1.032070 0.0000 \ 610 300.00 337.2 1.031590 1.032000 0.0000 ! 611 300.00 278.0 1.031550 1.032040 o . o o o o T '"612"" 145.00 420.7 "T."03T9"56" ' . 03'2096 1 .5915 1 235 [""2 36  H  36.830 51. 970 45. 080 36.300 37. ,310 35.850 28. 810 35.720 21. 250 35.600 17. 050 34.980 12. 580 35. 190 10. 040 3*5 • 280 7 . 810 . 35.320 5 . 160 35.490 3. 460 35.700 1. 820 35.670 16. 190 35.700 21"."130" 3*57690 2 . 020 23.450 5. 850 23.630 8 . 880 23.760 14.,110 23.776 18. 000 23.720 23. 830 237780 28. 270 23.830 4. 980 17.600 19. 970 17.440 40. 230 17.410 36. 605 17.450 51. 640' r7.'32'"6 63. 130 17.350 90. 150 17.390 9 9 . 550 17.310 35. 110 17.32a 53. 200 17.280 9 . "630 17.270 j  C  i  TABLE 2-9 (CONTINUED)  r  •'• RUN : NO. 613 614  WS  140,00 200.00 191.00 r 6 5 7 ~~ 295.00 | 658 658 2 9 5 . 0 0 _ 328". 00 i'659 659 328.00 245.00 660 245.00 660 661 285.00 661 285.00 262.00'. 1662 262.00 662 I 663 280.00 i 663 280.00 664 295.00 664295.00 310.00 [~66 5 665 310.00 285.00 4 666 285.00 666 667 340.00 667 340.00 "'668 3 00.'00 J 668 300.00 j 66 9 110.00 669 110.00 189.00 670 189.00 670 "263 365.00 ! 264 340.00 1 265 375.00 375.00 1 1 267 365.00 268 390.00 • 269 365.00  1  S I  2  1  i  —  6  6  TI  PO  PBO  PC  j  2-20  H  U  » i  i  224.9 330.6 1114.7 761.0 761.0 123778 1237.8 1072.0 1072.0 596.8 596.8 465.4 465.4 406.6 406.6 326.6 326.6 341.2 341.2 268.6 268.6 295.6 295.6 246.5 246.5 632.6 632.6 817.9 817.9 250.1 248.0 290.0 317.0 335.6 399.8 397.0  1.032110 1.031490 1.031550 1.032080 1.046800 1.048050 1.046850 1.047750 1.046850 1.047750 1.04.7710 1.046940 1.047710 1.046940 1.046890 1 .047730 1.046890 1.047730 1.047720 1.046830 1.047720 1.046830 1 ."046940 " l ."047770" 1.047770 1.046940 1.047800 1.046920 1.047800 1.046920 1.047760 1.046940 1.047760 1.046940 1.047030 .1 .047800 1.047800 1 .047030 1.047880 1.046990 1.047880 1.046990 1.047880 1.047040 1 .047880 .1 .047040 i.~047900" 1.047020 1.047900 1.047020 1.047810 1.047080 1.047810 1.047080 1.047190 1.048120 1.047190 1.048120 1.044240 1.044"56'd~ 1.044640 1.044240 1 .044730 1.044240 1 ,044740 1.044230 1.044250 1.044670 1.044630 1.044240 1.044240 1.044540  1 .5915 17.190 30,.465 1 .5915 .660 17.270 28. 1 .5950 41.350; 3«.035 0.8767 42.300| 36..640 1 .5934 42.300' 11..490 0.8763 42.050 17..460 1.5932 42.050; 5..480 0.8767 41.820 13..075 41.820 1.5930 4. 160 1 .5929 41.590 17. 260 0.0000 41.590' 8.,980 1 .5929 24.. 180 42.010 42.010; 0.0000 12.,535 1 .5933 36.. 145 41.960! 0.0000 18.,970 . 41.960 0.0000 32.. 800 42.080 13.5426 42.080' 2.,740 0.0000 42.480 33..250 13.5423 42.480 2.,785 0.0000 ,710 .42.300; 45. 13.5429 42.300; 3.,860 0.0000 42.480i 53..990 42.480; 13.5431 4..640 0.0000.. 61.,816 42.480J 13.5431 . 5.. 170 42.480; 0.8769 42.630! 7. 150 1 .5933 42.630; 2.,415 0.8778 43.150; 12. 890 1.5943 4. 130 43.150" 1.5924 36.040, 35. 150 1 .5927 ,860 35.990' 30. 1.5931 36.010^ 27. 340 1 .5933 36.010. 22. 850 1 .5929 19. 080 36. 070 j' 1 .5927 36.010J 15. 350 1.5924 36.010J 13..530 !  1  1  :  ] f  TABLE  WS  RUN  335.00 271 25 Oj_0_0_ 325.00 I 272 320.00 i 273 j 2 7 4 375.00__ f'2"7 5" "375"."00 290.00 I 371 2 3 0 . 0 0 | 372 2 5 0 . 0 0 280.00 373 | 374 _325.00 f 3 7 5~ 2 9 0 . 0 0 " 295.00 584 145.00 584 145.00 585 265.00 585_ 2 6 5 . 0 0 "586 "2 3 0700" 586 230.00 _587_ 3 3 5 . 0 0 587 335.00 360.00 588 360.00 588 "589" •"335.00" 335.00 589 590- _ A J L _ 365.00 590 335.00 591 335.00 591 "592" " 2 3 5 . 0 0 " 592 235.00 2 00 00_ I 6 3 7 "2'3"0.0"0 I 638 3 4 0 . 0 0 f 639 355.00 r"6'4'b~ ' T i o V o o " !  3  5  0 0  JL  TI  PO  2-9  PBO  1.044590 1 .044240 1.044630 1.044260 1.044580 1.044500 1.044510 1.044220 1.044400 1.044170 TT04*42T0~ " l . " 0 4 4 4 0 0 " 1.044390 1.044190 1.037200 1 .036760 1 .036740 1.037190 1.036710 1.037140 1.036760 1.037150 TT03684CT "l70371*3"0" 1.037010 1.037200 1.031890 1.031280 1 .031280 1.031890 1.032260 1.031780 1_.031780_ 1 . 0 3 2 2 6 0 ~1 ."03*1846 " l " . 0 3 2 3 5 0 " 1.031840 1.032350 1.031850 1.032380 1.032380 1.031850 1.032430 1.031980 _ 1 . 0 3 1 9 8 0 _ 1_.032430 1,0 3*1980 " 1 . 0 3 2 4 2 0 " " 1.032420 1.031980 1.032600 1.032080 J _0_L _ 2~30.8 1.032080 1.032600 301.2 1.032060 1.032590 301.2 1 .032060_ 1.032590 ~3 2 0 . ' 8 " " 1 7 0 3 2 1 2 0 T . 0 3 2620' 1.032120 1.032620 320.8 1_._0_3_22_00_ 1.033090 402.7 342. 8 "1.032180 1.032950 1.032210 381.4 1.032960 1^032210 340.1 1^032800 " 2 5 574"" Y . 0 3 2 23*6" " l . 0T273Cf 394.2 _3_ _?JL 469.6 538.0 696.8 "8 1 2 7 7 " 743.2 919.2 678.0 568.4 505.3 "39676" 340.0 314.3 314.3 356.8 3 56.8 " 2 3 3 . 5~ 233.5 287.4 287.4 269.0 269.0 "*229"."8~ 229.8 23  3  8  2-21  (CONTINUED)  PC  1.5924 1 .5926 1 .5922 1 .5918 1.5914_ T.5913 1.5911 1.5897 1 .5894 1.5889 1_. 5 8 8 5_ " l . 5 881 1.5880 1 .5918 0.0000 1 .5917 0.0000 l .5917 0.0000 1.5917 0.0000 1 .5917 0.0000_ " l . 5Vl*7 0.0000 1.5917 0.0000 1 .5917 0.0000 "1 ."5'9'2"0~ 0.0000 1.5927 1.5923 1.5923 1.5916 "1759*1*2"" N  H  11. 4 8 0 9, 450 580 600 ,593 ,"468" ,425 060 2 270 ,3 9 3 0 6 710_ 8 740 12 360 1 ,963 0 ,933 5 .096 _ ,470_ 9 "320 4 560 13 2 4 0 6 565 17 3 5 0 8 810_ 21 "205 10 320 25 3 4 0 12 3 0 0 12 , 0 9 0 _5 8 3 5 5",0'55" 2 .465 3 990 7 310 13 140 18 300 25" 15*0* 2  U  36.010 36.100: 35.910' 35.990: _35.82_0 ' 3*5.960"" 35.880 23.000 22.820: 22.620| 22.550 "22 . 550" 22.820' 16.940 16.940* 16.780. 1 6 . 7 8 OJ "16/750, 16.750' 16.770' 16.770, 16.790, 16.790, " l 6 • 82 0, 16.820, 16.810 16.810 16.800 16.800 "167920" 16.920 17.490 17.450 17.510'_17.500! 17 .~5 9 0 ;  2-22  TABLE 2-9 (CONTINUED) [ RUN [NO.  WS  350.00 390.00 642 330.00 643 |644 295.00 1699 330.00 [ 6 9 9 "3*30.00 307.00 [700 307.00 1700 ] 701 295.00 295.00 701 { 702 3 0 0 . 0 0 300.00 {702 "703 340.00 1 703 3 4 0 . 0 0 704 375.00 704 375.00 705 410.00 410.00 "705 706 405.00 706 405.00 249 370.00 370.00 250 j 251 350.00 345.00 "252 1253 345.00 1 254 360.00 i 255 365.00 370.00 256 257 330.00 : 2*58 3 2 5 . 0 0 1 259 4 0 0 . 0 0 i 260 3 5 0 . 0 0 261 290.00 262 285.00 359 245.00 3 59 24*5.00 : 1  TI 262.8 262.7 205.2 298.9 1166.2 1166.2 913.8 913.8 628.0 628.0 416.2 416.2 358.3 358.3 356.9 356.9 327.6 327.6 280.8 280.8 235.0 238.4 244.9 258.5 265.7 290.1 318.8 331.0 325.0 353.8 506.9 594.0 662.2 1539.2 655.0 655.0  PO ^  PBO  PC  1.032250 1 .032800 1.032230 1.032280 1.047680 1.047680 1.047410 1.047410 1.047250 1.047250 1.047220 — 1.047220 1.047230 1.047230 1.047120 1.047120 1.047280 1 . 0 4 7 2 80" 1.047090 1 .047090 1.044340 1.044280 1.044290 1.044190 1.044190 1.044160 1.044130 1.044090 1.044110 1.044060 1.044100 1.044160 1.044100 1.044180 1.036500 1.036500  I .032710 1 .032750 1 .032700 1 .032700 1 .048 0 0 p _ 1• 0 4 8 6 6 6 1.048100 1.048100 1 .048160 1 .048160 1 .048160 .648~160 1 .048210 1 .048210 1.048190 1.048190 1 .048210 1 .048210 1.048170 1 .048170 1 .044790 1 .044590 1 .044720 1*. 0 4 4 7 8 0 1 .044810 1 .044700 1 .044690 1.044490 1 .044490 1 .044420 1 .044280 1.044330 1.044200 1 .044100 1 .035990 1 .035990  1.5910 1.5910 0.0000 1.5907 0.8765 1.5911 0.8767 1 .5916 0.8769 1.5920 1 .5922 0.0000 1.5924 0.0000 1.5923 0.0000 1.5924 0.0000 1.5924 0.0000 1.5939 1.5917 1.5935 1.5933 1.5933 1.5929 1 .5928 1.5922 1 .5919 1.5915 1.5910 1.5912 1.5906 1.5903 1.5870 0.8736  H .  U  17.570 : 3 0 ..810 17.540 38. 4 9 0 17.590 • 24..866 1 7 . 5 9 0 '• 16.,346 4.>210____45.30.0j 45.300 1..387 44.100 5..530 44.100 i 1..895 1 1 .. 100 4 3 . 3 2 0 43.320 3 ,565 43.240 8..350 43.240 4 . ,290 43.230 i 14.,450 43.230 i 7.,540 , 830 4 2 . 8 0 0 [ , 17. 42.800 j 9.,260 2 5 ..586 42.880 42".'"88 0~ 13.,360 42.620 ; 33 ,885 42.620 i 17.,820 13<, 100 36.. 390 I 36.200; 12.,710 36.240! 9.,530 35.970: 9<,370 36.000 8.,830 3 5.880 i 8<,030 7.,020 35.820 6.,540 35.690 35.780 5. 310 4. 4 0 5 35.670 • 35.740 i 3..367 35.890 1..861 35.710 1..018 o..201 35.870'23.5701 0<.750 23.570! 2..460 ;  !  1  1  :  !  .  :  .  _  j 1  [RUN {NO.  .  .  TABLE 2-9 (CONTINUED)  ;  2-23 j 1  WS  TI  PO  PBO  PC  1.5867 671.6 1 .036590. l7036000 0.8734 671.6 .1.036590 1.036000 1.5864 398.6 1.036020 1.036590 0.8733 398.6 1.036020 1.036590 1.5872 267,4 1.036620 ' 1.036400 0.8737 267.4 17036400 17036620 1.5865 249.4 . 1 .036960 1.036580 0 .8733 2 4 9 . 4 1 . 0 3 6 5 8 0 1 . 0 3 6 9 6 0 j 366 1.5864 184.9 1.037640 {367 1.037080 0.8733 184.9 1.037640 367 1.037080 1.5867 408.4 1368 1.037170 1.036900 "408 .4~ 1 . 0 3 7 1 7 0 0.8734 |368 ~3 007o6 1.036900 369.3 0.8734 1.036990 1.037310 j 369 2 2 0 . 0 0 0 .8735 6 2 3 . 8 1370 240.00 1.037390 1.037090 1.5925 i578 342.4 1.032120 220.00 1.031710 342.4 220.00 1.032120 0.0000 578 1.031710 249.7 1.5923 1.032110 1.031690 ! 5 7 9 210.00 2 4 9 . 7 ~ 7 o 3 1 6 9 6 ~ " l . 0 3 2"l 10 0 . 0 0 0 0 [579 210.00 1.5927 281.2 1.032190 325.00 1.031760 [580 0 .0000 2 8 1 . 2 1 . 0 3 2 1 9 0 3 2 5 . 0 0 1 . 0 3 1 7 6 0 i 580 1 .5921 1581 2 3 3 . 5 1 . 0 3 2 1 8 0 330.00 1.031770 2 3 3 . 5 581 1 . 0 3 2 1 8 0 0 . 0000 330.00 1.031770 1.5922 213.2 350.00 [582 1 .031800 1.032250 2 1 3 . 2 "T. 0 318do " 1 . 0 3 2 2 5 0 0.0000 t 5 8 2" 3 5 0 . 0 0 208.8 1 .5920 360.00 1.032210 1.031760 ^,583 1.5920 1.032210 1.031760 ! 583 360.00 • 208.8 3~8"1 ."7 1 . 0 3 1 6 7 0 1.032080 1.5913 [Gl~5~ 2 8 0 . 0 0 1 .5914 305.4 1.032160 310.00 616 1.031590 617 266.3 1.5915 1.031550 1.032160 330.00 1.5914 2 57.4" 1 . 0 3 1 6 2 0 1.032170 : ~6'i8~~ 3 8 0 . 0 0 " " 1.5917 223.9 1.031680 1.032170 I 619 375.00 1.5915 5 1 7 . 2 1 . 0 3 2 1 7 0 1.031670 ,'6 20 2 0 0 . 0 0 1.5915 5 2 5 . 7 J621 1 . 0 3 2 2 0 0 265.00 1.031600 0.8780 ! 671 287.00 534.6 1.048190 1.047010 1.5948 671 534.6 1.048190 287.00 1.047010 0 .8783 3 8 3 . 6 " 1.047030 1.048260 "672 " 3 0 0 . 0 0 f360 [360 361 361 | 363 [363 366  j  340.00 340.00 275.00 275.00 285.00 285.00 260.00 260.00 225.00 225.00 300.00  H  i  u  1. 3 4 0 2 3 . 5 7 0 ; 4.550 23.570 ' 2.520 23.470 ! 8.530 23.470 ; 6.025 23.410 1 20.350 23 7410 ; ' 5.790 23.610 ! 19.780 23.610 7.755 23.660 26.610 23.660 2. 8 7 0 2 3 . 7 0 0 9.780 237700 6.420 23.720 2.820 23,750 i 1 .256 1 7 , 0 6 0 ! 0.590 17,060 2 . 180 17.010 ' 1.020 17.010 , 4.250 17.010 : 2.065 17.010 ! . 6.530 17.030 j 3.185 17.030, 9.040 , 16,990 i 4.410 167"99"0 ; 10.010 1 6 , 9 1 0 ! 10.010 1 6 , 9 1 0 ; 2.917 17,430 5.460 17.330 ; 8.460 17,280 12.035 17.360 15.880 17,430: 0.838 17,420 1.236 17.340 4.372 4 2 , 4 0 0 ;1 .560 4 2 . 4 0 0 i 9.940 42.500J :  ;  ;  ;  1  t  J  [  TABLE  2-9  2-2U  (CONTINUED)  1  • WS I'RUN • L NO. 6 7 2 300.00 I|673 310.00 \ 673 310.00 340.00 1 1 674 340.00 fr— ' -365.00 -—~-~ $67 5 .365.00 ! 67 5 390.00 !| 676 677 405.00 677 405.00 [678 415.00  t  TI  PO  PBO  PC  H  U  !  1;-  6 7 4  383.6 311.4 311.4 331.2 331.2 295.2 295.2 309.7 285.4 285.4 269.4  1.047030 1.048260 1.048250 1.048720 1.048250 1.048720 1.047710 .1.048470 1.047710 1.048470 1.047740 1.048330 1.047740 1.048330 1.047500 1.048210 1.047500 1.048490 1.047500 1.048490 1.047020 1 .048130  1.5951 0.8778 1 .5949 0 .8773 1.5944 0.8770 1.5939 0.8768 0.8773 1 .5932 1.5924  3. 200 15.930 5.063 17.445 5.490 24.150 7.820 26.060 35.050 10.485 12.276  42.500 46.380 46.380 44.800. 3j4_.800j 4~4.900 ! 44.900 44.400 44.140 44.140 42.740 !  :  TABLE  2-10  2-25  DATA RUN NO.  WS  ORTFTCE "TYPE  "TT  PBO  PC  H  U  SPECIAL 15  135. 00 423.8 ""210 . 00" "2 7 8'. "2" 257. 00 813.4 240. 00 575.4 480.7 250. 00 407.2 268. 00 311.9 250. 00 ~3"4 07 00" ~3 5*5T6~ 255.8 280. 00 257.4 320. 00 310.00 222.6 280.00 199.2 _2 90.00 196^2 2 3 5.00" 4 75.8" 137.00 778,2 137.00 778.2 772.0 210 .00 772.0 210 .00 j 689_ 240 .00 ^84_.JL | 689 "24b .00 484.9 f 690 290 .00 384.0 285 .00 295.0 692 295.9 3 50" ,00 692 350 ,00 ' 295.9 | 693_ 385 ,00 330. 2_ T693 "385" , 00 3"30"V2 | 694 205 ,00 511.4 [_6_9_4_ 205 ,00 511.4 1 69 5 401.2 247 .00 ' 696 245 .00 504.8 69 6_ _2_45_00_ 504.8 697 2 05" • 00 5*7 2". 3~ 622_ "623 624 _>2_5_ 626 627 628 "629" 630 _631_ 6 32 633 _634 6"35" 687 687 I 688 688  PO  _1__032170 1.5915 10j» 860_ 1.0' 32150" "b'.oo'bb" "36 ."230 11.000 1.031950 1.5901 19.505 1.031880 1 .5899 1.031870 1.5897 30.640 1.032100 27.460 0.0000 1_.0 3236_0_ _0.0000 _41j_170 " l .032 360 oTdbo'b" 59.390" 1.032250 78.540 0.0000 1.032310 102.070 0.0000 1.032300 0.0000 128.220 1.032310 0.0000 131.035 1_.031340 13.5411_ __11.900 " l .032300"~"T ."5919 2 7. "580" 1.047910 0.8 763 9.840 1.047910 1.5916 3.250 1 .047930 0.8763 24.520 1 .5915 1.047930 7.710 1^5916_ 1.047970 26. 250_ T."0'479"70"' ~6.6ooo 13.756 1.048000 33.100 0.0000 1.048030 55.290 0.0000 0.0000 1.048100 85.246 1.048100 13.5407 7.095 '1.048090 _0_._0000 j3_l!_730_ T. 0480"9b"" "13.5409" 6". 8"l"0 1 .5922 1.048190 17.200 1.048190 9.075 0.0000 1.046710 0.0000 1.048120 21.760 1 .046670 1.048170 1.5922 25.390 JL j_046670 1_.04817_0_ 0.0000_ _13.350 1 • 04"6 8 6'6" "l."6"4"8"246 T."5"9T5 13.~6b"6"  1.031700 To"03i64'0~ 1.031640 1 .031600 1.031550 1.031510 1.031600 T.0315 b<f 1.031550 1 .031490 1.031510 1.031490 _1.031670_ 1.031540 1.046840 1.046840 1.046770 1.046770 1_.046710 T .0467" 10" 1.046740 1.046760 1.046760 1.046760 1 ._04_6 780 T . 046"780" 1 .0468 00  17.480: T7T390" 17.700; 17.650 17.590 17.520 _17_?_640 17.500" 17.570 ; 17.490: 17.500. 17.480 1J.730 ~17T55"6" 42. 170. 42.170 42.000, 42.000' _41.800' 4l'".8bb" 41.900, 41.950 42.000 42.000 _4 2^0 0_0  42.000" 42.080 42.080 41.800 41.70041__7_00 "42.25b  i 2-26-  t  1  TABLE , 2 - 1 0  ;  (CONTINUED)  1 1  | RUN 1 NO e  WS  TI  [ 697  205,00  572.3  PBO  PO 1.046860  PC 0.0000  1 .048240  i  H 7 . 050  U  !  42.250  . TABLE 2 - 1 1 i !  !  DATA RUN NO,  -ORIFICE | 679 | 679 680 | 680  WS TYPE.  100,00 100.00 240.00 240.00 " r"68~r 3 0 2 7 0 0 " 302.00 681 I 681 3 0 2 . 0 0 I 682 2 0 0 . 0 0 | 682 2 0 0 . 0 0 340.00 S 6 84" "l'5076o" 150.00 ! 684 1 70.00 [_6_8_5_ 685 170.00 f 686 118.00 j 686 118.00 [""645" " 1 8 0 . 0 0 ' 646 200.00 _260.00 2 5 0". 0 0 " ; 648 5 649 2 9 0 . 0 0 270.00 650 ' 6 5 1 ' "3 5 0 . 0 6 "  TI  PO •  SPECIAL 640.8 640.8 682.5 6 8 2 . 5_ "5 9 577 595.7 595,7 237.1 237.1 4 2 0 . 1_ "51576 515.6 746.2 746.2 868. 1 868. 1 "531.7" 433.5 _440_ 3_ 3"5"5 . 2 328.8 2 58^0 "284.4" !  PBO  •  PC  H  U  30 1.047240 1.047240 1,046850 1 .046850 17 0 4 6 9 70™ 1 .046970 1.046970 1 .046900 -1.046900 0 4 6 9 00 T ."04'69 30" 1.046930 1.046970 1 .046970 1.047040 1.047040 T". 0 3 2 6 2 0 " 1.032500 1.032500 1.032450 1.032440 1.032400 T."03"2'300"  0.8765 8 . 220 1 .048040 1.048040 1.5916 2.617 1.047930 0.8763 41.417 _1.047930 1.5912 12^995 l 7 0 4 7 88" 6" T . " 5 90 9 "27.275"" 1 .047880 0.8792 87.900 1.047880 0.0000 14.220 1.047870 41.000 0.0000 1.047870 13.5392 3 . 300 1.047790_ __0.0000 _37.640_ T'."d4"7690 1 ."590 3" ""87780 1.047690 0.8758 27.890 1.047750 1.5903 5.450 17.215 1.047750 0.8760 2.545 1 .047740 1 .5904 6 .060 'l . 0 4 7 7 4 0 0.8759 T27210" "1 " . 0 3 3 4 9 0 " "175953"" 23.430 1.033210 1 .5937 39.356 1.033400 1.5947 0.0000 31.340 1.033450. 0.0000 50.233 1.033490 0^0000 __7l.660_ 1.033500 ~l."03"332b" "o". 0 0 0 0 " 10*67670  43.380 43.380 42.220 _42.220 427570 42.570 42.570 42.330 42.330 42_.330 "42 ."'46™b 42.460 42.560 42.560 42.800 42.800 Te  .""26'b  17.960 17.940 17.870 17.82017.780  T7763G •  i  TABLE 2-11 (CONTINUED)  ws  TI  350.00 36 0__) 0 T3*5T0"0 300.00 205.00  254.3 _2_35 .7 761^6 462.1 354.1  ( R U N •'; I NO. 652 653 "654 655 656  m-  PBO  n-;:  1.032300 1.033190 !• 0_3 22 20 1.033170 1.032290 1.033100 1.032110 1.033030 1.032200 1.033090  PC  2-27'  vr/j  u  ;• !  0.0000 126.970 17.630' 13.5430 12.8 9 6 17.440 1.5933 3.273 17.560 0.0000 26.540 17.240 1.5931 37.940 17.390 ;  !  APPENDIX 3 - ERROR ANALYSIS I  Tabulation o f the S t a t i s t i c a l Results A s t a t i s t i c a l a n a l y s i s was c a r r i e d out on each experimental run based on a method given by P a r r a t t (19) and summarized by Ratkowsky (20). A 95$ confidence i n t e r v a l was c a l c u l a t e d i n each case f o r K and Rerj. The e r r o r a n a l y s i s r e s u l t s were used i n two d i f f e r e n t ways.  Firstly,  the 95% confidence i n t e r v a l allowed a decesion to be made as t o whether an expermental r u n , represented by an apparently w i l d p o i n t , should be ••. repeated o r not. Secondly, i t allowed a check on the experimental graphs such as Figure 10 i n which a comparison between two curves gave the required information.  I n Figure 10, the n o n - i n t e r s e c t i o n o f confidence i n t e r v a l s on  K f o r the Sharp.and Standard O r i f i c e p l a t e s confirmed w i t h 95% confidence t h a t there was a s i g n i f i c a n t d i f f e r e n c e between curves." The other graphs were checked i n a s i m i l a r manner.  .'  The r e s u l t s o f these c a l c u l a t i o n s are contained i n Tables 3-1 t o 3-11 inclusive.  * .  :  TABLE  j f-RUN WO, !  95% C O N F I D E N C E I N T E R V A L . F O R K~~~~ '95% CONFIDENCE ' INTERVAL  j O R I F I C E TYPE fib 5 i 106 i 107 108 109 110  i 111 ; 112  113' 114 115 116 117 118 131 . i 132 1 133 ; 134  t 135 t 136 ' .137 138 139 140 14l I 142 :i43 • | 565 ! 506 ; 506 506 r  r  f  3-2  3-1  N  0,6205 0.6196 0.6197 0.6215. 0.6217 0.6213 0.6237" 0.6237 0.6267 0.6282 0.6301 0.6337 0.6391 0.6791 0.7091 0.7100 0.7107 0.7036 0.7138 0.7172 0.7199 0.7209 0.7212 0.7264 0.7247 0.7128 0.6735 0.7144 0.7095 0.7124 0.7053  1.0  INCH  STANDARD  0.6246 0.6237 0.6239 0.6256 0.6259 0.6255 0.6279 0.6279 0.6310 0.6325 0.6344 0.6381 0.6435 0.6840 0.7139 0.7148 0.7155 0.7084 0.7187 0 .7220 0.7248 0.7258 0.7262 . 0.7316 0.7302 0.7196 0.6880 0.7194 0.7145 0.7175 6.7103 •  0.6163 0 .6154 0.6155 0.6173 0.6175 0.6171 0.6195 0.6195 0 .6225 0.6240 0 .6258 0.6294 0.6347 0.6742 0.7043 0.7051 0.7058 0.6988 0.7090 0.7123 0.7149 0.7159 0.7161 , 0.7212 0.7193 0.7060 0.6590 0.7094 0.7045 0.7074 0.700 2 ;  K AND R~ED  7144.39 6560.13 5936.95 5493.18 5166.01 4742.51 4322.81 3963.72 3541.20 3132.65 2727.95 2361.19 2178.30 2042.48 213.04 205.33 2 0 5 .57 191.83 176.88 160.53. 151.17 124.31 109.53 84.58 71.85 47.07 24.18 209.21 209.21. 217.65 "2 I T . 6 5  RED' '95%' CONFIDENCE INTERVAL  7150.54 6565.84 5944.27 5499.83 5171.92 4747,68 4328.58 3969.35 , 3546.46 • 3137.41 2732.69 2365.75 2182.37 2048.18 213,34 205.61 205.85 ' 192.12 177,11 160.74 151,38 124.48 109.73 84.73 72.02 47.24 24.30 209.57 209.57 218.08 218.08  7138.25 6554.41 5929.62 5486.53 5160.11 4737.35 4317.05 3958.09 3535.94 3127.89 2723.21 2356,62 2174.23 2036,77 212.75 205,05 205.29 191,55 176.65 160,33 150.96 124,13 109.33  .!  84,42 71.68 46,91 24.06 20 8,8 5 208.85 217.21 217.21  1 i  i  ; i  , ; ! i j ! | J i ; j  i  i  I  jj  T A B L E 3-1  \509  . 509 510 510 511 1 511 f 512 \ 513 1514 515 ;  0.7033 0.6997 0.6885 0.6955 0.6771 0.6821 0.6674 0.6716 0.6637 0.6680 0.6612 0.6574 0.6529 0.6486  0.7082 0.7045 .0.6932 0.7019 0.6816 0.6872 0.6719 0". 676'2 0.6681 0.6725 0 . 6 6 56 0.6618 0.6572 0.6529  0.6984 0.6949 0.6839 0.6890 0.672 5 0.6771 0.6630 ' 0 . 6"6"7 0 0.6593 0.6635 0.6568 0.6531 0.6486 0.6443  TABLE 95 % CONFIDENCE  "ORTFTC E "7 YP E !  f  87  I "8 898™ 90 r~9T ? 92  i! 9 493" ~  0.6209 0.6212 0.6219 0.6222 0.6"235 0.6249 0.6266 " 0.6264  1 T 5 ~ T N CH  294.03 294.03 427.67 427.67 5'8"2T6'0 582.60 746.83 746.83 861.09 861.09 993.38 1122.20 1260.22 1385.54  294.59 294.59 428.37 428.37 583.43 . 583.43 747.72 747.72 862.03 862.03 994.52 1123.43 1261.60 1387.05  293.46 293.46 426.97 426.97 581.78 581.78 745.95 745.95 860.15 860.15 992.24 1120.98 1258.85 1384.03  3-2  INTERVAL  FOR  95 % CONFIDENCE INTERVAL.  | RUN  3-3 95$ J^ONFID_ENC_E_ INTERVAL  RED  95 % CONFIDENCE^ INTERVAL"  f RUN E NO. j.507 ,;50 7 •| 508 :508  (CONTINUED)  K RED  AND  RED 95%  CONFIDENCE INTERVAL  STANDAR D  0.6238 0.6179 "0". 6 2 4 1 ' — o .6' 18 3 0.6248 0.6190 0.6251 0 .6193 "0"T6~2~6'5 0". 6"206 0.6278 0.6220 0.6295 0.6236 "0V6 29 3 0*76 2 35  10009.03 10018.14 10027.25 9 3 6 6 7 3 0 " ~"9'3 5 07 3"9" 9 3 5"8T 3'4 8691.61 8698.91 8706.21 8 1 3 9 . 1 6 _ 8 1 2 4 . 3 8_ 8131^77 7169.69 717"5 . 70 ~7r81772 6353.80 6 3 6 4 . 19 6359.00 5590.97 5595.98 5600.99 50T5". 3 T 5"0 2 07l"3" 50"24'796"  TABLE  f f I  95 96  I-— 97i  98 99  roo  101 102 "103 104 L 151 152 [ 153 |' 154 "155 i 156 1 157 158 !! 159 i 160 r ~16 l " j 162 522 522 523 I t t 523 *> f 524 \i 5 2 4 525 iL 525 526 i 526 "5 2 7 528 f. 5 2 8 529 529 i 530 Lf- 5 3 0 i  i  <  1  0.6267 0o6272 0.6296"" Oo 5 9 0 2 0.6283 0.6319 0.6319 0.6364 0 76426™ 0.6621 0.7080 .0.7099 0.7128 0.7153 "0.7186 0.7218 0.7244 0.7284 0.7288 0.7303 "o".7'293. 0.7175 0.7-176 0.7143 • 0.7110 0.7048 6. 7 0 0 7 0.6964 0 . 6956 0.6836 Oo 6 7 5 6 0.6768 0.6688 0.6640 0.6681 0.6597 "0.6661 0.6564 0.6602  3-2  0.6296 0.6238 0.6243 0.6302 6."6 32 5 0 .6266 0.5874 0.5930 0.6314 • 0.6251 0.6349 0.6289 0.6289 0 .6349 0.6334 0.6395 0.6456 0.6396 0.6655 0.6586 0.7115 0.7046 0.7133 0 .7065 0.7094. 0.7162 0.7187 0.7119 0.7220 0.7151 0.7252 0.7183 0.7279 0.7209 0.7321 0.7248 . 0.7325 0.7250 0.7343 0 .7263 6". 7 3 4 6 0 . 7 2 3 9 0.7079 0.7270 0.7212 0.7139 0.7183 0.7103 0.7146 0.7074 0.7086 0 o7010 0.7041 0.6974 0.6998 0o6931 0.6989 0.6922 0.6868 0o6804 0.6787 0.6725 0.6813 0 . 6 7 2 3 •' 0.6719 0.6657 0.6671 0.6609 0.6716 0.6646 0.6628 0.6566 0.6694 ,0.6628 0.6595 0.6533 0.6634" 0.6569  (CONTINUED.) 4560.79 4564.76 4068.81 4072.78 3690.07 3693.78 3790.95 3794.82 3704.82 3712.15 3223.77 3227.11 2993.42 2996.68 . 2580.15 2583.21 2096.39 2098.41 1424.92 1427.33, 323.12 323.48 302.80 303.10 278.83 279.09 261.87 262.11 236.40 236.62 206.02 206.23 179.84 180.00 155.76 - ^ 155.94 136.85 137.03 111.56 111.68 79.50 79.64 • 51.64 51.76 261.24 261.58 261.24 261.58 292.31 292.72 292.31 292.72 401.12 401 . 5 5 401.12 401.55 587.33 588.00 587.33 588.00 734.96 735.68 734.96 735.68 889.20 890.10 1043.71 1042.61 1043,71 1042.61 1196.54 1197.69 1196.54 1197.69 1314.13 1315.43 1314.13 1315.43  3-U 4556.81 j 4064.84 1 3686o36 3787.08 ; 3697.48 3220.43 2990.16 2577.08 2094.38 1422.51, 322.76 302.50 278.56 261.63 236.18 205o80 179.67 i 155o57 136o67 ' lllo43 79.37 . 51.52 260.89 260.89 j 291.91 291.91 i 400.70 : 400.70 ; 586.66 | 586.66 , 734o24 : 734.24 888o29 ! 1041.51 1  1041.51 1195.39 1195.39  1  1312.83 1312.83  j ;  \  i  TABLE  95 % CONFIDENCE RU N NO.  '"" ~ K  ORIFICE 1 119  120 121 122  123 124  i  12 5 "  126 i 127 128 t< 129 130 r~ 7 . 4 4" I 145 f 146 j 147 r 148 [ 149 "150" 1*  j" 1 5 1 :  t  152153 . 154  155 u "516"  :  I  i  I-  517 517 518 518 519 5  1  9  3-5" • i  3-3  INTERVAL  FOR  95%  CONFIDENCE INTERVAL TYPE  2.0  INCH  K. RED  AND  RED 9 5~% CONFIDENCE INTERVAL  STANDARD  0 76196 07~6T4~8* 0.6172 0.6191 0.6215 0 .6167 0.6186 0.6138 0.6162 0.6228 0.6181 0.6205 0.6184 0 . 6 2 0 8 . 0.6231' 0 . 6 2 4 5 0 .6197 0.6221 0 7 6 2 36 ""0 7 6 2 6 0 "076212 0.6671 0.6646 0.6620 0.6264 0.6217 0.6240 0.6268 0.6292 , 0.6244 0.6314 0 .6264 0.6289 0.6399 0.6348 0.6374 0.6934 0.6962 0.6906, 0.6997 0.6941 0.6969 0.7014 0.7042 0.6986 0.7023 0.7051 0.7080 0.7115 0.7058 0.7087 0 . 4 3 8 4 0.4349 0.4367 0 7 7 1 7 8""* 0 .'7118" 0.7148" 0.7241 0.7179 0.7210 0.7243 0.7179 0.7211 0.7273 0.7202 0.7238 0.8445 0.8521 0.8369 0.56940 . 5 9 4 6 0.5820 0.6933" 0.6897 0.6860 0.6815 0.6842 0.6870 0.6761 0.6788 0.6815 0.6787 0.6733 0.6760. 0.6719 0.6744 0.6693 0.6652 0.6627 0.6602 0.6652 076696""" 0.6739.  1T6T8 . 21 T i " 6 2 " 9 . 7 7 10977.78 10987.79 10129.21 10138.07 9218.54 9226.71 7660.89 7667.58 6619.32 6624.74 5730.77 , 5735.97 5271.13 . 5276.06 4449.69 4453.33 3932.43 3936.52 3412.70 3416.62' 2480.51 2483.23 389.54 389.92 352.59 352.93 315.66 315.94 284.17 284.46 257.32 257.58 142.46 142.60 "T997?7*~ 199.60 172.68 172.87 160.05 160.20 136.12 136.25 9 6 . 16 96.28 39.44 39.33 316.77 317.15 510.15 510.70 510.15 510.70 662.96 663.56 662.96 663.56 907.38 908.19 907.38 908.19  '71606.65 10967.78 10120.35 9210.38 7654.20 6613.91 5725.56 5266.21 4446.05 3928.35 3408.79 2477.79 "389.16 352.25 315.39 283.89 257.07 142.32 199.15 172.50  , ".'  159.91 135.99 96.03 3 9.23 316.3*9 509.60 509.60 662.36 662.36 906.56  j . ' .' . ,  :  • •  ;  ! 1  ; i , j ! , j  ;  !j  906.56 i  TABLE  *  i 520  0.6571 0.6607 0"."670 5  ! 520 " 521  95% RUN' ~NO.  J  | S | |  i  1  16 1  7  18 19 20 21 22 23 24 25 26 65 66 67 68 69 7  0  71 72 163 164 165 166  CONFIDENCE  K  ORIFTCE \  0.6597 0.6641 0.6 73 3  '  TYPE 0.6305 0.6203 0.6195 0.6201 0.6208 0.6202 0.6249 0.6281 0.6285 0.6297 0.6268 0.6285 0.5978 0.6261 0.6294 0.6339 0.6370 0.6436 0.6379 0.6750 0.6745 0.6762 0.6784  0.6545 0.6573 6.6677  I N T E R V A L FOR  95J_ CONFIDENCE INTERVAL 1.0  INCH  0.6347 0.6245 0.6236 0.6243 0.6249 0.6243 0.6291 0.6324 0.6328 0.6340 0.6311 0.6328 0.6018 0.6303 . 0.6336 0.6382 676'4r5 " 0 .6484 0 .6430 0.6795 0.6790 0.6808 6.6829  3-6  3-3 ( C O N T I N U E D ) 1102.38 1102.38 662.00  K  AND  RED  1 1 0 3 . 41 1 1 0 3 . 41 6 6 3 . 03  1101.35 1101.35 660.97  RED 95 % CONFIDENCE INTERVAL  SHARP 6799.91 0.6263 6717.33 0.6162 6188.11 0.6153 6331.71 0 .6160 "0.6166 5918.92 6084.86 0 .6160 5527.69 0.6207 0.6239 4 9 5 9 . 0 2 .. 0.6243 . . 4598.91 0.6254 4168.44 0.6225 .3 7 0 5 . 2 0 0.6243 2919.13 0.5937 . 2709.57 0.6219 2371.52 0 . 6 2 5 1 .' 2 0 7 6 . 4 6 0.6295 ' 1982.85 0;"632 5 17 2 6"." 9 5 1146.59 0.6389 745.39 0.6328 0.6704 200.80 184.65 0.6699 0.6716 171.50 0.6738 153.90  6807.44 6725.16 6195.47 6339.23 5926.51 6091.96 5534.91 4966.07 4606.06 4175.25 3 712.77 2923.10 2713.89 2374.50 2079.69 1986.66 1731.29 1150.34 748.10 201.05 184.86 171.72 154.10  6792.37 1 6709.49 ! 63 12 84 0. .1 78 6 6 5911.34 6077.76 5520.46 4951.98 4591.75 4161.63 3697.64 2915.16 .2705.25 2368.54 2073.23 1979.04 172 2 7 6 1 1142.85 742.69 200.56 184.44 171.27 15 3.71  j ! j j 1 J | ! | j : ' ! ; | j f L i  TABLE  3-4  (CONTINUED)  3-7  i i  I  RUN I NO. | " "  K .  0.6831 167 0.6887 7 168 0.6888 \i 169 0.6966 170 0.6999 I 172 ' 0.7157 • 173 • 0.7207 174 0.6787 537 0.6769 537 0.6697 538 0.6674 538 0.6626 539 £.6595 i 539 0.6564 540 1 540 0.6620 0 .6534 • 5 4 1 1 6.6595 r 541 0.6513 1 542 0 .6560 5 4 2 I 0.6490 543 [ 0.6512 543 0.6504 . i 544 r 545 0.6466 0.6468 546 0 .6461 5 4 7 ' 1 0.6449 548 }  •  !  RED  -95%  __ "  CONFIDENCE "INTERVAL ' 0.6877 0.6934 0.6936 0.7016 0.7053 0.7215 0.7337 0.6840 0..6827 0.6745 0.6722 0.6671 0.6640 0.6608 0.6677 0.6578 0.6644 0.6556 0.6606 0.6532 0.6556 0.6547 0.6509 0.6511 0.6504 0.6491  0.6784 0.6839 0.6840 0.6917 0.6945 0.7098 . 0.7077 0.6733 0.6712 0.6649 0.6626 0.6580 0.6550 0.6520 0.6563 0.6491 0.6546 0.6470 0.6515. 0.6447 . 0.6468 0.6460 0.6423 , 0.6425 0.6418 0.6406  133.88 109.24 97.52 86.29 68.15 56.38 30.20 145.28 ' 145.28 235.26 235.26 333.53 333.53 4 3 2 . 18 432.18 550.09 550.09 • 653.24 653.24 761.79 761.79 852.31 980.63 1095.83 1236.41 1382.12  95 % CONFIDENCE INTERVAL 134.06 109.41 97.69 86.45 68.32 56.46 30.32 145.82 145.82 235.89 235.89 334.14 334.14 432.89 432.89 550.82 550.82 654.11 654.11 762.64 762.64 853.26 981.69 1097.09 1237.86 1383.76  133.71 109.07 97.34 86.13 67.99 56.30 30.09 144.75 • 144.75 234.63 234.63 332.92 332.92 431.47 431.47 549.35 549.35 652.37 652.37 760.94 760.94 851.37 979.58  ,  '  ' ' , ! j . ! !  1094.58 j 1234.97 1380.48 ;  1  !  I  TABLE 95$ |  RUN~~~  CONFIDENCE  K  3-5  INTERVAL  FOR  95%  NO.  CONFIDENCE'" INTERVAL  [  ~  K  AND  RED  "RED  95%  ;  CONFIDENCE INTERVAL  ii  j  ORIFICE  \  37 38 39 40 41 42 43 44 45 46 47 48 49 50 51  fI  1  i :  ' t  I : I  53 54 55 56  5 7  184 185 186 187 188 189 1*90 191 192 193  TYPE  0.6300 0.6224 0.6248 0.6243 0.6172 0.6236 0.6245 0.6253 . 0.6257 0.6225 0.6247 0.6261 0.6282 0.6284 0.6287 0.6290 0.6273 0.6317 0.6367 0 . 6 4 6 1 -. 0.6478 0.6688 0.6753 0.6704 0.6701 0.6753 0.6783 0.6826 0.6858 0.6903 0.6894  1.5  INCH  0 «. 6 3 3 0 0«. 6 2 5 4 0«. 6 2 7 8 0<, 6 2 7 3 0. 6201 0.,6265 0.,6275 .o< , 6 2 8 2 0«, 6 2 8 7 0 «, 6 2 5 5 0 «, 6 2 7 7 o.,6291 0 ., 6 3 1 2 0<, 6 3 1 4 o., 6 3 1 7 0-, 6 3 2 0 o.,6303 o., 6 3 4 8 o., 6 3 9 8 Q« , 6 4 9 3 , 0 «, 6 5 1 8 0 «, 6 7 2 0 o., 6 7 8 5 o.,6736 0 ., 6 7 3 3 0 «, 6 7 8 5 0 «, 6 8 1 5 0 «, 6 8 5 9 o., 6 8 9 2 0 .6938 0« . 6 9 3 0  SHARP 0«, 6 2 7 0 0.,6195 0.,6219 0 ., 6 2 1 3 0 .,6142 0, , 6 2 0 6 0, , 6 2 1 5 Oi, 6 2 2 3 0, , 6 2 2 6 0, , 6 1 9 6 ' 0 ., 6 2 1 7 0 ,, 6 2 3 2 0 ,, 6 2 5 3 0 ., 6 2 5 3 0 .. 6 2 5 7 0 ., 6 2 6 0 0 .. 6 2 4 3 0 ., 6 2 8 7 0 «, 6 3 3 5 0 .. 6 4 2 8 0-,6438 0 ., 6 6 5 6 0, , 6 7 2 1 •' 0 ., 6 6 7 2 0 ,• 6 6 6 8 0<, 6 7 2 0 0 .. 6 7 5 0 0 ., 6 7 9 3 0 .. 6 8 2 4 0 .. 6 8 6 8 0 .6857  9804.79 9815.86 9495.39 9505.25 8945.35 8954.35 8481.05 8491.33 7756.71 7747.66 7124.94 7134.26 6303.56 6311.98 5727.81 5720.33 5162.66 5169.84 5129.09 .5134.87 5041.33 5047.55 4753.90 4759.35 4593.81 4588.63 4249.41 4243.25 3849.29 „ 3854.03 3650.79 3655.86 3331.77 3336.30 2942.11 2946.38 2464.44 2468.46 1779.95 1783.01 1076.96 1079.69 311.59 311.86 244.91 244.70 283.47 283.73 272.72 273.01 224.32 224.52 194.86 195.02 172.63 172.78 156.19 156.34 136.59 136.72 121.60 121.76  9793.72 ; 9485.52 . 8936.34 ! 8470.77 7738.61 7115.62 ; 6295.15 i 5 7 1 2 . 8 5 ij 5155.48 j 5123.31 ! 5035.12 ; 4748.45 i 4583.46 ! 4237.09 j 3844.54 ! •3645.71 | - 3327.23 | 2937.84 | 2460.41 j 1776.89 1074.23 ! 311.32 ; 244.50 i 283.21 j 272.44""; 224.12 ; 194.71 ; 17 2 . 4 9 ; 156.04 I •136.46 { 121.44 | : :  TABLE 3-5 (CONTINUED)  j RUN I NO. I h 194 — 195 557 557 ! 558 i 558 |_ 559 h 559 ! 560 L 560 7  ft  "56T  561 562 562 563 563 564 564 565 565  I  K  95 % CONFIDENCE ' " ~~ TNTERVAL 0.6988 0.7030 0.6946 0.7067 0.7149 0.6984 0.6724 0.6760 0.6688 0.6672 0.6711 0.6634 0.6695 0.6728 0.6662 0.6640 0.6672 0.6608 • 0.6655 0.6687 0.6623 0.6613 0.6644 0.6582 0.6560 0.6590 0.6530 0.6583 0.6631 0.6535 6.6537 0.6567 0.6507 0.6578 0.6619 0.6536 0.652O , 0.6550 0.6489 0.6519 0.6556 0.648 2 0.6516 0.6546 0.6485 0.6548 0.6583 0.6514 0.6498 0.6529 0.6467 0.6548 0.6581 0.6515 0.6520 0.6552 0.6489 0.6554 0.6586 0.6521 TABLE 3-6 95% CONFIDENCE INTERVAL FOR  RUN NO.  K  95%  CONFIDENCE / INTERVAL  RED 97.70 57.19 257.55 257.55 382.01 382.01 485.69 485.69 652.66 652.66 746.50 746.50 858.98 858.98 984.58 984.58 1150.08 1150.08 1255.43 1255.43 K AND RED  SHARP  |  7~3 : 74 75 7  "6.6140^ T.2438.10 0.6147 11411.53 0.6146 10830.65 "0.6T37 9918784  6  1  ;  :  ;  i  ORIFICE TYPE 2.0 INCH 6T6T9T 0.6195 0.6193 0Y6184'  95$ , CONFIDENCE INTERVAL" 97.85 97.54 1 57.33 57.05 • 258.06 257.04 | 258.06 257.04 382.55 381.47 ; 382.55 3 81.47 j 486.27 48 5.12 486.27 485.12 : 653.36 - 6 51.96 • ' 653.36 651.96 ' 747.16 745.84 | 747.16 745.84 859.94 858.03 j , 859.94 858.03 985.66 983.51 ; 985.66 983.51 1151.33 1148.82 | 1151.33 1148.82 j 1256.80 1254.07 : 1256.80 1254.07 j i  j  0T6T66 0.6171 0.6170 o". '6161  3-9  1  RED  I i  i  95 CONFIDENCE INTERVAL  j 1i j ;  j  12453.53 12422.68 j 11422.23, 11400.83 !10839.88 10821.42_J 9927.29 99T6739 >  TABLE  (CONTINUED)  • 95£ CONFIDENCE^ "'"INTERVAL  RUN NO. 77 ~7T 79 80 ~8f 82 _8 3_ 84 85 __86_ 172 173 174 175 176 177 T78" 179 180 181 182 183 "549" 550 550 549 551 551 "552"" 552 553_ 5"54 555 556  3-6  0.6188 "6V6T6"0"  .0.6204 0.6200 "6 ."6 2 06™ 0.6218 _0._622A 0.6207 0.6281 _0.6358_. 0".657i 0.6590 0.6597 0.6610 0.6642 0.6662 0."6727" 0.6760 0.6781 0.6846 0.6816 0.6835_ "0.6660 0.6590 0.6550 0.6579 0.6561 0.6526 076518" 0.6499 0.6465 0.6479 0.6461 0.6459 L  6212 6T84" 6227 6223 6230" 6242 6_248_ "6231 6306 6384 6 5*98" 6617 6623 6636 6669 6689 6754 6788 6812 6879 6863 692 3_ "6691 6617 6578 6617 6587 6551 6 544" 6524 649 0_ '6 564 6486 6484  0.6165 0.6137 0.6180 0.6176 "6'76183~ 0.6194 0.6200 0.6184 0.6256 _0.6332 0".6 545~ 0.6563 0.6571 0.6583 0.6616 0.6635_ "676699 0.6731 0.6750 0.6813 0.6769 0.6747 ~0".""6629"" 0.6563 0.6522 0.6540 0.6535 Oj.6 501' " 0 . 6"49~2" 0.6475 0.6440 0.6454 0.6436 0.6434  3-10 95£ CJDNFI DENCE_ " INTERVAL  RED  9016.61 7969.73 6846.89 5844.42 ""5386.lV 4708.66 _4204. 60 3345.72 2502.12 _2007.80__ 428.1*9 403.00 350.90 333.95 287.86 244.02 "20 5.64" 179.11 165.90 137.51 97.30  _ _7 6 5  8  275". 09" 400.22 400.22 275.09 518.83 518.83 62"9"."20" 629.20 795.39 713.47 914.26 1007.60  9009, 0_4_ 9024.19 7 9 6 2 . 87 7976.60 6852.71 6 8 4 1 . 07 5849.32 5 8 3 9 . 51 5 3 90.7 3" "5381". 58 4712.82 4 7 0 4 . 49 4208.31 4 2 0 0 . 89 3348.76 3 3 4 2 . 68 2505.26 2 4 9 8 . 97 _2010_.14 2 0 0 5 . 45 428.62" 4 2 7 . 75403.41 4 0 2 . 59 351.21 3 5 0 . 58 3 3 3 . 65 334.26 2 8 7 . 62 288.10 24 3. 79_ 244 25_ 20V. 45 205.84 178. 92 179.29 1 6 5 . 67 166.13 137.64 137. 38 97.42 9 7 . 19 6 5 . 70 _ » J T 7 4 . 74 2 75" .~4 4" 3 9 9 . 78 400.66 3 9 9 . 78 400.66 275.44 2 7 4 . 74 519.31 5 1 8 . 35 519.31 5 1 8 . 35 ""62 87 62" 62 9 .7 9" 6 2 8 . 62 629.79 7 9 4 . 55 796.23 714.25 7 1 2 . 69 915.11 9 1 3 . 40 1008.54 1006. 66  r  JL  6 5  8  TABLE 95% RUN NO.  CONFIDENCE INTERVAL FOR  K  ~~ 95% CONFIDENCE' INTERVAL  l r !ORIFICE  TYPE  j  0.7238 0.7173 0.7165 0.7152 0.7134 0.7068 0.7008 0.7260 0.7014 0.7140 , 0.7157 0.7167 • 0.7034 0.6975 0.6890 0.6748 0.6653 0.6559 0.6526 0.6541 0.6521 0.6492 0.6464 0.6421 0.6269 0.6258 0.6241 0.7133 0.7143 0.7160 0.7162  !  226 227 [ 228 ! 229 230 1 231 f~232  j|  233 384  r~38 3865 396 397 39P 399 400 401 ! 402 403 404 - 405 . 406 : 407 408 I '09 j 410 \ 411 j 211 . 4  ;  212  :  213 214  i  3-11  3-7  G. S.  K ~  AND  RED  !  RED 95"%'  CONFIDENCE INTERVAL  BETA = 0.2  i  0.7142 0« 7 3 3 3 0.7077 0. 7 2 6 9 7 2 6 1 0.7069 0. 7 2 4 8 0 .7056 o. 7 2 2 9 0 .7039 o. 0 .6971 7 1 6 4 o. 7 1 0 4 0 . 6911 o. 7 3 6 2 0 . 7 159 o. 0 . 6 917 o. 7 1 1 0 7 2 4 3 " 0 . 7 0 38 0« 0.7058 0. 7 2 5 7 0 .7 2 6 3 0.7070 0.6940 0. '7129 0.6881 0« 7069= 0.6797 0. 6 9 8 3 6 8 3 7 . 0 .6659 o. 6 7 4 1 0 .6566 o. 6 6 4 4 0 . 6473 o. 6 6 1 2 0 . 6440 o. 6 6 2 6 0 . 6 456 o. 6 6 0 6 0 . 6 436 o. 6 5 7 6 . 0 . 6 407 . o. 6 5 4 8 0 . 6 3 81 0« 6 5 0 5 0 . 6 3 38 o. 6 3 5 1 0 . 6 1 88 0« ,6339 0 . 6 1 77 o. 6 3 2 2 0 . 6 1 6 1 07 1 9 8 0 . 7 0 6 9 0« 0 .7078 0« 7 2 0 8 0.7095 o. 7225 6.7096 6". 7 2 2 8 ;  61.36 56.37 51.29 47.22 42.48 36.53 29.84 23.57 137.65 96.53 58.07 71.60 116.32 136.50 158.32 176.96 195.98 218.60 239.59 272.81 305.05 336.56 362.10 395.03 423.14 449.97 474.05 85.11 80.66 76.79 74.51  61.23 61.50 56.55 56.19 1 51.12 i 51.46 47.06 j 47.37 42.35 j 42.60 36.38 1 36.68 29.70 | 29.98 23.45 ! 23.69 137.02 i 138.27 97.11 95.94 i 57.79 58.34 7 1.33 : 71.86 1 1 5.89 ; 116.76 1 3 6.01 ] 137.00 1 5 7.74 ! 158.90 176.44 j 177.49 195.54 ; 196.42 218.15 j 219.05 239.04 j 240.13 272.35 273.27 304.57 305.54 335.99 j 3 3 7 . 13 361.62 i 362.58 3 9 4.43 .' 395.62 422.42 i 423.85 449.32 450.62 4 7 3.47 ; 474.63 8 4 . 9 5 ;85.28 80.82 • 8 0.49 I 76.65 i 76.92 . 74.33 j 74.70 I  |, ) RUN l_ NO. j 215 216 217 1 .2 1 8 219 if" n 220 ! 221 222 223 224 393 394 421 . 422 f 423 i. 4 2 4 ! c~42 5 425 426 427 . 428 r 429 ~430~"~ 431 432 433 i 434 435 "196 1 197 ' 198 i w 200 201 . 202 ' If  1 1  |_  r i ;  r~  L  TABLE 3-7<C0NTINUED) K  95%  -  CONFIDENCE "INTERVAL"  ~~"  RED  3-12 95%  CONFIDENCE INTYRVXL  0 . 7 1 7 5 ' 0• 7 2 4 1 0.7109 70.21 70.38 0.7161 65.84 0.7095 65.99 0 • 7227 58.57 0.7114 0 . 7 1 8 2 . 0. 7 2 5 0 58.75 52.04 0.7169 52.21 0.7101 0 .7237 0.7158 0.7093 46.84 46.92 0 .7223 .• 4 1 . 8 4 0.7152 0.7083 0 .7220 41.98 0.7136 . 7 2 0 5 0 . 7 0 6 8 , 3 6 . 1 4 36.27 0 32.81 . 7 1 8 5 0.7116 0 . 7 0 4 8 3 2 . 7 0 0 0.7091 28.97' 0.7021 29.07 0 .7160 23.76 0.7009 0.6938 23.85 0 .7081 0.7082 0 . 7 0 1 8 ' •. 9 3 . 7 9 0 .7146" 93.93 122.61 0.7035 122.30 o. .7100 0.6970 0.7049 101.41 0.6982 101.05 0 .7117 0.6909 0.6848 1 4 6 . 5 2 .. 0 .6971 146.76 186.64 0.6699 0.6760 187.04 0 .6821 0.6678 210.25 ,0.6619 210.57 0 .6737 0 . 6 4 1 1 229.65 0.6469 230.05 o"r6"52"7" 0.6626 235.23 0.6567 235.64 0 .6686 261.48 0.6558 . 6 6 1 6 0.6500 0 261.76 .0.6393 324.02 0.6451 324.57 0<, 6 5 0 9 0.6497 0.6439 296.60 297.090 .6555 0.6348 337.64 0.6292 o. ,6405 338.13 359.07 0.6736 6 •67 96" 6",685 6" 359.45 0.6437 0.6379 390.52 0 .6494 391.18 0.6381 434.90 0.6324 0 .6438 435.60 . 6 4 1 1 0 . 6 2 9 8 463.72 464.34 0.6354 o. 0.6321 0.6265: 517.12 .517.81 ,0 .6377 570.49 0.6290 0.6234 o . ,6346 571.24 0.7008 1 0 9 . 1 8 ."705 7" 109.33 0.6959 ."6. 104.76 .0.7029 0.6980 •. 1 0 4 . 8 9 0 .7078 98.88 ' 0.7035 0.6986 99.02 0 ,7084 0 . 7 0 6 4 . 0 .7X14 0.7014 . . 92.63 92.78 0 . 7 0 7 6 • •'; o.7125 0.7026 86.51 , 86.64 . 0.7099 80.50 0 .7149 • 0.7049 . 80.64 7 1 . 4 5 71.58 6 . 7 1 2 0 r -Q-.7176 6."7069 :  :  70.04 j 65.69 58.38 j 51.87 : 46.76 : 41.70 i 36.02 ; 3 2.60 i . 28.87 : 23.67 93.66 j 121.98 ; . 100.70 j 146.2 8 | 186.24 i 209.93 ! 229.24 ; 234.82 ! 261.20 ! 323.47 | . 323976..1151 |j 358.69 i 84 9. .2 80 7 ij 43 3 • 463.10 | 516.43 ! . 569.75 j ••1 10 04 9. .6 02 3 : j 98.75 ! 9 2 . 4 8 i8 6.37 I • 80.37 I  71.321  I  3-13  TABLE 3-7<C0NTINUED) 95* CONFIDENCE """INTERVAL™  RUN NO. f 203 i 204 !  20 5 206 207 208 209 210 . 387 388 i 389 | 390 : 391  I  t  3  9  2  412 . 413 ! 414 ! 415 J 415 1 4 1 6  I r  •  4  1  7  418  4  1  9  f 420  •  0.7954 0.7135 0.7143 0.7131 0.7134 0.7099 0.7009 0.6900 0.6599 0.6624 0.6705 0.6760 0.6835 0.7000 0.6902 0.6747 0.6629 0.6433 0.6542 0.6472 0.6429 0.6381 0.6360 0.6331  -  0.8011 . 0.7186 0.7194 0.7185 0.7190 0.7157' 0.7073 0.6987 0.6645 0.6670 0.6753 0.6807 . 0.6884 0.7052 0.6951 0.6794 0.6675 0.6477 0.6586 0.6516 , 0.6473 0.6425 . 6.6403 0.6374  0.7896 0.7083 0.7091 0.7077 0.7079 0.7042 0.6945 0.6812 0.6553 0.6577 0.6658 0.6712 0.6786 0.6949 0.6852 0 . 6 700 0.6584 0.6389 0.6497 0.6427 0.6385 0.6338 0.6316 0.6288  95% .  RED  •  .  64.37 49.86 64.15 45.62 40.26 34.48 27.56 17.90 241.23 218.35 194.35 174.12 150.34 100.24 137.90 185.55 225.85 263.72 268.18 302.45 333.30 369.27 401.64 427.41  _CONFIDENCE_ I NTERVAL"  '  64.51 . 49.96 64.29 45.75 40.39 34.59 27.68 17.98 241.54 218.66 194.70 174.36 , 150.65 100.45 138.19 185.87 226.19 264.04 268.50 302.82 333.67 369.66 402.12 427.89  64.24 49.75  : !  64.01 i 45.49 ! 40.14 i 3 4.36 ' 27.44 1 . 17.83 240.93 , 218.05 : 194.01 ! 173.88 1 ;  150.04 j 100.04 I 137.62 i 185.23 225.51 i 263.41 j 267.86 j . 302.08 J 332.93 | 368.87 j 401.17 426.93  I  I  TA8LE 95%  \  \  RUN NO.  CONFIDENCE  3-8  I N T E R V A L FOR  95-% CONFIDENCE INTERVAL  K  3-lU K  AND  RED  RED 95* CONFIDENCE INTERVAL  [  i  >  ! ORIFICE r 278  .279 280 281 282 [ 283 284 285 286 i— 2 8 7 : 288 289 290 335 | 336 337 338 i 339 340 341 342 343 452 453 454 455 1 it 4 5 6 457 458 459 460 1  r I i  j i  j  •  TYPE 0.7139 0.7167 0.7180 0.7190 0.7208 0.7228 0.7229 0.7213 0.7185 0.7000 0.7197 0.6943 0.6786 0.6994 0.7016 0.7043 0.7070 0.7101 0.7136 0.7176 0.7197 0.7142 0.9785 0.6877 0.6830 0.6918 0.6763 0.6729 0.6647 0.6607 0.6620  G .S.  ' BETA= 0.4  6T7188" 0.7215 0.7229 0.7238 0.7257 0.7277 0.7279 0.7265 0.7239 0.7055 0.7256 0.7007 0.6904 0.7042 0.7064 0.7090 0.7118 0.7150 0.7185 0.7226 0.7248 0.7194 0.9853 0.6924  "0V6876  • 0.6964 0.6808 0.6774 0.6692 0.6651 "'"0.666'5"  0.7091 0.7119 0.7132 0.7141 0.7158 0.7179 0.7178 0.7162 0.7132 0.6945 0.7137 0.6880 0.6667 0.6946 0.6968 0.6995 0.7021 0.7051 0.7086 0.7125 0.7145 0.7089 0.9716 0.6830 0.6784 0.6872 0.6718 0.6684 0.6603 0.6563 . 0.6576  203.62 186.42 172.33 158.10 139.34 116.23 100.66 85.06 73.41 54.29 50.74 41.82 25.05 331.74 317.44 285.37 260.99 230.09 200.43 179.89 148.41 118.62 403.45 374.82 466.74 371.20 550.00 605.94 759.65 867.73 . 985". 50  203.88  186.58 172.56 158.27 139.54 116.35 100.84 85.23 73.61 54.39 50.86 41.91 25.12 332.22 317.92 285.67 261.34 230.54 200.81 180.27 148.73 • 118.90 404,27 375.55 467.58 371.72 550.82 606.80 760.78 868.80 986.73  203.35 , 186.25 172.10! 157.93 139.14 116.12 100.48 i 84.89 i 73.22| 54.19; 50.61> 41.73! 24.97, 331.25| 316.96! 2 8 5.07| 260.64; 229.63i 200.06; 179.52 i 148.081 118.35: 402.63 1  374.09 i 4 6 5.891 370.67J 549.18 I 605.09' 758.53J866.66 984.26  TABLE  3-8<CONTINUED>  3-15* |  • K  RUN NO,  461 462 463 496 496 497 497 498 498 499 500 500 500 501 502 503 504 291 292 293 294 295 296 297 298 299 300 301 302 327 327 328 328 329 330  1  95 # CONFIDENCE INTERVAL  0,7476 0 .7527 0.6784 0 .6829 0,6505 0 .6549 0.7104 0 .7156 0.7036 0 .'708 8'" 0.6889 0 .6937 0.6865 0 .6912 0.6751 0 .6796 0.6831 0 ,6883 0.6693 0 .6737 0.6719 0 ,"6767 0.6619 0 .6663 0.6667 0 .6713 0.6634 0 .6679 0.6640 0 • 6684 0.6553 0 .6597 0.6498 0 .6542 0.5983 0 .6007 0.6977 0 ,7005 0.6997 0 .7025 0.7056 0«,7084 0.7088 0 ,7116 0.7142 0 .7170 0.7155 0 .7184 0.7192 o.,7222 0.7220 0 • 7253 0.7237 0 ,7273 0.7253 0 .7298 0.7456 0 .7534 0.7265 0 .7330 0.7237 0 .7374 0.7196 0 • 7232 0.7088 ' 0 .7136 0.7215 0 ,7264 0.7146 0«.7177.  95$  RED  "  0.7425 0.6739 0.6462 0.7052 0.6983 0.6841 0.6818 0.6706 0.6779 0.6648 0.6672 0.6574 0.6621 0.6590 0.6596 0.6509 0.6455 0.5959 0.6949 0.6969 0.7028 0.7060 0.7113 0.7126 0.7162 0.7186 0.7201 0.7208 0.7378 0.7201 0.7100 0.7159 0.7040 0.7166 0.7115  ;  i  CONFIDENCE " INTERVAL "  1275.14 ! 1276.92 1278,69 1290.18 1291.58 1288.77 | 1396.27 j 1397.93 1399,59 210.29 i 210.85 211.42 210.29 210.85 211,42 417.73 418.54 419.34 418.54 417.73 ! 419.34 580.68 ' 581.53 582.38 580.68 581.53 582.38 664.59 1 • 665.31 "\ 666.0 2 665.31 666.02 664.59 j 854.14 j 855.50 856.86 854.14 855.50 856.86 862.45 i 863.51 864.58 954.64 955.68 953.60 j 1062.88 1061.49 ! 1064.27 1162.73 j 1164.00 ' 1165.27 336.02 336.37 335.66 , 368.35 ! 368.70 369,05 331.71 332.03 331.38 j 281.64 j 281.87 282.11 .' 252.29 252.07 j 252.51 225.03 225.24 224.82 203.61 203.42 j 203.80 180.14 179.92 ' 180.35 148.91 149.15 148.67 i 120.58 . 120.45 120.72 95.76 9 5.66 j 95.86 70.16 . 70.09 j 70.23 . 78.70 78.52 j 78.88 78.69 78.51 i 78.88 191.95 191.70 . 192.20 191.95 191.70 192.20 143.33 j 143.53 143.74 239.19 238.98 238.77 j :  :  t  ;  TABLE RUN NO_  !  K  0o7108  329  3-8(CONTINUED)  95% _____ C O N F I D E N C E ^ INTERVAL 0.7157  0.7058  RED  95% CONFIDENCE INTERVAL  143.53  143.74  143.33  330  0o7047  0.7094  0.7000  238.98  2 3 9 . 1 9  2 3 8 . 7 7  331  0 . 7 0 9 6  0.7126  0.7066  2 8 6 . 1 7  286.51  2 8 5 . 8 4  331  0 . 6 9 9 6  0.7043  0 . 6 9 4 9  286.17  286.51  2 8 5 . 8 4  I "3 32". "  0 . 7 0 4 2  0.7071  0 . 7 0 1 4  318.67  3 1 8 , 9 7  3 1 8 . 3 6  i  0 . 6 9 5 6  0.7002  0.6909  0 . 6 9 4 7  0.6975  0.6919  3  3  1f 1  2  334 334  '  318.67  3 1 8 . 9 7  3 1 8 . 3 6  404.51  4 0 4 , 9 3  4 0 4 . 0 9  0.6850  0.6896  0.6803  404.51  4 0 4 . 9 3  4 0 4 . 0 9  344  0 . 9 3 1 4  0.9379  0.9249  179.07  179.33  178.81  344 345  0 . 9 1 7 4  0.9238  0 . 9 2 1 5  0.9260  0 . 9 1 7 0  345  0.9168  0.9230  346  0 . 7 8 4 5  0 . 7 8 7 9  0.7469  0.7520  \  1 4~4 7 34  6  .  .  179.07  0.9110  .  179.33  178.81  249.13  2 4 9 . 4 2  2 4 8 , 8 4  0.9105  249.  249.42  2 4 8 . 8 4  0 . 7 8 1 2  318.97  319.41  3 1 8 , 5 4  ;  3 1 8 . 9 7  3 1 9 . 4 1  3 1 8 . 5 4  i •  0.7418  13  ,  0 . 9 2 7 7  0.9315  0.9238  6 7 6 . 3 0  6 7 4 . 9 4  i  675.62  0.9498  0.9549  0.9446  4 6 8 . 9 5  4 6 9 . 4 7  4 6 8 . 4 4  |  0 . 9 1 9 6  0.9233  0 . 9 1 6 0  813.82  8 1 4 . 6 0  8 1 3 . 0 4  •  0 . 9 1 4 5  0.9109  8 8 9 . 7 6  8 9 0 . 5 7  8 8 8 . 9 5  i  I  0.9180  0 . 9 1 2 2  0 . 9 1 5 7  0.9087  1036.19  1037.09  1035.29  i  0 . 9 0 9 3  0.9128  0.9058  1142.35  1143.31  1141.40  ;  2 6 3 . 9 7  2 6 3 . 2 4  |  446 """"448  1  450 451  '  J  488  0 . 6 9 7 5  0.7011  0.6940  263.61  I  288  0 . 6 8 7 4  0.6921  0 . 6 8 2 7  263.61  2 6 3 . 9 7  2 6 3 . 2 4  !  2 7 1 . 3 6 2 7 1 . 3 6  j j ,  .  1  289  0 . 7 0 4 1  0.7076*"  077005  271.72  272.08  )  289  0 . 6 9 3 1  0.6976  s  0 . 6 8 8 5  j  271.72  272.08  0 . 6 9 6 2  0.6991  s  0 . 6 9 3 2  376.22  376.60  3 7 5 . 8 4  ;  490 490  0 . 6 8 9 7  0 . 6 9 2 9  0.6865  376.22  376.60  3 7 5.84  :  4 9 i  0 . 6 7 7 2  0.6799  0.6745  581.04  5 8 1 . 6 3  58 0 . 4 4  1  :  491  0.6741  0.6767  0.6714  581.04  581.63  5 8 0.44  .:  f f I  492  0.6720  0.6747""  0 . 6 6 9 3  6 6 7 . 0 1  6 6 7 . 7 0  6 6 6 . 3 2  ,  0.6709  0.6658  6 6 7 . 0 1  6 6 7 . 7 0  6 6 6 . 3 2  i  493  0.6658  0.6683  0.6632  795.39  7 9 6 . 1 9  7 9 4 . 5 9  j  |  493  0.6738  0.6793  0 . 6 6 8 2  795.39  796.  7 9 4 . 5 9  i  494 494  0 . 6 6 0 1  0.6626  0.6576  9 1 5 . 2 1  9 1 6 . 0 3  i-  915.21  9 1 6 . 0 3  9 1 4 . 3 9 9 1 4 . 3 9  495  0 . 6 5 8 3  I. "  492  •  0 . 6 6 8 4  0.6579  0  .6621  "6"."6~66"8"  0.6536 0".6558\  1  1629.21  19  loso.ii .  f 6 2 8 . 30"  !  3-17  TABLE 3-8(C0NTINUED) RUN NO, 495  ~3~0T  304 __305 I 306" I 307 i 308 309" 310 i  312 313 \ 314 J  I  95%  jCONFIDENCE "INTERVAL "  0.6622  6659 7066 0 . 7 0 5 4 7088 0 . 7 0 7 0 7105_ "o77108" 7142 0 . 7 1 4 7 7181 _0o7l84 7219 0.7190" .7226 . 0 . 7 2 1 9 .7256 0.7243 0 .7282 "bV7238"' 0 .7278 0.7227 0 .7276 0.7151 0 .7232 6934 0.6901 6971 0.6937 7013 0.6979 "7052" Oo "7618" 7097 0.7062 0.7123 0 7159 0.7173 7209 0.7198 0 7238 0.7244 0 7291 0.7205 7323" 0.6884 6918 0.6928 6962 0.7040 0 7092 0.7104 0 7156 0.7152 0 7204 0".'7176 0 722 9" 0.7258 0 7312 0.7444 Q 751 2 0.6944 6 '7007 0.7284 0 7416 0.7226 0 7270 0".To'87~ 0 0.7032"  Yl~4b"  0.6584 0.6998 0.7020 0.7036 "0770 7 4* 0.7112 0.7150 0.7155. 0.7182 0.7204 0.7197 0.7179 0.7071 0.6867 0.6904 0.6945 "b".6"98 5~ 0.702 7 0.7087 0.7137 0.7159 _0 .7197 oT7o"86~ 0 .6851 0.6894 0.6989 0.7051 0.7100 "077 12 3" 0.7204 _?j_7 37__ 0.6881 0.7152 0.7181 "67"70"34"  RED 1029.21 300.94 283.29 260.44_ "236". 74 206.74 179.56 159.70 130.89 111.85 99.09 77.55 51.05 442.42 398.75 361.42 "319790*" 263.33 238.30 209.49 166.05 _128o_90  6~67  55"  4 4 2 . 6 3 4 1 1 . 3 4  263.33 238.30 209.45 T6"6"."0"5" 128.90 __66__55 63.87" 63.87 140.19 "1*40". 1~9"  95% CONFJDENCE_ INTERVAL 1030.11 301.22 283.53 260.66_ "23 6. 94 206.93 179.71 159.89 131.04 112.02 99.20 77.68 51.10  1028.30 300.66 283.04 _260.21 236."55~ 206.56 179.42 159.51 : 130.74 111.67 ; 9 8.98 77.42 i 5 0.99 4 4 2 . 7 9 442 .06 | 399.10' 398 .41 361 . 8 4 . 3_61 • 01_ "320"o'l9 "3 19"."61 2 6 3 . 6 4 263 .02 238.63 237.96 209.69 209.29 166.29 165 • 81 J.29. 10 12 8 •I? 66".74" 6~6.37" 443.13 442 .14 411.87 410 .82 263.64 263.02 ; 238.63 237.96 i 2 09_>66_ _20 9.25_J "166.29 16"5"78 "i j 129.lo 128 .70 | 66.74 66 .37 ; 64.08 63 .67 64.08 63 .67 140.46 13 9.93 "14*6746"" 1"3 ' "9"793" 1  TABLE RUN NO, 349 349 350 350 ~3 5 1 " 352 _353_ 354 355 _3 56 357" 358 j437_ 4 38 439 _440_ 441 442 443 444 445 479 f 479" 480 _ 480 "48"1" 481 _482 "483" 483 4 8 4_ 484 485 485 ~486"  3  RED  95%  CONFIDENCE^ "INTERVAL 7157 0 , 70 5 8" 0 , 7100 0 , 7021 "6 m7 0 4 7 " o. 7004 o. 6956 0 . 6960 0 , 6934 0 . 6913 ~07 6 8 9 6 " Oo 6 8 9 8 Oo 9 6 6 6 _ "o. 9 536 0 . 9467 Oo 9 4 0 6 " o . 93 74" 0 . 9340 0 . 9362_ 0 . 935 3 o. 7878 0 . 7143 Oo 7 0 5 3 " 0 . 6957 Oo 6 9 2 0 _ o. 6868 Oo 6 8 5 0 0 . 6768 "Oo 6 6 8 5 " 0 . 6810 0 . 6649_ Oo 6 7 1 9 0 . 6594 0 . 6612 ~o. 6 5 7 3 "  _?_• 7 1 9 5 0o7110 0.7136 0.7072 "6.708 2" 0.7038 0.6990 0.6994 0.6968 _0.6947_ 0.692 9 0 .6932 0.9720 0.9583 0.9512 0.9450_ "o"o"94~19 0.9384 Qo9406 0.9398 0.7916 0.7181_  "o77695 0.6991 0.6954  0.6902 0.6882 0.6800 "0.6716"' 0.6857 0.6760 0.6625 0.6648 "0."6604~  3-18  3-8(C0NTINUED)  0o7119 Oo7006 0.7064 0.6970 "0~."7'oT2" 0.6969 0 .6921 0 .6926 0.6900 0.6879_ ~0"o6862 0.6864 0o9612 0.9489 0.9422 0_«93_61 " 0 . 9 33"0~ 0.9296 0.9317 0.9307 0.7840 0_. 7 1 0 4_  "0 ."7611  0 .6923 0.6887 0.6834 0.6817 0o6736_ 0"."6653 0 o6764 0.6617 0.6678 0.6563 0.6577 "6".'6"541"  95%  CONFIDENCE INTERVAL 194.79 194.79 239.89 239.89 "281.77" 327.84 J_54__40_ 375.89 394.78 411.20 "4 32 7 3 9 " 441.65 402.29 580.49 685.97 8 32.95 "94 5"773~ 1100.91 1032.21 1194.11 1142.75 _245.79 2 4 57"79"" 382.68 382.68 496.48 496.48 5811.04 "702 .98"" 702.98 796.80 796.80 946.59 946_. 59  TO  75  710"  195.07 195.07 240.18 240.18  "28 2".T"2~ 328.23 354.89 3"76.31 395.21 411.68_ "432".'84 4 4 2 . 15 402.87 581.24 686.67 J33.JB0 946.71" 1102.00 1033.27 1195.58 1144.08 __246.21_ 2 4 6 721 383.14 383.14 497.09 497.09 581 73_ "7 03 . 78 703.78 797.84 797.84 947.62 947.62 TO 7 6 . 27" JL  194.51 l 9 " 4 . 51 2 3 9 . 59 23 9_. 59_ "281." 43 3 2 7 . 44 3 5 3 . 91 3 7 5 . 46 3 9 4 . 36 4 1 0 . 72_ "43 l". 9 5 4 4 1 . 16 4 0 1 . 70 5 7 9 . 73 6 8 5 . 27 8 3 2 . 10 ""9V4." 7 5 " 1 0 9 9 . 82 1 0 3 1 . 16 1 1 9 2 . 64 1 1 4 1 . 42 _ _ 2 4 5 . 36 2 4 5 « 36" 3 8 2 . 22 3 8 2 . 22 4 9 5 . 87 4 9 5 o 87 _5 8 0 . 3_5 70 27 19" 7 0 2 . 19 7 9 5 . 75 7 9 5 . 75 9 4 5 . 56 9 4 5 o 56 I T0'7 3~." "9'2~j :  f  TABLE  Ii  95$ • CONFIDENCE INTERVAL  RUN NO. 486 ~4~87~ 487  0j_6611 "0T6530 0.6586  0_6645 "0T656T 0.6619  3-19  3-8(CONTINUED>  0.6576 0.6499 0.6553  RED  1075.10 1164.74 1164.74  95$ _CONF I DENCE__ •INTERVAL" 1076.27 1165.91 1165.91  1073.92 1163.57 1163.57  TABLE  3-9  1-  1.  r  95  i  !  1 i  \  ris ,i ,*  l i r >*  j  *  TYPE  •  K  AND  1 i i  RED 95%  RED  ;  CONFIDENCE  INTERVAL  INTERVAL  BETA=0.6  235  0o8126 0 . 8 1 7 5  0.8214  237  0 . 8 1 5 7  0.8196  238  0 . 8 0 8 5  0 . 8 1 2 4  239  0.8052  0 . 8 0 9 0  0.8165 •  ;  4 7 6 . 4 1  ;  0.8088  476.85  4 7 7 . 2 9  0  .8136  4 5 3 . 1 1  4 5 3 . 5 5  0 . 8 1 1 8  4 1 6 . 4 3  4 1 6 . 8 4  4 5 2 . 6 7 i 4 1 6 . 0 1 1  0.8047  363.93  364.22  3 6 3 . 6 3  0.8013  312.23  3 1 2 . 4 9  3 1 1 . 9 7  ;  240  0.8139  0.8178  0.8099  2 8 7 . 5 7  287.88  2 8 7 . 2 6  i  241  0 . 8 1 6 1  0.8202  0 . 8 1 2 1  246.16  246.45  2 4 5 . 8 7  .  0 . 8 2 1 1  0.8128  219.56  2 1 9 . 8 3  0.  0.8113  193.10  193.38  242  0 . 8 1 6 9  243  0 . 8 1 5 6  .  8200  2 1 9 . 2 9  i  1 9 2 . 8 3  j  244  0 . 8 1 8 6  0.8233  0 . 8 1 3 9  156.73  156.93  245  0 . 8 1 0 3  0.8158  0.8048  126.32  126.53  246  0 . 7 9 1 4  0.7996  0 . 7 8 3 2  8 9 . 5 7  8 9 . 7 8  8 9 . 3 7  275.22  2 7 4 . 4 9  247  0.8150  0.8190  0.8109  274.86  0.8168  0.8208  0.8128  314.89  315.25  377  0.7810  0.7885  0.7736  142.64  142.90  3 1 4 . 5 4 142.38  378  0.7992  0.8037  0.7946  246.39  246.81  2 4 5 . 9 6  ;  379  0.8159  0.8201  0 . 8 1 1 7  308.15  3 0 8 . 5 6  3 0 7 . 7 4  '  380  0.8098  0.8138  0.8058  3 8 6 . 1 7  3 8 6 . 6 3  381  0.8128  0 . 8 i 6 7  0.8088  4 3 7 . 4 9  4 3 7 . 9 2  3 8 5 . 7 1 4 3 7 . 0 5  I •  382  0.8072  0.8111  0.8033  498.52  4 9 9 . 1 0  4 9 7 . 9 4  :  383  0.8053  0.8092  0.8014  540.58  5 4 1 . 2 0  5 3 9 . 9 6  ;  0.8078  0.8125  0.8031  312.02  312.45  3 1 1 . 6 0  ;  0 . 8 1 1 7  0.8157  0.8076  6 3 3 . 5 4  6 3 4 . 5 3  604  0.7940  0.7979  0.7901  881.16  882.33  605  0.7809  0.7845  0 . 7 7 7 2  1120.07  1121.29  1118.85  |  0 . 7 7 3 2  0.7768  0.7697  1327.22  1328.43  1326.02  ;'  0.7679  0.7715  0.7642  1454.81  1456.39  1 4 5 3 . 2 2 !  608  0.7588  •0.7624  0.7552  1714.03  1715.68  1712.38  609  0 . 7 5 4 7  0.7583  0 . 7 5 1 1  1799.72  1801.50  610  0.7818  0.7854  0.7781  1106.50  1107.70  0.7668  1345.38  1346.8 5  603  607  •'"611  .  '  0 . 7 7 0 4 '  ""0.7740"  '  156.52 i 126.11 1  248  606  I:  G . S .  FOR  CONFIDENCE  236  !— .  INTERVAL 95 %  NO.  602  .  CONFIDENCE  K  RUN  i I 1 i ORIFICE ti  %  i  !  6 3 2 . 5 5 j 8 7 9 . 9 8 ;  ,  1 7 9 7 . 9 4 L 1 1 0 5 . 2 9 i  —~1343  .'921  TABLE 3-9 (CONTINUED) [ RUN ? NO. \  """""''""" ~  612 613 614 657 658 658 659 659 660 660 661 661 662 662 663 663 664 664 665 665 666 666 667 667 668 668 669 669 670 670 263 264 265 266 267  0.8110 0.7977 0.7992 0.6983 0.8131 0.8129 0.8042 0.8047 0.8024 0.7968 6.8174 0.8175 0.8142 0.8157 0.8144 0.8111 0.8090 0.8106 0.8081 0.8086 0.8049 0.8021 0.8028 0.7930 0.7940 0.7951 0.8258 0.7954 0.8188 0.8078 0.8101' 0.8120 0.8135 0.8139 0.8192  It  r 1  \ \ f  j  ! 1  t— i  1 i  t  \ \  l  f i  }  i  L  _____  i  j t*i  K  95$ ^CONFIDENCE ""INTERVAL"'  ' RED  __  •  0.8154 0.8065 429.73 0.8020 0.7934 780.21 . 754.60 0.8032 '. 0.7952 0.7034 0.6932 87.96 " 6 7 8 1 88 0.8073 194.53 0.8170 0.8089 194.53 0.8099 0.7986 133.75 0.8092 0.8002 133.75 0.8081 0.7967 116.00 0.8018 0.7918 116.00 0.8214 0.8134 243.73 0.8215 0.8134 243.73 0.8182 0.8102 284.45 0.8196 0.8118 284.45 0.8184 0.8104 348.38 . 0.8149 0.8073 348.38 0.8128 0.8053 455.62 0.8167 0.8045 455.62 0.8119. 0.8044 453.90 0.8146 0.8026 453.90 0.8011 532.35 0. 8087 0.8071 0.7971 532.35 0.8065 0.7991 574.61 0.7976 0.7885 • 574.61 0.7977 0.7902 608.10 0.7995 0.7906 608.10 0.8323' 0.8193 86.56 0.8023 0.7884' 86.56 0.8248 0.8129 113.64 0.8129 0.8027 113.64 0.8132 0.8071 . 585.54 0.8151 0.8089 550.82 0.8166 0.8105 519.25 0.8170 0.8109 475.03 0.8222 0.8161 . 436.00  95$ CONFIDENCE "INTERVAL 430.70 782.03 755.83 88.12 194.74 194.74 1 33.89 133.89 116.16 116.16 244.01 244.01 284.81 284.81 348.79 348.79 456.13 456.13 454.37 454.37 532.96 532.96 5 75.7i6  575.16 608.76 608.76 86.82 86.82 113.84 113.84 586.07 551.35 519.70 475.44 436.39  428.76 778.38 753.37 i 87.81 \ 194.31 : 194.31 l 133.62 •! 13 3.62 ; 115.85 ' 115.85 : 243.45 243.45 : 284.10 ; 284.10 347.98 347.98 455.12 ! 455.12 i 45 3.42 : 453.42 j 531.74 ; 531.74 ! 574.05 | 574.05 ; 607.43 | • 607.43 | 86.30 ; 86.30 ! ;  llT.45 !  113.45 | 585.02 ' 5 5 0.29 f 518.80 474.61 i 435.61 j ;  TABLE 3 - 9 (CONTINUED) • ; RUN (__NO. \ ' "  K "  95%"  ___CONFIDENCE___ " INTERVAL"  "  RED  3-22 95%  CONFIDENCE '"TNYERVAL  j  j j  0o8193  0.8224  0.8162  391.71  392.04  269  0o8226  0.8258  0.8195  369.19  369.52  3 6 8 . 8 6  .  'l 2 7 0  0o8255  0.8287  0  341.25  3 4 0 . 9 2  :  if  341.58  271  0o8265  0.8300  0.8231  309.25  309.66  308.85  i  272  0.8274  0.8309  0.8239  278.61  278.89  278.33  1  273  0.8276  0.8315  0.8238  238.98  239.22  2 3 8 . 7 4  274  0.8271  0.8313  0  217.27  217.46  217.08  275  0.8162  0.8210  0.8113  185.55  185.71  276  0.8255  0.8318  0.8192  157.26  157.44  371 •"372  0.7994  0.8120  0.7867  158.44  158.67  0*.'80 5 2  0.8117  0.7987  235.34  235.64  2 3 5 . 0 3  !  373  0.8179  0.8224  0.8134  317.19  317.56  316.82  J  374  0 . 8 1 7 5  0.8211  0.8139  415.41  415.83  4 1 4 . 9 9  ;  375  0.8146  0.8180  0.8112  472.23  472.76  ' 4 7 1 . 7 0  376  0.8128  0.8160  0.8096  553.62  554.23  553.01  636  0.8144  0.8190  0.8098  415.44  416.11  4 1 4 . 7 6  ;  637  0.8129  0.8165  0.8093  562.41  563.21  561.61  !  638  0.8056  0.8087  0.8025  744.71  745.43  7 4 3 . 9 9  !  639  0.7998  0.8028  0.7968  872.58  873.39  871.78  1  640  0.7934  0.7965  0.7904  1009.32  1010.39  1008.26  ;  641 .  0.7868  0.7898  0.7838  1108.80  1109.83  1107.76  :  642  0.7845  0.7874  0.7816  1237.54  1238.57  1236.50  !  643  0.7776  0.7804  0.7747  1337.40  1338.72  1336.07  j  819.93  ;'  fI— 2 6 8 ! >\  | f t  L i |  L i IS  S  i  | } 1 (  i •  644  .  0.8007  .8223  .8230  -  391.38  ;  185.39 • •  157.09  ,  15 8 . 2 2  i  ;  0.8038  0.7976  820.84  821.75  699  0.8098  ' 0 . 8 1 5 7  0.8039  90.03  90.12  8 9 . 9 4i  699  0.7929  0.8027  0.7831  90.03  9 0 . 12  8 9 . 9 4  :  700  0.8394  0.8452  0.8336  109.82  109.94  109.71  ]  700  0.8052  0 . 8 1 2 7  109,82  109.94  109.71  i  701  0.8286  0.8340  0.8233  156.34  156.52  1 5 6.17"""""  701  0.8206  0.8254  0.8158  156.34  156.52  156.17-  702  0.8226  0.8260  0.8192  240.35  240.61  '240.0.9  f  702  0.8268  0.8226  240.35  2 4 0 . 6 1 •  2 4 0 . 0 9  i  703  0.8232  0.8310 0.8264  0.8201  316.53  316.84  3 1 6 . 2 3  703  0.8211  0.8244  0.8179  316.53  316.84  316.23  "704  0.8207  354.33  3 5 3. 72  "  6".8237  .  .  0.7977  "0"."8T76""~  354.03  "  .  !  |  ~j  TABLE 3-9 (CONTINUED) I  RUN NO.J  i  """  r  704  [7"705  705 i 706 r 706 249 250 251 252 253 254 1 255 f 256 1 257 258 259 260 261 1 262 359 359 360 I 360 t 361 361 363 363 ' 366 r8 366 367 1 367 i 368 I 368 369 370 J  1  :t  1  i,  3-23 ]  95% RED 95% CONFIDENCE__ ; CONFIDENCE " "~ * "'INTERVAL" " " INTERVAL 0.8205 0.8236 0.8174 354.03 354.33 353.72 ! 0.8158 0.8189 0.8128 420.81 421.15 420.48 i 0.8135 0.8164. 0.8106 420.81 421.15 42 0.48 ! 0.8170 0.8201 0.8140 488.01 488.40 487.61 : 0.8118 0.8147 0.8090 488.01 488.40 487.61 i 0.8183 0.8212 0.8154 .474.53 474.95 474.11 ' 0.8204 0.8233 470.24 470.66 0 .8176 469.83 i 0.8711 0.8744 • 0.8679 432.53 432.94 432.13 ! 0.8206 0.8236 0.8176 407.00 407.38 406.61 0.8225 0.8255 395.64 396.01 395.26 0 .8194 0"«8276~ 0.8214 379.39 379.73 0".824 5 379.05 ; 0.8137 0.8169 .0.8105 • 350.63 350.94 350.31 ' 0.8234 0.8267 0.8201 343.59 343.89 343.29 1 0.8303 0.8339 0.8266 311.31 • .. 311.62 311.00 ' 0.8249 0.8290 0.8209 282.52 282.80 282.24 j 0.8108 0.8155 0.8062 242.21 242.41 242.01 « 0.8142 0.8218 0.8067 180.09 180.26 179.92 ; 0.8186 0.8320 0.8052 134.53 134.68 134.38 ! 0.7790 0.8424 0.7157 56.62 56.69 56.56 i 0.8141 0.8320 0.7962 175.37 175.60 17 5.13 i 0.8280 0.8356 0.8204 175.37 175.60 175.13 r 0.8245 0.8349 . 0.8142 237.33 237.56 237,10 i 0.8236 0.8295 0.8177 237.33 237.56 237.10 \ 0.8196 0.8256 0.8137 324.81 325. 19 324.42 : 0.8192 0.8246 0.8138 324.81 325.19 324.42 i 0.8186 0.8221 0.8151 503.05 503.63 502.48 , 0.8194 0.8247 0.8142 ' 503.05 503.63 502.48 ! 0.8173 0.8209 0.8137 487.72 488.33 487.11 ; 0.8114 487.72 488.33 0.8 167""" 0.8062 487.11 ; 0.8251 0.8286 0.8216 568.03 568.85 567.20 ! 0.8139 0.8192 0.8086 568.03 568.85 567.20 1 0.8127 342.29 342.66 0.8180 • 0.8233 341.91 !• ' 0.8125 0.8178 0.8073 342.29 342.66 341.91 j0.8075 277.31 277.73 0.8130 • 0.8186 276.90 ! 0.7921 0.7989 0.7854 178.86 179. 10 178.62 |  K  ;  TABLE  I  j  I>  671 672  •  f( 667723 "' I 673 I 674  674 675 t 675 | 676  { Sll 611 '  i  678 678  1.0884 1.0740 1.1868 1.1547 1.0672 1.0760 1.1494 1.168 2 1.0553 1.0501 1.1195 1.1101 1.0407 1*0364 1.0995 1.0930 1.0269' 1.0231 1.0788 1.0840 l 7 0 214""~" 1 . 0 2 5 2 1.0214 1.0252. 0.8055 0.8106 0.8183 0.8147 0.7991 0.8021 0.7981 0.8009 "0.7907 0.7880 0.8078 0.7922 0.8619 0.8503 0.8665 0.8726 0.8094 0.8182 0.8376 0.8429 0.8231 ~0.8 28 0" 0.8394 0.8445 0.8329 - 0.8367 0.8268 0.8318 0.8288 0.8252 0.8461 0.8512 0.8 363" 0.8331 0.8293 0.8343 0.8063 0.8112 0.8293 0.8264 0.8297 0.8325 0.8299 0.8267  3-2U  (CONTINUED)  95 % ' CONFIDENCE INTERVAL  RUN L. NO o 578 578 > 579 '. 5 7 9 • 580 • 580 } 581 581 582 582 ! "583 ' 583 1 615 ij 6 1 6 617 • 618 619 620 1 621 I 671  3-9  RED  1.0596 1.1225 1.0584 1.1307 1.0448 1.1008 1.0321 1.0865. 1.0192 1.0736 1.0176 1.0176 0.8003 0.8112 0.7960 0.7953 0.7853, 0.7765 0 .8388 0.8603 0.8005 0.8324 0.8181 0.8342 0.8291 0.8217 0.8216 0.8409' 0.8299 0.8243 0.8015 0.8235 0.8268 0.8236 ;  418.10 418.10 548.86 548.86 754.23 754.23 921.18 921.18 1072.41 1072.41 1131.88 1131.88 467.22 650.34 796.33 944.18 1066.81 246.45 322.77 138.51 138.51 201.31 201.31 234.53 234.53 250.51 250.51 301.04 301.04 310.11 351.51 351.51 394.29 394.29  95% CONFIDENCE INTERVAL 418.72 418.72 549.72 549.72 754.99 754.99 922.09 922.09 1073.41 1073.41 1132.91 1132.91 467,77 . 651.02 797.12' • 945.00 1067.74 ' 246.86 3 2 3 ,17 138.67 . 138.67 201.53 201.53 234.78 234.78 250.75 250.75 • 301.31 301.31 310.37 351.79 351.79 394.60 394.60  417.48 417.48 548.01 548.01 753.47 753.47 920.27 920.27 1071.41 1071.41 113 0.85 1130.85 466.68 649.65 795.54 943.37 106"5 7 8 8 246.05 322.38 138.35 138.35 201.09 201.09 234.28 2 3 4.28 250.27 250.27 300.77 • 300.77 309.85 351.22 351.22 393.98 393,98  !  ; i ' i I 1  : • ; : : i : ; : ;  ! ! •' ! ]  i; 1  j : ; | ; 1  j  TABLE 3 - 1 0 95% RUN" NO,  CONFIDENCE  " K  622  0 » 7 0 2 7  i  623  i  624 625  i  1 i— 8 l'  FOR  K  AND RED  RED  95%"~  95%  CONFIDENCE" INTERVAL  i TYPE l ORIFICE ;ii 3  INTERVAL  3-25  SPECIAL 1 5  CONFIDENCE INTERVAL  BETA=0 . 4 1 266.71  267.36  2 6 6 . 0 7  :  0.6679  635.33  636.32  6 3 4 . 3 4  '.  0.6898  261.27  260.93  i  0.6840  345.90  261.60 346.37  345.43  i  4 3 3 . 3 4  4 3 2 . 2 0  !  550,55  549.20  !  0.7066  0.6988  0o6711  0.6744  0o6933  0.'696 8  0 » 6 8 7 4  0.6908  626  0o6839  0o6873  0.6806  432.77  627  0 » 6 7 2 2  0.6753  0.6690  549.88  *  628  0o6685  0o6717  0.6653  665.13  666•00  664Y26  !  i I  629  0.6640  0.6671  0.6609  799.88  800,65  799.11  \  630  O066IO  0.6642  0.6579  912.00  9 1 0 . 9 4  •  j  631  0.6585  0.6617  0.6554  1040.52  913.06 .  1041.59  1039.46  632  0o6582  0.6613  0.6550  . 1 1 6 4 . 9 1  1166.13  1163.68  f  633  0.6571  0.6603  0.6539  1177,14  1178.51  1175.77 1  |  634  0 » 6 5 8 6  0.6619  0.6553  1 2 2 0~. i"6  1221.53  1218.78  635  0.6835  0.6869  0.6802  411.95  412.52  411.38  687  0.7311  0.7366  0.7256  60.22  60.36  6 0 . 0 7  687  0.7148  0.7200  0.7096  60.22  6 0 . 3 6  6 0 . 0 7  |  688  0.7157  0.7208  0.7106  93.42  9 3 . 5 7  9 3.28  i  688  0.7172  0.7210  0.7133  93.42  93.57  93.28  !  689  0.7072  0.7107  0.7037  170.81  171.04  !  1 1i  L i  1 f f if  J  |  '  i i ! ;  170,57.;  689  0.7036  0.7070  0.7002  170.81  171.04  170.57  690  0.6921  0.6954  0.6889  260.00  260.  2 5 9 . 7 1 1  691  0.6850  0.6882  0.6817  332.19  332.57  331.80  .  692  0.6755  0 . 6 7 8 7  0.6724  406.30  406.68  4 0 5 . 9 2  ;  692  0.6782  0.6817  0.6747  406.30  406.68  4 0 5 . 9 2  i  693  0.6800  0.6832  0.6768  400.47  400.81  4 0 0 . 1 3  ;  30  j  693  0.6823  0.6858  0.6788  400.47  400.81  4 0 0 . 1 3  :  694  0.7073  0.7109  0.7037  137.42  137.63  137.20  ;  '•  694  0.7015  0.7051  0.6980  137.42  137.63  137.20  695  0.6959  0.6992  0  212.49  212.77  2 1 2 . 2 1  696  0.7049  0.7083  0.7014  167.89  168.12  167.67  696  0.7003  0.7037  0.6969  167.89  168.12  167.67 j  .6926  !  TABLE 3-10(CONTINUED)  95% CONFIDENCE^ "'"INTERVAL"  RUN NO e 697 i 69 7  0.7106 0.7112  0.7142 0.7150  RED 122.29 122.29  0.7070 0.7074  95 %  JL° J ^ _ ENCEINTE RVAL N  122.49 122.49  D  122.10 12 2.10  TABLE 3-11  RUN "NO."  95  ^ORIFICE TYPE I 645  CONFIDENCE INTERVAL FOR K AND RED 95 95 RED CONFIDENCE CONFIDENCE INTERVAL INTERVAL SPECIAL 30  0.7069 0.7105 0.6998 0.6963 646 0 . 6 8 7 1 0.6905 6 4 7 J 0.6764 0.6796 648 0.6726 0.6695 j 649 i 650 0.6683 0.6651 \ 0.6631_ 651 0.6600 i 0.6573 652 0.6604 0.6608 0.6576 653 0 .7212 654 • 0.7160 0.6814 0.6782 655 0.6904 0.6869 J 656 0.7193 0.7136 6 7 9 L """"0V710 5" 0 .7166 ""6'79"~ f t 680 0.7214 0.7163 0 .7224 0.7188 680 ' 0.7155 0.7190 • 681 0.7151 681 0.7201 0.7167 0.7133 681 0.6989™ ~0~".702'4~ '682'*"  r  r r  BETA=0.4 0.7032 0.6928 0.6837 0.6731 0.6663 0.6619 0.6569 "b".~6~542" 0.6544 0.7108 0.6750 0.6835 0.7080 0.7045 0.7113 0.7151 0.7120 0 .7100 0.7099 0 .6954  271.98 272.48 375.67 ' 376.29 481.39 482.00 576.02 576.78 723.87 724.68 860.86 861.90 1021.05 1022.00 Tl'4l799 1143.06 1282.07 1280.90 147.65 148.00 . 550.90 551.50 486.97 487.75 51.87 52.04 51.87 52.04 120.14. 120.30 120.14 120.30 171.76 171 .95 171.76 171.95 171.76 171.95 287.39 287.86  2 71.49 : 375.06 ! 480.79 575.27 : 723.05 ; 859.81 1020.09 ' 1140.93 ; 1279.74 j 147.29 ! 550.30 : 486.20 J 51.70 j 51.70 ; 119.97 ' 1  ;  11 9.5 9 7 ;j 17 171.57 L 171.57 ! 286.92 j  I  3-27  TABLE 3-11(CONTINUED)  \ RUN \_NO» . . ! 682 :  683  1  6 8 4  i ;  1  i  I  68 4 685 685 686 686  K 0o7135 0»6999 0.7239 0.7217 0.7195 0,7194 0.6282 0.7235  95%  CONFIDENCE^' .0 . 7 1"YMTERVAL" ~" 85 0.7085 0.7032 0.7279 0.7270 0.7238 0.7247 0.6335 0.7293  0.6966 0.7199 0.7164 0.7153 0.7142 0.6229 0.7178  RED "  287.39 275.75 .98.82 98.82 77.20 77.20 45.80 45.80  95%  CONF I DENCE_ INTERVAL' 286.92 287.86 276.02 99.04 99.04 77.35 77.35 45.93 45.93  275.49 98.61 98.61 : 77,05 77.05 : 45.67 ' 45.67 ;  :  U-l APPENDIX 1| - CALIBRATIONS  The C a l i b r a t i o n of Thermocouples and Thermometers. The c a l i b r a t i o n of thermocouples 1,  2 , 3> h  5 and thermometer  t  1  was c a r r i e d out using a s t r a i n - f r e e Platinum Resistance Thermometer, No, 169 3 l U , made by the American Instrument Company,  The  was calibrated by the National Research Council i n 1959*  thermometer The following  quadratic equation describes the temperature resistance curve,  |£-  -  1  A  -  0,00393298  B  - -5,8138 x I O "  Rb  -  where  •  AT  +  (30)  BT2  7  /  2,5121  R© «  resistance i n ohms a t the f r e e z i n g point of water  Rt »  resistance i n ohms a t temperature T  T  measured temperature, °C  «  A, B  - constants  The method used was e s s e n t i a l l y that recorded i n Appendix I I of Galloway's (U;) Ph.D. t h e s i s .  The r e s u l t s f o r tiae 5 thermocouples and '  thermometer are recorded i n Table 1*-«1  ^  Least-square-fit equations were calculated and appear as follows: 1  Teal, "?  - 1*5,29751 x EMF(volts) • 32.3721*1*9  (31).  T  - UU-289022 x EMF(volts) • 3 3 . 5 7 U 6 3 0 ' " .-•  (32)  0  T  ,°F  cs3*°  T T  c g 2  csli  F  ,°F  cs5*°  tmal* * 0  F  - W.337977  x  EM~"(volts) + 33.1*8391*6  - U*,236682 x EMF(volts) + 33.1*18095'  •  —  (33) , , (31*)  " UU.U75782 x EMF(volts) • 33.301*903  (35)  - 1.789271 x T , ° C  (36)  ml  • 31.91*788.  TABLE U - l DATA FOR THE CALIBRATION OF THERMOCOUPLES 1, 2, 3, U, 5 AND THERMOMETER 1 Muller  Resistance  Bridge  Thermometer Thermometer  Ohms  Resistance  oc  °E  Thermocouple E.M.F.  Thermometer 1  1  2  Op  Volts  3  U  5  2.6850  63.68  17.6  17.70  0,690  0.680  0.681  O.683  0.685  2.6552  58.19  1U.55  lU.70  0.577  0.562  0.56U  0.566  0.565  2.71U*  68.99  20.55  20,70  0,805  0.797  0.796  0.799  0.301  2.7U19  73.9U  23.30  23.55  0.919  0.910  0*913  0.918  0.912  2.772U  79.61  26.U5  26.55  1.037  1.03U  1.035  1.0U0  1.035  2.80U1  85.37  29.65  29.80  1.168  1.168  1.168  1.172  1.165  2.8313  90.32  32.Uo  32.65  1,277  1,280  1.282  1.288  1.282  2.8671  96.80  36.00  36,30  1.U2U  1.U30  1.U30  1.1435  1.U30  2.8995  102.7U  39.30  39.55  1.558  1.565  1.565  1.568  1.566  ''  I  ro  TABIE h-2 CALIBRATION DATA FOR THERMOMETERS 2 AND' 3 Thermometer  Thermometer 1 Corrected b y E q . 36 oF  Thermometer  26.25 26.6  78.91 79. Sh  79.1 79.9  79.2  28.5  82.9h  83.U  83.3  35.1  9U.75  95.0  95.1  30.6  86.70  87.0  87.O  29,6  8U.91  85.6  85.5  26.U  79.18  79.U  79. h  2U.U5  75.69  75.8  75.85  22,65  72*1*7  72,7  72.65  19, h  66.66  66.7  18.0  61iol5  6U.2  66.65 61* . 2 0  1  °C  F  2  °F  Thermometer  3  °F  79.85  > 6  .7  .0  .0  THERMOCOUPLE  1.0  I.I  1-2  •  E MF  FIGURE 4-1 CALIBRATION OF THERMOCOUPLE  I  > 6  .7  .©  1.0  THERMOCOUPLE  E MF  .8  I.I  FIGURE 4-3 CALIBRATION OF THERMOCOUPLE  1.2  3  U-8  7  .8  .9  THERMOCOUPLE FIGURE 4-5  I.D  I.I  1.2  E MF  CALIBRATION OF THERMOCOUPLE  5  TABLE U-3 CALIBRATION DATA FOR CARBON TETRACHLORIDE Thermometer  1  OC  Density C C l ^ gnio/c.c o  1.5869 1.5705 1.5712  25»0  3U.2 33 6 23oU 28 o9 31.95  1.5*901  1.5798 1.5739 1.5657 1.5930 1.5975 1.5992 1.6020  36.1*0  21.75 19.20 18.1*0  16.52 26.10  1.581*8  TABLE k-h CALIBRATION DATE FOR BENZENE  Thermometer Op  2  D e n s i t y C6H6 gra./c.c.  79.3  Oo8722  77.8  0.8731  76.0  0.871*1  7U.5 73 oO  0.87U8 0.3757  69.6  0.877U  71.8  0.3761  U-io C a l i b r a t i o n o f Thermocouples and  Thermometers  The d a t a from Table U-l f o r thermocouples 1, 2 , 3, U, thermometer 1 a r e p l o t t e d r e s p e c t i v e l y  i n F i g u r e s U-l, U-2,  5 and U-3,  U-U,  U-5 and U-6. Thenncmeters 2 and 3 were c a l i b r a t e d u s i n g thermometer 1 as a s t a n d a r d . The d a t a a r e r e c o r d e d i n T a b l e U-2.  U s i n g e q u a t i o n (36), a c o r r e c t e d  t e m p e r a t u r e , based on the r e s i s t a n c e  thermometer was c a l c u l a t e d f o r  thermometer 1 i n °F. are  The r e c o r d e d t e m p e r a t u r e s o f thermometers 2 and 3  compared v/ith the c o r r e c t e d temperature o f thermometer 1 t o c a l c u l a t e  t h e i r l e a s t s q u a r e s c a l i b r a t i o n equations.Thermometer  (37) (38)  plotted  i n F i g u r e s U-7  and lj-< . D  J 6 6  I  I  I  68  _J  I  7 0  RESISTANCE  'FIGURE k-lt  I 7 2  I  I 74  I  1  I  1  76  7 8  THERMOMETER  ° F  CALIBRATION CF THERMOMETER #2  .  L  'FIGURE l i - 9 :  CALIBRATION OF CARBON TETRACHLORIDE  U-16 C a l i b r a t i o n of Manometer F l u i d s  A l l d e n s i t y c a l i b r a t i o n s i-rere c a r r i e d out u s i n g t h e C h e m i c a l E n g i n e e r i n g D e p a r t m e n t ' s s e t o f p r e c i s i o n Hydrometers The m a n u f a c t u r e r c a l i b r a t e d them a t 60° F . a t temperatures between 60° F and 80° F .  ( C h » E . 11)66)  „  They were u s e d , however, A Westphal balance, u s i n g  d i s t i l l e d w a t e r as an a b s o l u t e s t a n d a r d , was employed t o check the hydrometers a t the h i g h e r t e m p e r a t u r e s .  The hydrometers u s e d were  found to be i n e r r o r by no more t h a n 0.3$.  Therefore,  d e n s i t y r e a d i n g s were a c c e p t e d as c o r r e c t w i t h i n - 0 . 3 $ . f o r the c a l i b r a t i o n o f c a r b o n t e t r a c h l o r i d e  the  hydrometer  The  results  ( s a t u r a t e d w i t h PEG) and  benzene ( s a t u r a t e d w i t h PEG) appear r e s p e c t i v e l y i n T a b l e s U-3 and U-U.  L e a s t - s q u a r e e q u a t i o n s f o r the two l i q u i d s a r e  DENSITY f C C l ) -  1.632717 -  0.001833  x Tm2  (39)  DENSITY (C H ), -  0.91U061 - 0.000527  x T_3  (U0)  

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