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Head losses resulting from flow through wyes and manifolds Wang, Hua 1967

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HEAD LOSSES RESULTING FROM FLOW THROUGH WYES AND MANIFOLDS  by  HUA WANG B.S., Taiwan Cheng Kung U n i v e r s i t y , 1964  A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF APPLIED SCIENCE i n the Department of Civil  Engineering  We a c c e p t t h i s t h e s i s as conforming required  to the  standard  THE UNIVERSITY OF BRITISH COLUMBIA September, 1967  In p r e s e n t i n g  for  thesis  an a d v a n c e d d e g r e e  that  the  Study.  thesis  Library  for  agree  scholarly  or  publication  without  shall  I further  Department  or  this  of  of  make i t  that  freely  Civil  thesis  may be g r a n t e d  September  for  permission.  Engineering,  The U n i v e r s i t y o f B r i t i s h V a n c o u v e r 8, Canada 1967.  for  Columbia  It  of  British  available  permission  purposes  this  fulfilment  the U n i v e r s i t y of  by h i-;: r e p r e s e n t a t i v e s .  my w r i t t e n  Department  at  in p a r t i a l  for  the  Columbia,  I  reference  and  extensive  by  the  requirements  copying  gain  this  Head o f my  is understood  financial  of  agree  shall  that  not  be  copying  allowed  i  ABSTRACT  L a b o r a t o r y t e s t s were conducted t o determine the head  losses  i n wyes and m a n i f o l d s o f c o n v e n t i o n a l type, both w i t h and w i t h o u t an i n t e r n a l t i e - r o d a t the t h e o r e t i c a l  c e n t r e o f the wye.  These  wyes and m a n i f o l d s , h a v i n g 45°, 60° and 90° subtending a n g l e s of the wyes, were symmetrical about the l o n g i t u d i n a l  axis  o f the main p i p e .  The apparatus and method o f t e s t i n g used i n the t e s t s a r e d e s c r i b e d . The experiment spans a range o f Reynold's numbers from 85,000 t o 420,000 i n the i n f l u e n t main p i p e .  The a n a l y s i s  i s based on the energy e q u a t i o n o f B e r n o u l l i condition. graphical  o f e x p e r i m e n t a l data  f o r the one-dimensional  The r e s u l t s o f the t e s t s a r e g i v e n i n both t a b u l a r and form.  I t appears t h a t  the c o e f f i c i e n t of the form  loss  (the  r a t i o o f the form l o s s o f a wye or m a n i f o l d t o the v e l o c i t y  head  i n the main p i p e ) i s a f u n c t i o n  water  o f the p r o p o r t i o n a l  flow o f  through the branches, the s i z e of the t i e - r o d used and the  subtending a n g l e o f the wye.  ii  TABLE OF CONTENTS PAGE ABSTRACT  i  TABLE OF CONTENTS  ii  LIST OF TABLES  iv  LIST OF FIGURES  vi  LIST OF PLATES  ix  NOMENCLATURE  x  ACKNOWLEDGMENT  xii  INTRODUCTION  1  PREVIOUS RESEARCH  3  CHAPTER I  DESCRIPTION OF EXPERIMENT  5  1.1  Layout  5  1.2  Model  7  1.3  Instrumentation  14  1.4  E x p e r i m e n t a l Measurements  15  BASIC CONCEPTS RELATING TO HEAD LOSSES  18  2.1  Form Losses o f Wyes  19  2.2  Form Losses of M a n i f o l d s  20  2.3  H y d r a u l i c Power Losses i n Wye and M a n i f o l d  20  CHAPTER I I  Arrangements CHAPTER I I I  EXPERIMENTAL INVESTIGATIONS  22  3.1  Preliminary Investigation  22  3.2  Flow P a t t e r n s  23  iii  PAGE CHAPTER IV 4.1  EXPERIMENTAL PROCEDURES D e t e r m i n a t i o n o f F r i c t i o n Losses  24 i n Main  Pipe and Branch Pipes  24  Sequence o f Experiment  26  RESULTS AND CONCLUSIONS  27  5.1  Results  27  5.2  Conclusions  29  HEAD LOSSES IN ELBOWS  31  4.2 CHAPTER V  APPENDIX BIBLIOGRAPHY  33  iv  LIST OF TABLES  TABLE NO.  TITLE  PAGE  I  -1  Areas of M a i n ,  I  -2  O r i f i c e Arrangement  36  D i s t a n c e from T h e o r e t i c a l Center o f Wyes to  37  II-l  Branch and I n l e t Pipes  36  P i e z o m e t r i c Rings on Main and Branch Pipes (For Wye Arrangement) II-2  D i s t a n c e from T h e o r e t i c a l Center of Wyes to P i e z o m e t r i c Rings on Main and Branch (For M a n i f o l d  IV-1  ±  IV-2  Pipes  Arrangement)  Data of S k i n F r i c t i o n Loss i n Main Pipe f o r Length SS  37  (3.375  ft.)  Data of S k i n F r i c t i o n Losses i n Branch Pipes f o r Length BB^ (9.0  38  39  ft.)  V -1  Form L o s s Data f o r 9 0 ° Wye w i t h o u t T i e - r o d  40  V -2  Form Loss Data f o r 9 0 ° Wye w i t h TR1 T i e - r o d  42  V -3  Form Loss Data f o r 9 0 ° Wye w i t h TR2 T i e - r o d  44  V -4  Form Loss Data f o r 9 0 ° Wye w i t h TR3 T i e - r o d  46  V -5  Form Loss Data f o r 9 0 ° Wye w i t h TR4 T i e - r o d  48  V -6  Form Loss Data f o r 6 0 ° Wye w i t h o u t T i e - r o d  50  V -7  Form Loss Data f o r 6 0 ° Wye w i t h TR2 T i e - r o d  52  V -8  Form Loss Data f o r 6 0 ° Wye w i t h TR3 T i e - r o d  54  V -9  Form Loss Data f o r 6 0 ° Wye w i t h TR4 T i e - r o d  56  V -10  Form Loss Data f o r 4 5 ° Wye w i t h o u t T i e - r o d  58  V  LIST OF TABLES - -  TABLE NO.  (Continued)  TITLE  PAGE  V -11  Form Loss Data f o r 9 0 ° M a n i f o l d w i t h o u t T i e - r o d  60  V -12  Form Loss Data f o r 9 0 ° M a n i f o l d w i t h TR3 T i e - r o d  62  V -13  Form Loss Data f o r 6 0 ° M a n i f o l d w i t h o u t T i e - r o d  64  V -14  Form Loss Data f o r 6 0 ° M a n i f o l d w i t h TR3 T i e - r o d  66  V -15  Form Loss Data f o r 4 5 ° M a n i f o l d w i t h o u t T i e - r o d  68  V -16  Data of H y d r a u l i c Power Losses i n Wye Arrangements  70  V -17  Data of H y d r a u l i c Power Losses i n M a n i f o l d  73  Arrangements A -1  D i s t a n c e from T h e o r e t i c a l Center of Elbows to P i e z o m e t r i c Rings on S t r a i g h t  76  Pipe  A -2  Head Loss Data f o r 4 5 ° Elbows  77  A -3  Head Loss Data f o r 3 0 ° Elbows  78  A -4  Head Loss Data f o r 22%° Elbows  79  vi  LIST OF FIGURES  FIGURE NO.  TITLE  PAGE  I-l  Details  of G e n e r a l Arrangement  80  1-2  D e t a i l s o f Wye Arrangement  1-3  Model Layout and Manometric L o c a t i o n s  81 for  82  Wye Arrangement 1-4  D e t a i l s of M a n i f o l d Arrangement  1-5  Model Layout and Manometric L o c a t i o n s Manifold  83 for  84  Arrangement  1-6  Details  of Main Pipe from C o n t r o l V a l v e to Wye  1-7  Geometrical D e t a i l s  1-8  Details  1-9  D e t a i l s of Manifolds  88  I-10  D e t a i l s o f Elbows  89  1-11  D e t a i l s of P r e s s u r e Tap  90  of 9 0 ° Tapered Wye  of Wyes  85 86 87  II-l  H y d r a u l i c & Energy G r a d i e n t L i n e s  f o r Wye  91  II-2  H y d r a u l i c & Energy G r a d i e n t L i n e s  for Manifold  92  III-l  Flow P a t t e r n s "in M a n i f o l d s w i t h o u t T i e - r o d  93  III-2  Flow P a t t e r n s i n M a n i f o l d s w i t h T i e - r o d  94  IV-1  S k i n F r i c t i o n Loss  95  IV-2  Experimental  Set-up  Losses i n Branch  i n Main Pipe f o r Measuring S k i n F r i c t i o n  96  Pipes  IV-3  S k i n F r i c t i o n Loss  i n R i g h t Branch Pipe  97  IV-4  S k i n F r i c t i o n Loss  i n L e f t Branch Pipe  98  vii  LIST OF FIGURES - -  FIGURE NO. V-l  TITLE Form Loss C o e f f i c i e n t s (Symmetrical  V-2  Form Loss C o e f f i c i e n t s  V-6  Form Loss C o e f f i c i e n t s  Form Loss C o e f f i c i e n t s  102  f o r 6 0 ° Wye  103  f o r 6 0 ° Wye  104  f o r 4 5 ° Wye  105  f o r 4 5 ° Wye  f o r Wyes  107  Flow) for Manifolds  108  for Manifolds  109  Flow)  Form Loss C o e f f i c i e n t s (One-leg  106  Flow)  Form Loss C o e f f i c i e n t s (Symmetrical  V-ll  f o r 6 0 ° Wye  Comparison of Form Loss C o e f f i c i e n t s (Unsymmetrical  V-10  101  & O n e - l e g Flows)  (Unsymmetrical V-9  f o r 9 0 ° Wye  Flow)  Form Loss C o e f f i c i e n t s (Symmetrical  V-8  100  Flow)  (Unsymmetrical V-7  f o r 9 0 ° Wye  Flow)  Form Loss C o e f f i c i e n t s (One-leg  99  Flow)  Form Loss C o e f f i c i e n t s (Symmetrical  V-5  f o r 9 0 ° Wye  Flow)  (Unsymmetrical V-4  PAGE  Flow)  Form Loss C o e f f i c i e n t s (One-leg  V-3  (Continued)  Flow)  viii  LIST OF FIGURES -- (Continued)  FIGURE NO. V-12  TITLE  PAGE  Form Loss C o e f f i c i e n t s  f o r Manifolds  110  (Unsymmetrical Flow) V-13  Comparison  o f Form Loss C o e f f i c i e n t s  & Manifolds without V-14  Comparison  f o r Wyes  111  f o r Wyes  112  Tie-rod  o f Form Loss C o e f f i c i e n t s  & M a n i f o l d s w i t h TR3 T i e - r o d V-15  H y d r a u l i c Power Losses i n Wye Arrangements  113  V-16  H y d r a u l i c Power Losses i n M a n i f o l d Arrangements  114  A-l  E x p e r i m e n t a l Set-up f o r Measuring Head Losses  115  i n Elbows A-2  H y d r a u l i c & Energy G r a d i e n t L i n e s f o r Elbow Testing  A-3  116  Set-up  Elbow Loss C o e f f i c i e n t s  117  ix  LIST OF PLATES  PLATE NO. 1  TITLE Model Layout f o r Wye Arrangement L o o k i n g  PAGE 6  Downstream 2  Model Layout f o r M a n i f o l d Arrangement Looking  6  Upstream 3  Tapered Wyes i n V e r t i c a l View  10  4  Tapered Wyes i n H o r i z o n t a l View  10  5  Elbows  10  6  O r i f i c e s and T i e - r o d s  12  7  Top View of Wye i n P l a c e  12  8  Top View of M a n i f o l d i n P l a c e  13  9  Manometric Board w i t h Gauge Tanks  13  X NOMENCLATURE  The  f o l l o w i n g symbols a r e used i n t h i s  A  = Average i n t e r n a l  D  = Average i n t e r n a l diameter,  thesis:  cross-sectional  area,  i n sq. f t ;  i n inches;  2 g  = Acceleration of gravity,  i n ft/sec ;  h^'  = Skin f r i c t i o n  hp  = P r e s s u r e head i n p i e z o m e t r i c r i n g ,  h^  = Velocity  ^ h  = Form l o s s  A hg Ah P  = Elbow l o s s , i n f t ; - D i f f e r e n c e o f p r e s s u r e heads i n p i e z o m e t r i c r i n g s  l o s s o f pipe, i n f t ; in ft;  head, i n f t ; of wye or m a n i f o l d ,  in ft;  main pipe and one o f branch p i p e s , i n f t ; k  = Form l o s s  kg  = Elbow l o s s  L  = Length o f p i p e ,  N  r  c o e f f i c i e n t of wye or m a n i f o l d ; coefficient; in ft;  = Froude number;  p  = H y d r a u l i c power l o s s  P^  = H y d r a u l i c power l o s s ,  P  = H y d r a u l i c power i n main p i p e , i n f t - l b / s e c ;  m  i n dimensionless i n ft-lb/sec;  Q  = Discharge  i n pipe, i n c f s ;  Re  = Reynold's number  t  = Time i n t e r v a l , i n s e c ;  V  = Mean v e l o c i t y  Js  = Kinematic  i n pipe, i n fps;  viscosity,  expression;  i n ft/sec;  between  XL  NOMENCLATURE -- (Continued)  w  = U n i t weight of water, i n l b / c u . f t ;  W  = Weight o f water, i n l b s ;  Subscripts: m  = Occurrence i n main p i p e ;  b  = Occurrence i n branch  r  = Occurrence i n r i g h t branch  1  = Occurrence i n l e f t branch  i  = Occurrence i n i n l e t  pipe;  pipe.  pipe; pipe;  xii  ACKNOWLEDGMENT  The his  author  constant  i s i n d e b t e d to h i s s u p e r v i s o r ,  encouragement  D r . E . Ruus,  and i n v a l u a b l e guidance  for  throughout  the p r e p a r a t i o n of the work. He wishes to express h i s a p p r e c i a t i o n to P r o f e s s o r Muir  f o r suggestions  the s t a f f  and c r i t i c i s m i n p r e p a r i n g t h i s  of the C i v i l E n g i n e e r i n g Instrument  J.F.  thesis,  Shop f o r  to  their  a s s i s t a n c e i n the c o n s t r u c t i o n of the models, and to the N a t i o n a l Research C o u n c i l of Canada f o r f i n a n c i a l support g i v e n through g r a n t s i n a i d of t h i s  research.  1  INTRODUCTION  In  r e c e n t h y d r o - e l e c t r i c development,  a power p l a n t of h i g h  c a p a c i t y i s o f t e n proposed w i t h a l a r g e diameter penstock t o convey water from the overhead r e s e r v o i r t o the powerhouse.  A detailed  study o f the head l o s s i n the penstock becomes n e c e s s a r y f o r an economic d e s i g n o f the p e n s t o c k .  A major p o r t i o n o f the t o t a l  head  l o s s i n the penstock r e s u l t s from the f l o w through branched p i p e junctions .  Research i n h y d r a u l i c s i s r e q u i r e d t o determine the  exact amount o f the head l o s s e s a t these p i p e j u n c t i o n s and t o study the  v a r i o u s parameters g o v e r n i n g such head l o s s e s .  The author  d e a l s s p e c i f i c a l l y w i t h those i n v e s t i g a t i o n s t h a t concerned the head l o s s e s a t wyes and m a n i f o l d s . The study d e s c r i b e d i n t h i s t h e s i s was made t o determine the head l o s s e s f o r v a r i o u s f l o w c o n d i t i o n s a t s y m m e t r i c a l l y branched p i p e j u n c t i o n s h a v i n g d i f f e r e n t subtending angles of the wyes.  It  i s p r i m a r i l y concerned w i t h the form l o s s e s r e s u l t i n g from the flows through wyes and m a n i f o l d s . D e f i n i t i o n o f Terms A wye ( o r a b i f u r c a t i o n ) i s a branched f i t t i n g used to connect an i n f l u e n t main p i p e t o two e f f l u e n t branch p i p e s . F i g u r e 1-8) .  When a branched f i t t i n g  (See  i s used t o connect an i n -  f l u e n t main p i p e t o three e f f l u e n t branch p i p e s , i t i s c a l l e d a trifurcation. A m a n i f o l d i s a branched f i t t i n g wherein the e f f l u e n t branch p i p e s a r e brought back p a r a l l e l  t o the i n f l u e n t main p i p e by the  2 connection of elbows to each limb of a wye.  The subtending  angle  of a manifold i s considered to be the angle between the limbs of the wye.  (See Figure 1-9).  45° wye  For example, a 45° manifold consists of a  followed by two 22-1/2° elbows connected  limbs of the  to the downstream  wye.  The form loss i s the head loss a r i s i n g from turbulence i n a branched pipe system excluding the skin f r i c t i o n loss of head i n the system. The form loss c o e f f i c i e n t i s the r a t i o between the form loss of a wye  or manifold and the v e l o c i t y head i n the main pipe.  When the experimental results are adopted to estimate the head losses i n geometrically similar prototypes, the application of Froude law (N„ = V / / gD ) as the c r i t e r i o n f o r dynamic s i m i l a r i t y F i n interpreting the hydraulic models w i l l lead to r e l i a b l e prediction of prototype performance.  3  PREVIOUS RESEARCH  The  e a r l i e s t important e x p e r i m e n t a l i n v e s t i g a t i o n of the head  l o s s e s i n branched  who  p i p e systems was  d e a l t o n l y with p i p e t e e s .  undertaken  L a t e r i n 1929,  i n 1928  by Vogel (2)  Petermann  (1)*  ,  made a  d e t a i l e d study of the head l o s s e s i n p i p i n g b i f u r c a t i o n s w i t h a main p i p e t h a t c o n t i n u e d s t r a i g h t a f t e r the j u n c t i o n , a branch which subtended  of  a t an angle of 45° to the l o n g i t u d i n a l a x i s of the  main p i p e . Since 1957,  numerous t h e o r e t i c a l and e x p e r i m e n t a l  of h y d r a u l i c behaviour  i n many c o u n t r i e s .  i n branched  p i p e systems have been (3)  In S w i t z e r l a n d , C a r d e l  the head l o s s e s produced  i n s e v e r a l types of wye  i n diameter was  60 mm  the angles between the branches  135°.  undertaken  made t e s t s to  main p i p e 150 mm to 150 mm,  investigations  branches  determine  where the  j o i n e d by branch p i p e s r a n g i n g from  In I t a l y , M a r c h e t t i and N o s e d a ^  v a r y i n g from 45° to  i n v e s t i g a t e d the h y d r a u l i c  behaviour o f f i v e symmetrical b i f u r c a t i o n s w i t h the angles between the branches  v a r y i n g from 60° to 180°.  conducted model t e s t s on a 60° wye internal ribs  Salvesen^  using i n turn four d i f f e r e n t  i n the f o r k of the wye  lowest head l o s s .  In Norway, F r i t j o f  to f i n d which r i b p r o v i d e d the  I n Canada, a t the U n i v e r s i t y o f B r i t i s h  Columbia,  (6) Ahmed  conducted  a s e r i e s of head l o s s t e s t s on f i v e  wyes of c o n v e n t i o n a l and s p h e r i c a l and 60° between the branches.  symmetrical  types h a v i n g the angles of  90°  In the U n i t e d S t a t e s , s e v e r a l b a s i c  s t u d i e s of the mechanism of i n s t a b i l i t y of f l o w through a s y m m e t r i c a l l y * Numbers i n parentheses r e f e r to the B i b l i o g r a p h y .  branched p i p e system were made a t the U n i v e r s i t y o f Kansas H y d r a u l i c model s t u d i e s t o determine the head l o s s i n a m a n i f o l d c o n s i s t i n g o f a 45° wye f o l l o w e d by two 22-1/2° elbows were conducted by s t a f f members a t C o l o r a d o S t a t e U n i v e r s i t y  .  t e s t s was made by G l a d w e l l , Tinney and K r e u z e r ^ ' Washington  A s e r i e s of model '  at  S t a t e U n i v e r s i t y on a l a r g e penstock t r i f u r c a t i o n t o  determine f l o w p a t t e r n s , s t a t i c and dynamic p r e s s u r e s , energy and the shed v o r t i c i t y from a c e n t r a l  tie-bar.  losses  5  CHAPTER I DESCRIPTION OF EXPERIMENT  1.1  LAYOUT The  experimental  Laboratory  i n v e s t i g a t i o n was  conducted  i n the H y d r a u l i c  a t the U n i v e r s i t y of B r i t i s h Columbia i n 1966-67.  The water was  pumped from a sump i n t o an overhead tank w i t h a  s u r f a c e l e v e l about 55 f t . above ground and h o l d i n g about 1760  cubic  f e e t of water.  test  section.  Through a c o n t r o l v a l v e t h i s supply l e d to the  The p i p e s and f i t t i n g s of the model r e s t e d upon a wooden  frame, the t i g h t n e s s of a l l j o i n t s b e i n g under o b s e r v a t i o n . a r e a extended from the c o n t r o l v a l v e to the o u t l e t s of the pipes.  From the o u t l e t s of the branch p i p e s r a n two  enabled  the f l o w through  each branch  The model branch  troughs  p i p e to be guided  which  into a  weighing  tank or the sump as r e q u i r e d i n the experiment. The  g e n e r a l arrangement of the model i n e l e v a t i o n i s shown i n  Figure I - l .  The p l a n views of a wye  1-2  and P l a t e 1.  and 1-3,  are shown i n F i g u r e s 1-4 Due  arrangement are shown i n F i g u r e s  The p l a n views of a m a n i f o l d and 1-5,  and P l a t e 2.  to the e x i s t e n c e of many elbows and  to e n t e r i n g the model a r e a , a g r e a t amount of pressure fluctuations occurred.  arrangement  Two  tees on the l i n e  turbulence-induced  f l o w s t r a i g h t e n e r s each 2 f t .  l o n g were p r o v i d e d i n the upstream main p i p e to dampen these t i o n s as w e l l as to o b t a i n a symmetrical entrance  s e c t i o n of a wye  prior  or m a n i f o l d .  fluctua-  v e l o c i t y d i s t r i b u t i o n i n the These flow s t r a i g h t e n e r s were  made of t h i n aluminum tubes v a r y i n g from one  to two  inches i n  diameter.  PLATE 1  Model Layout f o r Wye Arrangement Looking Downstream  PLATE 2  Model Layout f o r M a n i f o l d Arrangement Looking Upstream  7 The  first  one was l o c a t e d downstream from the bend below the c o n t r o l  v a l v e , and the other downstream from the f i r s t r e d u c e r ,  as shown i n  F i g u r e 1-6.  1.2  MODEL The model was made of l u c i t e except f o r the p o r t i o n upstream  from the second reducer used.  t o the c o n t r o l v a l v e where s t e e l p i p e s were  (See F i g u r e 1-1).  T h i s set-up  had the advantages o f (1) en-  a b l i n g the d i f f e r e n t p a r t s o f the model t o be r e p l a c e d e a s i l y , (2) p e r m i t t i n g the h y d r a u l i c behaviour throughout the model a r e a t o be observed c l e a r l y , and (3) showing any entrapment o f a i r which would a f f e c t the p i e z o m e t r i c A.  heads.  Main Pipe and Branch Pipes The main p i p e , o f l u c i t e , comprised o f three s e c t i o n s o f  equal  l e n g t h , had an i n t e r n a l diameter o f 5.25 i n c h and a t o t a l  of 13.5 f t .  I t was f i t t e d on both ends o f the s e c t i o n s w i t h  length  lucite  f l a n g e s which connected the p i p e s t o each o t h e r and t o the upstream f a c e of a wye o r m a n i f o l d . s e c t i o n with  the f a c e p e r p e n d i c u l a r  r i n g s were f i t t e d its  ends.  Each f l a n g e was g l u e d to one end of a t o the p i p e l i n e .  Two p i e z o m e t r i c  on the downstream s e c t i o n o f t h e main p i p e c l o s e to  A v e l o c i t y t r a v e r s e s t a t i o n was s e t up a t 6 inches  the downstream end o f the main p i p e .  from  D e t a i l s of the main p i p e from  the c o n t r o l v a l v e t o a wye a r e shown i n F i g u r e 1-6. Four s e c t i o n s o f the branch p i p e s , d e s i g n a t e d and D, h a v i n g  an i n t e r n a l diameter o f approximately  l e n g t h of 4.5 f t . , were f i t t e d w i t h  as A, B, C  3.75 i n c h and a  l u c i t e f l a n g e s and p i e z o m e t r i c  r i n g s to from the r i g h t and l e f t b r a n c h e s .  Throughout the experiment,  8 s e c t i o n s A and C formed the l e f t branch, right  reducer  diameter for  s e c t i o n s B and D  the  branch. The  first  and  l e n g t h of the main p i p e from the downstream end to the upstream end of a wye  r a t i o b e i n g 75.  each of the branch  The  pipes .  was  length-diameter T h i s r a t i o was  of the  33 f t . , the l e n g t h r a t i o was  equal to 30  c o n s i d e r e d adequate to  o b t a i n a r e a s o n a b l y u n i f o r m v e l o c i t y d i s t r i b u t i o n , and  to  achieve  a c c u r a t e p r e s s u r e head measurements a t the downstream p i e z o m e t r i c r i n g s a t the branch  pipes.  An i n l e t p i p e was in  the branch p i p e s and  IV-2  used to determine the s k i n f r i c t i o n l o s s e s  the head l o s s e s i n the elbows.  and A - l ) . B.  Wyes Three s y m m e t r i c a l l y  tapered wyes w i t h subtending  60° and 90° r e s p e c t i v e l y were i n v e s t i g a t e d . and dimensions of the wyes are: i l l u s t r a t e d and P l a t e s 3 and 4. rical  angles  45°,  D e t a i l s of the o u t l i n e s  i n F i g u r e s 1-7  and  1-8,  These c a r e f u l l y c o n s t r u c t e d models were symmet-  about the l o n g i t u d i n a l a x i s of the main p i p e . I n p r e p a r i n g each wye,  The  (See F i g u r e s  t h e o r e t i c a l c e n t r e and  the outer f a c e s were f i r s t machined.  the l e n g t h from the t h e o r e t i c a l c e n t r e to  the p o i n t s of i n l e t and o u t l e t s were determined.  The  c o n i c a l water  passages were turned on a l a t h e ; the i n n e r s u r f a c e of the wye  was  p o l i s h e d by emery paper, then by crocus paper, and f i n a l l y by  polish-  i n g . l i q u i d to make the i n n e r s u r f a c e of the wye for  the purpose of d e c r e a s i n g s k i n f r i c t i o n For a l l wyes, the diameter  of  both o u t l e t s 3.75  as smooth as p o s s i b l e  loss.  of the i n l e t was  i n c h ; the t a p e r i n g was  5.25  i n c h and  done a t an angle of  10°.  9 C.  Manifolds Three symmetrical  m a n i f o l d s w i t h 45°, 60° and 90° subtending  angles of the wyes were i n v e s t i g a t e d .  The 4 5 ° m a n i f o l d c o n s i s t e d of a  45° wye f o l l o w e d by a 22-1/2° elbow, which was b u i l t up from a 15° and a 7-1/2° elbow, connected  t o each downstream limb o f the wye.  A s i m i l a r set-up was made f o r the 90° m a n i f o l d , r e p l a c i n g the 45° wye w i t h the 90° wye and the elbows w i t h 15° and 30° elbows.  F o r the  60° m a n i f o l d , 3 0 ° elbows, one on each limb o f the 60° wye, were used. D e t a i l s of the o u t l i n e s and dimensions  of the m a n i f o l d s  are i l l u s -  t r a t e d i n F i g u r e 1-9. These elbows, o f c o n s t a n t diameter,  consisted of a series  of s m a l l - a n g l e m i t r e bends j o i n e d together w i t h o u t any rounding a t the p l a n e s o f i n t e r s e c t i o n .  Each elbow was designed a c c o r d i n g to the  (12) recommendation o f B i e r times  the diameter  , w i t h bend r a d i u s (15 inch) equal to f o u r  o f the m i t r e bend (3.75 i n c h ) and a d e f l e c t i o n  angle o f 7-1/2° between segments.  D e t a i l s of the o u t l i n e s o f the  elbows a r e shown i n F i g u r e 1-9 and P l a t e 5 . S i n c e the segments o f the elbows were glued t o g e t h e r , machining  final  o f the f l a n g e s a t the ends o f each elbow was n e c e s s a r y i n  o r d e r to a c h i e v e a c c u r a t e alignment.  (It i s essential  t h a t the main  p i p e and the branch p i p e s a r e p a r a l l e l and l i e i n the same h o r i z o n t a l plane.)  When two elbows were connected  to form a r e q u i r e d d e f l e c t i o n  angle f o r a m a n i f o l d , two l o c a t i n g p i n s were i n s t a l l e d on each s i d e of the elbow f l a n g e s to e l i m i n a t e any d i s t o r t i o n i n the h o r i z o n t a l p l a n e and t o f i x the combined elbow i n t o f i n a l  position.  PLATE 5  Elbows  11.  D.  Tie-rods Four t i e - r o d s d e s i g n a t e d  diameters 0.187, 0.380, 0.562 and  as TR1,  TR2,  TR3,  and  of them were made of l u c i t e except the TR1  made of b r a s s .  Each of the f o u r t i e - r o d s was  t h e o r e t i c a l c e n t r e of a wye, E.  manifolds.  t i e - r o d which  was  placed i n turn at  the  screwed t i g h t to i t s i n n e r s u r f a c e .  Orifices The  by  and  having  0.754 inches r e s p e c t i v e l y were  used i n the i n v e s t i g a t i o n of the head l o s s e s i n wyes and All  TR4  v a r i a t i o n of d i s c h a r g e s was  the c o n t r o l v a l v e and  a t the two  c o n t r o l l e d a t the  o u t l e t s by o r i f i c e s .  and P l a t e 6 show the d e t a i l s of the o r i f i c e s . p l a c e d , one  inlet  Table  1-2  These o r i f i c e s were  a t a time, a t the downstream end of the branch p i p e .  Each o r i f i c e was  machined on one  edge f r e e from b u r r s . p l a c e d i n such a way  s i d e to o b t a i n a c l e a n and  sharp  Throughout the experiments, the o r i f i c e s were t h a t the sharp edges were f a c i n g the f l o w  with  the c e n t e r l i n e s of the o r i f i c e s a t the same e l e v a t i o n . F .  Set-up of Model (1)  For wye A wye  arrangements:  was  f i r s t b o l t e d to the branch p i p e s .  were checked by hand to ensure a proper of the wye two to  to the main p i p e  alignment.  (see P l a t e 7) was  The  made w i t h  The  joints  connection the h e l p  of  l o c a t i n g p i n s i n s t a l l e d i n the downstream f l a n g e of the main p i p e e l i m i n a t e any (2)  o f f s e t between the wye  For m a n i f o l d  and  the main p i p e .  arrangements:  Elbows were f i r s t b o l t e d to the branch p i p e s , then to a wye  (see P l a t e 8 ) .  PLATE 7  Top View of Wye i n P l a c e  PLATE 9  Manometric Board with Gauge Tanks  14 For the f i n a l  set-up  of the whole system, the main p i p e  was a l i g n e d by means of a t h e o d o l i t e , and the p i p e s were l e v e l e d a c c u r a t e l y with a carpenter's l e v e l .  L e a t h e r b e l t s were used on the  main p i p e and a t p l a c e s c l o s e to the o u t l e t s of the branch prevent  1.3  p i p e s to  vibration.  INSTRUMENTATION The  f o l l o w i n g i n s t r u m e n t a t i o n was used to measure p r e s s u r e  heads, and determine d i s c h a r g e s . A.  P r e s s u r e Taps A t y p i c a l pressure  tap w i t h an opening  shown i n F i g u r e I-11, was used i n the experiment.  o f 1/8 i n c h , as The b r a s s tube was  h e l d i n p o s i t i o n by a 1/8 i n c h N a t i o n a l Taper P i p e threaded (NTP) i n a 7/8 i n c h l u c i t e tube.  The NTP i n t u r n was connected  3/16 I m p e r i a l threaded nut w i t h rubber nate p o s s i b i l i t y of any The  opening  leakage.  of the p r e s s u r e tap should be s m a l l enough to  normal to the w a l l and f r e e from any b u r r s .  manometer B.  to a  r i n g a t the j u n c t i o n to e l i m i -  p r e v e n t any d i s t u r b a n c e i n the f l o w along the p i p e w a l l .  opening,  screw  I t must be  Any i n c l i n a t i o n of the  e i t h e r towards or away from the f l o w , may cause  false  readings. Piezometric  Connections  The p r e s s u r e taps on the p i e z o m e t r i c r i n g s were to manometers and gauge tanks by f l e x i b l e , manometers were i n s t a l l e d as shown i n P l a t e 9.  connected  transparent tubing.  i n groups and connected  The  to the gauge tanks  F i g u r e s 1-3 and 1-5 show the connections  of the  15 manometer tubes and gauge tanks to the p i e z o m e t r i c r i n g s on the main p i p e , and  the l e f t and r i g h t branch p i p e s f o r both wye  and m a n i f o l d  arrangements. C.  Gauge Tanks, Hook Gauges and V e r n i e r s In  s p i t e of e f f o r t s  to minimize  the  turbulence-induced  p r e s s u r e f l u c t u a t i o n s by p r o v i d i n g the f l o w s t r a i g h t e n e r s , small o s c i l l a t i o n s of the water l e v e l s i n the manometers were The water l e v e l s levels  observed.  i n three gauge tanks c o r r e s p o n d i n g to the  i n the manometers were used  average  to measure the p r e s s u r e heads i n  each of the p i e z o m e t r i c r i n g s i n o r d e r to a c h i e v e a s a t i s f a c t o r y degree of a c c u r a c y .  The p r e s s u r e f l u c t u a t i o n s i n the manometers were  a u t o m a t i c a l l y smoothed out i n these In 5.5  tanks.  t h i s s e r i e s of t e s t s , three gauge tanks, each of  i n c h e s , connected  w i t h f o u r c o r r e s p o n d i n g manometers on the main  and branch p i p e s , were f i t t e d w i t h hook gauges and v e r n i e r s to c a t e the average  diameter  indi-  p r e s s u r e heads i n the r e l a t e d p i e z o m e t r i c r i n g s .  Each p r e s s u r e head was  measured to one  use of e x t e n s i o n rods f i t t e d  thousandth  of a f o o t .  By  the  to the hook gauges when r e q u i r e d , the  range o f d i f f e r e n c e i n p r e s s u r e heads would be i n c r e a s e d from 2 f t . to  3 f t . (i.e.,  6 i n c h a d d i t i o n a l a t the top and 6 i n c h a t the bottom)  u s i n g the same v e r n i e r s . set  an a r b i t r a r y 0.210  stream  1.4  gauge tanks  The v e r n i e r i n the upstream gauge tank  was  f t . h i g h e r than those i n the c e n t r a l and down-  to f a c i l i t a t e  measuring.  EXPERIMENTAL MEASUREMENTS A.  Measurement of Weight of Water A weighing  tank w i t h maximum c a p a c i t y of 20,000 l b s . was  16 used to measure the weight of water.  The s c a l e s of the weighing  tank were checked and found c o r r e c t b e f o r e s t a r t i n g the experiment. B.  Measurement of Time The time i n t e r v a l f o r a p a r t i c u l a r weight o f water,  which  was c o l l e c t e d i n the weighing tank, was r e c o r d e d by an e l e c t r i c to 0.1  clock  second. C.  Measurement of  Temperature  For each t e s t , the temperature o f water was r e a d by thermometer and the d e n s i t y and the k i n e m a t i c v i s c o s i t y were determined f o r the purpose o f c a l c u l a t i n g d i s c h a r g e s and Reynold's numbers  (Re =  V D lis ) i n the c o r r e s p o n d i n g main and branch p i p e s . D.  Measurement of P r e s s u r e Head The p r e s s u r e head was measured from the water l e v e l s of t h r e e  gauge tanks under the assumption t h a t the f l o w was i n the steady s t a t e c o n d i t i o n , and t h a t the water l e v e l s  i n the gauge tanks were c o n s t a n t .  S i n c e the a r e a r a t i o of a manometer tube (1/4 i n c h i n diameter) to a gauge tank (5.5 i n c h c ; i n diameter) was a p p r o x i m a t e l y 1 : 480, a p e r i o d of n o t l e s s water l e v e l s  than 2 hours was c o n s i d e r e d n e c e s s a r y t o a d j u s t the  i n the gauge tanks t o the steady s t a t e  I n measuring i n the f l e x i b l e  the p r e s s u r e heads, the presence o f a i r bubbles  t u b i n g connected to the p i e z o m e t r i c p o i n t s  g r e a t l y a f f e c t the a c c u r a c y . a i r bubbles were removed p r i o r E.  condition.  G r e a t c a r e was  will  taken to ensure t h a t a l l  to t a k i n g any r e a d i n g s .  Discharge Determination The d i s c h a r g e was determined from the weight o f water  charged w i t h i n a c e r t a i n time i n t e r v a l ,  Duiring the experiment,  dis-  d i s c r e p a n c i e s were found  i n measuring the weight of water u n l e s s a  s u f f i c i e n t l y l o n g time i n t e r v a l was i n t e r v a l of approximately an a c c u r a t e d i s c h a r g e The  300  o b t a i n e d from the formulas  h  v  seconds was  For a l l t e s t s , a  time  r e q u i r e d i n o r d e r to achieve  determination.  d i s c h a r g e and  Q = W / (t x  adopted.  the v e l o c i t y head i n each p i p e  was  as f o l l o w s :  w)  (1)  =  (2)  i n which Q = d i s c h a r g e , i n c f s ; W = weight of water, i n l b s ; t = i n t e r v a l , i n sees; w = u n i t weight of water, i n l b s / f t velocity  i n pipe, i n fps; h of g r a v i t y ,  in ft/sec  ; V = mean  = v e l o c i t y head, i n f t ; and g =  2 eration  3  .  time  accel-  18  CHAPTER  II  BASIC CONCEPTS RELATING TO HEAD LOSSES  When water flows through a c l o s e d c o n d u i t , are  certain  resistances  c r e a t e d which oppose the m o t i o n , and depend upon the  geometrical  form o f the c o n d u i t .  They are  d i r e c t i o n and c r o s s s e c t i o n , other  causes.  is  c o n v e r t e d i n t o heat energy  As f a r as  the head l o s s e s  f o r d i v i d e d flows i n branched p i p e systems continuity,  i n flow  merging and d i v i d i n g of flows and from  K i n e t i c energy  the a c t i o n of t u r b u l e n c e .  caused by f r i c t i o n , changes  momentum, and energy e q u a t i o n s ,  theory have been a p p l i e d to e v a l u a t e  are  at  the  concerned,  and the  through junctions  the  free-streamline  the approximate head l o s s e s  flow through b i f u r c a t i o n s and t r i f u r c a t i o n s A c c u r a t e d e t e r m i n a t i o n of such head l o s s e s ,  ' i f required,  (^),  for  (16)^  can o n l y be  o b t a i n e d by model t e s t s . In t h i s  study,  the model t e s t s of the head l o s s e s  resulting  from the flow through b o t h a wye and a m a n i f o l d were based on the energy e q u a t i o n of B e r n o u l l i f o r the o n e - d i m e n s i o n a l c o n d i t i o n . These l o s s e s were c a l c u l a t e d under the f o l l o w i n g (1)  the mean v e l o c i t y at  of the flow a t (2)  that  each c r o s s - s e c t i o n  is  representative  section.  the flow p a s s i n g through the c r o s s - s e c t i o n where the  ment of p r e s s u r e head was made i s (3)  assumptions:  measure-  i n steady and i r r o t a t i o n a l m o t i o n .  the l o n g i t u d i n a l a x i s of the whole system i s h o r i z o n t a l .  19 2.1  FORM LOSSES OF WYES The  energy e q u a t i o n  o f B e r n o u l l i f o r the one-dimensional con-  d i t i o n s t a t e s t h a t the t o t a l head -- c o n s i s t i n g o f the sum o f the v e l o c i t y head, p r e s s u r e head and geometric head o f the f l u i d -- above an a r b i t r a r y h o r i z o n t a l r e f e r e n c e p l a n e must be equal the same r e f e r e n c e plane vening  head l o s s e s .  to t h a t above  a t any s u c c e s s i v e s e c t i o n , p l u s the i n t e r -  F o r a h o r i z o n t a l wye arrangement as shown i n  F i g u r e 1-3, the energy g r a d i e n t l i n e s a r e e x t r a p o l a t e d t o the theoretical  c e n t r e o f the wye on the b a s i s of a sudden t r a n s i t i o n a t t h a t  point.  (See F i g u r e I I - l ) .  The form l o s s of the wye i s determined as  the d i f f e r e n c e between the energy g r a d i e n t l i n e s upstream and downstream o f the wye measured a t i t s c e n t r e . be  expressed  from the energy e q u a t i o n  h  =h,+ h  +h pm  vm  pb  L  +  vb  T h i s form l o s s ,  ^ h , can  as f o l l o w s :  dh + L + L , fm fb  --- (3)  or -  h  -  - p h  +  < vm " vb> h  h  "  ( h  fm  +  V  -  —  -  (  4  )  i n which h , h and h_ = p i e z o m e t r i c head, v e l o c i t y head and s k i n pm vm rm f r i c t i o n l o s s o f head i n the main p i p e , i n f t ; p i e z o m e t r i c head, v e l o c i t y head and s k i n f r i c t i o n of the branch p i p e s , i n f t ; and ^ h ' ' p r  r  = h pm  *Vb ^ an  ^fb  =  l o s s of head i n one  - h , = d i f f e r e n c e of pb  p i e z o m e t r i c heads, i n f t . The  wye l o s s c o e f f i c i e n t , k, based on the v e l o c i t y head i n the  main p i p e can be expressed as  vm  20 When the v e l o c i t y , the s k i n f r i c t i o n l o s s and  the p r e s s u r e head  a t the p i e z o m e t r i c r i n g on each p i p e f o r a p a r t i c u l a r d i s c h a r g e known, the form l o s s of a wye The  can be o b t a i n e d from E q u a t i o n ( 4 ) .  l o s s c o e f f i c i e n t of the wye The  i s determined  from E q u a t i o n  d i s t a n c e from the t h e o r e t i c a l c e n t r e of each wye  piezometric rings Table I I - l . The  on the main and branch skin f r i c t i o n  losses  i n S e c t i o n 4.1.  (5). to the  pipes i s tabulated i n  f o r the p a r t i c u l a r l e n g t h s from  S to T i n the main p i p e and from T to are determined  are  or  i n the branch  pipes  The p r e s s u r e heads a t the p i e z o m e t r i c  rings  are o b t a i n e d from the steady water l e v e l s of the three gauge  tanks  connected  from E q u a t i o n  2.2  to the manometers.  The v e l o c i t y heads are  obtained  (2) .  FORM LOSSES OF MANIFOLDS F o r a m a n i f o l d as shown i n F i g u r e I I - 2 , the energy e q u a t i o n  be d e r i v e d i n the same way of a m a n i f o l d i n s t e a d  as E q u a t i o n  of a wye.  a manifold i s obtained.  (3) where ^ h i s the form l o s s  From E q u a t i o n  ( 4 ) , the form l o s s  d i s t a n c e from the t h e o r e t i c a l c e n t r e o f each wye  piezometric rings  of  The m a n i f o l d l o s s c o e f f i c i e n t , k, based on  the v e l o c i t y head i n the main p i p e i s o b t a i n e d from E q u a t i o n The  can  on the main and branch  (5).  to the  pipes f o r manifold  arrange-  ment i s g i v e n i n Table I I - 2 .  2.3  HYDRAULIC POWER LOSSES IN WYE  AND  MANIFOLD ARRANGEMENTS  In most i n s t a n c e s , the d e t e r m i n a t i o n of the h y d r a u l i c  power  l o s s r e s u l t i n g from the p a s s i n g of flow from the main p i p e i n t o branch p i p e s i s n e c e s s a r y .  T h i s study was  made to a s c e r t a i n  the  the  21 relationship between the hydraulic power loss and the  proportional  flow of water through the branches of the wye and manifold arrangements . The hydraulic power loss i n a branched pipe system can be expressed as P  (6)  = w (Q ^ h r r  v  u  1  in which P^ = hydraulic power l o s s , i n f t - l b / s e c ; charges i n the r i g h t and l e f t branches ^h^ and  and  = dis-  respectively, i n c f s ; and  h^ = form losses of wye or manifold r e s u l t i n g from the  flow passing through the wye or manifold into the r i g h t and l e f t branches respectively, i n f t . The above equation can be made more useful for d i r e c t applicat i o n by reducing a l l the terms of i t into a dimensionless expression. The hydraulic power i n the main pipe, P , i s expressed as  (7)  P = w Q h m m vm Then Equation (6)  p  =  can be converted into a dimensionless form as k  ^m  r  Qr_+ % i  k i  5i_  (8)  ^m  i n which p = hydraulic power loss i n dimensionless form; charge i n the main pipe, i n c f s ; and  = dis-  and k^ = the c o e f f i c i e n t of  -^h^, and of ^ h^ based on the v e l o c i t y head i n the main pipe.  22  CHAPTER I I I EXPERIMENTAL INVESTIGATIONS  3.1  PRELIMINARY INVESTIGATION In the i n i t i a l  s e t up and  as f o l l o w s :  Symmetrical  V e l o c i t y - D i s t r i b u t i o n i n Main P i p e C l o s e to  Horizontal velocity  These t e s t s were made by Ahmed  who  completely  A f t e r the l e n g t h of the i n f l u e n t main p i p e was and  two  wye.  p r o v i d e d maximum d i s c h a r g e of  c f s i n one branch w i t h the o t h e r branch  diameters  Wye  t r a v e r s e t e s t s were performed a c r o s s  the main p i p e a t a s e c t i o n about 6 inches upstream from the  0.92  was  subsequently m o d i f i e d to meet c e r t a i n proposed h y d r a u l i c  requirements A.  stage of the study an e x p e r i m e n t a l model  closed.  i n c r e a s e d to 75 p i p e -  f l o w s t r a i g h t e n e r s i n s t a l l e d i n the upstream main  p i p e , the t e s t showed t h a t a symmetrical  v e l o c i t y - d i s t r i b u t i o n about  the l o n g i t u d i n a l a x i s of the main p i p e a c r o s s the t e s t s e c t i o n was achieved.  Since the symmetrical  v e l o c i t y - d i s t r i b u t i o n was  the f l o w p a t t e r n s f o r a symmetrical branch  p i p e s would have to be B.  demonstrated,  f l o w c o n d i t i o n i n each of the  identical.  C h a r a c t e r i s t i c V e l o c i t y - D i s t r i b u t i o n at Piezometric Stations a t Branch P i p e s The  d i s t u r b a n c e a r i s i n g from the f l o w p a s s i n g through  a  wye  or m a n i f o l d can i n f l u e n c e p r e s s u r e r e a d i n g s f o r some d i s t a n c e downstream  of the wye  or m a n i f o l d .  d i s t a n c e of 25 p i p e - d i a m e t e r s  E x p e r i e n c e has i s necessary  shown t h a t a minimum  f o r gradual m o d i f i c a t i o n  of the v e l o c i t y d i s t r i b u t i o n to a c h a r a c t e r i s t i c form through  the  remainder o f the s t r a i g h t p i p e .  T h e r e f o r e , a p i e z o m e t r i c r i n g was  p r o v i d e d a t the downstream end o f each branch p i p e , r e s u l t i n g i n a length-diameter C.  r a t i o o f approximately 30.  C o n d i t i o n of Discharges Large  troughs were p r o v i d e d a t the o u t l e t s o f the branch  p i p e s t o ensure atmospheric  3.2  i n t o Free Atmosphere a t O u t l e t s  p r e s s u r e a t the o r i f i c e s .  FLOW PATTERNS A few o f many p o s s i b l e f l o w p a t t e r n s under d i f f e r e n t flow con-  ditions,  i . e . , symmetrical,  shown i n F i g u r e s I I I - l  unsymmetrical  and I I I - 2 .  and o n e - l e g f l o w s , are  I t was observed  t h a t the r e g i o n  of the eddies formed i n a wye or m a n i f o l d was i n f l u e n c e d d i r e c t l y by the d i s c h a r g e , the v e l o c i t y , the s i z e o f the t i e - r o d , the subtending angle of the wye and the p r o p o r t i o n a l f l o w of water through the branches.  24  CHAPTER IV EXPERIMENTAL PROCEDURES  4.1  DETERMINATION OF  SKIN FRICTION LOSSES IN MAIN PIPE AND  BRANCH  PIPES The (4) w i t h  form l o s s of a wye  or m a n i f o l d was  o b t a i n e d from  Equation  the s k i n f r i c t i o n l o s s e s i n the main and branch p i p e s  determined i n advance.  F o r any  g i v e n l e n g t h s , the s k i n f r i c t i o n  l o s s e s i n e i t h e r the main p i p e or each branch p i p e under v a r i o u s charges were determined by e m p i r i c a l equations A.  dis-  i n t e r p o l a t i o n and by p r o p o r t i o n from  the  as d e r i v e d below.  S k i n F r i c t i o n Loss I n Main P i p e The  i n s t a l l a t i o n , as shown i n F i r u g e 1-3,  was  used to  determine the s k i n f r i c t i o n l o s s i n the main p i p e f o r l e n g t h (3.375 f t . ) .  Two  SS^  of the gauge tanks were connected to the p i e z o m e t r i c  r i n g s a t the c r o s s - s e c t i o n s of S and  S^.  (See F i g u r e 1-3).  As  the  v e l o c i t y heads a t these s e c t i o n s were e q u a l , no v e l o c i t y - h e a d c o r r e c t i o n was  r e q u i r e d , t h e r e f o r e the d i f f e r e n c e of p r e s s u r e heads  between these  two  s e c t i o n s i n d i c a t e d the s k i n f r i c t i o n  The main p i p e was from 0.32  to 1.50  c f s and  loss.  tested with various discharges  ranging  the r e s u l t s t a b u l a t e d i n Table IV-1.  When  the r e s u l t s were p l o t t e d on a l o g - l o g s c a l e as shown i n F i g u r e  IV-1,  a l i n e a r r e l a t i o n between the s k i n f r i c t i o n l o s s and d i s c h a r g e was f o r curve  the  corresponding  d e t e c t e d . Hence, by u s i n g the method o f l e a s t  fitting,  the f o l l o w i n g e m p i r i c a l e q u a t i o n was  squares  obtained.  25 h  i n which h SS  f  (  )  °'  =  0 8 2 5  Q  1  ,  7  8  9  (  , x = skin f r i c t i o n t (,bb^/  9  )  l o s s i n the main p i p e f o r l e n g t h  in ft.  1 }  B.  S k i n F r i c t i o n Losses The  friction is  S S l  experimental  set-up  f o r the d e t e r m i n a t i o n o f the s k i n  l o s s , f o r l e n g t h BB^ (9.0 f t . ) , i n each o f the branch  shown i n F i g u r e IV-2.  which determined for  i n Branch P i p e s  The t e s t s were conducted  the s k i n f r i c t i o n  similarly  l o s s i n the main p i p e .  pipes  t o those  Correction  v e l o c i t y head between the upstream p i e z o m e t r i c r i n g o f the i n l e t  p i p e and the downstream p i e z o m e t r i c r i n g o f the branch p i p e was made i n the computations. Each branch  p i p e was t e s t e d w i t h v a r i o u s d i s c h a r g e s  from 0.32 t o 0.75 c f s and the r e s u l t s  ranging  t a b u l a t e d i n Table IV-2.  When  the r e s u l t s were p l o t t e d on l o g - l o g graph papers as shown i n F i g u r e s IV-3 for  and IV-4,  s i m i l a r l i n e a r r e l a t i o n s h i p s f o r each branch  the main p i p e were found.  the e m p i r i c a l equations  By u s i n g l e a s t squares  f o r the f r i c t i o n  curve  p i p e as fitting,  l o s s i n each branch  pipe  were o b t a i n e d as f o l l o w s : (1)  F o r the r i g h t branch h  (2)  f r  = 1.0696 Q  1  ,  8  2  pipe  ( S e c t i o n s B and D) (10)  1  F o r the l e f t branch p i p e ( S e c t i o n s A and C) h  £ 1  = 1.0667 Q  1  ,  8  1  (11)  1  i n which h.. and h ~ = s k i n f r i c t i o n fr f1  l o s s e s i n the r i g h t and l e f t  branches p i p e r e s p e c t i v e l y f o r l e n g t h B.. Bj (9.0 f t . ) , i n f t .  26 4.2  SEQUENCE OF EXPERIMENT In each t e s t i n g  made to determine  arrangement,  the l o s s e s  a s e r i e s of head l o s s  t e s t s was  i n the wye or m a n i f o l d under  different  flow c o n d i t i o n s . The t e s t s were s t a r t e d w i t h symmetrical f l o w c o n d i t i o n . fices  of equal s i z e were p l a c e d a t  the o u t l e t s  Ori-  of the branch p i p e s  and the c o n t r o l v a l v e was then a d j u s t e d to the r e q u i r e d  discharge.  F o r each t e s t the d i s c h a r g e  approximately  1.50,  1.10,  levels  0.92,  0.75,  0.50  i n the main p i p e was s e t and 0.32  cfs  i n turn.  i n the gauge tanks became c o n s t a n t ,  discharge, pressure  When the water  the measurement  r i g h t and l e f t branch d i s c h a r g e s ,  head from the gauge r e a d i n g s  at  of combined  the measurement  and the measurement  of  of water  temperature were t a k e n . The t e s t s of unsymmetrical f l o w c o n d i t i o n s were c a r r i e d next.  O r i f i c e s of d i f f e r e n t s i z e s were p l a c e d to c o n t r o l  t i o n a l f l o w of water through each of the branches . branch d i s c h a r g e  to  a constant discharge testing  and 0.92  The r a t i o  the main p i p e d i s c h a r g e v a r i e d from 0 to  For the purpose of comparing the form l o s s e s  the  the  out proporof 100%.  of wyes and m a n i f o l d s ,  i n the main p i p e was m a i n t a i n e d a t 0.75  cfs  for  arrangements w i t h the subtending angles .of 9 0 ° and 6 0 ° ,  cfs  f o r t h a t w i t h the subtending angle of 4 5 ° .  were then taken as  Measurements  i n the f o r e g o i n g p a r a g r a p h .  The t e s t s of o n e - l e g f l o w c o n d i t i o n s , where one branch was comp l e t e l y b l o c k e d o f f and an o r i f i c e of a p p r o p r i a t e the o u t l e t  s i z e was p l a c e d  of the o t h e r b r a n c h , were f i n a l l y c o n d u c t e d .  i n the open branch v a r i e d from 0.32  to 0.92  cfs.  The  at  discharge  27  CHAPTER V RESULTS AND  5.1  CONCLUSIONS  RESULTS A.  Form Losses o f Wyes T a b l e s V - l t o V-10 g i v e the h y d r a u l i c computations o f the  form l o s s e s and l o s s c o e f f i c i e n t s f o r the 9 0 ° , 60° and 45° wyes i n the wye  arrangements: T a b l e s V - l to V-5 g i v e the computations f o r the 90° wye w i t h o u t any t i e - r o d , and w i t h the TR1, TR2, TR3 and TR4 t i e - r o d s p l a c e d i n t u r n a t the t h e o r e t i c a l c e n t r e o f the wye  respectively.  T a b l e s V-6 t o V-9 g i v e the computations f o r the 60° wye w i t h o u t any t i e - r o d , and w i t h the TR2, TR3. and TR4 t i e rods  respectively.  T a b l e V-10 g i v e s the computation f o r the 45° wye w i t h o u t any  tie-rod.  The r e s u l t s o f the above computations a r e p l o t t e d i n F i g u r e s V - l t o V-9: F i g u r e s V - l , V-4 and V-7 show the form l o s s c o e f f i c i e n t v s . d i s c h a r g e under symmetrical f l o w c o n d i t i o n s f o r the 9 0 ° , 60° and 45° wyes  respectively.  F i g u r e s V-2, V-5 and V-7 show the form l o s s c o e f f i c i e n t v s . d i s c h a r g e under o n e - l e g f l o w c o n d i t i o n s f o r the 9 0 ° , 60° and 45° wyes  respectively.  28 F i g u r e s V-3, V-6 and V-8 show the form l o s s c o e f f i c i e n t v s . the r a t i o of branch d i s c h a r g e to the main d i s c h a r g e under unsymmetrical f l o w c o n d i t i o n s f o r the 9 0 ° , 60° and 45° wyes respectively. F i g u r e V-9 shows the comparisons o f the form l o s s c o e f f i c ients (a)  among the three wyes w i t h o u t any t i e - r o d , and  (b)  between the 90° and 60° wyes w i t h the TR3 t i e - r o d ,  under unsymmetrical f l o w c o n d i t i o n s . B.  Form Losses o f M a n i f o l d s T a b l e s V - l l to V-15 g i v e the h y d r a u l i c computations o f the  form l o s s e s and l o s s c o e f f i c i e n t s f o r the 9 0 ° , 60° and 45° m a n i f o l d s in  the m a n i f o l d arrangements: T a b l e s V - l l , V-13 and V-15 g i v e the computations f o r the 90°,  60° and 45° m a n i f o l d s r e s p e c t i v e l y w i t h o u t any t i e - r o d .  T a b l e s V-12 and V-14 g i v e the computations f o r the 90° and 60° m a n i f o l d s r e s p e c t i v e l y w i t h the TR3 t i e - r o d . The r e s u l t s o f the above computations a r e p l o t t e d i n F i g u r e s V-10 t o V-14 under s y m m e t r i c a l , o n e - l e g and unsymmetrical flow conditions  respectively.  F i g u r e s V-13 and V-14 show the comparisons  o f wye and mani-  f o l d l o s s c o e f f i c i e n t s w i t h o u t any t i e - r o d , and w i t h the TR3 t i e - r o d under unsymmetrical f l o w c o n d i t i o n s  respectively.  The same c o o r d i n a t e systems f o r p l o t t i n g have been adopted as i n S e c t i o n 5.1.A.  29 C.  H y d r a u l i c Power Losses Tables V-16  power l o s s e s  and V-17  f o r the wye  F i g u r e s V-15 r a t i o of branch  i n Wye  and M a n i f o l d Arrangements  g i v e the computation of the  and m a n i f o l d arrangements  and V-16  show the h y d r a u l i c  hydraulic  respectively. power l o s s v s . the  d i s c h a r g e to the main d i s c h a r g e f o r both  arrangements  respectively.  5.2  CONCLUSIONS (1) The  of  form l o s s c o e f f i c i e n t of a wye  the p r o p o r t i o n a l  f l o w of water through  the t i e - r o d used and (2) Separate indicated two  angle of the  t h a t the form l o s s of a m a n i f o l d  and  tends  the s i z e of  wye. and  of the i n d i v i d u a l form l o s s e s  and of  i n t e r n a l t i e - r o d p l a c e d a t the t h e o r e t i c a l c e n t r e of a  i n the downstream branched f l o w , as w e l l (4) The necessarily  as i n c r e a s i n g  form l o s s c o e f f i c i e n t of a wye  a minimum f o r a symmetrical  (5) F o r a symmetrical  flow  flow condition,  of a wye  or m a n i f o l d i s n o t g r e a t l y  charge.  The  any  elbows  -- c o n s i s t i n g of a wye  to c r e a t e c o n s i d e r a b l e p r e s s u r e f l u c t u a t i o n s  of the wye  function  elbows.  (3) An  without  the branches,  head l o s s t e s t s f o r wyes, m a n i f o l d s  elbows -- i s l e s s than the sum  the wye  wye  the subtending  or m a n i f o l d i s a  and  disturbance  the form l o s s .  or m a n i f o l d i s not condition. the form l o s s c o e f f i c i e n t  a f f e c t e d by the amount of d i s -  form l o s s c o e f f i c i e n t i n c r e a s e s as the subtending  and  the s i z e of the t i e - r o d are i n c r e a s e d .  t i e - r o d i n e i t h e r the 45° wye  lowest form l o s s c o e f f i c i e n t .  The  angle  system  or the 45° m a n i f o l d had  the  30 (6) For a one-leg flow condition, due to the turbulence associated with eddies i n the closed branch of a wye or manifold, the head loss i n the closed branch i s generally greater than the head loss i n the open branch. (7) A l l the tests indicate that a one-leg flow condition i s the most i n e f f i c i e n t . (8) For an unsymmetrical  flow condition, the form loss c o e f f i c -  ient of a wye or manifold i s greatly affected by the proportional flow of water through the branches and the size of the tie-rod.  For  any fixed r a t i o of branch discharge to the main discharge, the form loss c o e f f i c i e n t increases as the size of the tie-rod i s increased. (9) For an unsymmetrical  flow condition i n a wye or manifold  without any tie-rod, the form loss c o e f f i c i e n t i s a minimum when the r a t i o of branch discharge to the main discharge i s approximately 0.6. Under the same flow condition with a tie-rod, the form loss c o e f f i c i e n t i s a minimum when the r a t i o of branch discharge to the main discharge i s approximately 0.4. (10) Referring to Figures V-13 and V-14, the curves of form loss c o e f f i c i e n t vs. discharge r a t i o obtained for both a wye and a manifold are similar under the conditions that (1) no tie-rod i s used i n either the wye or manifold; (2) i f a tie-rod be used, i t s h a l l be i d e n t i c a l i n both arrangements; and (3) there s h a l l be an i d e n t i c a l subtending angle of the wye.  31  APPENDIX HEAD LOSSES IN ELBOWS  The head l o s s i n an elbow i s c o n s i d e r e d h e r e i n to be the l o s s i n excess arily  o f t h a t i n a s t r a i g h t p i p e o f equal l e n g t h .  I t i s prim-  caused by the induced s p i r a l motions o f flow i n the elbow which  are p r o b a b l y  independent o f i t s l e n g t h and c r e a t e a c o n s i d e r a b l e  d i s t u r b a n c e downstream.  The motion around the elbow tends  to take on  the c h a r a c t e r i s t i c s o f a f r e e v o r t e x h a v i n g a l a r g e r v e l o c i t y a t the i n s i d e o f the elbow than t h a t a t the o u t s i d e .  C o r r e s p o n d i n g l y , the  p r e s s u r e a t the i n s i d e i s l e s s than t h a t a t the o u t s i d e .  At the  downstream end o f the elbow, the v e l o c i t y d i s t r i b u t i o n depends on the f l o w i n the elbow.  T h i s d i s t r i b u t i o n changes g r a d u a l l y i n the  downstream s t r a i g h t p i p e u n t i l  i t assumes the c h a r a c t e r i s t i c form o f  that i n a s t r a i g h t pipe. T h i s study i s m a i n l y  concerned  w i t h the head l o s s e s o f the  elbows which a r e used to c o n s t r u c t the m a n i f o l d s . the study  The purpose of  i s t o determine the head l o s s e s i n the elbows a l o n e .  From the set-up  shown i n F i g u r e A-2, f o r h o r i z o n t a l p i p i n g , the  l o c a l i z e d elbow l o s s can be expressed  from the energy e q u a t i o n as  follows: h  + h . = h, + h , + b vb v i1  Ah  + h_. + h f i fb  (12)  ) - (h_. + h _ )  (13)  E  or ^h. = E  Ah  p  + (h . - h vi  vb  f i  fb  i n which A L = head loss i n an elbow, i n f t ; h ., h . and h... = E pi' vi f i piezometric head, v e l o c i t y head and skin f r i c t i o n loss of head i n the upstream i n l e t pipe, i n f t ; and hp^j  n v  ^  a n c  *  =  piezometric  head, v e l o c i t y head and skin f r i c t i o n loss of head i n the downstream straight pipe, i n f t . The elbow loss c o e f f i c i e n t , k^, based on the mean v e l o c i t y head i n the upstream pipe i s thus expressed by Ah "E - — 5 —  (14)  V ^ / 2g i n which  « v e l o c i t y i n the upstream pipe.  Table A - l gives the distance from the theoretical centre of each elbow to both upstream and downstream piezometric rings.  The  downstream piezometric ring has a distance of approximately 30 pipediameters downstream of the elbow. The results of the tests are tabulated i n Tables A-2, A-3 and A-4 for 45 , 30  and 22-1/2  elbows respectively.  The loss c o e f f i c -  ients of the elbows versus discharges are p l o t t e d i n Figure A-3.  33  BIBLIOGRAPHY  V o g e l , G.,  "UNTERSUCHUNGEN UBER DEN  VERLUST IN RECHTWINKLIGEN  ROHRVERZWEIGUNGEN", M i t t , des Hydr. I n s t i t u t s der Technischen Hochschule, Munchen, No.  2,  1928.  ( I n v e s t i g a t i o n s o f the L o s s e s i n R i g h t Angle P i p i n g  Bifurca-  t i o n s .) Thoma, D. and C o l l a b o r a t o r , " T r a n s a c t i o n s of the Munich H y d r a u l i c I n s t i t u t e " , B u l l e t i n 3, T r a n s l a t e d by A.S.M.E., C a r d e l , A.,  1935.  "LES PERTES DE CHARGE DANS LES ECOULEMENTS AU  TRAVERS DE BRANCHEMENTS EN TE", B u l l e t i n Techique de l a S u i s s e Romanda, Nos.  9 & 10,  1957.  (The Loss o f Head i n the Flow through Tee M a r c h e t t i , M. and Noseda, G.,  Branches.)  "PERDITE DI CARICO NELLE BIFOR-  CAZIONI SIMMETRICHE A DIAMETRO CONSTANTE, DELLE CONDOTTE FORZATE", L ENERGIA ELLETTRICA NO. 1  (Loss of Head i n Symmetrical i n a Penstock Fritjof  4,  1960.  B i f u r c a t i o n s of Constant  Diameter  Conduit.)  S a l v e s e n , " H y d r a u l i c Losses i n B r a n c h p i p e s " , The Water  Power L a b o r a t o r y , The T e c h n i c a l U n i v e r s i t y of Norway, O c t . Ahmed, S.,  "Head Loss i n Symmetrical  Bifurcations",  T h e s i s , U n i v e r s i t y of B r i t i s h Columbia, H e r a k o v i c h , C a r l T.,  and O t t s , J.V.,  Master's  1965.  " C h a r a c t e r i s t i c s of Flow  through Symmetrical L a t e r a l s " , Report No.  13, S t u d i e s i n Engrg.  Mechanics, C e n t e r f o r Research i n Engrg. S c i e n c e , U n i v . of Kansas ( L a u r e n c e ) ,  1962.  1962.  (8)  Karake,  S. and R u f f , T.F., " F i n a l Report o f H y d r a u l i c Model  S t u d i e s f o r D i v e r s i o n , Power and I r r i g a t i o n Tunnels",  Civil  E n g i n e e r i n g Dept., C o l o r a d o S t a t e U n i v . , Jan. 1965. (9)  G l a d w e l l , J . S . and Tinney, E.R., " H y d r a u l i c S t u d i e s o f Large Penstock T r i f u r c a t i o n " , J o u r n a l o f the Power D i v i s i o n , ASCE, V o l . 91, No. P01, 1965.  (10)  G l a d w e l l , J.S. and Tinney, E.R., "Round B u t t e Penstock  Tri-  f u r c a t i o n " , B u l l e t i n 260, Washington S t a t e I n s t i t u t e of Techn o l o g y , D i v . o f I n d u s t r i a l Research, Washington S t a t e U n i v . , 1962. (11)  G l a d w e l l , J.S., T i n n e y , E.R. and K r e u z e r , H., "The Round Butte Penstock T r i f u r c a t i o n T i e - B a r " , Research Report No. 63/9-80, Washington S t a t e U n i v . , 1963.  (12)  B i e r , P.J., "Welded S t e e l Penstocks, Design and C o n s t r u c t i o n " , E n g i n e e r i n g Monography No. 3, U.S. Bureau o f R e c l a m a t i o n .  (13)  F a v r e , H., "On the Law which Govern the Movement o f F l u i d s i n C o n d u i t s h a v i n g L a t e r a l A b d u c t i o n s " , Rev. U n i v . Minnes., 1937.  (14)  McNown, J.S., "Mechanics  of M a n i f o l d Flow", T r a n s a c t i o n s o f  ASCE, V o l . 119, 1954. (15)  McNown, J.S. and Hsu, E.Y., " A p p l i c a t i o n to D i v i d e d Flow", P r o c e e d i n g s , Midwestern Dynamics (ed. by J.W. Edwards),  (16)  Mapping  Conference on F l u i d  M i c h i g a n , 1951.  Lakshmana Rao, N.S., Syamala Rao, B.C. and Ramaswamy, R.I., " P r e s s u r e Losses a t T r i f u r c a t i o n s of  (17)  o f Conformal  i n Closed Conduits", Journal  the H y d r a u l i c s D i v i s i o n , ASCE, V o l . 93, No. HY3, May 1967.  Freeman, J.R., "The Flow o f Water i n P i p e s and P i p e F i t t i n g s " , P u b l i s h e d by A.S.M.E., 1941.  35 (18)  Yarnell,  D.L.  and N a g l e r , F.A.,  "Flow of Water Around Bends  i n P i p e s " , T r a n s a c t i o n s o f ASCE, V o l . 100,  1935.  (19)  A.S.M.E., " F l u i d M e t e r s " , 4 t h ed.,  (20)  S t r e e t e r , V.L., " F l u i d Mechanics", M c G r a w - H i l l , 1962.  (21)  Jaeger, C ,  (22)  Rouse, H.,  "Advanced Mechanics of F l u i d s " ,  (23)  K i n g , H.W.  and B r a t e r , E.F., "Handbook of H y d r a u l i c s " , 4 t h ed.,  " E n g i n e e r i n g F l u i d Mechanics", McGraw-Hill, 1962.  McGraw-Hill, (24)  1937.  Bakhmetefv, Univ. Press,  John W i l e y , 1959.  1954. B.A., 1941.  "The Mechanics of T u r b u l e n t Flow", P r i n c e t o n  36  TABLE 1-1  Areas of M a i n , Branch and I n l e t  Description  Mean Diameter  Mean Area  (sq.ft.)  (inch)  Pipes  Diameter a t Piezometric Ring (inch)  Area a t Piezometric Ring (sq.ft.)  Main P i p e  5.252  0.1503  5.251  0.1503  R i g h t Branch  3.746  0.0764  3.750  0.0766  L e f t Branch  3.750  0.0766  3.748  0.0766  3.734  0.0759  Inlet  Pipe  TABLE 1-2  O r i f i c e Arrangement  Numerical D e s i g n a t i o n of o r i f i c e  External Diameter (inch)  Internal Diameter (inch)  X  3.720  3.622  1  3.720  3.300  2  3.720  3.175  3  3.720  2.913  4  3.720  2.749  5  3.720  2.490  6  3.720  2.000  7  3.720  1.342  8  3.720  0.840  9  3.720  0.542  Remark  ) )  Rounded edge orifices  37  TABLE I I - 1 D i s t a n c e from T h e o r e t i c a l Centre of Wyes to P i e z o m e t r i c Rings on Main and Branch P i p e s * (For Wye Arrangement)  Particulars  Distance SS. 4  Distance S.T 4  Distance ST  Distance TS, o r T S 1  0  Distance Distance S..D.. TD. o r TD„ 2 1 1 1 2 or S D 2  2  (ft)  (ft)  (ft)  (ft)  (ft)  (ft)  90° Wye  0.500  0.125  0.625  0.374  8.833  9.207  60° Wye  0.500  0.083  0.583  0.497  8.833  9.330  45° Wye  0.500  0.060  0.560  0.608  8.833  9.441  * See F i g u r e I I - l  TABLE I I - 2 D i s t a n c e from T h e o r e t i c a l Centre on Main and Branch P i p e s ** (For M a n i f o l d Arrangement)  Particulars  Distance Distance ST TSj^ o r T S  2  o f Wyes t o P i e z o m e t r i c Rings  Distance  Distance  1 1 or S C  1 1 or C F  S  C  C  2  2  F  2  2  Distance F D 11 or F D  Distance  (ft)  2  2  1 1 or T C D T C  D  2  (ft)  (ft)  (ft)  (ft)  (ft)  90° M a n i f o l d  0.625  0.374  0.641  0.500  8.833  10.348  60° M a n i f o l d  0.583  0.497  0.333  0.333  8.833  9.996  45° M a n i f o l d  0.560  0.608  0.370  0.238  8.833  10.049  ** See F i g u r e I I - 2 .  2  OA  Ul  -P-  OJ  Ui  h-> O O  h-» Ul O  VO  VO  O O  O O  O O  OJ  OJ  Ul Ul Ul Ui  O O  OJ  OJ  ho ho  ho O J I O w  OA N> - J  OJ  o  Ov Ki  OOJ hO  O  O  hO hO  OJ ho  •  OOJ N>  o  vO vo vo vo  . ho  1  Ul  OA OA IO - J  OA  OA  ho  -J  l->  o  o  Ul  -J Ul h-  VO  to 00  VO VO  o bo -Po  o  I-  o  00 Ul 00  vO  i-  M  to  o  I-  o  OJ  OJ  vO  to  o o  o  H-  1  hO VO vO  i>  vO  1  1  b  b  OA  VO  to  I-  1  1  o o  OJ  b  h-> VO VO  Ul  to  Ito  1  o  o  o  ho  to I-  to  to  o  o  o o  o  o o  o o o  o  o  o  o  o vO  00  o  o  o  o  o  o  o o  o o o  o o o  o o o  o  o  t->  o IO  . o  •  •  o  •  . o  to  •p-  VO  o  1—  . o  VO  OJ  1  . OJ  vO  •p-  •  •  ho  to  o o  -p-  •  OA  . o  hO  I-  •  •  to  -p-  VO  o  1  Hook Gauge Reading i n Downstream Tank ( f t . )  vO  Vernier  I-  V e l o c i t y Head C o r r e c t i o n ( f t . )  Correction ( f t . )  o  o  t-  00  1  ^1  .  Hook Gauge Reading i n Upstream Tank ( f t . )  o  o  1  Discharge ( c f s )  1  hO  1  OA  oo  O  I-  (sees)  Temp, i n °F & S p e c i f i c Wt. o f Water ( l b / c u . f t . )  O O J U i OJUi OJ Ui hO O hO 0 hO O  o  o o  Ave. Time I n t e r v a l  .  o OJ  (sees)  t-  00  .  Time I n t e r v a l  UlUi  i>  •  Weight o f Water from Main P i p e ( l b s .)  ho  O O  vO VO  OA OA ho-^j o •  1  VO  0J  VO  8£  I-  oo oo  o  OA ho OA i — '  OJ  ho ho  OJ hO  1  •  O  OJ  I-  o o 4>4> Ui O J O J Ui  OJ ho Iho Ul  Ul Ul hO Ul  OJ  ho ho  T e s t No.  1  >->  o o  OJ  to  •  Ul  1  o  II-  h-  1 1  1  to  F r i c t i o n Loss ( f t . )  Reynold's Number (xlO )  Left Branch  O O O  ON  o o  •vl v j  ui U l •p- -p-  OJ  ro ro •P- O N  w  ro ui ro  o  00 to ro  ro •  00 • ro  ON O N  ro O N . oo ro oo u> o U l U l ro M o  o  o  vO  Ul oo  -p-  00  •  *  00  M  -PON  •  i->  o  •p-  1  •  vj  o  ON  o o  u> ro ro 00 o o •P- •P-  u> U l 00 o o •p- U l 00 o  U)  o o 00  ON  ro O N • oo ui o ro  «vl Ul h-»  O  vO Ul ro  o  ro ro  • VD  •  ON roo> Ul ro  00  u>  O U l U l o  M  VUJl Ul  i-  t-  1  1  1  •  Weight of Water from Main Pipe (lbs.)  Ul  o o o  U)  Ul  ro ro  u> ro  -vl VO • Ul  oo  ON M ON  W i-  Ul ro  Ul o  o  •  •  o  o  •p-  00  -p-  VJ  ro •  i—  •  VJ  1  • o  •  ON  Ul  t~*  ro  ro  i> ro  i-  ro  00  b iUl  o  o  o  •  •  ro i-  ho I-  ro  o  o  ro M  -p-  1  VO  I-  b  1  o  U)  o  o  o  • ro i-  *  o  o  o  o  o  o  o  o  o  o  o  b  o o  o i-  o o  b  ro  o oo  o  Ul  o o oo  IUl  b ro  o  o  O  o  o  o  o  ro VD  o  Ui  ro  Ul  ON  •P-  Ui vO vO  ro  i-  i-  ro  o  o  o  i->  o o  Ul  ON  o -vl  • ro  1  iVD 1  o  l-» Ul  •  1  1  oo ro  o  1  VD  -P-  u>  •vj ro  •  1  o •P-  Ul ro  1  00  Hook Gauge Reading i n Downstream Tank ( f t . )  Vernier Correction ( f t . )  O  ON  Velocity Head Correction ( f t . )  F r i c t i o n Loss ( f t . )  1  M  ro  VO I-  vj  1  Hook Gauge Reading i n Upstream Tank ( f t . )  oo o  • ro t->  ro  Discharge (cfs)  -p-  VO  1  ON  Ul  -P-  o o  Temp, i n F & Specific Wt. of Water (lb/cu.ft.)  o  Ui  vO ON  Ul  o  -vi  VD  Time Interval (sees)  Ave. Time Interval (sees)  •  ON ON r o o o  1  Ui  vj  Ul  o  •  Description  00 00  Ul Ul  ro  ON ON M O O  Ul  vg v j vO VO  U)  •P-  .  u>  Ui Ul -vi  Ul  o  1  U)  oo  IVO I-  •  o o o  u>  o •  ro o o o  VO  ON  u> ro 00 • •P-  o  ro  w o  oo  I-  ro «  ui o o o  VO  o  •  6£  Ul  oo  u>  ON  o> oo  Ul  VO VO  u>  vl  u> • •p-  ON  Ul  -J -J  -vl  •  ro o o o  VO  -p-  Right Branch  •p-  Reynold's Number (xlO )  1*  o.  I -  s:  ...  «.  J  ;  J  ;  O r l f l c a to.  111 ! I I 1 1 i i I I I I 1 I I I i 1 I I I I I i I  mm  sSSSss • - i, i ^  t i l  *- '» 3  u  mm  ~ S s s S S 5 -  s  -  -  i. b b b. c  5 s s -  5 £ * ~ s a  S 2. 11I  mm  s -s -s  i n  u  £  c  i  r  i  1  i  5  I  i  1  I I I  1  ii  ii  ii  ii  II  I1  II  11  S £ S  o  -  s if5  I  I 1 1 1 1 I i I I 111  I  SISSIES* S S s s a s 0. b b 1- b b  £t  T » p . » C r . In °F .ao S p e c i f i c W.lsht of W.t.r ( l b . / c o . f t . )  s  i  i  I  i 5  I  i  I  i  I  i  I  I  I  i  I  i  I  1I  U  111  I I I  5  -  *—<•"••>  -  1  I  rip.!  g s  i  I I  f r o i * * Hole  o  1  s  11  11  Op.tt.«.*T.»k ( f t f )  ~<-> or Hi La Pip* & U f t Broach  i  I  i  i  I  I  I  i  s  P i p . for Uagch 5.J75 I t .  i  i  i  i  I  I  I  i  I  F r i c t i o n U i . ( f t . ) Io r k l o P i p . for U a B t a ST  Ii  II  11  II  I I  I I  I  3  11  11  P r l c t l o a U . . . ( f t . ) to I l . h t or U f t Broach for Uagtb 9.0 f t .  Ii  11  11  11  I I  II  II  11  11  P r l c t l o a Loo. ( f c . ) l a R l h c or U f t Ironch for Uagch TO,.,™,  11  II  11  11  I I  I I  I I  11  J1  i I  i  II i  II  I  II Ii i = ^  07  I i  II II  II II  i  i  I  5  I  i  1  I  I  I  Tot.l Prlctloa U i . (ft.)  I  V e l o c i t y l a PkUn P i p . ( f t / u c )  I  y . l o c l c ; B u d l a rfclo P i p . ( f c . )  11  i i  11  11 •  V . U c t t y l a I t i h c or U f t Ir.aca ( f t / . . e )  1 i. I I  11  I I  11  I1  Voloclt? Boo. l a l l j h t or U f t Broach ( f t . )  I I  II  I I.  ?? § :  II  For. U . 0 (ft.)  111  H!  ? ? ? = I|  11 i  1I  1 1  II  II  11  b  i  s  S fcs°  II  i fe  2  ? sill  =5  b fc fc fc  For. U * . C M f f l c U a t  s  I"  .ii  o i l  . s  jg.  i  o  §s *o>  b.  z  i :  •» - » o . V  u «  5.  s  • =  *-  i  * ;  S " 8o  1 I o  o  o  »•„  1 i s8 8 8  s s  S  I  o  b o b b  • u ~  I  s  s  s  o>  ! II I I  2  S g2  3 s  s *. I * 111 1 111 s 1111 111 i l l 1 I £ 1 § S i s 1 i o o £ 5 3 i 5 1 I 1 5 s 1 5 1 A o A _ 1 g 1 5 I1 Is- S S S i  s  5 *.  5 * 0.291  0.293  0.000  0.306  -0.025  I i  H 0.009  o  1 0.114  0.000  0  I  !  I  1  1  o  0  0.117  0.000  1  s  o  o  s  ° =  s  I  111  O  S S §1 S 58  —  11 11  s  S  I  S5  ii  i I  ii  Z  1; Ig  1 11  5  I £  o  2 S  11  o  o  o  o  O  M **  i  i  1  i  s s  2§  11  15  5  s  K S S bis  O  o  M  o  o  M  2k 8 2b 8 S5  s '=  s  Branch  Discharge f U c i o ( D i s c h a r g e In Branch P i p e / D i s c h a r g e In KB In P i p e )  P r t e t t o n L o s s ( f e . ) In M a i n P i p e f o r L e n g t h 3.375 f t .  F r i c t i o n U I I ( f c . ) In M a i n P i p e f o r L e n g t h ST  s:  f r i c t i o n L o s s ( f t . ) In R i g h t o r L e f t Branch f o r Length 9 . 0 f t .  5  m e t : t o n L o s s ( f t . ) In R i g h t o r l e f t Branch f o r L e n g t h T D j o r TD^  S  T o t a l F r i c t i o n Loss ( f t . )  s  s  s  Velocity  s  5  o  o  §1  o  I O  In M a i n P i p e  (ft/sec)  V e l o c i t y Head I n M a i n P i p e ( f t .  V e l o c i t y In R i g h t o r L e f t Branch ( f t / s e c )  25  1s i I 11 I I  ©  Vernier Correction ( f t .  **  1 §  >- •  Hook Cauge R e a d i n g In C e n t r a l tank (ft.)  or M a i n P i p e ft L e f t  §  II  Kook Ceuge R e a d i n g In U p s t r e a m Tank ( f t . )  Pr«tt«re Heed D i f f e r e n c e ( f t . )  o  s  I  E  1 1  Discharge ( c f i )  Hook Cauge R e a d i n g i n 0 o v n s t r e a » Tank ( f t . )  5  83  1 M  5  i  11  (..cs)  i-  -  1I  Int.rv.l  S p e c i f i c Weight o f W.ter ( l b . / c u . f t . )  i  o o  Weight o f H a t e r ( l b . . ) f r o n H . M»in P i p e ; R. Right B r . a c h ; L. l e f t Bt.nch  I5 -  «  I  5 2  0  1 1  L.  I  15  i 2 i  I I  *•  i  1  -  1 II  I I •1  1 I5  1  o 1 5  i  s 1i I I I  o  0  0  0.118  | 0.002  i I 1 I 1 i5 a oa 15 § j i 1  8  :T17  o  I  1 s I  1  1 l i  I  r  £ *.  o  ~  -  Te.t So. O r i f i c e Mo.  Tioe  5 = s  -  | 0.728  o  i  I  -  SSS555  '» b  M  . S g, s s, ' s s  s  ¥-  W  S  V e l o c i t y Head In R i g h t o r L e f t Branch ( f t . )  2  Pom Los. ( f t . )  B  (Average) ^  s s ; S  R e y n o l d ' s Nuober  ^  ^  (xlO ) 5  42  0.177  s  5  s «»  1 ss  \\\  S  5 5 .= 8 *.  1 e  £ 3  o  o •  ,  au.ioijjoco  2 2 !!  0.170  3  (0.178)  *  (0.17*)  t  0.170  ( 0 I » ) "°»>« t . p i o u i . ,  (•al)  S 5 I s S! § s 2 S s s S1  I I  < J J ) ..oi U O J  S s  i p o . J J j | r i JO  JO m l , ! 01  S  ijjooi.i  .SS  •„ J. 'oi aoj i p o i j g . ajoq »  S u l u O l (-1J) f l O l  OOJ331JJ  •3) 0'6 «J»»»1 J o , w i XI JO i q t n o, < J J ) ••«! o o i i a u i  IS vatD»i J O ) »dlj  =  JOJ a o u  • 3 ; Sit'C  2  ..  ~  IS :•  o  s-  3  I  SS  jj  2  5 22  s s SS SS IS SS 3 S !• S 5 I S ! 5 !  s s  S  I  2  !ss I s  i.  s  §  2  M  s s S s s ss S! ! !  ll  S  <•  SS  s s S! ss s ! !  IS \ \ s IS SS S I . ss ss ss s s11 IS 1 ! s ! ! ! S ! I s ! ! ! !  S! S! S! SI  !  !  S  S  s s s s SS M s s s S s ! s I S S  s  s sS S s s  IS  =  <  •  -  s s J I  —  - i  <•>»•«>/•«>  J»J»« JO 3l|»l»J| ' " l ^ S  <•  »  IqoooJB anSii 't oi-H -H ~ J J i r o n j o J»t,.» o« mjiJo •o»  mi  -  5  ss s §  1  s  -  CHI)  SS  \\\  5  S I sss  •» 3  •  \  s a 3ill iiiiia  ssSSSS  !  S  s  I  mm  IIS I I I 111  s  o"  s  s s s ! s IS s S sss SSS SSI SSI *3  = 3 *3  s Ss  s , ; ; s  s s - s -s s s 5 K §  siiiii  • ° =>-•-. -°. -. a S 5-588 s s s s s s  111  I  : s  : s  *3 III  §  n  = s? s  I I  111 : i  ^3  •«§  iii iSi 5555'i'I iiiiii I 11 I I § I H :  2  Ut  5  s  * »  " t-  ¥ -  " c-  320.3 320.4 324.0 323.9 366.4 348.2  320.7  317.9  328.65  a.  w  o  ii.  **' 3  62.29  o>  is ° M  Tett Ho.  M  Orifice No. Height of Uticer (lbt) from H . H A I O Plpo; R.Right Branch; L.Lefc Branch  *-  Time Intirvsl («ec»)  -  Average Time Interval (aect)  Os  0.752  0.595  0.157  0.751  0.556  0.195  0.751  1.717  1.060  b  -  M 15000  3400  R 12000  L  3t  320.7 320.7 317.9 317.9 328.6 328.7  320.8  o U  n  o T o»  1.863  1.277  2.216  o oo fr  s  fr a.  Temperature In °F and Specific Weight of Water (lba/cujl)  Discharge (cfi)  Gauge Reading In OB Hook Upstream Tank (ft)  Hook Gauge Reading In Central Tank (ft)  Hook Gauge Reading in Downatream Tank (ft)  |  i  sO  o<  0.686  1.210  -0.067  5  0.210  0.210  0.210  0.210  =  fr  | 0.210  o  o  0.208  0.792  0.639  =  o> o  o o  8 •o  8  0.050  o  Vernier Correction (ft)  Preaaure Head Difference (ft) between Main Pipe & Right Branch or Main Pipe & Left Branch Discharge Ratio (Discharge In Branch Pipe/ Discharge in Main Pipe )  0.009  0.009  Friction' Loss ( f t ) , in Main Pipe for Length 3.375 f t .  ;  o  0.009  sO  0.361  8  (Si  0.049  8  o  o 0.591  0.409  0.555  0.445  a  o  1.061  5  -0.154  o  8 fr  0.684  o  -0.122  0.375  o sO  |  1  0.009  .o  fr b  0.069  0.074  0.163  0.179  0.190  7.246  o  o  o  fr  Friction Loss ( f t ) . In Right or Left Branch for Length 9.0 f t .  =  Friction Loss ( f t ) . In Right or Left Branch for Length TDj or TDj  0B  Total Friction Loss (ft)  Velocity in Main Pipe (ft/sec) sO  o  0.368  0.063  o  o  o~<  7.252  0.607  0.072  o  o  o "  5 fr  2.551  0.195  0.059  o  o>  3  cr  3.561  1.490  o  0.545  6.251  9.795  0.000  0.078  o  0.000  0.113  o «-  0.000  0.053  o —  2  *•  a?  Friction Loss ( f t ) . In Main Pipe for Length ST  OS  Ul o  o  Velocity Head la Main Pipe (ft)  s  Velocity In Right or Left Branch (ft/sec)  B  Velocity Head In Right or Left Branch (ft)  1 0.080  bo  0.122  H  o  o  S s  b *—o  a.  fr  3  Form Loss (ft)  (Aversge) Form Loss Coefficient  M  2.11  i>  o  5  2.19  !fc> C* •>  o u?  0.77  § s s  Ut CD  0.071  1.61  2.25  1.30  o  0.00  *v* >o  "-J  1.82  —  b  0.00  o  SO  0.099  1O>  0.817  o  C  0.101  O.OTJ  . o  o  0.179  0.036  0.031  o  S  t>  0.069  t>  0.371  o  %  0.B1S  a  0.000  0.265  : 0.000  j  o io  5.807  0.000  c-  u» *•>  z  °  O  0.388  O*  o  s  0.387  0.387  0.212  0.069  o  sO sO  SO  o  =  o  s  3.001  o  0.425  JO  0»  o  «> sO  *> SO  o  0.038  3  0.375  O  X  0.057  0.159  O  0.367  O sO  0.055  O 10  o  0.295  0.222 ' 0.231  4>  0.112  0.150  u»  0.286  sO  o  ro o>  0.103  S  o  0.280  S  1 0.100  0.147  0.217  1 X  o  3  0.658  o  0.009  0  o  0.009  o  s  4>  0.360  o  8  o O o» 5 o  0.375  o  a  b * '*  O.OOS  0.133  1  o  0.000  0.000  o  O.OOS  0.004  0.002 0.132  0  0.000  o  S  *>  H 15000  o fr w  0.479  b 2  ie  0.127  1.904  0.029  0.011  © o  o  0.271  o  2.092  0.210  -0.167  1.062  -0.093  iS  8  a  335.3  o *-  1  0.370  0.210  0.210 o o»  o  s =  295.9  o U*  V-  0.210  o  sO  t*  5 **b  »o  8 fr  1.212  OJ  a o  I -  R 10000  0.750 i  0.750  0.000  0.555  0.555  0.000  0.445  0.445  0.000  0.317  0.317  0.000  8  o  o  c  320.8 ' 320.8 335.3 335.3 295.8 296.0  o  o o  o  8  5000  w o  0  o*  o  320.7  M  b  2  z ¥ "  OJ  fr «  325.9  313.3  321.0  308.3  336.25  320.9  320.9  318.25  318.25  324.95  324.93  355.0  355.0 o»  L  9000  320.7 320.7 325.8 326 .0 313.3 313.3  sO sO >A vO  321.0 311.0 308.5 308.5 336.2 336.3  318.2 318.3 318.2 316.3  314.9 .325.0 324.9 325.0  355.0 355.0 335.0 J55.0  • OOOO  II  X  6000  »  L  M 15000  C*  I H 15000  ]  i  f.  1 R 15000  §  O  0  X  L  0  7000  W  X o  H 11000  *  o  r*  > 11000  L  t-  ¥ -  o  0  -  L  i  s  k •:  S  Reynold's Number ( nlO^ )  -  5 "  ill  . 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Main Pip.; «.»l,ht Br.nch; L.UfC Br.nch  ? 2  ? °  9  gggsss  -  z (Dl.ch.rje In Br.nch Pip./  11  11 I1  s s  s  E £  'i i i  s  9  9  III  5 g 5 S 5 • is 5 - = s  o  s  .-  I 1I  SSSSgg  ? ».  s  IIS  Orifice No.  i i i  5 5 5 s * ;  = %  5  li  g g  s  in  i t I§  v..  v.bb  ni  p  I i 1I I I 552*5*  t . i t lb.  5 "  s  1; 11 11 11  I  1  p  3  i i  S  3 ? ? £ 5 ?  11  P  t i  us r  r  s a  i •; ?  p  1g1 » S  i  =  •  F r i c t i o n Lo>. ( f t ) . In tight or U f t  Iot.1 P r l c t l o n l o t . ( f t )  1  v . l o c l t r In Main P i p . (ft/a.c)  £ s  Velocltr Bea4 In Main P i p . ( f t )  1i I I  l o ' l l g h t or Laft Jr.nth  2  11 111 s  5 Si : * 8  P r l c t l o n l o . . ( f t ) . In U l n P i p .  F r i c t i o n lo.< ( f t ) . In «lght or L»ft Br.nch for Ungth 4.0 f t .  S  ?  F r i c t i o n Lo.i ( f t ) . In ».ln Pip. for Length 3.375 f t .  5  (fc/a.c)  In l l g b t or U f t Iranch (fc)  For. l o . . ( I t )  For. U>II C o . f f l c l . o t  z  C-  w ac  r  ii  o  r* ••  f  »  o  I  ae  .  « ?•  .  t r-  sr :  s:  at  S  r  *  i  o  II  r*  s>  JO  X  l-  I  O  t "  w1«- •»r-X  0.364  0.364  0.000  o  o  o  0  O  O  o  51 £ £§  § S #-  in  o  o  r  X  ut  s s s " O w" t>  u>  0 0 0  5—  S  O r i f i c e No.  »  0 0 0  5  ~*  U>  0 —  «-  ? ?St  Z  0 0 0 -4  *• *• 0 a>  u"  *•  —  S t-  io p  5  s>  's  o  O  o  o  o  0  p  0  p  o  o  o  o  o  0  5  0  5  o  e> o  1£  -4  o -»  o  a  —  8  S  p  p  _—  o  •>  9  r*  5 ?  XI  p  o  a  8  o b  o  a>  I  o  o  o  8  8  1  3 o  o  0  o  1 5 § s  0  o  o  o  8 3  * o  §I  § s  o  o  0  8  S  o O  o  0.177  0.003  § S  1  a o  ? 2 !*  o  1  o  o b  o  o  o  o  o  1 5  s  |  p  p  § I  4> »  o  O  •M  o  o ">  X)  o  o  0  ©  —  0  §  i  1I  a  o  a  o  o  a  1 2  p  9 9  p  w  o> - i  o  o  -  8  a is  9 9  = 3 — a o  o'  a t  o>  0  0  — -J  S  0  p  0  O  >»  M  0  O  p  —  p  p  p  s*  S  8  —  —  o  «  —  S  o o» •O r * "  3  S  8  3  5  8  * 5  p  S  £  0  •>  p  O  p  O  0  p  W M  JJ  O O O  0  a  0  1  O  S  O w *• '*t a- O •~t O v 8 0 S  »•  O  a  -  0  0  3 8  2 io  Vernier Correction ( f t )  =  Pressure Read D i f f e r e n c e ( f t ) between Main Pipe & Right Branch or Main Pipe 6, U f t Branch  =  Dteeharge R a t i o ( D l s c h s c g e In Branch Pipe/ D i s c h a r g e In K a l n Pipe ) F r i c t i o n t o s s ( f t ) In K a l n Pipe f o r Langch 3.375 f t .  9  =  0  0  0  0  0  s  b  «j  g  0  0  0  0  F r i c t i o n Loss ( f t ) . In K a l n Pipe f o r Length ST  F r i c t i o n L o s s ( f c ) . I n Right o r L e f t Branch f o r Length 9 . 0 f t .  s i  U»  Hook Caugr Reading In Upatrean Tank ( f c )  5  0  1  =  15  =  F r i c t i o n Loss ( f t ) , i n Right o r L e f t Branch f o r Length TDj o r T D 2  T o t a l F r i c t i o n Loss ( f t )  •> b 0  <o  0  * 2 0  0  S  io  0  0  0  3 S  8  *  -  O O  11  s i  O O  .°  ?  a  w  O  0  M  ^  ^  *>  w  <>  * 0S 8>oiS —  (ft/aec)  V e l o c i t y Head tn Main Pipe ( f t )  Velocity i n Right o r L e f t Branch  O  0  V e l o c i t y In Main Pipe  0  0  W  O O  (lba/cu.ft)  Hook Caugf? Reading In O o v n i t r c u Tank ( f t )  b  s  u >  Temperatura In P and S p e c i f i c Weight o f Water  0  0  5 0  «  8 S  9 9  o  p  0  b  •>  —  o  s '»  S  o  § .i  s  O  a  9  o  p  § S  § 5 § 5 1  %  0  0  O  0  5 8  P  •>  § S  o  S  0  o  O  o  M  p a>  :«  O O  «•  § s o  0 '—  <0  o  0.174  o  0  £ 2 1 1  0.170  0.000  0  o  0  8 £  0  p  —  0  p b  5  b ?  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P  i I5 5 I 5 5 I ? r  S  S  s * •=  5  S-  3  s  P r l c t l o n L o . . ( f t ) l o Right o r L e f t Branch f o r Length 9.0 f t .  P r l c t l o n Loaa ( f t ) , i n Right o r L . f t Br.nch f o r Length TO, o r T 0  1* t u ' o ' F l p ^ C f t )  £ 1  2  E'EiS  £ £  S  In'Sliht ot*L.ft Branch  ii  s  f  3 3  (0.167)  t.n  ill S I % % l?  'i  0.169  0.19  a '5  1 £ 1 £ 1£  **•  z  £  £ 1 s s ?? £1 8 5  (,c)  "  11  £  ? i  5 xrxgz  0.163  11  ?  s I  f o r Length 3.375 f t .  11  0.171  11  £ £  p  »  £1  (0.171)  ii. ? - .»  -££  ?  S i  .° 5  ;  0.170  5s  ~  £ £  2.16  11  5  11  1.51  ? .°  5  1  11  l.Sl  1I I£  s 5 p  "i 1 i£  0l.ch.rg. (cfa)  ii  £  i i  3  11  i 1 1  2  11  S t i f l e WelghC of Water ( l b . / c u . f c )  DlacherS. l o h a l n P i p . ' ) '  11  S 8  £1  (a.ce)  S  1 1  ii  £  ?  1  ii  I  I  1  0.122  i  ? .» 1 s  £  1  Average Tine I n t e r v a l  i -  i1  ii  1 1  £  1 £  0.112  1.711  -0.155  11  3  I  j 1.5U  I  201.4  J  £  0.757  1  ? = ? 5 ? 5  S  -  0. 757  s  i r i  0.920  £  0.461  i  0.459  3 •?  0.750  £  0.375  £  0.375  1  *  ii  ?  ]  £  ? ? r S s 2  Bench;  201.3 201.5  iI  0.496  p  0.250  p  s 5 =  0.246  0.748  0.736  0.012  0.748  0.716  0.032  ?  254.5  111  I * 1 1 1  254.45  313.85  5 5 5  - » s  No.  Weight o f U.c.r ( l b . ) f r c M. Main Pipe; R.Right L . U f t Branch  ll I ii 254.5 254 .5 254.4 254 .5  » V ~ V. V L>  I  276.9 276.8 320.5 320.5 320.6 320.5  55SSSS  313.3  Ul  I I I II  314.2  378.5  379.33  380.2  I l  i  s ;  313.9 313.8 313.3 313.3 3)4.2 314.2  SS3S33  I II 323.5 323.5 321.0 320.9 326.2 326.3  3J1.» 322.0 327.4 321.2 399.7 39B.5  = j ? .8 I  III  T.it  s ; • •s "  5 "  -  S  B  5  o t L . f r .ranch,,,...,  (ft)  Wa.Co.fflcl.ot  ^ . . ^ . r , W ,  2  i  :  i : r  »  i :  »  I  r  o>  o §§  c  W U* u » w IS* M M M •> *•  s  *>  u*  S "  w  *  ts>  »*»  §  §  f  o  V* U l Ul Ui  tU «>  o  » M  OS 0»  * u»  o  U>  o  o o  r*  P  H  I  O Q  § 2S 8  VI  Ui  U*  Ul  OH K» W Ul  OS 0S 0  o o  Ul Ui  OS M u> u>  u» Ul  M  o o\  o" OS 0  U U O O N N « >0 <3 4) M rg  •s*  Is* o  O  O  O  Ui u> so  -o  Ul u>  0*  00  ui  p  to  o  o  O  O  O  o  iS  X  U) M  *> Ul  0B  S  t-  p  O  U»  SO  U>  Ul  M OP  Ul o  o g  a  S  o -J so  O  s  o  o  o  o  ro O  Ul •—  2  o  o  o  §  8  8  K> oa  p  o  •sj  oa  p  p  *«"  Ul  O  o e» o  S  O  p  ui o  o r-  ui  o  Ui  -  Discharge (cfa)  o*  09  09  Hook Gauge Reading i n Upstream Tank ( f t )  SO  Hook Gauge Reading i n Central Tank ( f t )  o -J.  o  p  p  8  o S  o  2  ro  o o  o  p—  os  »—  vO  0  o  O  O  •-• Ul 09  ro >-* U  o  o  0.105  o  c  u>  0.000  o o o o  8  's  § 5  M OS W O*  p *• o»  »  o  8  O  Ul Ul  o  p  **  p  o  OS OS  09 'J  o  O  s  CO  00  o>  o  o  o  *•  Ul  *>  Ul  § 2  § I  § 5  w  V  3  ?  ui  o  b  o  o  p  p  p  p  p  § 2  o — o *• 5 o O ui  4  Ui  is* Ui M  Ui •— U»  p  O  O  O  O  O  8  2  o 3  o o *S 3 o • p  p  o> U  a  3  8  3 2  p  £  o Ul i — o o  bO  « V o> o  KJ M  •o  O  r— U>  OS  F r i c t i o n Loss ( f t ) . In Right or L e f t Branch f o r Length 9 . 0 f t .  O  <C  p  p  p  p  3  $  W  •»  8  8  3  W »J  -  i-  N  O  Total F r i c t i o n Loss ( f t )  o  p  p  r-»  =  V e l o c i t y Head Ln Haln Pipe ( f t )  B  Velocity in Right or L e f t Branch  Form Loss ( f t ) .  iUl  p r*  0B  is*  O  (ft/aec)  V e l o c i t y Head tn Right or Left Branch ( f t ) .  o  ro  V e l o c i t y i n Main Pipe (ft/sec)  o  81  p  >l  Discharge Ratio (Discharge l n Branch Pipe/ Discharge In Haln Pipe )  F r i c t i o n Losa ( f t ) , i n Haln Pipe f o r Length ST  o o o  u»  S  Pressure Head Difference ( f t ) between Haln Pipe & Right Branch or Haln Pipe & L e f t Branch  5  CD  p  S  § s  Vernier Correction ( f t )  F r i c t i o n Loss ( f t ) , i n Right or L e f t Branch f o r Length TD^ or TDj  sO OS Ul  w>  § £  Hook Gauge Reading i n Downstream Tank ( f t )  *•  O  o  (tecs)  F r i c t i o n Loss ( f t ) . Ln Main Pipe for Length 3.375 f t .  O i-*  §  o  *  O  b  (feet)  «•  O "u> OS  s  8  Ul  8  b  p  *•  ui a» Ul  o  p  o  ui  ui  b  8  O  o>  1 I  C*  SO  o  o  o  OS  O  o  o  o  =  =  1  8  o  -J  o  O  o  O  SO  8  § 5  O  p  O  O  O  o o  SO  s  o  o  o  o  o  OS  «  8  O  u»  Q  OS OS  o  O  p C  §  § S  2  Temperature i n °F and S p e c i f i c Weight of Water (lbs/cu.ft)  VI Ul 0  Ui  o  o  t  OS  K* IS* OS  <o  p  o 3  os  8  Average Time Interval  9  o  p u>  8  O  w  Ui  is*  a>'  u> SO  ' 1  b  °*.  Time Interval  O  •o  t:  O  »  so  IS)  b  o «•  O  Weight o f Water (lbs) from M. Haln Pipe; a.Right Branch; L.Left. Branch  X  ^^  c*  a  p  "o *»*  ie is  -  jo  is*  p 1st  o S  Orifice No.  Ul Ul Ul Ul U l U l N N N M M N SO SO O O N Ul  *j  O Kt  KJ  00  O  g i  \jl O  §  os  O  § 1  Ul U l ON K) *> —  ui u>  ON  *»  IS*  Cf  X  Ul Ul Ul Ul u> W 0> » M N fO N) *> *» •- P-  ,j  V 0  Ul  s  s  O  M  v -  NJ  O  O  >B  o  OS  •> SO  IS*  is  P"  Ul »— hJ  or.  #> O S E Q •5  #>  5  8  r"  i i § I i § ^ If i  N  O  ui  :  TtiC Ko.  O  ui <H oa CO  ui M 4>  o  X  o o o o  ' bob b w  P  f • ui  .  •*<  •O.  ISl  *• is*  -* O  (Average) Foro Loss C o e f f i c i e n t  Reynold's Number ( mto' )  T..C no.  i ^ s; if i 1 I 1 i l l  I i ii  I I II  I  ? 5  S 5 5 s  3 b  mm.  ? 5 3 * 3 J  1i1  i  i  .2  £  £  i  i  r  g  i  £  £  £  £  £  £  £ 5  £  i  -  i  i  ?  £  £  £  i  I  ? ? 11 £ 1 £1 i i ?2 3? 11 £1 £ 1 i i 5 1 ? P i i . 11 £ 1 i i 11 £  £  £  1  1  i  ?  \\ ? ?  ii  ££  i£  ii  £  i  1 £ £ i ? ? 11  C  W t > " *  or K i l n P i p . T u f t  11  for Length 3.375 f t .  s  0.252  (0.2S1)  0.250  i  ss z  p ? S  S  rS  b  S  C  3 3  K  *'  n  F t P  *  Prlctlon Loaa ( f t ) , i n tight or U f t  p p  Tot.. Prlctlon . . . . ( f t ,  % it  £  ?s  1  s  £ 3  r  s s  s  1  1 £ 11 £  .- .- r*  f f e )  Prlctlon Lots ( f t ) , i n l i g h t or U f t Branch Cor Length 9.0 f t  r  5  \ I  p ?  =  *  11  1 £  5 s  for Uo»th°"T  o . l o c l t ; In M i n P l o . ( f t / . . c )  in H i l n ' p i o . ( f t )  l J ' J l i h t or U f t Br.nch ( f t / . . c )  K.  In I l t h t or U f t Br.nch (ft)  S  S  P ? .b  BrSnch'™ °  a  1 £ § i i'i I s £ 1 £ 1 5 £ £ i i i ?s 1? ? 5? 1 £ ££ U S i l l I I I 5. i l £11 li  s» =I- =% 5  -  c  i  £  - ""rrS  S  1  £  £ £  i !  £1 i  £  £  -  i  ! 1 |  £  £  i I  0.407  ££  0.413  .  = =  |  11  ll !  0.940  i  |  I £ ii  0.471  i i  0.469  5 2  0.750  ? .-  li  £  S  Specific V . l j h t of W . t . r (Ib./cu.ft)  lis £  £  5 s  HE  r *  3 P  ? .-  Hi  I  1  1  1 £ £1  -  £  ?  SB.  *  i  1  11 11  -  £  ? i  IS  I  0.375  I  0.375  III  p §  II  U . l j h t of W.t.r (Ik.) f r o o H . K . ' n P i . . ; I . t l . h t Br.nch; L . L . f c Br.nch  £1-  .2  1 I  I  200.5 200.4 316.0  555555 ?  111  I  O r l f l c . Ho.  s *• i  £1  I  i;  316.9 316.9  > s b  337.75  3 5 5  £11 l i l  S s  I  I  338.13  u  I  ssSSSs 338.*  m  I  321.9 322.0  327.3 397.3 397.3  mm  s:  * »-  «  « b  b b =  S  s  -poo,,.  *•  U4  s :  I 'r m at  V  - I I  o  327.5 327.3  327.3 Ut tst  ^  Is* io <o  v  at  KI  to  o  §  §  on  ~i  »u» a  o  ct  0.392  0.392  0.000  o  B  g O  o  o  •*>  *•  9> <r> fo M  IS*  Ul K»  U* K>  u>  u»  b> w*  CD  OS IS*  -J f* 0  •si  o>  -J C*>  o  o o  m u»  o  8  ££  IS*  IS>  b  *  M i» ut IS*  sO U»  8  g  ** SO  is* O  o IS*  ro  w  »  ut  r-  p*  § i u> u> ui u> ui u* U U M H N N <OiflWW>«> M sli-i-Ois, u» U> sO ^4  o  K»  so  b  N N M N  Ui  s  r m • 3E  u>  O) <o o> <o  Ul  u> f  I1  V* o  X  Ul i> iff «•  o>  K»  H  w u u u  S £  Ul M  r"  u w u u %0 •»!  io  *• > «>  ^  t-  O  O  O  O  O  sO  SO  ut Ui »-  u> u* «— IS* Ul O *** OS Ut OS is* io OX  -4 m ut  O *» O  O -1 4> K)  OS  w  as  vf  ^  i  r  w  &  b  ut  o  o  o  i->  os u>  oUt  v> s»l  Ul OS OS Ul  Ul u O P  U) K> Ul M  m O* (St  o o U»  3  k> o>  -J U< ut 0  o *-  o -J  co  f  Ul Ul -J CD  «*. ©  o  o  b  U>  Average  OS -4 KI J> K> Ul -1 o  o>  Temperature l a ° F and S p e c i f i c Weight o f Water (lba/cu.ft)  o K*  o Ul  o  »  °  **  ts>  o  O  8 o  a  o  §5  Q O  ui 0D  O  O  o  ! 0.204  § z  0.003  O  0.202  O  0.000  o  0  o  8.  CD Kt Cjs  OS OS SO  Ut vO KI  so K>  Ul CD Ul  O CD Ul OB  O K>  o K>  O IS*  O  O  o IS* O.  o  1 S N  o  is  Ul  o>  o  o  o  *>  o  0»  o  § §  §5  o  o  o  o  § J  § is  o  o  o  o  (si  e*  o  o  o  o  o  ? 8  o  8  i  bSO b —I  5f  8 if S 8  98  b S  os  O  o>  0>  o o* M 0*  o U KI K»  8  S OS  o *• £»  o Ut ut W  p  o  a  o  vi m  O Q S CD  O OS o> W  CD  Time I n t e r v a l  (aeca)  Hook G a u g e  Reading  i n  (  UpaCream Tank ( f t . )  sO  Is* IsO  O i»  is» M  u> NO  § "5  b**  «• Ul K> i— o  o  o  8"  o is* U> CD  o O SO  o U> KI  o i— v* O  o IS) «> OS  O O CD KJ  u> K) X>  p »— Ul  o K> Ul Ui  o O  o Ul  f  o  Ut  OS o '  o I— Ul  o  0  o  O b> KI  U*  o  Ut  Total  Velocity  OS  o i*•  o C* CD  so  m  O  i n Main Pipe  (ft/aec)  V e l o c i t y Head i n Main Pipe ( f t )  o rLeft  Branch  K> KI  Velocity In R i g h t  Head orLeft  Branch ( f t )  KI W  Forn Losa ( f t )  KI •>  (Average) Forn Loae  O  sO  K>  o PS*  o I-" Ul KI  o 1—  o KI  o» CP *J  K» •«*  SO  O  CD i 1sO  F r i c t i o n Loaa ( f t )  Velocity in Right  K>  §.#-  S 5  o w f M  F r i c t i o n Loaa ( f t ) i nR i g h t o r L e f t Branch f o r Length TD. o r  *•  1 5  i-»  F r i c t i o n Loaa ( f t ) i n R i g h t o r L e f t Branch f o r Length 9.0 f t .  5  KI O '  o KI f*  o>  o»  o Ul CO Ul  o  Ul  F r i c t i o n Losa ( f t ) i n Main Pipe f o rLength ST  o Ul CB  —1  5 B  Ui  o Ul SO  3  Discharge Ratio. (Dlacharge i n Branch Pipe/ Dlacharge i nMain Pipe)  F r i c t i o n Loae ( f t . ) i n Main P i p e f o r L e n g t h 3,375 f t .  so  m  Correction ( f t . )  **  SO OS  SO  8  P r e a a u r e Head D i f f e r e n c e ( f t ) between M a i n P i p e & R i g h t Brmoch or Main Pipe & L e f t Branch  O  4>  8  o H*  ts>  SO Ut KI  *•  J—  Vernier  vO Ul CD  u> Ul U> CD  KI  -  sO  o iK) OS  S 1. bOS  Hook G a u g e R e a d i n g I n Dovnacream Tank ( f t . )  sO  sO  i i  O V  ?  8  *•  O  o  o  so  Hook Gauge R e a d i n g I n C e n t r a l Tank ( f t . )  U>  8  O  S0  o  os  CD K>  o  o  J>  O  o U) ICD  o Ul CO CD  SO  *s  o Ul C0  o j> IS*  SO  9 °  o is* O  4 o b » S  O  o  i—  so 0D  b ut 13 8  I-*  I: P  w  o K> o  O  O  i— is*  o»  » £  o  u* I-  o  u» <JS •*>  o  M  o  b  .° °  o  § 5 8 !  o  -*  §5 o  O  so  o*  o> v»  vO UJ OS  09  o  8  b  o>  O  6 W OS  o  3 §3  (aeca)  Discharge ( c f a )  k>  S  Ut  ut  .  IS* OS  bK»  b  m  -  Ul Ul f is* Ul IS* ~j so  m  CD  No.  WelghC o f Water (Lb«) f r e e M. MeID P i p e ; R. R i g h t B r a n c h ; L. Left Branch.  Time I n t e r v a l  K>  S  Orifice  «•  u> co Ul  is*  U*  § H If  OS Ul  4 ~ o o *•  x  U* Ul u> u> u* U* Ul W Ul U> Ul Ul OS A Ul U* ts* is* Os OS O O Ul Ul •si Ul W M N OS t » KI I— c> CD sO CO >j -si sO SO  Ui  IS*  O  K>  r  6  O M o  Tait Ho.  O  u*  s s —  K> UJ  taynold's  Coefficient  *aab«r  (alO ) 5  (ft/aec)  i ",  1 "  s: ill ii Iill ill t , u  S ! »  £  £  1  1  £  £  1  1  £  £  {  I  1  i i  £ £  ii  ;i  £ £  .  I I  £  £  Ii i i  £ £  5 a s w  •  »  i-  mn  s  fc -  £  5  i  £  £  £  £  £  £  £  s  saw  £  £  £  £  s  ' « » < « >  £ 1  s  i£  £ £  £1  £  £  £  £  I  £  £  £  £  £  £  £  I £ ii £I 5 ii ?  11  £ £  <*>  ?  1  £  £  £  £  £  £  £  £  £  £  £  £  £  £  £ £  £  £ £  5  £  £ £  £ £  £ £  £ £  £ £  SSTss W  Prletloo L o . . ( f t ) , l o U | M or U f t B r . n c h for U n « t h 9.0 ( t .  Prletloo L o . . ( f t ) . l o P.li«t o r  T o f l Prlct.ooLo.. < « >  v . l o c t t , to H . l o P i p . ( « / . . . )  s  ln'lfcln'pip^ft)  £ £  ££  £ £  £ £  £ £  s  £ £  £ £  s  £ £ £  s  s  95  or Haln Pipe & Left Branch  s  s I i ii £ 1 i£ £I i i 1 £ I i £1 1 £ £ i £ i 11 l i £ I i i £11 111 i l l i l l £ £j 5fcfcS 5 b s , fc5 S t s . 1 s S bi ; i s s : fc^  11  Book Gauge l e a d i n g In  s  £ £  £ £  Book Gauge leadIng In  for U n . t h 3.373 f t .  i i £I i£ i i I £S i i  5  < l C  £ £ 1-  £  11  (lta/«!!ft)  1  £ £ £  s  Ii  u«ltf>t o f H . t . r  ££I i  £  I £ I £ il I£ £1  *>  Z2  £  £ £  H. K . l n H p . ; B.'lliit'.rTncb; L. U f t Bench  -  111  £  1 £  11  £ £ £  Iz I  11  fc  £11 111  £ ££  £  i§  I  ££  i  I  111  S =•  in  Ii i i  1I  298.3 298.3 313.8 313.8 313 .4 313.2  •» ~ u  Orlflc. Ha.  333.3 333.2 331.8 331.9 332.4 332.2  111.2 111.2 334 .0 ill .a 112.9 132.9  321.B 111.I  SSS55S  127.1 197.2 197.0  ill mm in n j - is - I! S IfI  I « . t Ik.  s  Ufr.rLcolft) * * * '  For. L o u  (ft)  "  .  5  B  ! :  s: .  If  S  E  s  B  o  i i.  -mi  . S555 - ^ u •„  • 11 .  5 5  5  .SSSS  •mi mm  • 1I  - l l  b~b ~  Ik  s s  s 2 s a  i i ii i i S  i i S  ii  III  •  -  f r a M . Hot. H o i ; \. Eight Br.ocb; L. U f t Brooch  i i  1 •i  i  I  •i  i  I  i  i  i  I  1  **  i i£ ii Ii i i  * i =i  i  b«Cvcto Main Plp« & l l h t 8 r » n c h or K a l n P i p e & U f t Branch f  B  I I  Ii ii ii  F r i c t i o n Looo (ft), to f o r U n g t h 3.375 f t .  Ii Ii ii  F r i c t i o n L o . . ( f t ) . In l i g h t ot L e f t Bronco f o r L e n g t h 9.0 f t .  F r i c t i o n Looo  ( f t ) . In R i g h t o r  TD^or'Sj Totol F r i c t i o n Lo.. ( f t )  i  B  i  i  •  V e l o c i t y i n Hold F l p . (ft/o.c)  i i fe i fei1 ii ii  Kolo P i p .  f o r U n g t h ST '  i  ° ? § 5  T n p « r a c u r c to °F and S p e c i f i c W.liht of tet.r (lbe/eii.ft).  " " ' - — • • « ' >  h ii i  Ii ii il  -  S  ii ii i  2  =0  iii  I ii i i ii  «-  s i •= s  0.110  S 3 S  £  iii  ii ii  ii  i£ i i Ii ii  :  ! 11  0.143  *= s  0.410  ; : s fc k  0.190  s ss  ill j !I  t i .  Ill  *>  1  J  £=.  n  ii ii  11  :  ssssss  £ *.  i i i I i i I i i I i ii i i i § 5 i 1 i i i. i 1 I i 1 1 i 1 i S i ii i i tg i i ii i I I i i i i I i I ii Ii Ii Ii Ii 1 1 I i I i I i .i i I i Ii 1i I i i i !' i i i s i i 1 I i I i I i I i 'i i I i 11 Ii I1 i i ii i i I i 5 -5 i i iI  J  :  . I II i I§ i I i  11  s  c  i  V e l o c i t y In R i g h t o r U f t Bronch ( f t / . e c )  V e l o c i t y Hood I n B i g h t or U f t Bronch ( f t )  For.  Si k  V e l o c i t y Hood In H o l n M o o ( f t )  •  s  Lo.. ( f t )  M e C o . f f l c l . o t  loyn.ld'o  ftafcor  ( »10  S  )  58  111 Ui  3tl»T31I3*CO MO? lUOi  ! 8 13 ( J l ) n 5 0 . i l i i r ] a . l o l r l o)  3 8 33  (.../Jl) qoo.ao i i r ]  !  u  loz ao ,01 q i t o r , ao] uou.ifl J , ^ I  •1) 0 6 . 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I I I I I I :s : * :s  - -  iii  I Ii in  :i •>  -  1st  f , sa  r*  o» <-*  8  o  o  ac r* o» u>  so  r  ac t-  8- § § CJ  307.0 306.9 307.0 306.9  i  o  o  o  o o  o  «• ©  X  8 8 o  o  o  r-  »  ©  o ao  o o o  o  «• o O  O  o  o  *•  is* SO  is)  o  o  o  ©  S  £  i l l  ©  p  o  55  -NrJWW  OS O  * >8  f* • 6-  o  O O N p- k* Ul  p ^ 5 b  OS  •s> so  o  o  •  r  <o  o  t> »<  ui  *• s*  x  w m ~j  {> Ui  »  »J  sO y£>  u> w O  r*  36  8  ©  2  o  *• V-  o  **  O r i f i c e No.  at Ul  o  8 3 © o  }> b>  w> j .  *>  Os Kl  is ~  °  ©  ©  ©  ©  ©  OB W  *> rSl O Ul  i>  on  O*  Discharge (cfs)  u>  o>  o  OS  «•  K> kO  ?  o>  o  o  IS*  •s*  o  O  O  r-  so  sn  a>  o  o  CD  OS  o  o  a  a  ©  3  o  ©  O  • <o o  is*  OS  CD  w  u»  o  Temperature In °F and Specific Weight of Water (Iba/cu.ft)  ©  M  •*4 IS*  line Interval (sees)  Average Time Interval (aeca)  t> Li  b  >0 OS o  o>  «• ui u >  Weight of Water (lbs) from M.Maln Pipe; R.Right Branch; L.Left Branch  rs>  u>  e o  Test No.  r*  »  o o •«*  OS O  -  o  *> c  r*  s s s> s \t* Liw i - u> *-  OS so  8S  rr  »  'v  ' f ?9 is is  ©  o  7 *  o  a  *s>  2Os  OS OS  u>  «•  OS  CD  o O  o SW  o  o  S  CD vO  O  ©  VJl  o  o  o  O b 03  o  Hook Cauge Reading In Central Tank ( f t )  Hook Cauge Reading ln Downstream Tank ( f t )  Vernier Correction ( f t )  = Pressure Head Difference ( f t ) between Main Pipe & Right Branch or Haln Pipe & Left Branch  ui ui o> o>  o b  SO  Hook Cauge Reading ln Upstream Tank ( f t )  =  s  1  o  o b  o b  o  o b o  o b 1st  o b  Discharge Ratio (Discharge In Branch Pipe/ ' Discharge In Haln Pipe) F r i c t i o n Loss ( f t ) , ln Main Pipe for Length 3.375 f t .  SO o b o  o  1  0.150  0.000  o Ul  o O  S  8 B  o  o  ©  ©  ^  OS  O  OS  o O  8  o OS  i 0.157  0.000 0.002  0.159  o  o  o  S  8 O  o  ' O  O  o  o o  *>  o * * • 5 oo  — o  8  S  o  o  ©  o  —  b  *•  O  o  o  o  o  o  o  ? ?  §  o  S  ce  o  o  8  o  0»  o  o  o  o  ©  S  Ul  «•  •O  •si-  tS  -  8  ©  O  5 S8  o  o  O p-  it>  ©  o  o  ©  Ss  !o  OS  o  o  — O  Ul *•  2  Total F r i c t i o n Loss ( f t ) CD  OS  ©  o  o  O  CD OS  *4> sO o  CD  CD  o o  — o  O  i -  8  o  ui -• o  o  W  CD  O  -  o O  *-  -J  *> - ~ l Ul OS OS  O  O  o  o o  S  8 5 o  o  o  U» CD  -J -  ©  O  S2 2  b  *•* ^  Velocity in Haln Pipe (ft/sec) sD  Velocity Head In Haln Pipe ( f t ) O  Velocity In Right or Left Branch (ft/aec )  Velocity Head in Right or Left Branch ( f t )  B  Form Loss ( f t )  OS  o  ©  o  o  b CD  b S>  *pO  w  N  W  (Average) Form Loaa Coefficient  b  Ul M  <•*  F r i c t i o n Lose ( f t ) . L n Right or Left Branch for Length 9 . 0 f t . F r i c t i o n Loss ( f t ) . In Right or Left Branch for Length TDj^ or TD  O  o  *  ^  o © r"*> 4> O OS -J  4>  f» —  b iso  ** CD  OS  o u>  8  ©  CD O  f>  -o  o  o  sO OS  §s  o  o a>  a a>  S  8  o  O **  is»  OS  b sO  © o  8 5  8  o  o  F r i c t i o n Loss ( f t ) , in Main Pipe for Length ST  s b is  «  5  Reynold's Number ( xlO* )  TABU  Y~il  *•*» L M *  °*ta f o r 9 0 ° H a a l f o l d w i t h o u t  T U - r r d  y  a M  w •3 »> > <  o  •  i  •  Z*X  £  •  .  1 a  | H  t  a  M  J HM f 5 4  flu  tj s  •J  c  * 3  e M  o  B  c A  •O *.  s  •3 '  m •»< s i U j nn- U  o  a -S  SM  . S  3  8 !.  m ±T  j  M u O l  "* "u B  ^  "° £ at  ** 0 w  °  .  uo  ss  Jl 8|  EC <5  S B  • O • «  B  IT  £ C M « Mm d) */  5 3 -2rS. "3 "So.  **2  tJ c c 3 * -J  £i J S  •5  « -* o »*  w C B 3  til!  fail s i ; o o  a  i  •2 • +J  •2  "u **  «^ o  w • H  3 .3 3  2  s w 1.  31 G  X  s  1O 4i  h O I.  -  ° u2* • B  "  o *u %.  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( f t ) . In R i g h t or U f t Branch f o r U n g t h ID, o r t D ,  £ £  i  Pip. for Ungth St  t  1 £ 11  1  P r l c t l o n L o . . ( f e ) . lo K i l o H p . for U n j t h 1.175 f c .  P r l e t l o o L o . . ( f t ) . In « l , h t o r U f t Br.nch for L . n t h 9 . 0 f t .  £ £  £ £  ~ ' « >  £  £  £ £  -;oi'c.  -i  £  £ £  Specific Uet»ht of v . t . r (lb./c.ft)  -  •1  £ £  T9  I  £  i£ 1£ i£ i i SI I£ ii i i Ii J £  ii i i  -  1  £  £1  •  ' S S  £  £  £ £  l t f l t  11 £ £ 1 ££ £ £  £  £1  i i  £  «V>.  ss -  5  IK  fU  £  1  i  I II  320.1 320.2 124.2 324.1 323.5 121.7  £ £ £  Ortfte.  « . l t h t of w . c . r ( l b . ) fro. H. H.lo Pip.; » . , Ir.och; l . U f t b u t  |  £ £  !  £ £ £  5 s 5 s c«  320.6 320.6 318.0 318.0 326.6 325 !o  1  £  i I i l l ! I I-  I  320.9 321.1 302.1 302.2  320.9 321.0  {  |  • ! 1  *  124 .4  307.8  .•S5SS V- V  338.9  121.1 121.1 321.1 321.1  , § i . I I . I I. I I i i I i l l SSssss u • s •mi . s % • I I ss -s iss E S I -ll s is g * IK Iii ££1 ££i 1 1 •i  s * -  s  V.loclt,  i n M.IO P i p . ( f t / . , c )  v.iocitr a..d in W i n P i p . (ft)  V . l o c l t y ln Bight or U f t Br.nch  b b b  (ft/..e>  V . l o c l t y Hood l n l i t h e or U f t B e n c h  Por. L o . .  (ft)  (ft)  •  a  farnolo".  Knur  ( «10  5  )  (•11) n i l • « <  (1J) nra.li n r i q « T l 07 P'»H Jiioc-l*'  i i e i i° iqtTt 5 l i l o o l . i  fclooie.  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(•31) K l l 0 ™ «, pni i i , » o , e .  3 S  8  0.412  »  8  * »  1.1*7  S  0 0 0  s  11 2  -0.113  8  2.75  2.73  10070711.03  3.92  62  5  i i 1H i :1  : 1 »  6»>  s I I  I " . 11  .11  i i  :  i i  i  o  o  i  I  i  I  I  ii  : :  §S  0.000  0.186  0  o  0  o  0  1  H  13  i  5  i  s  o  C09'»  OOO'O  o  1 i 1 ii  Ii  il  I i  § §  81  i i  33  1.32  0.94  0.00  8  3 U  I  s  I  i  1  s  i §  i  i  s  o  o  ii  1 i  33  ii  I i  o  o  il  S  5  o  o  i  I  i  3  1  I  I  ii  ii  I  ii  11  i  e  o  o  o  **  Hook C a u g e R e a d i n g l n  B  ii  5  o  o  i  5  i  E  P r e a a u r e Bead D i f f e r e n c e ( f t . ) b e t w e e n H a l n P i p e 6> R i g h t B r a n c h o r M a i n P i p e 6. L e f t B r a n c h  C  (Dlacharge Discharge  C  =  S  i  3  I •  i §  i §  i i  » 'i •  8  s as  5  5 8  5  i  S  l n Branch P i p e / l n Haln Pipe)  F r i c t i o n Loaa ( f t ) i n Haln f o r U n g t h 3.375 f t .  Pipe  f r i c t i o n Loaa ( f t ) I n Haln f o r U n g t h ST  Pipe  o r Left  F r i c t i o n Loaa ( f t ) l n R i g h t o r Left S t a n c h f o r L e n g t h T D ^ o r TDg  T o t a l F r i c t i o n Loaa ( f t . )  Velocity  In Haln Pine  Telocity  Bend In f a i n P i p e ( f t . )  Telocity l n Right Branch ( f t / . . c )  s  Telocity  5 S is s  s s  Vernier Correction ( f t . )  **  4>  S5  s  s  i1  3  §3  (aeca)  Temperature Ln ° P and S p e c i f i c Weight o f Water (lb./cu.ft.)  Book Cauge R e a d i n g l n Central lank (ft.)  o  i  ii  Tine Interval  F r i c t i o n U a a ( f t ) l n Right Branch f o r . L e n g t h 9 . 0 f c .  5 8  E8  1 s - 5  s b  1  •i i  o  i 3  (aeca)  SO  o  * 3 .§ s  ii  § s  Interval  Hook Gauge R e a d i n g l n O p a t r e a n Tank ( f t . )  i  ii  ss  s  Average  o  o  I  £  \f  o  g  o  o  i  o  £  i  o  TtM  £  5  o  i  *-  2 5 §i 2 g  I i  i i  o  5 S 3 8  S =  o  0  2  §3  ii  g  ro  55  b  321.15  O  S  318.85  o  i  M  327.85  I  321.1 321.2 318.8 318.9  S  *  I  I  o  O  1  L." ^',>«o.  5 -  =S  §  5  i  8  321.0  l.M»  i  i  r  s i ss  327.55  8  Weight o f U . t e r (lba.) from H . Halo P i p s ; R. R i g h t B r a n c h ; L . U f t Branch  |  §  0 r l f l c « No.  i  ! *ti § i i  311.83  a  321.2  a  321.0 321.0 327.5 327.6 311.8 311.9  •SIS , 5 5. s s "S 8  Teit Ko.  i iI i i § III III  i  307.85  n  . I 1. i  337.65  323.13  323.13  •  s  B  s •  321.2 321.2 307.9 307.6 337.6 337.7  '<- *u <- u  c  i ;  321.0 321.1 321.0 321.1  •m  z  c  U f t  Bead  l n Right o r  B  For. U a . (ft.)  S S  S  Form L o t a  K  R e y n o l d a Number  5 8  orU f t  Branch ( f t . )  5 £  S  (ft/aec)  1  Coefficient  (xlO ) S  64  2  2  5  2 2 25 5 5 3  2 :  5.5  2 2 2  32 2  § 2 2 2 2  2 s  S n S i ! I I I 1 3 ! 1 3 3 33 3 3 33 33 ! ! .3! 3 ! 3 3 3 3 33 ! 3 3 3 !• 3 3 3 3 3 3 3 3 3 3 3 3.3 3 3 31 3 3 i^o^ 3 ! 2 :• ! ! I ! 3 3 3 3 3 3 3! 3 2 s <>> » "Jj,;™ I 3 3 3 •' 3 3 3 3 d *  ( « ) . . O l ..OJ  (Jl)  000.10  IO  l  JO  J n  Jul,,  =  11,  01  1  s  •(!,)  le'islra  •(?,) « 0 !  •«H o,W o, ^  uoii.jij  ..on.  8  *'I S i C ' t  Wi  <n««*i J o |  6  qsu.ig.  o » « H U,«M  i.  *  33 3 3 3 3 11 3 ! ! 3 3 ! 33 !•! 3 3 3 3 33 3 3 3 ! aoJj'JH 3 3 3 3 3 3 3 3 !! 3! 3! (,,) ..cr, oo, I 3 ! ! ! ! 3 5 ! I 3' 3 3 3 !! 33 33 3 3 3 3 3 3 3 3 M 3 3 3 3 3 3 3 3 i 3 ! 3 3 3 - § § 3 5 5 3 3 - 1 ! 3 3 H 3 o §33 !• 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 • * 3 1.3 3 s - , - S i ! S * » i s£ H I a S s Iii  i o >^T« o ,  '!  s  1! 3 3 3 3 3! 3! 3 3 ! 1 I 3 33 33  JO  M  s  s  .  ,  ,  o  l  ,  «  ^  Ct  S  <-~•prog  1W\  -  mm  asiiSa  8 51111 1 1 I  I  : s  1 «  : s  S  mm  3  3 3 ! 5 3 3 3 3 33 3!3 * s  ti s  ii i a 3 iaaaia  I I 1 111 I 1 * I : s  IJ  I i  11i  C  c  II  * »  _  t>  o  ° I1  w u u w KJ N M N o o o o m t> m »  r  CO  111 i -  r  Ul  u u u u w w O  o  4> w *•  o>  §  » s  X  r  m  x  C  U.  SO  C  s  i §  i §  w w w w w u a « *° KI (-> - J CH U) KI M  0B  T««t Ho.  O r i f i c e Ho. Weight  Ul  o f Water  (lfai).  from M . K a l n P i p e ; L . Left Branch  *>  Time I n t e r v a l  Ul  Average  CK  Temperature  KI  R. R i g h t  Branch;  (aeca)  Time I n t e r v a l  Specific  0.749  0.271  o -J  SO  KI  0.478  S>  o  0.731  o *•  .  0.443  S  —•  U> O  0.307  0.857  0,000  o Ut  KI  Ut KI  | 321.25  a  ut w  326.13  00  M  u» u>  320.35  M  w  Kt  O m  318.65  1  9  °  S 5 S  325.7  u» M O  0.857  § £ S  0B  I. KI  K>  O  0.730  o  K>  U» 1  0.750  o  °  ut Kt O Ul  0.000  OR  KI  0.501  m  rM I* M  O  Ui  0.501  ut  ut 1  313.8  u>  337 .0  m W  u»  0.000  o  t* U»  337.0  t  KI  r  wt x  320.5 320.6 325.7 325.7 313.8 313.8  l  X  337 .0 337.0 337 .0 337.0  w w u w  w  320.9 320.9 320.9 320.9  1  8  0  ° 8  r  * -  ui  00091 H  x  1  m  i :  :  0  r  i  M 10000  ; L  i  00091 8  s  (aeca)  i n ° ? and  Weight  o f Water  (Iba/cu.ft)  Dlacharge ( c f a )  , Kt « w  *> S0  Kt  | 1.172  8  b M O  5*  Kt  N  KI Kt c*  1  CD  o* 00  s  0B  -0.250  O Kt  o Kt  o Kt  o KI  o  o  o  o  0.210  K»  o  0.7S1  b  o  KI  o  ON -J  r  O  Kt  sO Kt **  N  P-  CD  S  0.352  1—  K>  SO  o  K>  0.103  0.689  -0.073  0.36*  -0.027  i  0B  Ul SO  Ul  o ut Ul Uf  o  b  w  i  o  o  ?  u> Ul  0B  VM  o  a  Rook Gauge R e a d i n g i n Upftream Tank ( f t )  Hook Gauge Central  Hook Gauge R e a d i n g I n D o m e treats Tank ( f t )  Vernier  KI  Reading i n  Tank ( f t )  Correction (ft)  o  4  o  KI KI  0* t> KI  b  KI  F r e a a u r e Head D i f f e r e n c e ( f t ) between Main Pipe & Right Branch or K a l n Pipe & L e f t Branch  ' O *£  i> i—  o b o  o  0.002  o  b  K» *-  O  k s KI  O  o  o  8  so  8  ?  o  o  Ut O  o  b  8  F r i c t i o n L o u ( f t ) . In Main f o r U n g t h 3.375 f t .  Pipe  F r i c t i o n Loaa ( f t ) , i n K a l n for Length ST  Pipe  Ul  so  o KI *U»  0.281  CK  F r i c t i o n L o i a ( f t ) . i n Right Branch f o rLength 9 . 0 f t .  o r Left  1  0.220  0.007  o f Kt *•  *>  o  i  so  Dlacharge Ratio (Dlacharge In Branch Pipe/ Dlacharge I n K a l n Pipe )  <o  SO  8  Ul  0B  o  8  SOTO  O  8  0.634  0.130  000*0  o  S is  V"  ui so  o  <o  1  o  O  K»  0.067  o  t-  0.000  O  CD  Ul  Ul  o KI  o  *>  <J* K>  to  Ut m u> ui  ,o  KI  Total  F r i c t i o n Loaa ( f t ) .  In Kaln Pipe  Kt o.  Velocity  Head  KI  Velocity Right  o r Left  Branch  KI  Velocity i n Right  Head or Left  Branch ( f t )  QS *• ui  F r i c t i o n Loaa ( f t ) , i n Right o r L e f t B r a n c h f o r L e n g t h TD^ o r T D ^  Velocity  sO  O  k »  (ft/aec)  In K a l n Pipe ( f t )  in  (ft/aec)  O K*  O  o  o  KI Ut  Form L o a a ( f t )  1  0.022  KI *>  *>  s *> sO  0.052  o  Ut w  o O  CD CD  8 3  5  Kt  o Ul  0.040  o  *~  OB  •» >o vo  0.020  5 Kt  KI *•  (Average) Forn Loaa  KI Ul  Reynold's  Coefficient  |  j U l SO m so  0.103  KI u>  0.052  0.061  o  t S  0.086  o  o  CO  b b  ^  |  0.323  0.552  o  Ul oUJ  o SO  0.134  0.276  0.110  0.211  0.056  0.095  0.039  0.026  o  o  O"  *> ut N  S?  § i  M  o Ul  is 11.189  9.792  980'1  o u> OB  o  O  P-  Ul 0.000  0.000  0.663  0.000  6.535  OOO'O  M  s  O Kt  o  0.280  o w»  0.272  C* —1  0.147  2.082  O  0.138  0.907  0.011  0.896  o  o  3 S  Ul W  0.239 o W  o  '•o  M  0.000 o Mi  0.000  |  8I  0.712  0.338 o  o  § I 0.009  0.000  0.146  0.002  0.163  0.000  o  o  2.29  3.21  0.00  2.00  2.81  IS  0.00  1.17 .  0.84  0.00  8 5  C> S 8  2  3 8  Humber  ( x i o ' )  lu  ())) •  ^,J)  u o i  u o o . i . ^ l r ] 10  » s  «!« o i ijiootoa w  01 p « .  H  s  =  =  lo^^ru-ds •»l 0-.« 01»o»i J O J o o o o i l M»1I  -1  CH)  a m  O M J O H 1  "<"1  =  2 2 32 2  322  2  133 133 113 133 33 3 3 ! 3 . 3 3 33 3 ! 3 3 ! 3 5 3 3 3 •3 3 3 3 333 3 13 33 33 33 3 3 33 33 3 ! 3 3 :3 3 ! ! !• 2 3 3 3 3 3 ?• 3 3 2 s 3 3 3 3 3 3 3 3 s. ! 3 ! 3 ! ! I! 33 33 3 3 !3 33 3 ! 3! 3! 33 1 3 3 3 3 3 . I i 3 3 3 ! 3 3 1 1 33 3 3 3 3 3 3 3! 31 !3 3 5 i 3 3 ! ! 3 3 3 ! ! ! 3 3 3 ! ! ! 3! 3! 33 33 i. o  3!  2  <  »  >  ~  —  3  •  Co)  .--p.,.  -  •o.  -  2  33  3 5 J  3!  13  33  3  3  3  3  3  !  3 1 3 1 5 3 3 3 3 3 ! 3 33 3 3 3 3 3 * 3 * \ v 3 s\  !J 3  35  M  3  3  3  3  5  3  2 3 3 3 •3 ? 3 3 3' ! 1 3 3 3 3 3 3 3 ! 3 3 33 3 3 %\ • 3 *3 «3 * 3  s  i l l \\\ : i s I 5 i a a ill a a s S ii l l S s a s a a mm mm iiiiii mm liaSli ii'ssss iasgli H I I I I 1 I I I 1 1 III ! I « 1 1 1 111 1 1 1 »  i  a  321.1 321,1 321.0 321.0 319.6  '»  0.11  l.ot  2 2 :•5 2 22 5 5 2 2 22 S 2  2.76  66  :s  :s  :s  :*  : t  ?  -  •  Test No.  S  O r i f i c e No.  15000  I  R  8000  Weight o f Water ( l b s ) from M . H a l n P i p e ; R.Right Branch; L . L e f t Branch  M 19000  L  H 19000  R U000  9000  19000  L  R  0  H 19000  L  H 15000  0  R ISOOO  L  OOOOI N  o  9 " H 13000  0  0  ro  ut  * r" R 13000  OOOOI I  «• +* o L  1  i :  s  406.7  505.05  667.93  0.750  0.477  0.274  1.080  2.270  1.302  1.955  o  0.210  0.210  0.210  0.210  0.210  1.215  0.210  -0.268  1.256  o  2.316  o  o  *>  O  0.557  M  0.443  -0.175  1.993  -0.136  1.139  -0.076  0.485  -0.030  2  ? ui » Lr>  £  o  5  o |  ro  ? o» Ul Ul  u>  o  0.061  0.049  0.013  o  *o  406.7 406.7 505.1 505.0 467.9 668.0  2.185  >e  Ut  Time I n t e r v a l  (aeca)  Temperature i n ° F and S p e c i f i c Weight o f Water (lbs/cu.ft).  Discharge  '*» M  te  O u> u>  (seca)  o 0. 749  co  OH  Ul  2.038  1.771  o  3  Time I n t e r v a l  Average  a  K>  **»  u»  407.3  0.847  o 0.416  0.847  424.7  70°  M  ~  0.332  62.30  M  ?  435.3  360.25  0.750  0.750  1 1.531  N  360.25  o  407.3 407.3 424.7 , 424.7 435.3 435.3  360.2 360.3 360.2 360.3  321.05  321.05  -  0.000  0.360  0.360  0.561  o  70°  u  0.561  -o  »• >o  62.30  •>  «• •o  321.1 321.0 321.1 321.0  429.3  s Ui "o  429.3 429.3 429.3  445.5 445.7 445.5 445.7 t W» '<*  *•  O **>  s  (cfs)  Hook Gauge R e a d i n g i n Upstream Tank ( f t )  Hook Cauge R e a d i n g l n C e n t r a l Tank ( f t )  Hook Gauge R e a d i n g I n Downstream Tank ( f t )  Vernier Correction (ft)  P r e s s u r e Head D i f f e r e n c e ( f t ) , between H a l n P i p e & R i g h t Branch or Main Pipe & L e f t Branch  Discharge Ratio (Discharge i n Branch Pipe/ Discharge i n Main P i p e ) .  '  Pipe  F r i c t i o n Loss ( f t ) , i n Main f o r Length ST  Pipe  1  P r l c t l o n Los* ( f t ) , i n Haln for Length 3.375 f c .  0.009  0.011  600*0  j  0.005  0.002  o  |  I  0.168  0.250  0.318  0.159  0.242  0.887  | 0.121  0.876  0.011  0.712  0.113  F r i c t i o n Loss ( f t ) , l n Right Branch f o r Length 9 . 0 f t .  o r Left  1  1  j  |1  1  0.009 •  0.110  a  0.279  o  •>  0.102  0.789  ! o.ooo  0.704  o»  0.000  0.634  0.000  0.421  0.000  o  0.005  0.189  0.002  0.374  0.186  o.ooo  0.000  0.000  0.168  o s S  o  = a  F r i c t i o n Loss ( f t ) . i n Right o r L e f t B r a n c h f o r L e n g t h TD^ o r T D ^  Total  F r i c t i o n Loss  (ft)  1  0  *>o a>  o Ul CO Ul  0.387  680  CD  0.493  0.387  0.216  5.633  3.731  2.397  *• vO  ro O  Velocity  l n Haln  Velocity  Head  In Main Pipe  Pipe  (ft/sec)  (ft)  | 0.225  0.051  ui  U  O*  aa  .J  M  0.115  **»  0.054  ro  ro Ul  V e l o c i t y In Right o r L e f t Branch ( f t / s e c )  V e l o c i t y Head i n R i g h t o r Left Branch ( f t )  Form Loaa  0.140  (Average) Form L o s e  0.2 97  0.132  0.306  0.463  0.626  0.472  0.623  0.471  0.638  p a  o ^4  0.601  j£ •O  s  *-  0.118  two  1.897  OOO'O  11.052  O  0.307  CD  «e  0.000  — *" ce  M  o  0.000  O  Q O  9.790  0.000  0.102  0.133  0.831  8  7.322  . o  0.000  0.000  4.703  o  8  o O  *•  (ft)  Coefficient  1  J  1.83  2.06  1.06  3.26  2.32  2.06  0.00  2.89  1.54  0.00  2.16  0.00  1.39  0.99  0.00  s sa  Reynold's  Number  ( xlO^ )  68  s a c « ~  «  a (aj)  .«n  s  0 O « . a . aj»l Jo J o l « 01 iaiooi.j  H  W  2  A  (3../ j) 5  . d  M  S3!  !!I  II  3!  1!  i  5. 5 o.  . o o , o, •am < a l » o i .  ll!  o.  !  i 3  « J « H «1 iaioot.j  3:  3  2 2 2 I 33  K  4  (JI)  5 5 :• 3  !!  .ao*  <aa> u.oo.a. aj»a j o auSia 01 P.-U < a , o o , .  (=»•/»»  8 2= ' ~~  n  -  d  o'  133 3  2 2  3  2  s  !  3  2 :• 3 R ~  SB ~  d  2 2 I  3 2 12  • 33 '53  33  3 2 22  3 5  ! 5  31  !!  s  I  -'  d  S3  1s  = °  2 -  22  35 2!  d  33  3  2  i5 o'  !3  5  i  S *  o'  2 3  2  2  5  5 •  5 .'  3  2 2 13 33 33 1! 3 ! ! ! 2! 22 2 1 3 i 3 3 3 3 5 3 5 5 ! ! ! ! 22 s 22 3 3 33 s s 3 3 5 3 3 ! ! 2 3 3' 2 i !• 5 3 5 3 2 3 3 § s I S 3 !• I ! 3 2 2! ! 2 2! 2 5 . s i 3 3 33 2.2 5 3 M M \ M i 3 3 3 3 3 3 3 5 2 5 ! 3 5 J J 2 2 2 ?• 5 3 3 3 2 5 3 s 5 - a _.' I 3 3 3 3 2 - 3 5 5 !22 3 3 ! 3 3 3 1 3 3 3-5 3 ! ! ! 222 222 - * 3 s3 ^3 * § • >. > 5 s 3 * S  •33 0 ' 6 H 3 » u » l JOJ 33*1 JO SIJIITH u i -.(a.)) aao*i u o n a i J i  IS  l i * " * ! JO;  o'  d  S  o  uauMa  »1 »lj»u3»ia)  ipuMfl. aj»i «j wlia ni*N Jo  d  «?  o'  «3»fl  t°u i » j i . 3 « J3T3T3»«li »dn»l  pu* i  3M«T"n  o  -  i3i  5 5  Uou.ag I j a V T au»T. ' 1  !»diJ.  'on . o i l f a o •on a . . i  -  III  - -  c  , S  s  1  s  iii  s s i i i 1iiiiii  iliiii !uoa«J«  3  III  I  I  §  a s s  ; s  III  iii S'S55sS  i Ii  2 *• °-  s  2 *  § || 1  I  I  1  !l  iiiiii  343.9 3*4 .0 357.3 357.3 423.3 423.9  <3)"«.»/"<n)  d  l i s  I  »S s s RSSRSK  I I I 1 1i  « * •>  5  s ;  i : r  tm  o  §  x  t-  «-  >•  ac  o  345.0 343.1 343.0 343.1  ui  *  O  O  o  »  x  ve  vo  §  §  b  i-  o  §  §  ui  04  Ok 0>  o> M  o> »  o  o  o  o  o>  t>  o  |  to  oo  o  ss  2  o  0>  CB  8  ve  o  u ut t  © o o  «-  0.  VO  *• M  0> M  2 ? 5  04 -O O  o Ul  o o Ul vB  4*  X  o  to  i  b  U>  o  o  «• Ui  o  ut  »  o  8  i  o  o  5  i  o  o  s  s  vO  U>  M  p  p  04  O  b  o  0.201  0.002  o  S  vO 0>  § g  o  o  o  o  p  8  'S  ui e>  e»  1  p  p  vB  § 5  §  8  0  o  o  mco  O  *  1 1 1 5  0.034  0.031  p  o *o»  p  p  o U>  5 5  M  o . Ul ve  o  o  *  2  8  a *  o  SS  o  Book Gauge R e a d i n g i n Dovmitreata Tank ( f t )  o UJ  p  p  5  s  i  p  o  S  E  U>  1 8 o O  p  p  vO  vB  8  o  o  o  5  to 0*  o  O  k  uu> i » V  =  Friction U a a (ft). f o r U n g t h ST  In M a i n  Pipe  -  P r l c t l o a Loae ( f t ) . I n R i g h t o r U f t B r a n c h f o r U n g t h TD^ o r TD^  at  Total Friction U a a  5  Ul  <o  (ft)  0>  o  (ft/eec)  V e l o c i t y Bead i n Main Pipe ( f t )  ss  Velocity In Right o r U f t Branch  p p to <o «o j-^  3»  V e l o c i t y In Main P i p e  o  <o  «-J o  0>  a  8  Dlacharge Ratio (Dlacharge i n Branch Pipe/ D l a c h a r g e i n HeIn P i p e )  Friction U a a (ft), lo tight or U f t B r a n c h f o r U n g t h 9.0 f t .  V  s b  o  (ft)~  Ok  Ul  o  •>  Vernier Correction  M  o  8  (lbe/cu.ft)  - F r i c t i o n Loaa ( f t ) . In K a l n P i p e f o r U n g t h 3.37S f t .  p  P M  =  V  •* o  Ui  0  p  V e l o c i t y Heed in Right o r U f t  (ft/aec)  Branch ( f t )  ui o  o  s s  'S  0V  O  1—  o  o  o  o  o  '8  8  8  ?  0"  Ul  M  S  ui  Form Loaa ( f t )  i3  o  S8  Book Gauge R e a d i n g l a C e n t r a l Tack ( f t )  o  b  ve  o>  o  vO  o  5 5 p  o  -*  p  O  o  <M  OJ  §  OOO'O  b  »  O  •-  o  (aeca)  T e n p e r a t u r e l a °P and S p e c i f i c Weight o f Water  Book Gauge R e e d l a 3 l o O p e t r e e n Tank ( f t )  b  to  o  fi  •*-  t i  o  o  o  Ui  8  o  a  § 5 § 3  Average T 1 M l o t e r v a l  Ct>  b  o  § S  o  MI'O  O.OOO  o  3  o  p  O  o  o  b  i  Ul  o  8  o  7  o>  =  o>  o  8  (eece)  P r e M u r e Bead D i f f e r e n c e ( f t ) between M a i n P i p e & R i g h t B r a n c h o r Main P i p e & L e f t Branch  u> ut  O  §  0.17«  000*0  8  Interval  Oteeharfje ( c f a )  o  O M  Tine  Branch;  o  p  o  § 2  o  o  o  o>  Weight o f Wecer ( l b i ) f r c a H . H a l o f l p e ; R.Right L . L e f t Branch  K  KI  o  0> ^0  tvt  p  D  Ui  0>  1**,  o  '8  a>  o  o  o  b  M  o  <o  O  b b  M  b  »vO <> o> vo Ul  9>  09  0V  o  ? S  X  "o>  to  o  O  o  b  §  . o  o>  Ui  M  M  vo  0>  M  8  1 § 1 »  «  «  o  Ul 0*  o  §  Si  O r i f i c e Ho.  t-  •> i> o> <£ o o  UT-  OM N  M  X  -o o* -a o>  CM-  S " "  o  et  T c i t Mo.  f-  Ul  •r*  e> at •e •e <« n at b b *  o  t "  f  •>(•<»«  «- b  la O  M  r>  5  n  uwwu  Ui o  M  O  I " ae  •  x &  i .I i ii  Ui o  z  Ul  C C S  s  (Average) F o r n Loaa  Coefficient  Reynold'a  Number  ( alo' )  TABLE V-16  A.  Data of H y d r a u l i c Power Losses  9 0 ° Wye Without T i e - r o d  Q (cfs)  Qb Qm  K  P  M 0.748 1.000  0.322  L 0.000  0.000  0.526  0 .322  M 0.752 0.984  0.290  L 0.012  0.016  0 .521  0 .294  M 0.748  K  P  0 .173  R 0.552  0.740  0 .149  L 0.195  0.260  0 .243  R 0.479  0.638  0 .148  L 0.273  0.362  0 .175  R 0.444  0.591  0 .126  L 0.308  0.409  0 .155  R 0.416  0.555  0 .134  L 0.334  0.445  0 .140  R 0.374  0.499  0 .146  L 0.375  0.501  0 .123  0 .158  M 0.753  R 0.717  0.957  0.264  L 0.032  0.043  0.493  0 .274  M 0.751  0 .138  M 0.751  R 0.674  0.895  0.210  L 0.078  0.105  0.429  0 .233  M 0.752  0 .137  M 0.749  R 0.595  0.791  0.166  L 0.157  0.209  0.296  Q (cfs)  Qb Qm  M 0.753  R 0.740  90  Q (cfs) M 0.747  R 0.748  B.  i n Wye Arrangements  0 .193  0 .134  Wye w i t h TR3 T i e - r o d Qb Qm  K  Q (cfs)  M 0. 7*8  Qb Qm  K  M 0.747  R 0.748  1.000  0.530  L 0.000  0.000  0.582  0.530  M 0.752  R 0.553  0.740  0.279  L 0.194  0.260  0.309  R 0.476  0.636  0.366  L 0.273  0.364  0.240  R 0.441  0.588  0.399  L 0.308  0.412  0.234  0.287  M 0.749  R 0.739  0.984  0.486  L 0.012  0.016  0.578  0.487  M 0.748  0.320  M 0.749  R 0.716  0.957  0.469  L 0.032  0.043  0.556  0.473  0.331  71 TABLE V-16 - Q (cfs)  (Continued)  Qb Qm  K  P  Qb Qm  K  P  0 .307  M 0.748  M 0.751 R 0.673  0.895  0.390  L 0.078  0 .105  0.496  0.401  R 0.414  0.553  0.358  L .0.334  0.447  0.244  R 0.375  0.501  0.323  L 0.374  0.499  0.312  M 0.749  M 0.748 R 0.592  0 .791  0.307  L 0.156  0 .209  0.367  C.  Q (cfs)  0.320  0 .317  6 0 ° Wye w i t h o u t T i e -•rod  Q (cfs)  Qb Qm  K  P  M 0.750  Q (cfs)  Qb Qm  K  P  0 .100  M 0.749  R 0.750  1 .000  0.292  L 0.000  0 .000  0.554  0.292  R 0.555  0.742  0.060  L 0.195  0.258  0.213  R 0.480  0.640  0.052  L 0.271  0.360  0.121  R 0.416  0.556  0.057  L 0.332  0.444  0.084  R 0.376  0.501  0.073  L 0.374  0.499  0.065  M 0.750  M 0.749 R 0.737  0 .984  0.274  L 0.012  0 .016  0.548  0.278  M 0.749  0 .077  M 0.749  R 0.717  0 .958  0.194  L 0.034  0 .042  0.518  0.207  M 0.750  0 .069  M 0.750  R 0.673  0 .897  0.135  L 0.079  0 .103  0.434  R 0.596  0 .793  0.086  L 0.157  0 .207  0.281  0.166  M 0.752 0.126  0 .069  72 TABLE V-16 -- (Continued)  D.  60° Wye w i t h TR3 T i e --rod  Q (cfs)  Qb Qm  K  E. P  45° Wye w i t h o u t T i e -•rod Qb Qm  K  P  R 0.844  1.000  0.484  0.484  L 0.000  0.000  0.538  R 0.863  0.960  0.390  L 0.035  0.040  0.499  R 0.836  0.906  0.270  L 0.086  0.094  0.424  R 0.729  0.789  0.130  L 0.193  0.211  0.236  R 0.646  0.700  0.063  L 0.275  0.300  0.146  R 0.588  0.637  0.035  L 0.334  0.363  0.102  R 0.540  0.585  0.028  L 0.382  0.415  0.081  R 0.462  0.501  0.041  L 0.460  0.499  0.051  Q (cfs) M 0.844  M 0.749 R 0.749  1.000  0.454  L 0.000  0.000  0.625  0.454  M 0.898  M 0.748 R 0.736  0.984  0.426  L 0.012  0.016  0.612  0.428  0.394  M 0.922  M 0.745 R 0.712  0.957  0.402  L 0.032  0.043  0.590  0.409  0.284  M 0.923  M 0.747 R 0.669  0.896  0.333  L 0.078  0.104  0.509  0.351  0.152  M 0.922  M 0.746 R 0.509  0.682  0.268  L 0.238  0.318  0.180  0.240  0.088  M 0.923  M 0.744 R 0.438  0.588  0.311  L 0.307  0.412  0.132  0.237  M 0.742  0.059  M 0.923  R 0.411  0.553  0.294  L 0.331  0.447  0.164  0.236  0.050  M 0.923  M 0.750 R 0.375  0.500  0.232  L 0.375  0.500  0.227  0.230  0.046  TABLE V - l 7 Data o f H y d r a u l i c Power Losses i n M a n i f o l d  A.  90° M a n i f o l d w i t h o u t T i e - r o d  Q (cfs)  Qb Qm  K  P  M 0.750  Qb Qm  K  P  R 0.555  0.736  0 .177  0.206  L 0.197  0.264  0 .286  R 0.478  0.637  0 .170  L 0.272  0.363  0 .234  R 0.442  0.590  0 .175  L 0.308  0.410  0 .216  R 0.417  0.557  0 .182  L 0.332  0.443  0 .207  R 0.375  0.499  0 .188  L 0.376  0.501  0 .180  Q (cfs)  Ob Qm  K  P  R 0.447  0.636  0 .383  0.349  L 0.273  0.364  0 .289  R 0.441  0.588  0 .405  L 0.309  0.412  0 .280  R 0.417  0.556  0 .370  L 0.333  0.444  0.286  Q (cfs) M 0.751  R 0.750  1.000  0.348  L 0.000  0.000  0.541  0.348  M 0.750  M 0.750 R 0.739  0.984  0.320  L 0.012  0.016  0.532  0.323  M 0.750  0.193  M 0.751  R 0.720  0.962  0.315  L 0.029  0.038  0.521  0.323  0.192  M 0.750  M 0.750 R 0.672  0.895  0.235  L 0.079  0.105  0.457  0.258  M 0.752  0.203  M 0.751  R 0.594  0.788  0.190  L 0.159  0.212  0.339  B.  Arrangements  0.221  0.184  90° M a n i f o l d w i t h TR3 T i e - r o d  Q (cfs)  qb  K  P  Qm  M 0.750  M 0.750  R 0.750  1.000  0.500  L 0.000  0.000  0.588  0.500  M 0.750  M 0.750  R 0.718  0.956  0.445  L 0.033  0.044  0.562  0.450  M 0.749  0.353  M 0.750  R 0.671  0.895  0.376  L 0.079  0.105  0.514  0.390  0.333  74  TABLE V-17 -- (Continued) Q (cfs)  Ob Qm  K  P  M 0.751  Qb Qm  K  P  R 0.374  0.499  0.318  0.315  L 0.376  0.501  0.313  Q (cfs) M 0.751  R 0.592  0.789  0.320  L 0.158  0.211  0.403  R 0.554  0.739  0.301  L 0.196  0.261  0.351  0.337  M 0.750  C.  0.314  60° M a n i f o l d w i t h o u t T i e - r o d  Q (cfs)  Qb Qm  K  P  M 0.750  Q (cfs)  Qb Qm  K  P  0.085  M 0.749  R 0.750  1.000  0.283  L 0.000  0.000  0.546  0.283  M 0.750  R 0.478  0.638  0.057  L 0.271  0.362  0.134  R 0.443  0.591  0.052  L 0.307  0.409  0.102  R 0.418  0.559  0.061  L 0.330  0.441  0.086  R 0.375  0.499  0.055  L 0.376  0.501  0.065  M 0.751  R 0.718  0.956  0.207  L 0.033  0.044  0.514  0.220  M 0.749  0.072  M 0.749  R 0.672  0.895  0.144  L 0.078  0.105  0.445  0.175  M 0.751  0.072  M 0.750  R 0.593  0.788  0.057  L 0.159  0.212  0.294  R 0.554  0.739  0.063  L 0.196  0.261  0.221  0.107  M 0.749 0.104  0.060  75 TABLE V - l 7 —  D.  (Continued)  60° M a n i f o l d w i t h TR3 T i e - r o d  Q (cfs)  Qb Qm  K  P  E,.  45° M a n i f o l d without T i e - r o d  Q (cfs)  Qb Qm  K  P  M 0.847  M 0.750 R 0.750  1.000  0.463  L 0.000  0.000  0.626  0 .463  R 0.847  1.000  0.516  L 0.000  0.000  0.536  R 0.853  0.962  0.382  L 0.034  0.038  0.499  R 0.836  0.906  0.272  L 0.086  0.094  0.426  R 0.728  0.790  0.118  L 0.1.94  0.210  0.236  R 0.646  0.700  0.057  L 0.276  0.300  0.135  R 0.587  0.638  0.045  L 0.334  0.362  0.086  R 0.538  0.584  0.036  L 0.384  0.416  0.061  R 0.459  0.499  0.031  L 0.461  0.501  0.041  0.516  M 0.887  M 0.751 R 0.718  0.955  0.419  L 0.034  0.045  0.595  0 .427  M 0.750  0.386  M 0.922  R 0.671  0.893  0.347  L 0.080  0.107  0.518  0 .365  0 .286  M 0.922  M 0.750 R 0.592  0.788  0.284  L 0.159  0.212  0.354  0 .299  M 0.750  0.143  M 0.922  R 0.555  0.739  0.264  L 0.196  0.261  0.274  0 .266  0.080  M 0.921  M 0.750 R 0.477  0.635  0.297  L 0.274  0.365  0.140  0 .239  0.060  M 0.922  M 0.749 R 0.416  0.557  0.306  L 0.332  0.443  0.132  0 .229  M 0.750  0.046  M 0.921  R 0.375  0.499  0.201  L 0.376  0.501  0.236  0 .218  0.037  76  TABLE A - l  Particulars  D i s t a n c e from T h e o r e t i c a l Center of Elbows to P i e z o m e t r i c Rings on S t r a i g h t P i p e *  Distance  Distance  Distance  Distance  Distance  s'c  CF ft.  FD ft.  SD ft.  0.5  8.833  10.141  SS* ft.  ft.  45°  elbows  0.167  0.641  30°  elbows  0.167  0.333  0.333  8.833  9.666  0.167  0.370  0.238  8.833  9.608  22%° elbows  Note:  .  the average r a d i u s of each elbow i s 15 i n c h e s .  •* See F i g u r e A-2  L e f t Elbow t-  o  o  OJ  u > Ul  u> OJ Ul  •P" - P -  ON NJ  OJ  o o  OJ  OJ  '—1 ~ J  (—  H-  OJ  OJ  -J  ^1  OJ  j>  -J  •P- -P1  O  O  .  o  o  OJ  o  OJ  Ul  VO  1  -P-  •P-  OJ U i h-» O  •p-  ON  ON  NJ VO  NJ  OJ I-  Ul  OJ I-  OJ I-  o  1  ON  Ul  o  1  ON  VO  o  1  o  o  Ui  .p-  vO INJ  r-*  o  o  o  00  vO  bo  vO  ON ON  o  I-  o  o  o  NJ NJ Ul  00 Ui  bo  0J  NJ  o  o  I-  oo  OJ  1  • I1  o  1  • I-  1  ON  OJ  o b  h-  o  ON  •p-  1  •P*  o  •p-  • OJ vO  o •  • pN>  I-  1  o  VO OJ  o  o  I-  OJ Ul NJ  NJ NJ  I-  b  1  co  O  o  o  o  o  o  b  b  b  b  b  NJ 00  •p-  Ui  r-» NJ  o  O  O  o  o  o  o  o  b  b  b  (-*  b  b  b  l-> OJ vO  Ni  -p-  vo  O  o  o  o  O  o  o  o  b  b  b  b  b  b  b  b  OJ  Ul  ON ON  OJ  NJ  CO Ui  LL  VO  OJ vO  •P-  ON  NJ  NJ NJ  00  ON  Ul h-  1  ^1 Ul  VO VO  ON  Discharge ( c f s )  Hook Gauge Reading i n Upstream Tank ( f t )  00  Hook Gauge Reading i n Downstream Tank ( f t )  vo  P r e s s u r e Head D i f f e r e n c e (ft) (Vernier Correct i o n 0.210 f t . )  1  b  M OJ  Temp, i n F & S p e c i f i c Wt. o f Water ( l b / c u . f t . )  ON  o  o  Ul  1  • I-  b  •p-  (sees)  1  o  NJ 00  (sees)  •p- Ave. Time I n t e r v a l  •p-  b  o  Time I n t e r v a l  1  ~J  1  OJ  ON  o  oo  Weight of Water from Main P i p e ( l b s )  OJ  •P-  NJ  o •  M 00  -p- •p-  NJ v o  O  ON  1  ON  o  ON  I-  ON  o  o  1  OJ  - J  OJ  O  -p-  oo oo  o  O  OJ OJ  o  o  NJ  VO  « J  I-  ON  OJ  ON  NJ  OJ  O • OJ CO  OJ  OJ OJ  •p-  t-o  o  OJ OJ  Ui  vO NJ 00  •  I-*  o  o  o  l-»  Ul  h-  Ui NJ  OJ  O  -~J  00 OJ  OJ  OJ  •P-  1  -p- -p-  o  ON  oo  0J Ivo  VO OJ  O Ui O  1  OJ IvO  OJ OJ OJ OJ  ON  NJ v o  o  o  OJ I-*  1  o  o OJ IOJ 1  o  o  ON  ON  OJ  o o  OJ I-  OJ Ul  • o  o o  o  NJ  1  00 OJ OJ OJ 4> -P-  o  ON «~4  o  Description  IVO  Ui  o o o  ON  OJ OJ  OJ  NJ  o  o o •p~ OJ  -p-  ON  NJ  o 0J OJ OJ OJ  OJ  ON  Ul  O  o  1  1  vo O  I—  1  t—'  (—  1  OJ  OJ OJ Ul  «-J  1—  1  ON  o  • o • o OJ O o  1  i-  1  o o o  ON  Ui  R i g h t Elbow  ON  T o t a l F r i c t i o n Loss ( f t )  o  1—  1  I-  1  (—  1  V e l o c i t y Head Correction ( f t )  Elbow Loss ( f t )  NJ  IOJ 1  Elbow Loss  Coefficient  Right Elbow  Left Elbow rUi  I-  1  O o o o  o o  LO LO  LO  U>  to ro oo oo  O O O  Lo LO r-> M «J -J  LO LO  •P- •P-  to to  r-» hvO VD 1  Ov Ul  VO  o o o  o o  LO LO  to to  as as as  Lo  LO  oo  LO  LO  IvO  1  o o o  LO  Lo r-» Ul  to  Weight of Water from Main Pipe (lbs)  1  O O O  LO LO  r-> !-• 00 0 0  i-» Ul  -^i  •~J ON  Ov Ov  LO  LO  LO  LO  to co  Ui  Ul  hUi • OV  to 00  •  r00 •  to to 00 0 0  Description  1  IUl  1  o o o o  1—  to to 00 00  VO  LO  oo  Time Interval  (sees)  i  LO  fD P O. O CO  co  LO LO  LO  • 00  •  r-  to  LO  LO  r-» VO •  1  to  as asl U •  to  •P-  as  as as ON as •to vO as to as •to • VO u> o LO o Lo o ILO — 1— lto  •  VO  1  o  1  1  o  • 00 r->  Ui  LO  ON  •  •  LO ON  ON  o  •  o  Ui  O  o  00  to  Ov vO O  •p-  •  Ul  o  OV Ov to vO LO  Ui  o  I-*  O  • VO  o  Lo  i o to  •  VO  r-  LO  VO  LO  r-> • O  •  O  •  Ul  to  o •  -po  O  •  LO  1  O  •  Ul 00  VO  O  o  LO LO LO  as oo  •  to  •  .o  o  O  o o  O  (->  to  o to oo  o  o  o  o  o LO  o  •  Ui  •  t-> ^1 o  . o  as -p-  •  •  ~J  O  •  o  Ul Ul  •  LO  o  O  h-  1  o •  o -pw o  • r-  1  O  r-»  o  O  o •P-  O  ON  H*  • Ul  •  •P-P-  • 00  •p-  o  I-  1  as o o  •  o to o  h-  1  Ui Ui  o  •  o  •  LO  as  •^J  •  t-  Ul O  o  1  t>  •P-  LO  Ul ^1 Ui  •  o  •P-  to vo  I-  • Ul  o  to  VO  O  1  • I-  • PLO  O  ON  •  o to o  o  o to oo  o  as  o  O  O  Lo  as to  •  •  to  ~J  o  o  • vO vO VO  O  •  o -pLO  .  O  o  r—  LO  O LO  O  o  O  o  o -p-  O •P-  Ul Ul  •  •  Ul  O  m  CO  as Discharge (cfs)  Hook Gauge Reading i n Upstream Tank ( f t )  00  Hook Gauge Reading i n Downstream Tank ( f t )  vO  Pressure Head Difference (ft) (Vernier Correction 0.210 f t . )  r—  Total F r i c t i o n Loss ( f t )  r-> I-  Velocity Head Correction ( f t )  r—  Elbow Loss ( f t )  1—'  Elbow Loss C o e f f i c i e n t  1  o  1  1  1  O  1  1  VO VO  LO  1  o  o to  rt  a o si  Ul Ul r->  •  P  I—  •  LO ~J  •  Temp, i n F & S p e c i f i c Wt. of Water (lb/cu.ft.)  o  • VO  o  •  Ui  o  O  LO LO  o  o  to  LO U l  o  o  O  o  «  (sees)  Hi O li  as  vO  as o  ILO  •  VO 00  to  -p-  Ui  h-  o  •  OV  Ul Ul  1  1  as  LO  Ave. Time Interval  Ul  •  •  •  O  •  a •P-  oo  •  LO  •  o o  M  Ui O  *  •  •  1  OV OV  to  o •p-  r—  •  1  as as  ^1  LO LO  1  as  o  •  .  1—*  1  to  LO  Right Elbow  Left Elbow O O  L o LO NJ NJ NJ NJ  LO LO I- l->  -P-  CN  1  oo 00  ON  ON  NJ CN VO Lo O  •  O  • NJ  vO VO  I-  1  • LO O  • CN O  LO  O  •  LO -^1  ON  LO LO NJ NJ O O  l->  LO N J  LO  -P-  ON  LO NJ  LO NJ  NJ CN VO LO O r->  •  O  • Ul  o -P" o  • VO  •P" NJ  1— • NJ 1  • o  Ui  ON  ON  NJ  ON  vO LO O  • I-  Ul  1  o  ON  NJ v o  • •  LO U l  o  — (*  o  o  • VO NJ I-  o  O  oo  ON  • Ul  1  •  #  o  -P-  NJ  O  o  l->  «  Lo  •P-  •  • O  NJ  vO  o  O  O  o  O  I-  LO NJ VO  ON  VO  • 1  NJ  00 O  • o o •po  • o  I-*  -po • o  Ul  00  6L  •  O  . O  I-* LO  O  •  -J  ON  o  • o  NJ -J  O  «  a  O  o  Lo LO  r->  O • O •P-  o • o •P-  vO  ON  • ON  •  Lo U l  o  o  •P-  o  a  Ul  J— •  1  •P-  1  • Ui  Ul  O  • ILO LO 1  O  00 o  NJ Ul  l-  1  o  O  o  I-  1  o •  vo ILO 1  o • 00  O  • LO  o  o • o  O • o  00  •p-  I—* NJ  Ul  Ul  LO I-  LO LO  1  • Ul  ON  ON  •  O  1  • >-*  NJ O N . VO LO O l-»  •  NJ  LO  O ON  • LO NJ Ul  O  •  1— • o  VO  Pressure Head Difference (ft) (Vernier Correction 0.210 f t . )  I-  Total F r i c t i o n Loss ( f t )  NJ  1  O  O  O  • O  NJ vo  O  • o •p•p-  O  1  VO CO LO  O  oo  00  o  o • o  o  LO  oo  I-  Velocity Head Correction ( f t )  1  NJ  • o  •  1  o  O  • o •p-  • o  Ul  Hook Gauge Reading i n Upstream Tank ( f t )  Hook Gauge Reading i n Downstream Tank ( f t )  VO NJ  00  Discharge (cfs)  00  ON  o •  NJ  ON  (sees)  1  o •  ON  • o  Temp, i n F & S p e c i f i c Wt. of Water (lb/cu.ft.)  •P-  O  O  Ul  -~J  LO NJ Ul  •  Ave. Time Interval  a  O  •  •P-  (sees)  O  •  00  o  Time Interval  1  o LO  LO  I—  o  •  Weight of Water from Main Pipe (lbs)  ON  vo O  vO NJ NJ  ON  NJ  M  IVO  t-> NJ  • o  I-  1  1  NJ NJ  o  Ul  Ui  1  NJ  •  O  L o LO L0 LO h- l->  1  •P-  •  • o 00 Ul  LO  o  1  NJ VO Ui  •  o  Ul  B  •  • o •p-  ON  • • I-  O O  O  I-  NJ vo LO  o  LO LO Il-  Ul  ON  ON  NJ VO  I-  NJ  *  • Lo  O  NJ  LO  O  -P-  o O  LO NJ  ON  NJ  o • 00 o  • Lo  ON •  ~J  LO NJ  Ul  H-* VO  o  ON  O  IUi  o  LO LO NJ NJ  CN Ui  Ln  O  Description  1  1  o o o  L o LO N J NJ l-> K-*  1  o o •  •P-  o o o  O  1  o  ON  LO LO NJ NJ Ih-*  LO  (jJ NJ NJ •  1  o o o  O  t-  hVO O  1  Ui  O  o o o  Ln  1—  h-»  CN  I-  LO Ui  I— NJ  Elbow Loss ( f t )  hLO  Elbow Loss C o e f f i c i e n t  1  1  GRAVITY SUPPLY fPOM TH£ OVERHEAD TSMK  1  £M> P/£CE  I—f/RST/?£&UCE# STAT/OA/  ECEVAT/OfV  FIGURE 1-1  Details of General Arrangement  81  82  MAM P'PZ  FIGURE 1-3  Model Layout and Manometric L o c a t i o n s f o r Wye Arrangement  COlieCT/NG  P'P£  .:  705UMP>  i i i —  C0UECTM6 W£/GH/rt6  P<P£ TANK  ro  TROUGHS  P/p£S eLBOWS G/)U6£  BOARD  \ mi*  PIPE  I  t  FIGURE 1-4  D e t a i l s of Manifold Arrangement  TANA'S  Pt£Z<yf£77?/C-  PVEZOAfETP/C KING  L£fT JBP/tfJCAf  p/p&  MPT  BAMMCM  DOWA/STPEAM GAU6E TANK  C£U77?A1L GA(/6& TANA  6  p/Ezoifm/c.  MAN0META7JC AWN  P/P£  TUBES 7  o  P/£ZQAt£r/ftCAf///G  AlAlN  PIPE UPSHREA)M GQUGE  FIGURE 1-5  Model Layout and Manometric L o c a t i o n s f o r Arrangement  85  3%d "IO  £l/C/T£  smrro// P/£ZOMEZRIC P/A/GS  5/* ID  me/re  AfAJN P/P£ • — i i  i  J i i  05  S~Sr/)A/£MPD &0W  06  ST/V)/&HT£H£P  5 P/PST  ST££L  p£DUC£R  P/A£ CP05S  S£CT/W  rsr/?/)/6//r£A/£P)  FIGURE 1-6  Details  o f Main Pipe  from C o n t r o l V a l v e  to Wye  OD  FIGURE 1-7  Geometrical D e t a i l s of 90° Tapered  Wye  FIGURE 1-9  Details of Manifolds  /=£/)Sr/CP/P/A/G  3//6" DMM£T£P &/9/ISS/°/P£  3P6* JMPWPM THREAD  7//6"D//W£T££t i  Pi/BBEP  #//)M£T£R  3/9"  f/8"  //rp  F*P£ IVfiLL  FIGURE I-11  Details of Pressure Tap  91  PLAN  FIGURE I I - 2  H y d r a u l i c & Energy G r a d i e n t  Lines f o r Manifold  93  94  Q»,  FIGURE I I I - 2  Flow P a t t e r n s  i n Manifold with T i e - r o d  95  FIGURE IV-1  Skin F r i c t i o n Loss i n Main Pipe  96  &JD  PIECE  P/EZOMETP/C PW6  BRANCH PIPE TO BE TESTED  P/J=ZOM£TP/C PING  . J'  IA/ZET P/PE  REDUC£P  A1AW  P/P£  SUPPLY  FIGURE IV-2 Experimental Set-up f o r Measuring S k i n F r i c t i o n Losses i n Branch Pipes  <>7i . •  1  I  -|  at,  —  as  ;—I  p  1  1  A  90" wy£ w/mouT  o  90'  .  90'W/£  wy£  MTH  TR/  1™  vs-ffoo T/£-/?0[>  WtTH Tft2 T/£*lOO  • x  90 W/£W/r// TR3 T/Ei?0O  GJ  90' W/£ W/TH Tft4 r/£S?OD  c  1  ;  —-|  —'  o./  3  I  i  03  <X4  FIGURE  • '  '  a6  i  i  i  i  i  a& f.O /1AW D/SCHARGE SCES)  i  12  I  S.4  V - l Form Loss C o e f f i c i e n t s f o r 90° Wye (Symmetrical Flow)  i  /5  100  CL7  0-6  05  I OA  "•si  0.3  02  —  OPEN BRANCH  —  CLOSED BPfANCH A.  9 0 '  WVE  w/rnour  77E-&OD  o 90' WYE MTH TR/ T/£-#OD  01  • Jo'wyE  w/rp  x 90'y/yE  W/W 7793  a 90' WVE H W W as  *4  z  r/p-poo  T/E-POO T/E-POD  _L  o.s o.6 . a.7 SfP/A/ O/SCP/jPGE: <CPS)  FIGURE V - 2 Form Loss C o e f f i c i e n t s f o r 90° Wye (One-leg Flow)  ae4  AO  FIGURE V-3  Form Loss C o e f f i c i e n t s  f o r 90° Wye  (Unsymmetrical  Flow)  102  07 -  Q6  - •  1  1  1  |  1  i  A  60' WE WITHOUT T/E-POO  ®  60' WE WITH TjRZ T/E-POO  •  €0' WE  o  60* WYE WITH TR4  -  WITH 7H3 T/E-&OD  -  77E-RQD  •  0.5  -  -  1  i  -  i  03  —  «  • -  cu.  9  -  -  ai  -  0-6  D/5CHPR6E  Form Loss C o e f f i c i e n t s  1  AO  0.8  MA/N  FIGURE V-4  1  I  1  /.2 (CPS)  f o r 6 0 ° Wye  (Symmetrical  1  /.<*  Flow)  /.5  103  0.6  X  OS  1 1« si  I OPEN — —  at  CLOSED BPA#CP  €0* WYE MTHOUT  ©  60' WYE  •  60' WYE MM  TR3  77Z-POQ  60' WYE  77=t4  77£-/fOO  WW  MTP  TP.2T/E-POO  O.B  0.4-  /YAM  FIGURE V-5  1  A  B  Q3  BPA/VCH  D/SO/PP6E  «7  0.6  YCPSJ  Form Loss C o e f f i c i e n t s f o r 60° Wye  (One-leg Flow)  FIGURE V-6  Form Loss C o e f f i c i e n t s  f o r 60° Wye  ^symmetrical  Flow)  105  1  1  1  1  |  1  45°WYEMrH0UT  -  A  SYMMETlR/CftL  © RJOW M  -  - n  m PWW/N  |  77E-RQQ. FLOW  OPENBRANCH OOSED  B&WCH  "• o -  -  •  -  -.  j •  -  —  -  •  •—-A a.3  a4~  FIGURE V-7  1  OS  1 MAIN  O.B  1  AO  DISCHPR6E (CPS)  Form Loss C o e f f i c i e n t s f o r 45° Wye (Symmetrical & One-leg Flows)  1  J.2.  1 AA  /-5  0.7  0~2  FIGURE V-9  o-3  out  Comparison o f Form Loss C o e f f i c i e n t s  0.5  o.e  0.7  f o r Wyes (Unsynimetr.ie.al Flow)  «9  t.o  108  &  90' MWFOW  O  40'M/W/FOLD MntOl/T  •  GO'/VM/FOW MM TP 3 77F-POO  *  a 4£'A/MiFOW  OS MAM  FIGURE V-10  T7S-P0O  W/rHOt/T 77£-POD  60°/fM/F0U>  O.A  tV/m TP3 7?f-P0O  MrPOUT T/E-POO  /.o £>/LSCP/)P6E  /J2.  /4  /3  (CPS)  Form Loss C o e f f i c i e n t s f o r Manifolds.(Symmetrical Flow)  109  OPEN  BAMGH  CLOSED  BPAMCti  A  WMAWFOLD  ©  90' AW/PO/0 ?//J7/0£/r 7/E-POD  T&3 PE-POD  &0 " PAAVfdlD  ' s  03  60'MQMPOLD  45' L  0.4-  H/tTA/ 7P3 77E-POO  wrmour  PE-POD  tPOCO MAHOUT 0.5  MA/A/  _l  L  PE-POD I  0.6  D/SCPPP67E  <\7  a 86  fCFS)  FIGURE V - l l Form Loss C o e f f i c i e n t s f o r Manifolds (One-leg Flow)  T  1  I I I  O  a/ FIGURE V - 1 2  1  [  I  I•  I  1  az  j  I  1  I  I  I  as  Form Loss C o e f f i c i e n t s  1  I  j  1  1  r  1  I  I  I  A5  ae  I  I  0.7  f o r ^ l a n i f o l d s (Unsymmetrical Flow)  I  0.8  I  I  0.9  I  /-o c  0.4  0.-5  D/SCH/IR6E FIGURE V-13  Comparison o f Form Loss C o e f f i c i e n t s  P.6  Q.7  .  XAT/O Oi/Offi f o r W y e s M a n i f o l d s without Tie-rod  1  •  1 •  i  1  1  1  1  90'  MAN/FOLD  60'A4AN/F0LD  A  k  \  g  °  \  5  -  04 -  £  -  \  *k \ V\ ^ \ \  Ay-  •  A X  c  \  -  ?• -  XN N.  N -  \ \  0.3  1  UNsyi L FLOW WETRICA  GO"  0.6 A  1  1  ^  ^  /  /  /  A  -  -  .  0.2 —.  -  1  • 1 A/  O.2.  1  1 0.3  1  l  04. 0.5 D/SCHA&GE  FIGURE V-14 Comparison o f Form Loss C o e f f i c i e n t s  O.S  A3AT/0  1  0.7 <St,/<Sm  1  1  1 0.8  0.9  f o r Wyes & M a n i f o l d s w i t h TR3 T i e - r o d  /o  113  *•  v>  •  .»  n  -*  <»  a-7  i  |  r—|  1  1  A  90'/VM/rOLD  e>  9O°A//W/F4!J>  H//7HOUT.  VE-AToO  •  eo'tfAMFOLO  W/TH 7P3  T/E-A?OD  *  €0*AfAMFOW  iV/THOUr  77£-POO  "a  45' A4W/P0LD  WATPOL/r  77S-POO  06  fr/TH  T#3  1  OJ  FIGURE V-16  Hydraulic  W£-FO£>  U/VSyMMETRICAL fiDW  a* Power L o s s e s  0.5  i n Manifold  «.«  o-T  Arrangements  0.9  AO  END PIECE PIEZOMETRIC  BPfiMCH  P/PE  ELBOW PlEZOtfErplC  PlN&  /NLET  P/PE  flMN  PIPE  SUPPLY  F I G U R E  1  A - l Experimental Set-up f o r Measuring Head Losses i n Elbows  116  FIGURE A-2  H y d r a u l i c & Energy G r a d i e n t  Lines  f o r Elbow T e s t i n g  Set-up  ao3o\  i  aa  i  1  i  os FIGURE A-3  1 0.6  L__  L  I  _|_ oa  o.r  D/SCHAGGB  (CPS)  Elbow Loss Coefficients  I  1  l  I  ! t-r  

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