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Head loss in symmetrical bifurcations Ahmed, Sirajuddin 1965

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HEAD LOSS IN SYMMETRICAL BIFURCATIONS BY S i r a j u d d i n Ahmed B.A., B.E., U n i v e r s i t y o f Hyderabad,  1943  A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGRISE OF MASTER OF APPLIED SCIENCE IN THE DEPARTMENT OF CIVIL ENGINEERING  We accept t h i s t h e s i s as conforming t o the r e q u i r e d  THE  standard  UNIVERSITY OF BRITISH COLUMBIA 1965  In p r e s e n t i n g  this  thesis  in p a r t i a l  fulfilment of  the requirements f o r an advanced degree at the U n i v e r s i t y o f British  Columbia,  available mission  for  I agree that the L i b r a r y s h a l l  r e f e r e n c e and study.  make i t  I f u r t h e r agree that  f o r e x t e n s i v e copying o f t h i s  thesis  for  freely per-  scholarly  purposes may be granted by the Head o f my Department o r by his  representatives . v  cation of this  thesis  without my w r i t t e n  Department o f  It  for financial  permission.  C i v i l Engineering,  The U n i v e r s i t y o f B r i t i s h Vancouver 8, Canada Date  i s understood that copying o r p u b l i -  Columbia  September 29, 1965 .  gain s h a l l  not be allowed  ABSTRACT F i v e symmetrical wye branches  o f c o n v e n t i o n a l and  s p h e r i c a l t y p e s were t e s t e d f o r h y d r a u l i c l o s s e s under symmetrical and unsymmetrical presented g r a p h i c a l l y . observed depending  flow c o n d i t i o n s .  R e s u l t s are  A wide v a r i a t i o n i n l o s s f a c t o r was  on the type o f wye and on f l o w c o n d i t i o n .  F o r a g i v e n wye the minimum wye l o s s c o e f f i c i e n t does not n e c e s s a r i l y o c c u r under c o n d i t i o n s o f symmetrical  flow.  ii  TABLE OF CONTENTS Page Noo ABSTRACT  1  TABLE OF CONTENTS ACKNOWLEDGEMENT  i i ix  INTRODUCTION  1  PREVIOUS RESEARCH  3  CHAPTER I .  INSTRUMENTATION AND APPARATUS  5  1.1  Lay Out  5  102  Apparatus  6  103  Instrumentation  9  CHAPTER I I .  BASIC CONCEPTS RELATING TO HYDRAULIC  15  LOSSES IN WYE 2.1  Theory  15  PRELIMINARY INVESTIGATIONS  19  3.1  P r e l i m i n a r y experiments and re s u i t s  19  3-2  Investigations  19  CHAPTER I I I .  •  3 * 3 . Modifications  20  EXPERIMENTAL PROCEDURE  2  3  4.1  F r i c t i o n losses  2  3  4.2  Areas o f main and branch p i p e s  25  4*3  Discharge and p r e s s u r e measurements  26  4*4  E x p e r i m e n t a l procedure  26  CHAPTER IV.  iii  TABLE OF CONTENTS (Cont'd) CHAPTER V.  RESULTS AND CONCLUSIONS  30  501  R e s u l t s o f experiments  30  502  C o n c l u s i o n s and d i s c u s s i o n  30  BIBLIOGRAPHY  33  APPENDIX NOTATION  35  iv TABLES Page Table  1  Areas, main and branch p i p e s  38  Table  2  Distance from t h e o r e t i c a l c e n t r e o f wye t o p i e z o m e t r i c r i n g , main and branch p i p e s  Table  3  Velocity traverse: preliminary  Table  4  Symmetrical  flow,  investigations  Velocity traverse:  39  Symmetrical  flow,  f i n a l t e s t set up Table  5  Velocity traverse:  39 One l e g flow,  final  t e s t set up  40  Table  6  F r i c t i o n losses  i n main pipe  Table  7  F r i c t i o n losses  i n branch  40  pipe  ( S e c t i o n s A & C) Table  8  F r i c t i o n losses  41 i n branch  pipe  ( S e c t i o n s B & D) Table  9  Reynolds' numbers  41 and f r i c t i o n  factors,  main and branch p i p e s Table 10  Wye  l o s s c o e f f i c i e n t s f o r 90°  s p h e r i c a l wye Table 10 (cont'd)  Wye  Wye  large  (symmetrical flow)  42  (unsymmetrical  and one l e g flow)  43  l o s s c o e f f i c i e n t s f o r 90° s m a l l  s p h e r i c a l wye Table 11  41  l o s s c o e f f i c i e n t s f o r 90° l a r g e  s p h e r i c a l wye Table 11  38  (cont'd)  Wye  (symmetrical flow)  44  l o s s c o e f f i c i e n t s f o r 90° s m a l l  s p h e r i c a l wye  (unsymmetrical  and one l e g flow)  45  TABLES  (cont'd)  Table 12  Table 12  Wye  l o s s c o e f f i c i e n t s f o r 90°  wye  (symmetrical  (cont'd)  Wye  t a p e r e d wye Table 13  Table 13  flow)  l o s s c o e f f i c i e n t s f o r 90° (unsymmetrical  and one  Wye  l o s s c o e f f i c i e n t s f o r 60°  wye  (A), (symmetrical  (cont'd)  Wye  t a p e r e d wye  tapered  l e g flow)  tapered  flow)  l o s s c o e f f i c i e n t s f o r 60° (A), (unsymmetrical  and one l e g  flow) Table 14  V/ye l o s s c o e f f i c i e n t s f o r 60° t a p e r e d wye  Table 14  (B), (symmetrical  (cont'd)  Wye  t a p e r e d wye flow)  flow)  l o s s c o e f f i c i e n t s f o r 60° (B), (unsymmetrical  and one l e g  vi FIGURES Page Figure  1  General  arrangement  52  Figure  2  D e t a i l s of main pipe from c o n t r o l l i n g  valve  to wye  53  Figure  3  Model l a y out and manometric arrangement  54  Figure  4  D e t a i l s of wyes  55  Figure  5  Geometric d e t a i l s o f 9 0 ° t a p e r e d wye  56  Figure  6  Pressure  57  Figure  7  O r i f i c e arrangement  Figure  8  9  58  . V e l o c i t y t r a v e r s e a c r o s s the main pipe near wye  Figure  tap  during preliminary i n v e s t i g a t i o n  V e l o c i t y t r a v e r s e a c r o s s main pipe near  59 wye  a f t e r m o d i f i c a t i o n i n the main pipe s e c t i o n F i g u r e 10  V e l o c i t y t r a v e r s e f o r one d i s c h a r g e o f 0.92  l e g flow  with  cfso  F i g u r e 11  F r i c t i o n l o s s e s i n main pipe  F i g u r e 12  Experimental  61 62  s e t up f o r measurement o f  f r i c t i o n l o s s e s i n branch p i p e s F i g u r e 13  F r i c t i o n l o s s e s i n branch pipe A and  F i g u r e 14  63 (Sections  C)  64  F r i c t i o n l o s s e s i n branch pipe  (Sections  B and D) F i g u r e 15  60  65  F r i c t i o n f a c t o r s versus Reynolds numbers f o r main and branch  pipes  66  vii .FIGURES (cont'd) Page Figure 16  90° large spherical wye, symmetrical and one l e g flow  67  Figure 17  90° large spherical wye, unsymmetrical  Figure 18  90° small spherical wye, symmetrical and  flow  one l e g flow  69  Figure 19  90° small spherical wye, unsymmetrical  Figure 20  90° tapered wye, symmetrical and one l e g  flow  flow 9 0 ° tapered wye, unsymmetrical  Figure 22  60° tapered wye (A), symmetrical and  flow  72  one l e g flow  73  Figure 23  60° tapered wye (A), unsymmetrical  Figure 24  60° tapered wye (B), symmetrical and  flow  one l e g flow 60° tapered wye (B), unsymmetrical  Figure 26  Wye loss c o e f f i c i e n t s f o r a l l wyes, symmetrical flow  flow  76  77  Wye loss c o e f f i c i e n t s f o r a l l wyes, one l e g flow (open branch)  78  Wye loss c o e f f i c i e n t s f o r a l l wyes, one l e g flow (closed branch)  Figure 29  74  75  Figure 25  Figure 28  70  71  Figure 21  Figure 27  68  79  Wye loss c o e f f i c i e n t s f o r a l l wyes, unsymmetrical  flow  80  viii PLATES Page Plate 1  Manometric board with gage tanks  81  Plate 2  Manometric board  82  Plate 3  Lay out of model looking downstream  83  Plate 4  Main pipe and control valve  84  Plate 5  Control  85  Plate 6  Wye i n place  86  Plate 7  90° small spherical and 60° tapered wye (B)  87  Plate 8  90° small spherical and 60° tapered wye (B)  ' 88  Plate 9  O r i f i c e s and end piece  valve  89  ix ACKNOWLEDGEMENT The author i s deeply g r a t e f u l t o h i s S u p e r v i s o r , Dr«  Eo Ruus who, i n s p i t e o f h i s m u l t i f a r i o u s  was always a c c e s s i b l e during  the p e r i o d  and a v a i l a b l e t o d i s c u s s  i n v o l v i n g the r e s e a r c h  t h e s i s from June 1964 t o September  activities, the problems  and w r i t i n g o f t h i s  I965•  He i s a l s o g r a t e f u l t o t h e Colombo P l a n and  the Department o f E x t e r n a l  the  f i n a n c i a l assistance  during  U n i v e r s i t y o f B r i t i s h Columbia©  1  Authorities  A i d , Government o f Canada, f o r the p e r i o d  o f h i s stay a t the  1  INTRODUCTION In s e v e r a l r e c e n t  h y d r o - e l e c t r i c power p l a n t s  u n i t s of c a p a c i t y up to 300,000 HP  have been  installed.  S t i l l l a r g e r u n i t s are proposed f o r f u t u r e p r o j e c t s . the  penstocks which serve these p l a n t s both the  and  water v e l o c i t y have been i n c r e a s e d  t o match the  increase  diameter  beyond p r e v i o u s l i m i t s  i n turbine discharge  A major p o r t i o n o f the  In  capacity.  total f r i c t i o n loss in  penstocks of l a r g e diameter c a r r y i n g water at high v e l o c i t y i s due  t o bends, o u t l e t s , wyes and  determination of hydraulic  valves.  An  accurate  l o s s e s i n these d e v i c e s  f o r an economical d e s i g n of the This thesis describes  i s necessary  penstock. a model t e s t program t o  determine h y d r a u l i c l o s s e s i n l a r g e symmetrical wye In t h r e e  conventional  type o f wyes t e s t e d the  branches.  influence  the magnitude o f the angle between the branches o f the was  investigated.  o f the were  s i z e o f the  In two  s p h e r i c a l wyes t e s t e d , the  sphere and  the  of wye  influences  rounded pipe i n t e r s e c t i o n s  studied. The  i n v e s t i g a t i o n was  p r i m a r i l y concerned w i t h  h y d r a u l i c l o s s e s r e s u l t i n g from wyes. l o s s e s i n the  Therefore  friction  i n d i v i d u a l p i p e s were deducted from the  l o s s t o o b t a i n the form l o s s of the  wye.  the  total  2 The flow i n g e n e r a l was w e l l w i t h i n the t u r b u l e n t range, the Reynolds number v a r y i n g from 50,000  to 375,000.  When the r e s u l t s o f the experiments are a p p l i e d t o estimate the l o s s e s i n a g e o m e t r i c a l l y s i m i l a r p r o t o t y p e , the Froude number i s used as the c r i t e r i o n f o r dynamical  similarity.  F o r convenience the wye l o s s c o e f f i c i e n t s K are r e l a t e d to the v e l o c i t y head  i n the main p i p e .  3  PREVIOUS -RESEARCH Considerable research has been undertaken f o r the computation of hydraulic loss i n bends, elbows, tees, branch outlets and symmetrical  b i f u r c a t i o n s , but most of i t i s  confined to small pipes as part of losses i n pipe f i t t i n g s . Hinds, Thoma, Shoder, Weisbach and o t h e r s ^ ) have shown i n graphical form head l o s s i n bends f o r various ratios.  radius-diameter  Model t e s t s have been made on small tees and branch  outlets at the Munich Hydraulic I n s t i t u t e . (2)  Gardel(3)  describes t e s t s on water flow through eight tees with main pipe diameter of 150 mm joined by pipes ranging from 60 to 150 mm at angles ranging from 45° to 135°». The t h e o r e t i c a l basis has been developed by F a v r e ^ and McNown(5) f o r l a t e r a l b i f u r c a t i o n s only.  The character-  i s t i c s of flow and pressure pulsations i n l a t e r a l b i f u r c a t i o n s have also been a subject of study at the University of Kansas (6),  (7),  (8). Marchetti and Noseda (9) have made experiments on  f i v e b i f u r c a t i o n s constructed by welding 70 mm diameter pipes with included angles between the downstream branches varying from 60° to 180°.  The laboratory r e s u l t s were presented f o r  d i f f e r e n t conditions of flow i n graphical form enabling determination of hydraulic l o s s e s .  For symmetrical b i f u r c a t i o n s ,  the value of wye l o s s c o e f f i c i e n t K varied from 0.27 f o r a 60° b i f u r c a t i o n to O.96 f o r a 180  bifurcationo  The Reynolds  4 numbers v a r i e d from 97000 t o 322000 f o r these G l a d w e l l and T i n n e y ^ ^ 1 0  experiments.  conducted i n v e s t i g a t i o n s  on a t r i f u r c a t i o n , the t e s t s i n c l u d i n g measurement of head l o s s f o r d i f f e r e n t conditions of flow.  With the centre pipe  c l o s e d and flow e q u a l l y d i v i d e d , the value of K f o r a g i v e n d i s c h a r g e was ively.  The  0.73  and 0 . 9 4  f o r r i g h t and l e f t l e g r e s p e c t -  l a r g e d i f f e r e n c e appears t o be due  upstream o f the  trifurcation.  t o the bend  5 CHAPTER I . INSTRUMENTATION AND APPARATUS 1.1.  /  LAYOUT:  The r e s e a r c h p r o j e c t was conducted i n the  ——————  H y d r a u l i c L a b o r a t o r y as shown i n F i g u r e 1 and P l a t e 3o supply i s from an overhead tank and hence no dynamic f l u c t u a t i o n s are i n t r o d u c e d i n t o the f e e d i n g During  The  pressure  system.  the p e r i o d i n which the experiments were  under way care was taken t o ensure t h a t t h e r e were no w i t h drawals at any o t h e r p o i n t i n the l a b o r a t o r y and, thus, f o r each experiment a s t a b l e £low c o n d i t i o n under constant  head  was e s t a b l i s h e d . The  g e n e r a l arrangement o f the model i s shown i n  F i g u r e s 2 and 3 and P l a t e 3»  The supply t o the model could  be d i v e r t e d t o one o r both o f the branch p i p e s l e a d i n g t o left  and r i g h t flumes ( F i g u r e 1)  a c c o r d i n g t o the requirements  o f the experiment. The  turbulence  induced  pressure  fluctuations, intro-  i duced i n t o the system due t o the many elbows and t e e s between the overhead tank and the v a l v e c o n t r o l l i n g flow t o the wye, were dampened by p r o v i d i n g two flow l o n g as shown i n F i g u r e 2.  s t r a i g h t e n e r s each 2 f t .  The f i r s t  one was l o c a t e d down-  stream from the bend below the c o n t r o l v a l v e , and downstream from the reducer near the f i r s t  the other  straightener.  The  s t r a i g h t e n e r s c o n s i s t e d o f t h i n aluminium t u b i n g v a r y i n g i n  6 diameter  from one t o two The  the wye,  inches.  l e n g t h o f the main pipe on the upstream s i d e o f  comprised  the,length-diameter  r a t i o being 75-  e q u a l l e d 30 f o r the branch  The  the wye  ratio  c o n s i d e r e d adequate  by passage o f water  and thus assure o b s e r v a t i o n o f c o r r e c t pressure  heads at p i e z o m e t r i c p o i n t s on the branch 1.2.•  length-diameter  p i p e s , which was  to e l i m i n a t e flow d i s t u r b a n c e s caused through  33 f t . ,  o f s t e e l and l u c i t e s e c t i o n s , was  APPARATUS:  L u c i t e was  pipes.  used throughout  a p o r t i o n o f the main p i p e and the branch  f o r a l l the wyes,  pipes.  T h i s set up  allowed: (i) (ii)  t o r e p l a c e the d i f f e r e n t t o observe  l o s s e s occurred, (iii)  v i s u a l l y the p o r t i o n i n which h y d r a u l i c and  t o see t h a t t h e r e was  p a r t which might a f f e c t ,  were 90°  no entrapment o f a i r i n any  the p i e z o m e t r i c heads.  DESCRIPTION OF WYES:  symmetrical,  parts  A t o t a l o f f i v e wyes, a l l o f them  were used f o r conducting the experiments.  wyes and the remaining  two were 60°  wyeso  The  wyes have been d e s i g n a t e d as ( i ) Large S p h e r i c a l Wye, S p h e r i c a l Wye Tapered Wye  and  ( i i i ) Tapered Wye;  (A) and  ( i i ) Tapered Wye  the 60° (B).  The  90°  ( i i ) Small  Wyes as ( i )  For a l l wyes, the  c o n n e c t i n g main pipe and branch p i p e s had diameters and 3*75 inches r e s p e c t i v e l y .  Three  different  o f 5*25  wyes are shown  7 i n F i g u r e 4 and P l a t e s 6, 7 and 8 .  Although dimensions o f  the wyes were chosen a r b i t r a r i l y , t h e shapes f o l l o w a c e r t a i n p a t t e r n as i n d i c a t e d i n F i g u r e 5«  geometrical  90° Large S p h e r i c a l Wye: the sphere had a diameter o f 7.5  As shown i n F i g u r e  4»(a),  i n c h e s e q u i v a l e n t t o twice  the diameter o f the branch p i p e s .  On the o u t l e t s i d e the  i n t e r s e c t i o n o f sphere and pipe was rounded a t a r a d i u s o f 3/8  inch. 90° Small  S p h e r i c a l Wye:  As shown i n F i g u r e  sphere had a diameter o f 5*85 i n c h e s .  the were  4»(b),  The i n t e r s e c t i o n s  sharp. 90° Tapered Wye:  As shown i n F i g u r e s 4 and 5 the  cone angle f o r the tapered wye was kept at 2 0 ° . 60° Tapered Wye  ( A ) : As shown i n F i g u r e  the t a p e r i n g was done at an angle 60° Tapered Wye t h i s wye contained it  4.(d),  o f 10°•  ( B ) : As shown i n F i g u r e  a 3 i n c h l o n g tapered p o r t i o n .  4«(e),. Otherwise  i s s i m i l a r t o the 60° tapered wye (A) i n a l l r e s p e c t s . The  f i g u r e 4*  t h e o r e t i c a l c e n t r e s o f the wyes are shown i n  Distances  from the t h e o r e t i c a l c e n t r e s t o the  p o i n t s o f i n l e t and o u t l e t o f the wyes are g i v e n i n Table P r e p a r a t i o n o f Wyes: and  accurate  the models. and  2.  In order t o o b t a i n dependable  r e s u l t s , great care was taken i n p r e p a r a t i o n o f Accuracy was c a r r i e d t o one-thousandth o f an i n c h  i n t e r n a l surface o f the wyes was made as smooth as p o s s i b l e .  3 During and  p r e p a r a t i o n o f a wye,  the t h e o r e t i c a l c e n t r e , angle  the f a c e s were machined  o f symmetrical  l e n g t h from the t h e o r e t i c a l centre;  bifurcation,  to p o i n t s o f i n l e t  and  o u t l e t , and p o s i t i o n o f h o l e s f o r connection with main  and  branch p i p e s were l a i d out.  A f t e r t u r n i n g the c o n i c a l and  c y l i n d r i c a l water passages on a m i l l i n g machine, p o l i s h i n g of i n n e r s u r f a c e o f wyes was then by crocus paper. l i q u i d . ..Two  done by emery paper f i r s t  F i n a l p o l i s h i n g was  done by p o l i s h i n g  l o c a t i n g p i n s were i n s t a l l e d on the main pipe  t o e l i m i n a t e any o f f s e t between the wye Main and Branch P i p e s :  and the main p i p e .  As shown i n F i g u r e 3»  L u c i t e s e c t i o n o f the main pipe, approximately comprised of three s e c t i o n s .  Flanges made from L u c i t e were  p i p e s t o connect the d i f f e r e n t  smoothened was  connecting  r i n g s 1/8  branch  Each f l a n g e , w i t h the  end  then glued, to the pipe  the f a c e p e r p e n d i c u l a r t o centre l i n e o f p i p e . annular  branch  s e c t i o n s of the main and  p i p e s or the p i p e s w i t h the wye. f a c e machined and  the  13 f t . l o n g ,  f i t t e d on both ends o f each s e c t i o n of the main and  •leakage,  and  To  with  stop  i n c h wide were machined on  the  f a c e s i n which rubber r i n g s l / 8 i n c h diameter  were p l a c e d . Setting: up o f Apparatus: the main pipe was  a l i g n e d by means o f a t h e o d o l i t e . " The  p i p e , branches and wye carpenter's levelo  For the f i n a l t e s t  were l e v e l l e d a c c u r a t e l y w i t h  setup main  a  Measures were a l s o adopted t o e l i m i n a t e  9 d i s c o n t i n u i t y at a l l j o i n t s on the main and branch p i p e s , and p a r t i c u l a r l y at j o i n t s w i t h the 1.3o  INSTRUMENTATION:  wye.  P r i m a r i l y i t c o n s i s t e d o f means t o  measure p r e s s u r e , d i s c h a r g e , temperature, Pressure Taps: taps i s t h a t the openings  The  and  time.  standard requirement  f o r pressure  should be f l u s h w i t h the conduit  w a l l and f r e e from b u r r s , while the a x i s o f the p i e z o m e t r i c tube  should be p e r p e n d i c u l a r t o the c e n t r e l i n e o f p i p e .  .The t a p should be f r e e from  leakage.  The p r e s s u r e tap used i n these experiments i n F i g u r e 6.  The piezome'ter had an opening  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  screw i n a 7/8  i n c h L u c i t e cube.  The  of 1/8  i n c h NTP  NTP  i s shown  inch.  The  threaded  i n t u r n was  connected  t o a 3/l6 i m p e r i a l threaded nut, w i t h rubber r i n g at the j u n c t i o n t o e l i m i n a t e p o s s i b i l i t y o f any P i e z o m e t r i c Connections:  leakage.  Piezometers were i n s t a l l e d  i n groups ( F i g u r e 3 and P l a t e s 1 and 2) and connected tanks.  T h i s arrangement was  s u i t a b l e because the water l e v e l  i n the manometric tubes c o u l d be observed any  s i n g l e p r e s s u r e r e a d i n g which appeared  be checked  immediately.  t o gage  s i m u l t a n e o u s l y and out o f l i n e c o u l d  The p r e s s u r e t a p s were connected  to  manometers by f l e x i b l e t u b i n g w i t h p r o v i s i o n f o r removal o f a i r bubbles trapped i n the system.  Numbers i n F i g u r e 3  i n d i c a t e these c o n n e c t i o n s on the p i e z o m e t r i c r i n g s , manometer  10 tubes and gage tanks t o main, l e f t respectively. fitted  and r i g h t branch  The gage tanks 5.5 i n c h e s i n diameter  pipes were  w i t h hook gage rods and v e r n i e r s t o o b t a i n r e a d i n g o f  water s u r f a c e s . tank connected  There were t h r e e gage tanks,  ( i ) the upstream  t o the f o u r p r e s s u r e t a p s forming the p i e z -  ometric r i n g and the c o r r e s p o n d i n g manometers on the main p i p e , ( i i ) the c e n t r a l tank connected  t o corresponding  manometers  and p i e z o m e t r i c r i n g on the l e f t branch pipe and ( i i i ) the downstream gage tank connected  t o the manometers and p i e z -  ometric r i n g on the r i g h t branch p i p e .  The board c o n t a i n i n g  the manometer tubes a l o n g w i t h the d i f f e r e n t gage tanks i s shown i n P l a t e s 1 and 2. The gage v e r n i e r i n the upstream tank was s e t 0.210 f t . h i g h e r than the^gage v e r n i e r s i n the c e n t r e and downstream t a n k s . The range o f pressure heads t h a t c o u l d n o r m a l l y be observed  by the gage rods was o n l y 2 f t . and h e i g h t o f gage  tanks was a l s o about the same.  With the a i d o f e x t e n s i o n  rods t o the gage p o i n t s i t was p o s s i b l e t o measure p r e s s u r e head d i f f e r e n c e s up t o 3 f t . o f water. O r i f i c e s f o r v a r i a t i o n o f d i s c h a r g e through Main and Branch P i p e s :  The experiments  were conducted  c o n d i t i o n s o f flow; symmetrical, unsymmetrical as e x p l a i n e d subsequently  i n more d e t a i l .  f o r different  and-one l e g ,  F o r symmetrical  flow the t o t a l d i s c h a r g e s used v a r i e d from 0.32 t o 1.5 c f s ;  11  f o r unsymmetrical 0.92  flow, the t o t a l d i s c h a r g e was  c f s , whereas the d i s c h a r g e r a t i o i n the two  v a r i e d from zero t o 1.0. v a r i a t i o n was The was  0.75  from 0.32  t o 0.92  l e g flow the  branches  discharge  cfs.  v a r i a t i o n o f d i s c h a r g e through  accomplished  i n F i g u r e 1.  For one  and  the main pipe  p a r t l y by o p e r a t i n g the c o n t r o l v a l v e shown  F o r a p a r t i c u l a r experiment i t was,  a t the  same time, necessary t o c r e a t e c o n d i t i o n s so t h a t pressure d i f f e r e n c e s c o u l d be o b t a i n e d by o b s e r v a t i o n o f water l e v e l s i n a l l the t h r e e gage tanks s i m u l t a n e o u s l y . o r i f i c e s of d i f f e r e n t  F o r t h i s purpose  s i z e s , which are shown i n F i g u r e 7 and  P l a t e 9, were p l a c e d i n end p i e c e s attached t o the pipes.  These o r i f i c e s had d i f f e r e n t diameters  and,  on the d e s i r e d p a r t i c u l a r d i s c h a r g e i n each branch,  branch depending orifices  of c e r t a i n diameters were p l a c e d i n the end p i e c e s a t t a c h e d t o the b r a n c h - p i p e s .  I f f o r a p a r t i c u l a r wye  and a p a r t i c u l a r  flow c o n d i t i o n , water l e v e l i n the gage tanks c o u l d not observed  s i m u l t a n e o u s l y due  t o manomotric l e v e l s being  be lower  o r h i g h e r than the l i m i t s o f o b s e r v a t i o n imposed by the hook gages, diameter was  o f the o r i f i c e s i n one or both the branches  changed u n t i l the d e s i r e d r e s u l t was  o r i f i c e s were machined from one sharp edge f r e e from any b u r r s .  achieved.  These  s i d e t o o b t a i n a c l e a n and In a l l experiments the  o r i f i c e s were p l a c e d i n such a way  t h a t the sharp, undamaged  edges o f the o r i f i c e s were f a c i n g the  flow.  12 Measurement o f Time:  A degree o f accuracy up t o  0.1 second was o b t a i n e d f o r d e t e r m i n i n g time i n t e r v a l s i n which a p a r t i c u l a r weight o f water was c o l l e c t e d i n the weighing  tank.  F o r t h i s purpose an e l e c t r i c  clock reading  d i r e c t l y up t o 0.1 second was used. Measurement o f Temperature:  To determine  Reynolds'  numbers f o r the corresponding f r i c t i o n l o s s c o e f f i c i e n t s i n the main and branch  p i p e s , temperatures  were recorded by  u s i n g a thermometer, and r e a d i n g s obtained t o t h e n e a r e s t h a l f degree o f F a h r e n h e i t . Measurement o f Weight o f Water: means o f a weighing  T h i s was done by  tank having a maximum c a p a c i t y o f 20,000  l b s . , the s c a l e s o f which were t e s t e d and found c o r r e c t b e f o r e s t a r t i n g the experiments. Pressure Measurements:  In spite o f the f a c t that  supply was from an overhead tank under constant head c o n d i t i o n s i n which no dynamic p r e s s u r e f l u c t u a t i o n s c o u l d have been p o s s i b l e , and t h a t two s e t s o f s t r a i g h t e n e r s were p r o v i d e d at the upstream end o f a l o n g s t r a i g h t main p i p e , some p r e s s u r e f l u c t u a t i o n s were observed  i n t h e manometric tubes  connected  t o t h e d i f f e r e n t p i e z o m e t r i c r i n g s . , I t c o u l d be d e f i n i t e l y e s t a b l i s h e d by process o f e l i m i n a t i o n t h a t these were t u r b u l e n c e induced p r e s s u r e f l u c t u a t i o n s .  I t was observed  t h a t maximum  f l u c t u a t i o n i n water l e v e l was o f the order o f 0.05 f t . The  13 pressure f l u c t u a t i o n s , as observed  v i s u a l l y , were i n the  neighbourhood o f 30 c y c l e s per minute.  The  c o r r e c t i v e measure  adopted f o r o b t a i n i n g p r e s s u r e d i f f e r e n c e s t o the r e q u i r e d degree of accuracy was  to adjust  the water l e v e l s i n the  d i f f e r e n t gage tanks c o r r e s p o n d i n g t o average l e v e l s i n the manometric tubes, the a r e a r a t i o o f the tube (diameter, to the gage tank (diameter, 1:480 i t was  5i  inches) b e i n g  and then allow 2 t o 3 hours t o e l a p s e . observed  £ inch)  approximately By t h i s  procedure  t h a t water s u r f a c e s i n the tanks assumed  constant l e v e l s , a u t o m a t i c a l l y averaging out f l u c t u a t i o n s i n the manometric  pressure  tubes.  Discharge Measurements:  As the degree o f  accuracy  i n o b t a i n i n g v e l o c i t y heads at p o i n t s o f p i e z o m e t r i c r i n g s was  d i r e c t l y r e l a t e d t o d i s c h a r g e , i t was  necessary t o measure  the d i f f e r e n t d i s c h a r g e s a c c u r a t e l y . Combined d i s c h a r g e through by a l l o w i n g both the branch weighing  obtained  p i p e s t o d i s c h a r g e i n t o the  tank s i m u l t a n e o u s l y .  branch p i p e s was  the main pipe was  The  d i s c h a r g e from each o f the.  then o b t a i n e d s e p a r a t e l y .  I t was  observed  t h a t d i s c r e p a n c i e s o c c u r r e d i n measurement o f d i s c h a r g e s 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  provided.  For combined  * r Note: T h i s measure was adopted to reduce the p e r i o d r e q u i r e d f o r the water l e v e l s to become steady i n the gage tanks. Water was e i t h e r poured i n t o or taken out from the tank u n t i l i t s l e v e l approximated the average water l e v e l i n d i c a t e d i n the manometric t u b e s .  14 d i s c h a r g e and f o r the d i s c h a r g e from the r i g h t branch p i p e the necessary time i n t e r v a l was found t o be about 300 seconds, whereas f o r the l e f t branch pipe the r e q u i r e d time i n t e r v a l was,500 seconds.  For a l l the experiments conducted, the time  i n t e r v a l s mentioned above were adhered t o , and Column 3 o f T a b l e s 10 t o 14  show t h a t the maximum d i f f e r e n c e i n time  i n t e r v a l s f o r weighing a p a r t i c u l a r q u a n t i t y o f water from the main, r i g h t , o r l e f t branch p i p e d i d not exceed about 0.1%.  The v e l o c i t y head c a l c u l a t e d on the b a s i s o f d i s c h a r g e  so o b t a i n e d was thus c o r r e c t up t o a thousandth o f a f o o t , the  degree o f accuracy r e q u i r e d .  15 CHAPTER I I . BASIC CONCEPTS RELATING TO HYDRAULIC LOSSES IN 2.1.  THEORY:  WYE  I t i s assumed t h a t the measurement of p i e z -  ometric heads has been made a f t e r s t a b l e flow c o n d i t i o n s have been e s t a b l i s h e d and a f t e r the water l e v e l s i n the gage tanks were  different  steady.  F o r a h o r i z o n t a l p i p i n g , the energy l o s s e s can expressed h  h  pm  pm  + vm h  +  h  vm  be.  from the energy equation o f B e r n o u l l i as f o l l o w s : 1  pr  h  +  = pl h  +  h  h  vr *  A  h  +  h  fmt  +  h  fr.  v l+  A  h  +  h  fm  +  h  f l  •••••  A  <  1}  B  (See Page 16). D e f i n i n g Q as d i s c h a r g e ; A, area; hp, v e l o c i t y head; h f , l o s s of head due  p r e s s u r e head;  to f r i c t i o n ;  h , v  V j , mean  v e l o c i t y i n the p i p e ; V"2>  v e l o c i t y at piezometric r i n g  d e s i g n a t i n g s u b s c r i p t s m,  r and 1 t o main p i p e , r i g h t and. l e f t  branch  r e s p e c t i v e l y the f o l l o w i n g equations  Continuity i s given Q  = Q  m  r  -t-  m  l  "  obtained.  by:  ..o..  Qi  (2)  Average v e l o c i t y i n the main pipe i s g i v e n V  can be  and  .....  A^I  by:  (3)  S i m i l a r e x p r e s s i o n s are v a l i d f o r average v e l o c i t y i n the r i g h t or l e f t at  branch;  Q, r  Qi, A i , r  An  being known.  the p i e z o m e t r i c r i n g S on the main pipe i s g i v e n  Velocity by:  16  Elevation.  17 v  Similar or D2  ~ Aj^2  m2  • <•.<>. (4)  e x p r e s s i o n s f o r v e l o c i t y at the p i e z o m e t r i c r i n g s DQ_ "the r i g h t or l e f t branch  o n  Qr»-'Ql> A r 2 and Ai2» distinguish  can be o b t a i n e d i n terms of  (3) and (4) are r e q u i r e d to  Equations  the average v e l o c i t y r e l a t e d  to f r i c t i o n  losses,  and the average v e l o c i t y at the p i e z o m e t r i c r i n g s which are related  to v e l o c i t y heads a t these Velocity  l e f t branch  The r  h  Ah  =  ( pm = A  r  P  h  v r  ,  h i i n the main, r i g h t v  once v e l o c i t i e s are  l o c a l i z e d l o s s o f wye -• ( fm  h  R  ,  and  obtained  (4)»  ~ pr)  h  y m  p i p e s can be determined  from equation  A  heads h  rings.  _ (h  h  +  + hf )  f m  r  h  fr)  (Km  +  + (h  can be expressed " vr) h  - h )  v m  as:  . 0 . . .  v r  (5)  Similarly *  h  l  Ah!  =  (h  p m  - h ) p l  = p]_ - ( h A  F i n a l l y wye  f m  - (h  f m  + h )  + (hvm  f l  + h f i ) + (hym  pipe i s g i v e n  h  " (6)  - h )  l o s s c o e f f i c i e n t K' f  - vl)»  v l  f o r the r i g h t or l e f t  branch  by: K=  lot  '  '* ,0  ,(7)  2g Equations l o c a l i z e d wye equation  ( 5 ) and  ( 6 ) have been used t o determine  l o s s at T, the t h e o r e t i c a l  c e n t r e o f wye,  and  ( 7 ) f o r d e t e r m i n a t i o n o f K f o r the f o l l o w i n g flow  conditions:  18 (a)  Symmetrical  Flow:  The  d i s c h a r g e i n the main  pipe i s d i v i d e d e q u a l l y between the r i g h t and l e f t  branch  pipes. (b)  Unsymmetrical f l o w :  The d i s c h a r g e i s d i v i d e d  u n e q u a l l y i n the two branches w i t h the d i s c h a r g e r a t i o r a n g i n g from 0 t o (c) to  One  S  1. Leg Flow:  the r i g h t or l e f t  The  discharge i s wholly d i v e r t e d  branch.  In the f i g u r e the h y d r a u l i c grade l i n e s and the energy grade l i n e s have been shown from S t o D i , D2, t h a t a l l wye  total  assuming  l o s s e s are l o c a l i z e d at the t h e o r e t i c a l centre  In a d d i t i o n to these l o c a l i z e d wye v e l o c i t y heads and l o s s o f head due  losses, piezometric  T.  and  t o f r i c t i o n at l o c a t i o n s  S, T, D i , D2 are a l s o i n d i c a t e d . The wye  d i s c h a r g e p a s s i n g from the main pipe through  i n t o the branch  p i p e s causes f o r m a t i o n o f v o r t i c e s  t u r b u l e n c e i n the wye.  wye  The  and  Mixing i s c a r r i e d a considerable  d i s t a n c e and e x t i n g u i s h e d s l o w l y w h i l e p r o c e e d i n g branch p i p e s .  the  i n the  e f f e c t of v o r t i c e s and t u r b u l e n c e i n the  i s extended i n t o the main pipe f o r a v e r y s h o r t d i s t a n c e  only.  The  d i s t a n c e o f S from T has, t h e r e f o r e , been kept  much s h o r t e r than the d i s t a n c e o f  and D£ from  T.  19 CHAPTER I I I . PRELIMINARY INVESTIGATIONS 3.1.  PRELIMINARY EXPERIMENTS AND RESULTS:  A complete  set of  experiments f o r symmetrical, unsymmetrical and one l e g flow was conducted f o r the 9 0 ° small s p h e r i c a l wye and the r e s u l t s t a b u l a t e d i n the way as shown i n T a b l e s 10 t o 14.  On exam-  i n a t i o n o f the r e s u l t s so o b t a i n e d , i t was found t h a t head l o s s i n the wye was  ( i ) the  . d i f f e r e n t f o r the two branches,  ( i i ) the p i e z o m e t r i c r e a d i n g s o f the c e n t r a l and downstream gage tanks d i f f e r e d c o n s i d e r a b l y ,  ( i i i ) t h e r e was v a r i a t i o n  i n c o n s e c u t i v e time i n t e r v a l s when a p a r t i c u l a r d i s c h a r g e was measured, ( i v ) d i s c h a r g e from the l e f t branch p i p e was consistently  l a r g e r than t h a t from the r i g h t branch p i p e and  (v) t h e r e was c o n s i d e r a b l e t u r b u l e n c e induced p r e s s u r e fluctuation 3.2..  (about 0.100  f t . ) i n the manometric t u b e s .  INVESTIGATIONS: These were undertaken w i t h a view t o  determine the causes and t o e f f e c t changes i n the apparatus u n t i l the d i s c r e p a n c i e s were removed.  A number o f t e s t runs  were conducted t o f i n d f a c t o r s r e s p o n s i b l e f o r the d i s c r e p a n c i e s observed. While a p a r t i c u l a r experiment was i n p r o g r e s s , i t was found t h a t a i r was trapped i n the f l e x i b l e t u b i n g connected  20 t o the uppermost p i e z o m e t r i c p o i n t s on the d i f f e r e n t  pipes  and hence the top p i e z o m e t r i c connections were pinched o f f t o e l i m i n a t e the source of t h i s By o b s e r v a t i o n i t was  error. found t h a t a r e l a t i v e l y l a r g e  q u a n t i t y o f a i r was  necessary to o b t a i n the c o n d i t i o n " d i s c h a r g e  i n t o f r e e atmosphere  11  and, hence, l a r g e wooden troughs were  p r o v i d e d f o r both branch p i p e s .  I t was  a l s o n o t i c e d t h a t the  maximum v a r i a t i o n o c c u r r e d i n measurement o f d i s c h a r g e from the r i g h t branch system. branch  pipe due  t o surge waves i n the  collecting  When the wooden trough c a r r y i n g water from the pipe was  extended so as t o d i s c h a r g e i n the r i g h t hand  flume ( F i g u r e 1) an immediate improvement was Velocity traverse: d i s t r i b u t i o n was  right  An unsymmetrical  found. velocity  found when a v e l o c i t y t r a v e r s e was made  a c r o s s the main p i p e about 6 i n c h e s from the wye, s t a t i o n b e i n g shown i n F i g u r e 3«  The  the t r a v e r s e  r e s u l t i n g flow  distrib-  u t i o n i s shown i n F i g u r e &M>ased on o b s e r v a t i o n s recorded i n Table 3 which c o n c l u s i v e l y proved u t i o n was 3.3.  not symmetrical  MODIFICATIONS:  t h a t the v e l o c i t y  distrib-  about the a x i s of the main p i p e .  To improve the p a t t e r n o f flow the  f o l l o w i n g m o d i f i c a t i o n s were c a r r i e d out i n the main p i p e section: (i)  The  4 i n c h standard s t e e l pipe was  r e p l a c e d by a  s e c t i o n o f 5 i n c h standard s t e e l pipe ( F i g u r e 2 ) .  new  21 (ii) provided (iii)  Two s e t s o f flow  s t r a i g h t e n e r s each 2 f t . l o n g were  i n p o s i t i o n s shown i n F i g u r e 2, The c o n t r o l l i n g v a l v e was r o t a t e d and made  symmetrical  w i t h the d i r e c t i o n o f f l o w . These m o d i f i c a t i o n s were proposed not o n l y t o improve the flow c o n d i t i o n s i n o r d e r t o e l i m i n a t e t h e d i s c r e p a n c y i n discharge  i n t h e two branches but a l s o t o p r o v i d e the maximum  s t r a i g h t p o r t i o n o f the main pipe w i t h a l a r g e r l e n g t h diameter r a t i o o f approximately  75 t o dampen t u r b u l e n c e  induced  pressure f l u c t u a t i o n s . A f t e r i n c o r p o r a t i n g the changes i n t h e main pipe s e c t i o n , t h e r e s u l t s o f the v e l o c i t y t r a v e r s e , made at t h e same p o i n t a t which t h e p r e v i o u s t r a v e r s e was made, and shown i n Table  4 and F i g u r e 9,  i n d i c a t e d an e n t i r e l y  symmetrical  v e l o c i t y d i s t r i b u t i o n about the a x i s o f the main pipe w i t h the maximum v e l o c i t y o c c u r r i n g a t the c e n t r e . Branch P i p e s :  Because the l e n g t h o f the branch  p i p e s was o n l y about 3.75 f t . , g i v i n g a length-diameter of about 12, i t was c o n s i d e r e d necessary  ratio  t o increase the  l e n g t h so t h a t most o f t h e v o r t i c e s and t u r b u l e n c e  created  i n the wye would be e x t i n g u i s h e d by the time water reached the p i e z o m e t r i c r i n g s on the branch p i p e s .  At the same time  too l a r g e an i n c r e a s e i n l e n g t h o f branch p i p e s would have r e s u l t e d i n magnifying  t h e e f f e c t o f f r i c t i o n l o s s e s , and  22 thus •would have .reduced the degree o f accuracy i n o b t a i n i n g the wye l o s s e s o  The branch p i p e s were consequently r e p l a c e d  by two s e c t i o n s o f pipe as shown i n F i g u r e 3»  The l e n g t h -  diameter r a t i o was thus i n c r e a s e d from 12 t o approximately 3 0 . L o c a t i o n o f P i e z o m e t r i c Ring on the Main P i p e : Some doubt was f e l t wye  about the p r o x i m i t y and i n f l u e n c e o f the  on the r e a d i n g s o f the piezometers  on t h e main p i p e  because o f t u r b u l e n c e and f o r m a t i o n o f v o r t i c e s i n the wye. In  o r d e r t o check t h i s s i t u a t i o n , a v e l o c i t y t r a v e r s e was made  under extreme c o n d i t i o n s o f maximum d i s c h a r g e o f 0 . 9 2 c f s i n the r i g h t branch w i t h t h e l e f t branch  completely s h u t - o f f .  The  v e l o c i t y p r o f i l e so o b t a i n e d , shown i n Table 5 and F i g u r e  10,  i n d i c a t e s p r a c t i c a l l y symmetrical  flow about the a x i s o f  the main p i p e , p r o v i n g t h a t the l o c a t i o n p o i n t o f the p i e z o m e t r i c r i n g on the main p i p e was o u t s i d e t h e i n f l u e n c e o f the wye • F r i c t i o n Losses i n Branch P i p e s :  As a r e s u l t o f  p r e l i m i n a r y i n v e s t i g a t i o n s , i t was a l s o d e c i d e d t o measure friction  l o s s e s a t more o r l e s s a constant temperature  i n t h e present case, was 6 5 ° F and t o keep t h e water d u r i n g the subsequent schedule o f experiments c l o s e t o t h i s temperature. friction  By adopting t h i s  which, temperature  on a l l t h e wyes procedure,  l o s s e s i n the branch p i p e s could be determined  a g r e a t e r degree o f a c c u r a c y .  with  23  CHAPTER IV. EXPERIMENTAL PROCEDURE The  p r e l i m i n a r y i n v e s t i g a t i o n s having  the p a t t e r n on which the experimental  work was  determined t o be  carried  out, the procedure as d e s c r i b e d below was  adopted w i t h a view  to  loss coefficients K  o b t a i n g r a p h i c a l r e p r e s e n t a t i o n o f wye  for  each o f the f i v e wyes f o r the cases of  unsymmetrical and 4.1o  one  l e g flow.  FRICTION LOSSES:  per equations  ( 5 ) and  symmetrical,  To o b t a i n the d i f f e r e n t wye ( 6 ) , i t was  f i r s t necessary  l o s s e s as  to determine  f r i c t i o n l o s s e s i n the main pipe f o r the l e n g t h S t o T ( F i g u r e 3 ) and  from T t o Dj' and D  2  i n the branch p i p e s .  F r i c t i o n Losses i n the Main P i p e : f r i c t i o n l o s s e s i n the main p i p e , two connected t o p i e z o m e t r i c  To  obtain  o f the gage tanks were  r i n g s at S and  as shown i n F i g u r e 3 *  F r i c t i o n l o s s e s were determined f o r d i f f e r e n t  discharges  r a n g i n g from 0 . 3 2 t o 1 . 5 c f s and r e s u l t s thus  obtained  (Table 6 ) were p l o t t e d on l o g - l o g s c a l e as shown i n F i g u r e 1 1 . These f r i c t i o n l o s s e s are f o r the l e n g t h S S i (Figure 3 ) which was  3 . 3 7 5  fto  For the l e n g t h ST the f r i c t i o n l o s s t h a t  corresponded t o any p a r t i c u l a r d i s c h a r g e was  determined from  the graph i n F i g u r e 1 1 .  ST f o r the  The  l e n g t h s SS^ and  d i f f e r e n t wyes are shown i n Table  2.  24  F r i c t i o n Losses i n the Branch Pipes:  The  experimental set up f o r determination of f r i c t i o n losses i n the branch pipes i s shown i n Figure 12o Four sections of pipes, designated with A, B, C, D, each having  3•75  inches  nominal ID and 4 * 5 f t . long, were duly f i t t e d with flanges and piezometric rings to form the right and l e f t  branches.  Different combinations were t r i e d so that f r i c t i o n losses f o r a l l discharges f o r these two legs would be equal.  I t was  found that the two branch pipes could be formed by putting Sections A, G and B, D together which then would have almost identical f r i c t i o n losses.  For the 90° wyes sections A and C  formed the r i g h t branch pipe and B, D the l e f t branch pipe. For 60° wyes i t was found that more symmetrical  discharges  and pressure elevations were obtained by having Sections A,. C as the l e f t branch pipe and B, D as the r i g h t branch pipe. F r i c t i o n losses were determined  f o r length B1B2  (- 9 f t . ) f o r Sections A, C and B, D (Figure 1 2 ) as i n the case of the main pipe f o r d i f f e r e n t discharges ranging from 0 . 3 2 to 0 . 7 5 c f s . , and the r e s u l t s thus obtained (Tables 7 & 8) were plotted on log-log scale as shown i n Figures 13 and 14.  I t may be seen from the two graphs that f o r high d i s -  charges, f r i c t i o n losses are almost the same; but f o r low discharges, the branch pipe formed by Sections A, C had somewhat l e s s f r i c t i o n losses than the branch pipe formed by Sections B, D.  25  F r i c t i o n l o s s e s from T to D]_, D the two  branch  2  (Figure 3 ) f o r  p i p e s were o b t a i n e d i n a s i m i l a r way  of the main p i p e .  The  l e n g t h s S D , S3D1, 2  2  T D i and  to that TD  2  (Figure 3 ) f o r the d i f f e r e n t wyes being the same f o r the two  branch  p i p e s , are shown i n Table  2.  Reynolds Numbers and F r i c t i o n F a c t o r s f o r Main & Branch P i p e s :  For the d i f f e r e n t d i s c h a r g e s f o r which f r i c t i o n  l o s s e s were determined  f o r the main and branch p i p e s , Reynold's  numbers and the corresponding f r i c t i o n f a c t o r s were  determined  (Table 9 ) and p l o t t e d on Moody's diagram i n F i g u r e 1 5 . be observed  It  t h a t the p o i n t s thus obtained f o r the branch  adhere very c l o s e l y to the curve f o r smooth p i p e s . shifted.  4.2.  BRANCH PIPES:  f o r the main and branch  pipes  Some o f  the p o i n t s on the main pipe are s l i g h t l y DETERMINATION OF AREAS OF MAIN AND  may  Both  p i p e s the f o l l o w i n g d a t a were d e t e r -  mined s e p a r a t e l y : (a)  Mean a r e a o f the pipe f o r c o r r e l a t i o n o f f r i c t i o n  loss  t o the mean v e l o c i t y i n the p i p e , (b)  Area a t p i e z o m e t r i c r i n g s t o c a l c u l a t e ' t h e v e l o c i t y heads  used i n equations  ( 5 ) and ( 6 ) .  F o r the main p i p e the a r e a was  determined  by measuring the  diameter near the centre and a t each end i n f o u r d i f f e r e n t p o s i t i o n s and then t a k i n g the average of the 1 2 v a l u e s . nominal ID o f the pipe was  5*25  inches but the mean  The  diameter  26 was  found t o be 5*252 i n c h e s .  was  a l s o found at the p i e z o m e t r i c r i n g .  The  same value of the diameter  F o r the branch p i p e s , the r e q u i r e d areas were found by measuring  diameters a t both ends of each s e c t i o n i n f o u r  d i f f e r e n t p o s i t i o n s and t a k i n g the mean of the 16 v a l u e s thus obtained.  Table 1 i n d i c a t e s the mean diameters and mean areas  and areas a t p i e z o m e t r i c r i n g s f o r the main and branch p i p e s . 4.3.  DISCHARGE AND  PRESSURE MEASUREMENTS:  determined by measuring was  the time and weight  Discharge  was  of water.  taken t o ensure t h a t a steady c o n d i t i o n was  Care  reached  after  any change i n c o n t r o l v a l v e p o s i t i o n . The  extent of p r e s s u r e f l u c t u a t i o n s i n the mano-  m e t r i c tubes connected t o the main and branch p i p e s  was  observed c l o s e l y and water l e v e l s i n r e s p e c t i v e gage tanks were a d j u s t e d t o r e p r e s e n t average p r e s s u r e at each o f the 3 piezometric r i n g s .  A p e r i o d o f not l e s s than 2 hours  was  c o n s i d e r e d s u f f i c i e n t f o r the water l e v e l i n the gage tanks to' assume p o s i t i o n s r e p r e s e n t i n g the a c t u a l p r e s s u r e s and o n l y thengage r e a d i n g s were t a k e n . 4.4.  EXPERIMENTAL PROCEDURE:  F o r each o f the f i v e wyes t e s t e d ,  h y d r a u l i c l o s s e s had t o be o b t a i n e d f o r t h r e e d i f f e r e n t c o n d i t i o n s o f flow, ( i ) symmetrical flow, ( i i ) flow and  ( i i i ) one l e g f l o w .  For each wye,  unsymmetrical  therefore, there  27  were three s e r i e s with a t o t a l number o f twelve to be performed.  experiments  Again, f o r each c o n d i t i o n o f flow, l o s s e s  had t o be e v a l u a t e d f o r s p e c i f i c d i s c h a r g e s f o r comparison of r e s u l t s .  F o r symmetrical  flow, d i s c h a r g e s f o r which  o b s e r v a t i o n s were taken were 0 . 3 2 , 0 . 5 , 0 . 7 5 , 0 . 9 2 , 1 . 1 and 1.5  c f s : f o r one l e g flow these d i s c h a r g e s were 0 . 3 2 , 0 o 5 ,  0.75  and 0 . 9 2 c f s .  In the case o f unsymmetrical  flow, as  a l r e a d y e x p l a i n e d , w i t h combined d i s c h a r g e maintained a t 0.75  c f s f o r 9 0 ° wyes and 0 . 9 2 c f s f o r 6 0 ° wyes, the d i s c h a r g e  r a t i o between the branch p i p e s was v a r i e d from 0 t o 1 0 0 % by p l a c i n g o r i f i c e s of d i f f e r e n t s i z e s i n t o the two branch 4.4.  EXPERIMENTAL  PROCEDURE:  pipes.  The sequence o f experiments  w i t h a p a r t i c u l a r wye was as f o l l o w s : (i)  The wye was f i r s t ^ b o l t e d t o the branch  Connection  between the wye and t h e branch p i p e s were checked  by hand so t h a t the j o i n t s were without possible.  pipes.  o f f s e t s as f a r as  The c o n n e c t i o n o f the wye was then made t o the  main pipe w i t h the h e l p o f the l o c a t i n g p i n s . (ii)  S t a r t i n g w i t h symmetrical  placing orifice  flow c o n d i t i o n s , a f t e r  No. 1 i n both the branches,  the opening o f  the c o n t r o l v a l v e was a d j u s t e d by t r i a l and e r r o r so t h a t the d i s c h a r g e was as near 1 . 5 c f s as p o s s i b l e .  After  observing  each p i e z o m e t r i c tube, water l e v e l s i n the gage tanks were a d j u s t e d and the n e c e s s a r y time allowed f o r the water l e v e l s  28 become c o n s t a n t .  O b s e r v a t i o n s were then made s e p a r a t e l y  f o r combined d i s c h a r g e , d i s c h a r g e from r i g h t and l e f t  branch  and f o r gage r e a d i n g s o f water l e v e l s i n tanks connected t o the..-main and branch The i n the branch  c o n t r o l v a l v e was then c l o s e d and No. 1  repeated f o r d i s c h a r g e o f 1.1  cfs.  This  was continued u n t i l a l l t h e experiments under t h i s  flow c o n d i t i o n were completed f o r t h e d i s c h a r g e s 1 . 5 ,  0.92, (iii)  orifices  p i p e s were r e p l a c e d by No. 2 o r i f i c e s and the  whole procedure procedure  pipes.  1.1,  0 . 7 5 , 0 . 5 and 0 . 3 2 c f s . The experiment f o r unsymmetrical  flow c o n d i t i o n was  c a r r i e d out next, a f t e r p l a c i n g d i f f e r e n t o r i f i c e s i n the branch p i p e s and r e p e a t i n g the procedure,  the s e r i e s was  completed f o r a v a r i a t i o n o f d i s c h a r g e r a t i o from 0 t o 100%. (iv)  F o r one l e g flow, one branch  b l o c k e d and o r i f i c e numbers 1,  pipe was completely  2 and 3 were p l a c e d one a f t e r  the o t h e r t o o b t a i n d i s c h a r g e s o f 0 . 9 2 , 0 . 7 5 , 0 . 5 and 0 . 3 2 c f s . S i m i l a r o b s e r v a t i o n s as i n the p r e v i o u s flow c o n d i t i o n s were then made. (v)  A f t e r completing  experiments on one wye another wye  was t e s t e d and a s i m i l a r procedure  adopted t o c a r r y out the  experiments. The t a b u l a t i o n o f r e s u l t s and g r a p h i c a l r e p r e s e n t a t i o n o f p o i n t s , d e t a i l s o f which have been g i v e n i n the  29 f o l l o w i n g chapter, were proceeded w i t h s i m u l t a n e o u s l y .  Any  d i s c r e p a n c y i n wye l o s s c o e f f i c i e n t o r d i s c o n t i n u i t y o f curve j o i n i n g the p o i n t s on the graph was c o r r e c t e d immediately r e p e a t i n g the experiment o r by a p p l y i n g o t h e r  by  remedial  measures i f r e q u i r e d . In p a r t i c u l a r , when i t was found t h a t f o r unsymmetrical  flow, the curve was not w e l l - d e f i n e d f o r d i s c h a r g e  r a t i o around zero, a d d i t i o n a l p o i n t s were o b t a i n e d i n the v i c i n i t y by u s i n g o r i f i c e s 7 and 8 i n the branch  pipe.  30 CHAPTER V. RESULTS AND CONCLUSIONS 5.1.  RESULTS OF EXPERIMENTS:  The wye l o s s e s and wye  loss  c o e f f i c i e n t s have been o b t a i n e d f o r a l l experiments on each of the f i v e wyes.  These have been shown from T a b l e s 10 t o 1 4 .  R e s u l t s o f experiments conducted wyes are shown g r a p h i c a l l y  on the d i f f e r e n t  on F i g u r e s 16 t o 2 9 .  Two graphs have been drawn f o r each o f the wye models.  The f i r s t  graph shows wye l o s s c o e f f i c i e n t K a g a i n s t  d i s c h a r g e i n the main p i p e .  The second graph shows the wye  l o s s c o e f f i c i e n t K versus d i s c h a r g e r a t i o branch  pipe and the main p i p e .  prises  3 curves f o r ( i ) symmetrical  p i p e and ( i i i ) c l o s e d branch 5.2.  ' between the  Again, the f i r s t flow,  graph com-  ( i i ) open  branch  pipe.  CONCLUSIONS AND DISCUSSION: Symmetrical  Flow:'  F o r symmetrical  flow  (Figure 2 6 ) ,  the wye ..loss c o e f f i c i e n t s f o r a l l the wyes show s l i g h t l y larger  v a l u e s f o r low d i s c h a r g e s .  F o r h i g h d i s c h a r g e s the  value becomes more or l e s s constant as g i v e n below:  31 P a r t i c u l a r s of wye  Value of K  90° large spherical  0,44  90° small spherical  0.30  90° tapered  0.16  60° tapered wye (A)  0.088  60° tapered wye (B)  0.080  The considerable v a r i a t i o n i n the value of K between the d i f f e r e n t wyes may be observed. K. f o r Open Branch:  In the case of 90° wyes the  value of K f a l l s with increase i n discharge as shown i n Figure 27, whereas f o r 60° wyes the value increases with increase i n discharge, but f o r a l l wyes the values seem to become constant f o r high discharges.  The value of K f o r  large discharges f o r the differentJwyes i s given below: P a r t i c u l a r s of wye  i  Value of K  90° large spherical  0.92  90° small spherical  0.86  90° tapered  0.47  60° tapered (A)  0.41  60° tapered (B)  0.41  For t h i s condition of flow also there i s a large v a r i a t i o n in value of K f o r the d i f f e r e n t types of wyes. K f o r Closed Branch:  For the closed branch there  i s l i t t l e change i n the value of K f o r a l l wyes as seen from  32 Figure 28, the smallest value of K being 0.45 value,  and the largest  0.60. Unsymmetrical Flow:  Figure 29 gives corresponding  values of K f o r d i f f e r e n t discharge r a t i o s f o r each of the f i v e wyes. A s i g n i f i c a n t fact that emerges f o r unsymmetrical flow i s that the minimum value of K need not necessarily occur f o r £ =• 0.5,  i . e . , when flow i s equally divided between  the two branches.  The minimum value of K and the  ing discharge r a t i o f o r each wye P a r t i c u l a r s of Wye ^  1  correspond-  i s given below:  Minimum value of K  Corresponding discharge r a t i o  90° large spherical  0.41  0.14  90° small spherical  0.26  O.38  90° tapered  0.17  0.50  60° tapered (A)  O.O85  0.54  60° tapered (B)  0.080  0.50  33 BIBLIOGRAPHY (1)  E n g i n e e r i n g Monographs No. 3 , Bureau of Reclamation, "Welded S t e e l Penstocks, d e s i g n and c o n s t r u c t i o n " by P.J. B i e r , I 9 6 0 .  (2)  Thoma, D. and C o l l a b o r a t o r s , " H y d r a u l i c Losses i n Pipe F i t t i n g s " , T r a n s a c t i o n s o f 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 No. 3 . T r a n s l a t e d A.S.M.E., 1934.  (3)  G a r d e l , A. B u l l e t i n Techn. S u i s s e Rom. and 10, pp. 1 4 3 - 8 , A p r i l and May 1957.  (4)  Favre, H. 1937. On the laws which govern the movement o f f l u i d s i n c o n d u i t s having l a t e r a l a b d u c t i o n s . Rev. Univ. Mines.  (5)  McNown, J.S. "Mechanics of M a n i f o l d Flow". V o l . 119, 1954. pp. 1103-18.  (6)  Herakovich, C T . 1962. " C h a r a c t e r i s t i c s of Flow at D i v i s i o n i n t o Symmetrical L a t e r a l s " . M.S. T h e s i s , U n i v e r s i t y of Kansas.  (7)  O t t s , J.V. 1962. "A Study of Pressure P u l s a t i o n s and Mass-Flow F l u c t u a t i o n s through Symmetrical L a t e r a l s . " M.S. T h e s i s , U n i v e r s i t y of Kansas.  (8)  McVickar, D.B. 1963. "An E x p e r i m e n t a l Study o f Flow at D i v i s i o n i n t o Symmetrical L a t e r a l s w i t h C i r c u l a r S e c t i o n . " M.S. T h e s i s , U n i v e r s i t y o f Kansas.  (9)  M a r c h e t t i , M. and Noseda, G. i960. "Loss o f Head i n Symmetrical B i f u r c a t i o n s of Constant Diameter In a Pressure Conduit", L ' E n e r g i a E l e t t r i c a No. 4 , PP» 289-301.  83,  9,  pp. 123-30  T r a n s . ASCE,'  (10)  G l a d w e l l , J.S. and Tinney, E.R. "Hydraulic Studies of 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. P 0 1 , May 1965.  (11)  " F l u i d Mechanics" by S t r e e t e r , V.L.  (12)  "The Mechanics o f Turbulent Flow." by Baklmeteff, P r i n c e t o n U n i v e r s i t y P r e s s , 1941.  McGraw-Hill.  1962. B.A.  34  (13)  "Modern Developments i n F l u i d Mechanics", S. Oxford U n i v e r s i t y P r e s s , 1938.  (14)  "Advanced Mechanics of F l u i d s " , by Hunter Rouse, Wiley,  by G o l d s t e i n ,  1959.  (15)  1  "Momentum T r a n s f e r i n F l u i d s " by Corcoran, W.H. and O t h e r s . Academic P r e s s I n s t i t u t e P u b l i s h e r s , New York, 1956.  35 Appendix Notation:  The f o l l o w i n g symbols have been used;  Ami  ~  i n t e r n a l average c r o s s - s e c t i o n a l a r e a o f the main pipe i n sq. f t . j  A i  =  i n t e r n a l average c r o s s - s e c t i o n a l area o f the r i g h t branch i n s q . f t . ;  r  A3,  =  i n t e r n a l average c r o s s - s e c t i o n a l area o f the l e f t branch pipe i n sq. f t . ;  Am2  =  i n t e r n a l a r e a o f the main p i p e at piezometric r i n g i n sq. f t . ;  A2  =  i n t e r n a l a r e a o f the r i g h t branch pipe at p i e z o m e t r i c r i n g i n s q . f t . ;  r  A12  =  i n t e r n a l area o f the l e f t branch pipe at p i e z o m e t r i c r i n g i n sq. f t . ;  Lni  =  l e n g t h o f the main pipe i n f t . from S t o T, the t h e o r e t i c a l c e n t r e of Wye, ( F i g . 3 ) ;  L  r  •  l e n g t h o f the r i g h t branch pipe i n f t . from T to D i , ( F i g . 3 ) ;  =  Li  -  l e n g t h o f the l e f t branch pipe i n f t . from T t o D , ( F i g . 3 ) ;  Qui  =  d i s c h a r g e i n the main pipe i n c f s ;  Q  =  d i s c h a r g e i n the r i g h t branch pipe i n c f s ;  r  Ql  v  ml  V i r  =  d i s c h a r g e i n the l e f t  branch p i p e i n c f s ; .  =  r a t i o o f d i s c h a r g e i n the r i g h t o r l e f t branch pipe t o d i s c h a r g e i n the main p i p e ;  =  average v e l o c i t y i n the main p i p e i n f p s ;  =  average v e l o c i t y i n the r i g h t branch p i p e in fps;  average v e l o c i t y i n the l e f t in fps;  branch pipe  v e l o c i t y i n the main pipe i n f p s at the p i e z o m e t r i c r i n g S, ( F i g . 3 ) ; v e l o c i t y i n the r i g h t branch pipe i n f p s at the p i e z o m e t r i c r i n g D i , ( F i g . 3 ) ; v e l o c i t y i n the l e f t branch pipe i n f p s at the p i e z o m e t r i c r i n g D , ( F i g . 3 ) ; 2  p i e z o m e t r i c head i n the main p i p e i n f t . at S, ( F i g . 3 ) ; v  p i e z o m e t r i c head i n the r i g h t branch pipe i n f t . at D (Fig. 3); lf  p i e z o m e t r i c head i n the l e f t branch pipe i n f t . at D , ( F i g . 3 ) ; 2  v e l o c i t y head i n the main pipe i n f t . at S, ( F i g . 3 ) ; v e l o c i t y head i n the r i g h t branch pipe i n f t o at D i , ( F i g . 3 ) ; v e l o c i t y head i n the l e f t branch pipe i n f t . at D , ( F i g . 3 ) ; 2  f r i c t i o n l o s s e s i n the main pipe i n f t . from S t o T, ( F i g . 3 ) ; f r i c t i o n l o s s e s i n the r i g h t branch pipe i n f t . from T t o D i , ( F i g . 3 ) ; f r i c t i o n l o s s e s i n the l e f t branch pipe i n f t . from T t o D , ( F i g . 3 ) ; 2  d i f f e r e n c e o f p i e z o m e t r i c heads i n f t . at S and D i , ( F i g . 3) ; d i f f e r e n c e o f p i e z o m e t r i c heads i n f t . at S and D , ( F i g . 3 ) ; 2  37 A,  n  x  -  l o c a l i z e d l o s s o f head o f wye between S and D^, ( F i g . 3 ) ;  at T  -  l o c a l i z e d l o s s o f head o f wye between S and D , ( F i g . 3 ) ;  at T  2  K  =  Wye  loss  coefficient.  38  Table 1  Areas, Main and Branch Pipes,  Description  Mean diameter (inches)  Mean a r e a (sq.ft.)  Main pipe 5.252 Branch pipe 3*746 ( S e c t i o n s A,C) Branch pipe 3*750 ( S e c t i o n s B,D) Table 2  Diameter a t Area at Piezometric Piezometric r i n g (inches) r i n g s ( s q . f t . )  0.1503  2.251  0 . 0 7 6 4  3*750  Ool503 0.0766  6.O766  3*748  0.0766  D i s t a n c e from T h e o r e t i c a l Centre o f Wye t o P i e z o m e t r i c Ring?* Main and Branch P i p e s  P a r t i c u l a r s Distance o f Wye from S to p o i n t of i n l e t Mft.) 90° large spherical 9 0 ° small spherical 9 0 ° tapered tapered 6 0 ° (A) 6 0 ° tapered  *• See F i g .  a  Distance Distance from TD ,TD point of ( f t . ) outlets,.^ to Di.D . (ft.) 1  2  2  0.243  0.743  0.355  8.833  9.188  0.500  0 . 2 4 0  0 o 7 4 0  O.36O  8.833  9.193  0 . 1 2 5  0 . 6 2 5  0 . 3 7 4  8.833  9 . 2 0 7  0 . 4 9 7  8.833  9.330  0 . 4 9 7  8.833  9 . 3 3 0  0.500.  3  Distance from T to point of(s ,Sjf outlet (ft.)  0.500  0.500 0.500  IB)  Distance Distance from ST (ft.) point of inlet to T (ft.)  0.083 0 . 3 1 8  .  0 . 5 8 3 0 . 8 1 8  39  Table 3  V e l o c i t y Traverse, Symmetrical Flow, Preliminary  Investigations.  I0IO7 c f s  Discharge  70° F  Temperature  Calliper reading (inches)  Station No.  Distance from Station 1 (inches) 0  Manometer readings (inches) 5.00  +  1.06  6.06  +  1.75  +  2.15  10.65 13.45  +  2.55  15.15  +  2.90  1  0 . 4 0 7  2  0.657  0 . 2 5 0  3  l o l 5 7  0 . 7 5 0  1.657  1.250  1 2 . 6 0  2 . 1 5 7  l o 7 5 0  1 3 . 4 0  6  2.657  2.250  7  3 . 1 5 7  2.750  3.657  3.250  4 o l 5 7  3o750  1 1 . 8 0  4.657  4o250  1 0 . 6 0 +  11  5 d 5 7  4 . 7 5 0  8.80  12  5.380  4.973  7.70  5.223  4.60  4 5  v  8 9 10  5.630  13  Table 4  13.50  12.75  + +  3.25  2.90  I6.4O  2.60  15.35  2.20  1 2 . 8 0  +  1.60  10.40.  +  1.10  8.80  +.1.00  5.60  + +  2.40  1 4 . 2 0  cfs  1.10  65 F  Temperature  Noo  13.75  16.30 1 7 . 0 0  V e l o c i t y Traverse, Symmetrical flow, F i n a l Test Set Up.  Discharge  Station  8.90  11.30  Velocity head (inches)  0  Calliper reading (inches)  Distance from Station 1 (inches)  Manometer readings (inches)  Velocity head (inches)  1  5.611  0o00  5o36l  4.70  +0.95  5.65  2  0 . 2 5 0  +  1.20  9.00  3  4.861  0.750  7.80  4o36l  1 0 . 0 0  11.35  +  1.250  1.85  12.40  + +  2.25 2.50  4  3 086I  5 6  3o36l  7  2  2.361  8  I086I  9  1.361  10 11 12 13  0861  .  O086I O06II  0o420  lo750 2.250  1 3 . 2 0  +  2.80  2.750  13.70  +  3.15  3.30  3.250  13.65  +  3 . 7 5 0  13.05  +  11.95  2.85  4 . 2 5 0  2.40 2.10  4.750  ,10.15  + +  5.000  8 . 8 0  +  1.80  5.191  5.10  +  1.00  11.85  1 3 . 6 0 1 4 . 9 0  I60  00  •16.85 16.95 15.90  14.35  12.25 10.60 6.10  40  Table 5  Velocity Traverse, One Leg Flow, F i n a l Test Set Up.  Discharge  0.917 c f s  Temperature Station No.  1 2 3 4 5 6  7 8 9 10 11 12 13  6 5 °F Calliper reading (inches) 0.410 0.660 1.160  1.660 2.160 2.660 3.160  3.660 4.160 4.660 5.160 5.410  5.620  Table 6 ~ Discharge (cfs)  Distance from Station 1 (inches) 0.00 0.25 0.75 1.25 1.75 2.25 2.75 3o25 3.75 4.25 4.75 5.00 5o20  Manometer readings (inches) 5.45 7.75 9o25 10.30 10.95 11.30 11.30 10.95 10.35 9.45 8.15 7.20 5.15  -.  1.25 0.85 0.55 0.45 0.25 0.12 0.10 0.10 0.20 0.25 0.55 0.90  Velocity head (inches) 4.20 6.90  8.70  9.85 10.70  11.18  11.20  10.85 10.15 9.20 7.60 6.30 4.20  - 0.95  F r i c t i o n Losses, Main Pipe. Temperature (*F)  Length (ft.)  Area (sq.ft.)  3.375' 3.375 3.375 3.375 3.375  0.1503 0.1503 0.1503 0.1503 0.1503  Friction (ft.)  i  ' 1.48 1.11 0.748 0.498 0.322  .  65 64.5 66 65 64  0.170 0.098 O.O48 0.022 0.010  41 Table 7  F r i c t i o n Losses, Branch pipe, Sections A and C.  Discharge(cfs)  Temperature (*F)  0.744 0.501 0.321 0.200  64.5 64 64 64.5  Table 8 ~  Temperature ( F)  0.746 0.499 0.321 0.198  65 65.5 64 63.5  Branch Pipe (Sections A-C) Branch Pipe (Sections B-D) ti  Main Pipe n  tt tt  n n  F r i c t i o n Loss (ft.) 0.604 0.300 0.136 0.059  0 . 0 7 6 4  O.O764  0 . 0 7 6 4 0 . 0 7 6 4  -  Length (ft.)  Area (sq.ft.)  9.00 9.00 9.00 9.00  0 . 0 7 6 6  F r i c t i o n Loss (ft.) 0 . 6 0 2  0 . 0 7 6 6  0 . 2 9 7  0 . 0 7 6 6  0 . 1 3 8  0 . 0 7 6 6  0 . 0 6 2  F r i c t i o n Factors and Reynold Number Main and Branch Pipes  Particulars  11  9.00 9.00 9.00 9.00  Area (sq.ft.)  F r i c t i o n Losses Branch pipe, Sections B and D.  Discharge (cfs)  Table 9  Length (ft.)  Discharge (cfs) 0.744  1.473  0.501 0.321 0.200 0.746  0 . 6 7 0 0.275 0 . 1 0 7 1.473  0.499 0.321 0.198 1.480  0.657  l o l l O  0 . 8 4 9  0.756 0.498 0.324 0.201  Length diameter  Velocity head (ft.)  0.273 0.103 1.508 0 . 3 9 2 0 . 1 7 0 0 . 0 7 2 0o029  ;  Friction factor  Reynold' Numbers (xl05)  28.7  .0142  2.71  28.7 28.7 28.7 28.7  .0155 .0172 .0193 .0142  1.79 1.14 0.72 2.72  28.7 28.7 28.7 7.71 7.71 7.71 7.71 7.71 7.71  .0156 .0174 .0207 .0146 .0150 • .0167 .0168 £0180 .0230  1.81 1.14 0.72 3.78 2.90 1.94 1.27 0.83 0.50  Vn Vn + vn  f w K  .f.p* f  t-  J?-\jJ-sl vjn vn O O O O O O O  U J  •*•  U J  »  3 tr" (-"(-• -vJVJlO O Vn O O O O O O O O O O O 1  rO N *• rO  U J  jo K  t-< so 3  H -0 vn  M H H vn O vo O Q O ' O O O O O O  vn O  O O  O O  f W S H H M vo vn vo O O O O O O O O O  4?- .p- vo U J u> U J J>-*-*-1-J?-tvn vn oa a* O ^ j  f-j^uwuvjo -a~3rorororo OO^WWOO  yimOOvOO  rorororonro  wu^>o>i>j CvOvOOCTvOv  vnvnvOvororo  H C>U H>0 M  -p-^lVovOp-p-  *-»0^->]0  OK»p- OOP" C*  p--vl-P" 0»-0-vl  w p00. •  ^vn . •p-  ro  \ J p^0 . M  vo O O . « •  O • H  Ov I  O  u>  U J U J  p-  Ov •  UJ  O • c* pOvC*  vn •  -j  ro ro •  c*  H  U  Ov  H  w  U  J  ro J ov  rovn  • vo vo O O O • • •  ro  ro  vn  vn .p- O U  O  )  »  H  U J  O O O » . «  vo ov  O  UJ  vn  CO  ^3  vn ro  0» oa  ro  H •  O •  **  0  O  O  ro  vo  co.  p-  H  UJ  o • ro  ro o • ro  Time i n t e r v a l (sees)  ro  H •  vn  O o .  o o ro  Discharge ( c f s )  01  Hook gage r e a d i n g i n upstream tank ( f t )  -p-  H  O •  O •  UJ  O-  O  Hook gage r e a d i n g i n c e n t r a l vO tank ( f t )  -O  o ro  U J  o  vO vn o •  <J< -0 o .  ro  ro  H O  H O  H H . . -ppvo p-  H O  H H  H  ro  roro  o v n  .  «  O O . .  O .  ~0 - J • *  W H  O  H  O •  O »  O «  O •  roro  OvO  0"> Ov v O - J  U J U J -O ON P -  O vn ^]  O O  O  O  O  O O - O C *  •  •  O  01  O  00  O  • 0  oaoa U  J  H  H  *-vn  vo O Ov ro O  •  vo vO'  O  0  .  vn vo p-  0.537  0  vn  O  O  •  cocu vo vo O O  0.537  .  .f\0  O H v O H  0.534  0  vn  r o w 0.534  \0 vO O * -  vOvO H  • 0.541  •P  O  0.536  1  v>  0  H  0.542  0 J£  • 0.555  0.611  0.597  O O •p- *UJ p-  H  vn vn *o  U J ON  p- p» •  vo vo  H .  .  oa  0  Pressure head d i f f e r e n c e ( f t ) between main pipe and r i g h t l e g or main pipe and l e f t l e g Discharge r a t i o , Discharee i n branch Discharge i n main pipe  H •F-  F r i c t i o n l o s s ( f t ) i n main pipe f o r length 3 . 3 7 5 '  H  F r i c t i o n l o s s ( f t ) i n main • pipe f o r length ST  vn H Ov  F r i c t i o n loss (ft) i n right or l e f t l e g , f o r length 9 . 0 '  H  Friction loss ( f t ) , i n right or l e f t l e g , f o r length TD-L o r T D  H  Total f r i c t i o n loss ( f t )  H vO  V e l o c i t y i n main pipe  (ft/sec)  ro  P -  O .  vo  u> .  H  Vernier correction ( f t )  2  H 0 . O  .  U J  U )  ~j  O v n  .  0.611 0.623 0.661  . O  O . H  ca  0.605 0.619 0.657  U J  UJ  O . 3 5 8 O.366 0.388  vn  0.356 0.363 O . 3 8 5  0.179 O.183 0.194  U J  ~o o . o:  Hook eage reading i n downstream tank ( f t )  UJ  UJ  o ro ro  vn  .  vo ro  O O  o  0.180 0.184 0.195  0.086 0.088 0.093  0.088 0.090 0.095  0.043  0.040 0.041 0.043  0.040 0.041  .  H  • H  U J  ->j ro H  o  • O vo oo o •  . H  O . O  K M « •  o  • O Poo o »  vn  ro  M H  o  • O  H H  c  vn  o ro ro o • o o  H  Temperature i n F and s p e c i f i c weight o f water ( l b s / c u . f t . )  -0  H  O • O  Average time i n t e r v a l (sees)  O  vn o» vo  O O • » oioa O O  O v O  H  vn  o  H O  O O • . U J vo vooa  ^]  Ott  H  H O  -0  O  UJ  O  O •  vn vn  w  O .« co  H  O •  H  H  U J  . ^ ] H  »C  5  O r i f i c e No. Weight o f water ( l b s F from M,main p i p e ; R,right l e g ; L,left leg  U J  vo O  H O  P-  U J  O  vo  O O • . • H H o> oa -  O O H H O O  O O H • ' •  if. vn  Test No.  p- p- U J U J ro ro  s  H H •p-  O O • • O O oaoa  UJ  vO «  H  o o • ro H o  P-  O .  O  ro  ro  U J U J H  ro ro  H  P-  H  p- ro ro -p- U J ro u» vo O H O Ov O 0v vn vo ro vn • • '• . . . o> » M I a» ov vn ov -a O*. O*. Ov 0 OvOv rovn ro J?M P - Ov • • • • • U J vn vo vn  p-  O * CJv  • rovn • vo  J^- -p- ui u> U J U J  P--p-ro ro ro ro  H H * H  0  .  vn  vo -s]  ro V e l o c i t y head i n main pipe ( f t ) 0  ro V e l o c i t y i n r i g h t o r l e f t l e g H (ft/sec) ro V e l o c i t y head i n r i g h t o r ro l e f t l e g ( f t ) ro Wye l o s s ( f t )  UJ  ro Wye l o s s c o e f f i c i e n t •tro vn Average wye l o s s c o e f f i c i e n t  (  W  w w + • xt-*  V  t  M 15000  R 14500  Weight of water (lbs) from M.maln pipe; R,right leg; w • L.left leg  0.575  0.177  320.2 65.5 0.751 62.33  404.2  451.8  1.365  1.822 r  * w o s  o  O  0.210  0.210 1.185  0.084 O a * c  o  vt o  O O ro "0 w r > -0 w h  -  o  VI  Average time interval (sees)  1 Temperature in F° and specific 0 'weight of water (lbs/cu.ft.) .. ^3  •Discharge (cfs)  t  [Hook gage reading in upstream ca : tank (ft) i*3  • Hook gage reading in central ' tank' [ft)  H : Hook gage reading in downstream O • tank ( f t ) H H  Vernier correction ( f t )  head difference ( f t ) H ]: Pressure between main pipe and right leg ro or main pipe and l e f t leg H  W  Discharge ratio, •Discharee in branch Dincharee in main Dioe  H  Friction loss ( f t ) in^main  H VI  Friction loss (ft), in main pipe for length ST Friction loss (ft) in right or left leg, for length 9.0'  *-  0.011  0.011 O.38O  0 H w H  0 ro *= r o  0 0 o w *- \o vi 0  H ^3  Friction loss (ft), in right or left leg, for length TD-, or TD,  0.056  H OO  Total friction loss (ft)  H  Velocity in main pipe (ft/sec)  8  , Velocity head in main pipe (ft)  7.51 0.876 0.296  ro H  Velocity in right or left leg (ft/sec)  ro ro  Velocity head in right or left leg (ft)  to w  Wye loss (ft)  O O *ro 0 w w  ro *r  Wye loss coefficient  c  W  c O  o V  v o 0 w c  i o a  i 2.32 O.O84 0.164  O O O 3 * - *- o> ro 03 H r o 0 co  5.70 0.505 0.238  1.06 0.019 O.I63  4.06 0.257 0.193  8.72 1.182 0.329 O 0 vt w  0.401  0.044  H  0.253  o  Orifice No.  0.142  c vi  5000  321.8 65 0.749 62.33  -  c  *  o 0  ro  0.237  -  H |Teat No.  0.128  W  O  0.611  0.207  * c  L  H 15000  0.668  H  0.011  0.515  0.023  0.494  0.013  9-33 1.355 0.345  O O CO VI vcro vi w  -  O  0.012  0.002 o  0.081  412.7  1.640 0.011  c Vi  0.44 0.003 0.202  0.19 0.001 0.210:  9-58 1.428 0.351  0.357  1  O O vOVl H*w cr*  W  -  O O  *  0.578  CJ*  9-78 1.485 0.208  0.073  Jo.072  J0.037  6.01 0.562 0.131  4.19 0.274  O O Vl\0 wro \o * -  o  r  H  *  H •  * - vi H co CJ* * -  0  o  0.556  c  W  •0.181 -  o o  W  0.210  0.210  1.893 0.011  0.012 o  W  * c -  H  ca  O O co H \o 0 ro c» O  0.606  0.001  0.583  0.011  j  -  o  349-2  *  0 0 v i o O H *- ro  *  8000  0  v« tr + . ropo 1  H  w H o 1  0 0 0 ro  -  9500  1.563 O  0 vi 0 -0  *  R  0.749  0.081  0.668  1.928 *  I  •0.167  *  H  *-*-wwww *-*-*-*-ww MH*-*-roro vtvioororo roro^\OHH r o H * - * - o o •Time interval (sees) , viorow^jco O O O * - H M *-  321.2 65  395-7  62.33 0.748 o  O O "ob v i * cr* * O a * c o c  0  L  2000  456.3  321.4  0.210  2.000  o  0  V  o  0.631  0.607  0.265  0.004  o s£)  w  ro V< 0  0 0 v i o \0 0 vi H  o c • 0  H  o  O 0 ro 0  o  O O V v O ro*ui M  -  0.011  !  0.004 0.256 1  c 0  w  O O "ob co H H *c O <D * o c  -  •0.162  2.087  •0.167 c  r o  3  0.210  0.210 0.819  •0.062  0.142  0.002  o  o ro • v£3 vi o r * v>  3  *- r* + w po  M 10000  R  L 19000  R 1000  ^  O  a * o  0.002| 0.137 O H VI O H H \0 co  \  l  + ow  K 15000  O  O H  ^  0.033  O  0.715  r co  *  486.8  *  426-3 65  O  H  r  L 19000  r  W  0 iro  w 0 O ^ H  W  2.085  *  0.210 0.412  L0.O32  0 *0  H 15000  0.734 2.357  o H  62.33 321.8 65 0.748 569-0 62.33 6.OI4  415.2  65.5 62.33 0.749  2.228 O 0  o -0  O M o b O O  I H  R 500  L 19000  1321-2 65.5 62.33  O.46O  1.772  r  H  »  O  O 0 o  H t-< + -o. w-  - 1  M 15000  R 15000  348.4  512.6 65-5 O.321 62.33  o  H  H  *  wc + oo w  W W W W f - p y i w w w *-*-*-*-ww *-*-wwww *-*. ro ro HHOO*roro rorocaoaroro vi vi\o*£r ro ro i coco i i HH f w c o ^ H H C3NC3-*OC*MH (>ff>wuiHH .*-*. ro ro *Ov<rooo^3c» H vi~o ooro c* C7*O*0*-o*-  i  r 0 *H v ~J  H H so + xtr*  M 10000  L  V1V* HH ro ro c»*-  i  R 10000  M 10250  -  R 10250  jL t  O  row + x r *  0 w c»  J?-  UJ  10  VI  f  UJ  IO  •»wi  •  . *-  • ro  O  rowi • • UJ 0 UJ  WI  . ->J  •  rowi  WW! UJ  UJ O UJ  O  0 >0 ro  *-  0 OJ * sO  O  .  0  .  ro  ro Cf< ro  - J Discharge  0.210  0.829 0.210  0.903 0.210  1.232  UJ  0  ca \0  1.098  1.083  0.605  0.599  0.295  0.298  0.133  0.147  0.063  0.065  oa Hook gage reading i n upstream tank ( f t )  NO  Hook gage reading i n c e n t r a l tank ( f t )  H O  Hook gage reading i n downstream tank ( f t )  H H  H IO  0.615  0 0 . . H H 00,00. -0 ~ J  U J U J  0 0 . . O O O - wi  0 . O ro \0  0 . O ro oa  .O .O O O \0 >0  O  O  .O .O O O O 0^  V O U J  ro .  .  H  l-i ->} UJ  O  rO .  W I U J  *-  0  F r i c t i o n l o s s ( f t ) , i n main pipe f o r length ST F r i c t i o n l o s s ( f t ) i n r i g h t or l e f t l e g , f o r length 9 - 0 ' F r i c t i o n l o s s ( f t ) , i n r i g h t or l e f t l e g , f o r length TDi or TD  H  Total f r i c t i o n loss  H 0  V e l o c i t y i n main pipe ( f t / s e c )  oa  .  WI vO u>  (ft)  0  ro V e l o c i t y head i n main pipe O  (ft)  ro V e l o c i t y i n r i g h t or l e f t l e g H (ft/sec) 1.532  0 « 0. roro 4> wi  Discharge r a t i o , Discharge i n branch Discharge i n main pipe  2  H UJ H  9.94 1.537  7.22 0.811  0  7.22 0.810  ro  0 . .0 H H H H  H WI  H  0  . o» ro  0  Pressure head d i f f e r e n c e ( f t ) . between main pipe and r i g h t l e g or main pipe and l e f t l e g  F r i c t i o n l o s s ( f t ) i n main H *- pipe f o r length 3.375'  H  H  .  UJ 0^ O  UJ O  Vernier correction (ft)  oa  -j  .  1  4.90 0.374  0» 0 O O wi wi  - 0 0 *  wi  .  4.92 0.377  3.23 0.163  0.068  -  2.10  0.069  «  . .O UJ UJ CO CKJ  oa  .  3.30 0.169  2.11  UJ  UJ UJ UJ O  . O -0  ro  oa  H UJ O  0 . 0. > O O roro  0.177 0.039  0.616  0 0 . . Q O <o oa J?-o»  . O• H 'H \ O v O  0.357  O  uj  0.358  O'  wi  fj*r-  0.182  M O  0.183  O  0.086  0.092  UJ  0.098 0.021  0.002 O  O.O48 0.011  0.022 0.005  0.010 0.040  0.042 O  (cfs)  O  .  UJ  -  0^ Temperature i n F ° and s p e c i f i c weight o f water ( l b s / c u . f t . ) '  H UJ  0 0 . .  leg;  M  .  0.374 0.210  CO  1.522  .  0.760  O  O NO H  0.761  w  UJ  0.297 0.210  M  rowi 0  UJ UJ  1.107  .  Weight o f water (lbs) from M, main p i p e ; R,right L , l e f t leg  WI  0.552  .  uj  O  rowi • • . UJ 0 0.553  .  O  or* a>  O  0.753  M  0.375:  .  0.3775  0.248  . O 0» wi  UJ  J  wi  rowi 0.501  0.253  0.321  0.161  0.161  M  •  ro O r i f i c e No.  t-J?-ro ro ro ro *-*-ro ro ro ro UJUJVOVO^J^J O C I P O O f-yioovjiw O O O H O O *- Time i n t e r v a l (sees) . . . . . . • • » • • • vO H ro 0**wi 0** 'wiwi O a O f O r N M *- ro ro U J V D ^ J O H O Wl Average time i n t e r v a l (sees) wi O wt O O O . » . • • • 0 wi wi 0 ro  . . . . . .  H  R 10000  • ro  O  L 19000  .\OUJOO>UJIO UJ UJ *ro H O ^ O v O  R 10000  *-0"OO^OWi j?- U J U J -j ro ro O UJ O  H  M H  M 19000  7500  * - * - ro ro H H VI O O 0 \ G vO  . . . . . .  L 15000  R  M 15000  fj>-wuwu  UJUJUJU) --j~j 10 to ro ro O^O^UJUJOO  Test N o .  H  +  + ro  UJ  L 10500  . O  5000  . oa  R  V O - J - J O* U J wi  7500  7500  3750  5000  ^•OU^-vnui. . . . . . . f-CSOOOO .r- U J U J  M 10000  L  M  R  L  UJUJUJUJ >©\O-0-J^J-0  • O  •  M 19000  wi  0  -0 vO  ro V e l o c i t y head i n r i g h t or ro l e f t l e g ( f t ) ro Wye l o s s  UJ  (ft)  H I O  0.309 0.302  0.295  i  0.293  0.290  0.307  0.297 0.294  0.290  0.290  0.295  0.289  0.301  0.324  0.310  ro Wye l o s s c o e f f i c i e n t •rro Average wye l o s s c o e f f i c i e n t  Wl  M  W W  w  H  r o w  R P t - w K  r  •si-Nj  •ViVi  1  1  1  8w-o^s 8w  f H M \o\0  »  E  r>  H H Q Q  w  w  M •»  f K  Vt w  c a w  H \D  H ui  S f i9 V J S  8wt o8ww fM- Pf8 8 - u i u8 iww OV<MOW  88  t CttsO NO*-  r  1 H H fvtNOvOHK CMO • - o w c o o o i o a -  N  w  w r r -  tr*  o  w »  H  H H v o r o v i  *- r  H W W K  «o w  e w x •  H H i v / i v i  ©Q  *-  f  f  H H r o v i u i  Q Q O  Q Q Q  888  888  w W  w K t  -  H  H  H  Test No.  N  Orifice No.  W  Weight of water (lbs) from M,main pipe; R,right leg; L,left leg  r o w w R  H oo. o  H vi  H H u i r o v i  8  8 vo n8 v n8 w w w8 w o*-*-roro  Q ro O  p - p - wo www MH-O^JMW roroOiOiOO oio-p-caoo  *-*-ioioww J£j>wwww M(o>j-jwro ooc£giroro «OOicaiC-roro H M O O H H ro oaovcoro*- * - i o . p - c a O N i o  ui  u; w O  HNOOtOH NOMOO>O  *- Time interval (sees)  320.8  65-0 0.750 62.33  0.574  0.176  349-0  501.6  0.437  0.312  0.752  62.33  65.0 O.748 62.33  0.667  320.0 66.0  412.3  376.6  321.8  0.079  360.6  401.7  0.033  0.713  0.748  0.734  0.014  0.745  O.5O2  0.746  62.33  65-5  62.33  65.O 62.33  65.O 62.33  65.O 62.33 0.324  322.3 65.O  979.2  427.0  321-7  569-4  415-0  321.8  319-2  371.9  Oi  c* Temperature  in F° and. specific weight of water (lbs/cu.ft.)  0.853  2.179  2.065  I.883  1.472  1.703  1.262  1.140  2.570  0.295  0.247  1.874  1.796  1.610  0.103  0.344  2.457  2.272  0.107  0.210  0.210  0.210  0.210  0.210  1.409 0.210  0.394 0.210  Hook gage reading in central tank (ft)  O  0.384 0.210  Hook gage reading in upstream tank (ft)  0.830  Discharge (cfs)  0.588  •<  03  o  a  O  b c  a  o  o  H  Discharge ratio,  0.011  O O W \o v  -  * - o i O - o - O H  H  Friction loss (ft) in main pipe for length ST  Friction loss (ft), in right or left leg, for length TDi or TDj  C0|  o»  1 0 - 0 w o i O W '  i n branch  t- Total friction loss (ft)  vQ  j  BnHsharKs  Discharge in main pipe Friction loss (ft) in main pipe for length 3.375'  H -J  0.398  •  left  Friction loss (ft) in right or left leg, for length 9.0'  0.387  H t » 0 - 0 * - H  Pressure head difference (ft) between main pipe and right leg or main pipe and leg  0.380  0.256  i  0.049 0.050 0.061  0.240  v O O W f H K >  O W co o  H ro  -  01  *• '10  O W  t Vernier correction (ft)  b Q  0.011  I O O O I H 00.0a  w  oa o  0.147  o  O W  0.136  VO "0 ro  Oi 01 ov  o  cn i  0.245  r  O W  0.133  -  ai  0.521  *ro w  O W  0.022  o  O H o p  -  0.011 VO  0.510  0.585  *-  \Q  0.011  0.012  - r - ' * -  w  -  o  0.499  0.574  0.606  0.002 0.002 0.013  0.562  0.001  0.630  0.011  0.595  0.619  0.314  0.005  0.583  0.606  0.309  0.142  0.002  0.001  0.302  0.140  w  H  iO  b o  0.011  o.ou  0.011  0.011  0.005  0.002  0.137  ro O Q S r  c  Hook gage reading in downstream c tank Tft)  O  b  c  O O to W O N 01 01  O  b  c  O O J r 01 HOft ff«fO  1.078  o  -0.132  i  O  b  0  o  O O H 0 » Q -3 C> W  0.504  O  0.117  O  O O * 0 O u i * 0 1 * *  1.575  O O , * 0 O Cc- H H v0  -0.192  b  I.846  O  -0.179  1.968  O  -0.172  2.045  -0.181  O.96O  -0.077  0.414  -O.032  O H Q.O O O 0 0  Average time interval (sees)  Velocity In main pipe (ft/sec) •O  8 Velocity ro H  head in main pipe (ft)  Velocity In right or left leg (ft/sec)  0.282  0.109  0.085  0.338  0.872  O.506 0.132  0.264  ro  O.5O4  0.154 0.40O  0.257 0.103  0.188 0.490  0.678  0.017  O.296 0.773  1.178 0.261  0.003  0.828  0.519  1.348  1.428 0.319  0.329 0.861  0.190 0.497  0.151 0.866  0.086 0.495  0.917  0.038 0.528  O.O65  0.001 0.200  1.468  0.669  0.278  head in right or left leg (ft) » Velocity Wye loss (ft) Wye  IOBS  coefficient '•  vn vn * vn  **+ f  V»J U J  H H Test No. M , • ro O r i f i c e No. t-J  ro  UJ +  ro • ro  •  f - o s  t - w s  t - w a s  t - w s  vn U J —3 O - N j v n O V J I O O O O  H VJI Q vn O O O O O O O O  M H O ^ J v n O v n O O O O O O O  1—'  O O O O  1—'  O  O O O O O O  »  •  f I—' vO  w  s  H H H N O vn N O O O O O O O O O O  *-*-UJUJUJUJ  *-*-UJUJUJUJ  *-*-UJUJUJUJ  ujuJUJUJUJUJ  * - * - U J U J ro ro  vn-^j;*-vnujuj H*-Orj.ro ov*-  -oo>vnf-HH vnUJ H O V U J 0**  caoaujuj ro ro O^UJOvfO  oo-o-o o a H H *- 0 V N O * - U J N O  caro I O U J * WHHwr>o  vOvo-o->a^j^  r---vjNO  *-  U - I * - N O  - 0  -vi  ro  *-  0"NC*N  .  vn O  0 -  *-  VJI O  *-  O  0  .  --J  H  ~o  weight of water  *-  ov - 0  oa  0.829  0.203  0.960  0.890  0.798  0.114  0.343  0.895 0.210  0.800 0.210  0.112  0.338 0.210  0.210  0.800  1.215 0.210  1.216  -J  Discharge  00  Hook gage reading i n upstream tank ( f t )  NO  Hook gage reading i n c e n t r a l tank ( f t )  H Vernier correction  O *o»  0.613 O.64I  O.6O4 0.632  00  0.833  1.530  0.383 rouj  (ft) in right l e f t l e g , f o r length 9 . 0 '  or  or  2  .  NO  NO.  i n main  (ft), in right l e f t l e g , f o r length TDi o r TD  vn  -  (ft), pipe f o r l e n g t h ST  H Friction loss  ro  ON  H Friction loss  01  0>  - 0  H->o  V  0.601  0.328  0.189  ro  O.3O6 0.313  0.180  0.191  - 0  0  H F r i c t i o n l o s s ( f t ) i n main *- pipe f o r l e n g t h 3 . 3 7 5 '  H Friction loss  NO  ON  Discharge Discharge  leg  ratio, i n branch i n main pipe  0  ^3  . . vnvn oaoa O O . . ON ON  0  H vn  . U>  . . oaoa oaov O O . ' . UJ UJ -  O  NO  .  * - * -  0  ro  0.328  0.176  0.182 0.171  O N O V  . 00  0.306 0.313  0.178  0.072 . . roro cq ro O O . « 4-> H  0  *-  . UJ ro  U J U J  .  0.028  0.004 O.O85 0.087 0.091  0.088 0.090 0.094  0.043  . . H H H O O O . . O O ONOV Nooa  U J  0  (ft)  or main pipe and l e f t  0.015  0.002 0.040 0.041  0.042 0.043 0.045  roro  ro . H v/i  .  0.009  0  O ro ro  downstream  H Pressure head d i f f e r e n c e ( f t ) ro between main pipe and r i g h t l e g  0.832  0.827  0.401  0.399  0.239  0.241  0.115  0.120  0.056  0.055  0  .  (cfs)  H Hook gage reading i n O tank Tft)  OJ  0  specific (lbs/cu.ft.)  -  H Discharge  . O H  (sees)  O Temperature i n F ° and  * - * - N O  H  (sees)  vn Average time i n t e r v a l  OvOv rouj UJVn *- ' O H . .  1.061  1  i  :  .  rouj UJvn *H .  Weight of water (lbs) from M,main p i p e ; R , r i g h t l e g ; L,left leg  *• Time i n t e r v a l  203.8  O .  U J U J - O  322.2  O .  r o r o * -  407.7  ro  0**C7V  ro*UJ *O .  O O W IM O O  301.6  0  O .  318.15  U J  H  O .  HHHHOO  318.0  UJ  10  OVCJV  ro*uj *O .  1  322.2  ON  323.45  O  U J  1  rorororororo  428.35  H  321.45  O .  324.85  H  rotUJ *O .  477.90  373.5  375-0  497.7  ONON  O .  -o~o ro ro ro ro  UJ  NO  . . 0 - 0 - 0 *H H . . *~ *Oa^J ujvn  Total f r i c t i o n loss  H Velocity  -0  (ft)  i n main pipe  (ft/sec)  ro V e l o c i t y head i n main pipe  0  ro V e l o c i t y H (ft/sec)  i n r i g h t or l e f t  ro V e l o c i t y head i n r i g h t ro l e f t l e g ( f t )  0.158  0.160  0.246 0.161  0.133  0.232 0.152  0.132  0.066 0.172  0.062 0.164  O.I56  0.159  0.168  0.236 0.214  0.181  0.181  0.032 0.187  0.017  0.030 0.175  0.013  ro Wye l o s s  (ft)  leg  or  (ft)  ro Wye l o s s c o e f f i c i e n t Fro Average wye l o s s  coefficient  IO ro t *  W  w  r*  H M  c  M  H  H  O p  1^  ns • 1  W  .  1  t3 s  H  0  N  W  \  •- fv  0  *  . n  0  i  i  o  r  O  N  •- » v  f0  0  i  i n downstream  f  .  O  -  0  W  O  N H  •  -  *  N  vo  •  C  O 0  p  •  »  0 •  O  H  s O  W  s¥  •  Discharge  o  O . H  w  O  w  .  H O H W  O  O  .  P-  H  F r i c t i o n loss ( f t ) , I n main p i p e f o rl e n g t h ST  W v • • vo O N v o v i  0  a s  O  N  Q .  ro  I  * *t-  0  w  a s  CO  •  0  W  O  O *  O  O O  N N  ••  friction loss ( f t )  H  -O V e l o c i t y I n m a i n p i p e ro 0  O  Velocity  head  (ft/sec)  i nmain pipe ( f t )  • o  Q r  o  • *  0  H  H  i nr i g h t  o rl e f t l e g  O  V e l o c i t y head i nr i g h t o r left l e g (ft)  O  H  0  £&  Total  0 » s e n vo H  O  .  H  r o - 0 ro V e l o c i t y r o v i H (ft/sec) ON W  r o * V cn 0  O vo  F r i c t i o n l o s s ( f t ) , i nr i g h t o r l e f t l e g , f o r length TDi o r TD  o  i  *  S  H  O N * -  0 V  O .  O  F r i c t i o n l o s s ( f t ) i nr i g h t o r l e f t l e g , f o r length 9.0*  H -J  C O  o  -  O O  ' H  W  o  - v j w  W  »  N  pipe  2  o  i nmain  F r i c t i o n l o s s ( f t ) i nmain pipe f o rl e n g t h 3 0 7 5 '  H  Ol  W  o  O a H • • 0 0 r o r j  O  b  * vo v  o  O H N  >  o  W  w  w*cnN)  w  n  * Co  r  o  a N *  0  v  o  O H  0  w  -  ratio,  BAasjiRrRs.in brans!.,  0  -  n  correction ( f t )  D i s0 charge  -  O  *  Vernier H  0  O  Q  W  V I Q ro O N  0  *  o  O •  H  0 0 *-  Hook gage r e a d i n g tank ( f t )  P r e s s u r e head d i f f e r e n c e ( f t ) between main pipe and r i g h t l e g or main pipe and l e f t l e g  ro  0  Co  o  O *  H  w  v>  <? \  -  C  *- b  *- 1 O * •  -  ,O H O cn  vi  Q  O  .  * o  * W  N  vO  1  O N - 0 . H  envoi  W  O  so  i n central  O  0.385 0.394 O.4O3  I  • «  O O *-Ch  *  a  vi O  O  v  0.047 0.048 0.057  O  H  0.128 0.131 0.140  O  w*-  o W  c  O  O O  0.231 O.236 0.245  O  O  -  a  0.011 0.011 0.020  O  Co  v  H  O N vi 0  *  -  •  O  O H 0  *  .  Hook gage r e a d i n g tank ( f t )  H  O  f  I  0  O  0  O  0.488 0.499 O.5O8  vi  -  o  o  O  1  ro  V  O  o p  0.002 0.002 0.011  o  * Co  o  0.564 0.577 O.586  O -o  -  w  .  I  O  -  a  0.001 0.001 0.010  1  ro O  *  Co  P  vg  V  i n upstream  *§ 0.585 0.597 0.606  .  P  *•  w  H  *  O  0.009  o . O  0.004  0.144  0.002  o  H  O  o  O  p a n  -  •  O  -  a  *  O  (cfs)  Hook g a g e r e a d i n g tank ( f t )  H  0  O *-  H  (sees)  a  3  •  »§ 0.583 0.597 0.606  0.142  0.297 0.304 0.308  0.139 r ^  O *  -  o  I  W  0.750  p  •  O  0  320.7  O *  .  W  -  0.577  O O  I  O p  V  vo  0.173  O H  .•  O  H  CO  H  Discharge  Q  O  O  0  347.3  •  O  O  O  441.2  t  O  O  vo  0  0.739  S S  O  \o  325.15  O  b  0  • * -  H  interval  i nF °and s p e c i f i c o fw a t e r (lbs/cu.ft.)  weight  O  O  H O • *  O O  cr  H  O  time  ovo*T e m p e r a t u r e  •  :  O W  H -  •J-l A v e r a g e  (sees)  O  •  -o H  O  *- T i n e i n t e r v a l  H  $  *  a Weight o fwater ( l b s ) from M,main p i p e ; R , r i g h t l e g L.left l e g  W  vi  0  H  >  Test No. Orifice No.  vo  H  •  w  '  H • H  O  H  ro  w H  ro*-  I  ro  -  H C  -  w  V  O  r*  320.5 320.4 347.4 347.2 441.5 440.7  O  O  v  O .  O H  0.433  H  O  H C  0.306  O  O H  523.60  G  o  '  O  370.30  H  325.4 324.9 370.5 370.1 523.8 523.4  O  0.746  O  322.75  O W  O  O N cr*  H •  • H.V  •  W  .  ro*w * -  H  O H  H  0.078  • Q  0.668  O  S  -  t H  s H  e  o  W  O  (3 O  H • W W vi  J  ro  •  H  *o \3  O  g  S  ro  •  o  351.55  O  «  ro  r v>n o  455.80  •  w  W  322.5 323.0 351.7 351.4 455.5 456.1  3 O  a H  O  •  r  A  0*ON  H  •  £ H  ro*w * -  O  • w  H  N  -  0.750S  3•  O H • S so O W O  320.4  0  O  vi ro  O  . w  f  H  H  w w  )  s  H  crvov  O  v  Q 0  O  •  H  rO  R  w  H  H  W w  *  •  O  H  O  . w  3  H v  ca  W  0.032|  O  H . .  O  w 0.719  -  vi *"  ov  0.749  O »  1  0.0139^  / •  w  w H  H  ro o\  w  0.735  0.741  0.498  0.322 O •  3  601.6  *  c« p  423.8  -  M  »  320.7 320.3 601.0 602.2 423.6 424.O  0* cn  row w i n -  *" t-i  H  321.45 321.22 321.00 578.50 578.90 579.30 414.50 414.75 415.00  *  v vi *-  O O • W  324.6 325.0  ro*-  w  w  w H  324.8  482.4  cr*  rov*.  w  H  i  I  H  c a w  f  H  482.8 482.0 -  497.3 497.0 497.15  O NO N  V  V  H  S ' p o S m S w w se t-> w a c >a &  O  H .  0  ro Wye l o s s ( f t ) VA>  v  S  Wye  r o w  ** ^  0  loss  coefficient  vn  *-  *+ *-  t«  w  ~J  vn  ^  vo  vo + vo  K (_. Q Q  2  O O Q O O O * - * - vovovovo o» oa (- »-" i—' i— ro t - i ^ j - j N O v o . . . . . . O o>0*»oavjnvn 1  1  r w a B M H  O O . . -g. -0 vn vn v n vo  i 0 \0 a  Test No.  r\  O r i f i c e No.  v.  Weight of water (Ibis) from M,main p i p e ; R,right l e g ; L , l e f t leg  *•  Time i n t e r v a l  VI  Average time i n t e r v a l  0  Temperature i n F ° and s p e c i f i c weight o f water ( I b s / c u . f t . )  . vn O 00  O  O  *Ca ro  oa  O  Discharge  0.210  vo *oa O vo *oa  0.739  0.739  0.423  0.423  0.301  0.300  0.218  0.212  0.111  0.102  Ni  Hook gage r e a d i n g i n c e n t r a l tank ( f t )  Hook gage reading i n downstream c tank ( f t ) 1-  t  Vernier correction (ft)  H t\  Pressure head d i f f e r e n c e ( f t ) between main pipe and r i g h t l e g or main pipe and l e f t l e g  1.564  O  t  •  w  -o  vi  O  O  Vi  "O  •  c»  w  W W  •  • • V i Vt vO W  0.145  0.139  (ft)  in  right  or  l e f t l e g , f o r l e n g t h 9.0»  F r i c t i o n l o s s ( f t ) , i n r i g h t or l e f t l e g , f o r l e n g t h TD, o r TD Total f r i c t i o n loss  (ft) (ft/sec)  V e l o c i t y head i n main pipe  (ft)  ro V e l o c i t y 1- ( f t / s e c )  i n r i g h t or l e f t l e g  rv V e l o c i t y ro l e f t l e g  head i n r i g h t or (ft)  IV Wye v>.  loss  ro Wye *-  loss coefficient  (ft)  1  O.O89  1 0.093 0.091  0.104  0.075 0.090 0.088  oa-o JV) - J  0.070 0.085  -f*  0.053 0.089 0.088  vi O  0.052 0.087  0.110  0.035 0.090 0.088  0.017  0.097  w w W w  0.032 O.O84  0.015  W W Q\ sO  0.030  O  w  0.174  0  oa  w  0.603 0.625 0.655  0  O  0.603 0.625 0.655  O  rv C  *0  •  Friction l o s 3  >-V e l o c i t y i n main pipe  vC  w  F r i c t i o n l o s s ( f t ) , i n main pipe f o r length ST  2  yaj  . O vo  -O-O  •  0  t-  O  OO**-  •  O  . Vo 0  0  Discharge r a t i o , Discharee i n branch Discharge i n main pipe  vn  0.829  •  0.098 0.017  p-  1  0.596  0  H vn  (cfs)  F r i c t i o n l o s s ( f t ) i n main i? pipe f o r length 3.375*  1-0  OV  .  0.388  •  O  •  V O N O  0.350 0.363 O.38O  0.198  O  0  •  w  0.350 0.363 O.38O  0.190  0.195  i\>  0.258 0.268 0.280  0.182  0.187  0 O  0.173  •  0.257 0.266 0.278  0.180  0.094 0.098  W W  0.070 0.012  0.048 0.022  0.022 0.004 0.091  0.087 0.090 0.094}  vn  .  (sees)  Hook gage reading i n upstream tank ( f t )  1V>  vo . vo *-  (sees)  a  O  to Ov vo O ro Ov vo  0.210  .  202.1  .  319.3  0.210  .  .  OvCJ> rowi . vo vo  0.210  H  r-> . Ov vn vo \-> . ov vn ro  .  oa -0 O oa I-"  o>  .  0.210  O  .  O O t . . . vn vn vn * O o a o  >-  f r o S S vOvnvO O O Q Q Q O O O O * - *-vovororo OOMMOO vo*-vovo ro \~> . . . . . . sOHvnOUtio  OvOv ro*. . vo v n vo  H . -J +vo  .  55  M  404.0  O oa M vO  so  H (-• «•  277.6  p o O *~ *- vo Cfl p ro >o jo * -  •  292.7  O O . vo >1 y i v n t - i vn O  .  f  ro • ro  r-< H vO Q vO O O O O Q Q O O O vnvnrorororo torovOvo-j^i M ro ro ro . . . . . . oarovOvn'^jvn  522.0  OvOv ro*. vo  .  O  330.0  OvOV rovn . vo vo  O  . vo vn O . vO O  347.3  O  . oa  521.3  O . vo sj v A vn  320.2  320.2  427.3  319-5  317.7  481.6  O O O . . . r o r o v n v n v n o O vo ro  f j o S  t—• I—" t—• vn Q O O O O O Q O O O vnvnvovjjvovo ro ro*-*-rovo i-'i-'-j-ovo o . . . . . . 0\orov/ivOO  Q ^ I v n Q ^ Q Q O O O O O f-f-wuvJUJ ro to ro ro to ro -o^j o o o o . » . . » . *ro MI-* ro  OvOv rovn . . 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Mo. vo W  '  1  O  O 1 t  O  1 I  O  v Ov H  n  ^  O  O  M  vo vO V O M H  -  o  O  -O  O  O  O  O Ca Ov  O M H  o M H  O fO H  P M H  M -0 vn  H CO ^3  £ Ov O w w  0.092  0.908  0.414  0  O 0  b ^1 0  b ^, O 0  b H M  b H M  b H M  b H M  b H M  O vn vO Ov  O  w " j c o ^ l ^ 3 V n  O  8.71  O  -O  Discharge ( c f s )  Hook gage tank ( f t )  reading  i n upstream  CO  vO  Hook tank  gage Tft)  reading  i n  H O  Hook tank  gage Tft)  reading  i n downstrean  intarval  l e g ;  (sees)  time  interval  (sees)  H H  Vernier  central  correction ( f t )  O  H  H H ^ I c o M M  Pressure head d i f f e r e n c e ( f t ) between main p i p e a n dr i g h t l e g o r main p i p e a n dl e f t l e g Discharge Discharee Discharge  r a t i o , in" b r a n c h i n main pipe  H -P-  F r i c t i o n l o s s ( f t ) i n main p i p e f o r l e n g t h 3.375'  H vn  F r i c t i o n loss ( f t ) i n main pipe f o r length ST  F r i c t i o n loss ( f t ) i n right l e f t l e g , f o r l e n g t h 9.0*  o r  F r i c t i o n loss ( f t ) , i n right o r l e f t l e g , f o rl e n g t h T D i or T D ?  v. vO jr3.32  H  7.06  4.99  1.10  10.92  0.46  11.53  O  O C O H v n v O W  0.522  O vn VO W  M  Temperature i n F ° and specific, weight of water ( l b s / c u . f t . )  H CO  Ov  O  O  0>  H  H vo  vj. ~0 vO  O O O O v W O O  0 n H 0  Ov  0  O H O C T H O  Average  H Ov  H -f-  VT. -0 vO  O t O  0 O v v O 0 > 0.108  H W  O  0.492|  v  0  0.093  O  0.205  0.768  v  0 0 H V O v O V . W Q V 0.368  0.025  O H O  0.343  0.728  Ov H O  0.187  0.013  0.842  0.014  0.802  M w H  0 b -j O 0  0.002  ^ M  0  ° ^ l V n f -  vn  H w  b  P O H W  O j  .  0  P P O c o O W M O  Time  H M  vo vo p- w  b 0 O 0  P P O C O O O V H M  *-  f  o P  0.276  M vn vn M v n v n  i  P [0 H  P  0.586  " o a . vn -o. o v o  0.962  P  O  O TO H O  o  M  0.038  -  o  O O  0.21  co ^  ^  W  O O 1—' o  11.78  ^ H  v  -O -O VO  Cc W  6 w  Weight o f water ( l b s ) from M !nain p i p e ; R , r i g h t L . l e f t l e e  H  P" -O vO  H  O O  H  va  M  W  No.  p  to °^ H O CO Ov  0.874  w C n  o  tn ^ p -0 M -o  v  H  11.98  Ov ov Ov  O H O v  9.77  0  O O  p  Ov vO M °? K v n ^ J M  o °v O  0.013  -  O C  o  w Ov O  0.832  W  f  o  Sj  0.001  V ~  o  w vn vO ™ C K M H V O .  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H  f  ?.°rr-p.° Y??'.PP.  vo  O  o  »  M  r^rfpp  IO -J O  o.  M  M  jM  VO  O M  o  *  f  t  i  W  M J  W  tr> 3)  3  Cl -p-  OH  o  O  W  r<  u  b v o v o O O a v O O , Q > v 0 H O H W CO H <>»VOM O v M « v v n V O O t t V . O V H  OO  b H O p  H  O M l-  3  *•  M  * t -  M  H  W  M VO VO M VO VO O vn VO vn o o o o o o o o o o o o o o o o o o o o o o o OvOvWVOWW WWWVoWW r , ^ M > W U vO^*->WvO -o-^O-OvwW rOM^r-tjW  cnOv roo. Co VO  OO  p  J  '  O  O H  O  »  o  w -pM  "  H O M N QV WM H W  O  O  o  M  O  H  *-  vK V O OO H O O O  O  *  H -vl  V  O  o lO  1 1  M J  Ov P"  H  Co  O  -*0 ? vO  W  t-  -T  i  ^ Ovn v v n 'W ovoW W  OCTro-pwvn W  O  vn O M  ^  f pf-yj  O  C.O. iv. 4-— vovn W  X 3 o o o WOJ O U  W  H , "  »  »> 3  1  S  w  over tovn vo W  | | V O M vo  rovn vo  »  MH-O-OPM  i j  C  u  tr  IO VO 5 O O vn o o o o o o S o o VOW v n v n W W NOVO D O W W  i i  c oVo ol  -J  JT-  Total  f r i c t i o n  loss  Velocity  i n main  Velocity  head  M H  Velocity (ft/sec)  i n right  M M  V e l o c i t y head l e f t l e g( f t )  H vC M O  Wye  loss  Wye  loss  pipe  i n main  (ft/sec)  pipe  ( f t )  o r l e f t l e g  i n right  ( f t )  M W  M  ( f t )  coefficient  o r  UJ  --- -p- uj uj uj uj  N  *_n \nJ uj uj uj uj uiu%w uj ro ro j  o .  uj  o . o  1  o vO  no  uj  O --j. *-o  .  O H . -o -f-p- vO in ro  .  o • *oa On o  v/i  vo o -o MO  ro -o.  u> ro ro  no  ro -o  -o oa  no  o • 00. o  o o  -o  o uj h-  1  uj  \~*.  y-  1  0.210  0.210  0.210  o no  OnOn rovn UJ  0.210  coO  O oo. ro u> O oa ro \-i  0.210  .  vo O O  ONON rovw  O O O O H . . . . * .p- vo \j- njon UJ \_n -poo oa o no  oo. u» ro  -J so ro  204.3  o .  O  . -o o  O r i f i c e No.  Weight o f water ( l b s ) from M,maln p i p e ; R , r i g h t l e g ; UJ L . l e f t l e g  .p- .p- uj uj ro ro  323.1  O  ro  oororooo oo-oujuj.p-.f- •F- Time i n t e r v a l (sees) HvoOHwro 408.0  O  « . ' uj -o -O. -0 vji no oa -o  uj  277.2  O . uj  306.7  O O O . . r o r o * fy i vO oo o no  o  OvO"* rout ui  uj  .  521.8  uj  324.8  342.8  512.0  317.8  340.0  423.7  318.8  .337.1  486.5  010* ro*UJVn  Test No.  1  +h>  oubhmuvj ro ro-t-*-h I- h i- *-*-ro ro p y o o - j - j on on 0000.-0-0 u u o o > ) - i ro h ro ro.p-*- hi-onon-o-o oorONO-OH»o vflyi o o c a - J ro oa-o oo-o oo -ti«onoo.i- uj  ro*u> vn  r-  t—'  L  0006T W j  0006T W 0006T 1  OOOOT H  •  0006T 1  OOOST W  H  *- .p- ui uj uj uj 1  .  M + ro  0005T H,  •,  0006T W 0006T 1  (O + ro  0008  OOOOT 1  H 0005  00S0T W  1 OOSZ.  + •t-  .  005OT H  UJ tuj  •p-  Average time i n t e r v a l  vn  (sees)  Temperature i n F ° and s p e c i f i c ON weight of water ( l b s / c u . f t . )  -J  Discharge ( c f s )  00.  Hook gage reading i n upstream tank T f t )  Hook gage reading i n c e n t r a l NO tank ( f t ) , Hook gage reading i n downstream I- tank ( f t ) 0 1  M Vernier correction ( f t ) }-•  0.740  0.739  0.423  0.426  0.317  0.321  0.217  0.219  0.112  0.102  Pressure head d i f f e r e n c e ( f t ) I- between main pipe and r i g h t l e g or main pipe and l e f t l e g 1  ro  Discharge r a t i o , Discharee i n branch UJ Discharge i n main pipe 0.171 0.042  0.098 0.024 0.596 0.619 0.661  0.599 0.622 0.664  0.352 0.365 O.389  0.354 0.367 0.391  0.267 0.277 0.294  0.267 0.277 0.294  0.184 0.191 0.203  0.182 0.189 0.201  0.091 O.O94 0.099  H F r i c t i o n l o s s ( f t ) i n r i g h t or ON l e f t l e g , f o r length 9-0' 1  •—' F r i c t i o n l o s s ( f t ) , i n r i g h t or l e f t l e g , f o r length TDi or TD  -J  2  Total f r i c t i o n loss (ft) CO  lA  On  ro  -p-  0  ro -p-  uj 0  vo ro  NO  •0 H* -0  0 » uj no -F-  0 . 0 0 NJ1  ro  0 . 00  w . m uj  0  NO  O  O  O  . . -0 O N O hoo  oa  9.75  7.17  O  « . 0000 -p- 0  NO  7.18  6.11  O  h-  V e l o c i t y i n main pipe  ro  V e l o c i t y head i n main pipe ( f t )  ro H  Velocity i n right or l e f t l e g (ft/sec)  ro ro  V e l o c i t y head i n r i g h t o r left leg (ft)  ro  Wye l o s s ( f t )  1  1  M M . . F- -P-JON cono  O.O83  0.140 O.091  0.127  0.087  0.067 0.081 0.080  0.065 0.078  0.048 0.079 0.079  0.030 0.076 0.079  1  0.016 0.094 O.O94  0.016 0.094  Nj-ui  O.O48 0.079  O  6.13  4-93  O  • « ujuj OO-O. 000 0.032 0.081  4.95  3.28  3.23 1  0.072 0.017  0.049 0.012  0.022 0.005  0.086 0.089 0.094  O O  F r i c t i o n l o s s ( f t ) , i n main VI pipe f o r length ST  UJ uj  O  . . t— H ONON ro -0  t-» F r i c t i o n l o s s ( f t ) i n main •F- pipe f o r length 3-375'  (ft/sec)  UJ ro  Wye l o s s c o e f f i c i e n t  •Fro  Average wye l o s s c o e f f i c i e n t  *-  W  +  W  4  +f;  W  fC  iO W  M  X  Ir*  M l - '  H  W  W  *-  I -  M  '  W  +  +  M . M  W w W  H  * W  M  * PO  X tr*  Co  I-  - o f  O  f  M NO  H NO O  W  + C-* •  w  1 f W X r w K t - S J ^ K . l - ' w S  • .« W J> vtv. i a  •I-  1 NOVO . .  Kiro M  j  |  o l  V  O  O  .  W  ^  J O w  w  O  t  l  ^  J V i p  *0 H  O  -  l  O  N  w o  O  O  .  •  .  0  o  o  O M O  vo vO O M N O O  O  O  W  o  . . .p-  M  0 W  t> o  o  o v  W  H  Ov  -o  O  O  *~ CO p-  v i  r o  0 0 M(a a ' WV? VI  -  o  p-vl -0 vo  0.718  1.626  2.185  O  .  0 O O O - > ] O i  '  M N  O  0.723  0.277  0.U5  0.585  0.961  0.039  0.070 0.017  0.070 0.017  0.070 0.017  0.070 0.017  0.529  0.092 0.096 0.115  0.494 0.512  0.354 0.371  0.030  0.188| 0.195 0.212  0.341  0.013  0.018  0.727! 0.744 O.76I  0.013  0.001 0.001  0.798 0.827 0.844  M M  0.580  0.582  0.586  0.583  ON  ON  O  8.67 1.168 0.081  0  O  3.32 0.171 O.O98  0.169  5.00 0.388 0.054  0.216  7.04 0.770 0.052  1.10 0.019  10.91 1.849  0.47 0.003 O.264  11.52 2.063 0.210  0  O O v Q V O W  0  0  M M W Q v v O C O  bischarge  ratio,  Discharge i n main pipe  M  F r i c t i o n loss ( f t ) i n main pipe f o r length 3*375  1—'  F r i c t i o n l o s s ( f t ) , i n main  H  F r i c t i o n l o s s ( f t ) i n right or l e f t l e g , f o r length 9o0*  1  \n pipe f o r length ST  F r i c t i o n l o s s ( f t ) , i n right or l o f t l e g , f o r length TDi or  oa Total f r i c t i o n l o s s ( f t )  M -F-  0  Pressure head d i f f e r e n c e ( f t ) between main pipe and r i g h t l e g or main pipe and l e f t l e g  1  ON  0  Vernier correction ( f t )  M H  I—  M W  W W - O v O M O  O  -O  ON  0  Hook gage reading i n downstream tank ( f t )  M  w  M M  0  Hook gage reading i n upstream tank ( f t ) Hook gage reading i n c e n t r a l tank ( f t )  vO  M W  M W O M w M  O vO  P - W w O v V i W  03-  O  O  0.280  0.039  0.218 0  O  W  Temperature i n F° and s p e c i f i c weight of water {lbs/cu \> f t •) Discharge ( c f s )  M  0.576  0.21 0.001 0.262 0  P - W V i - O V i v o  O  W M M v O —J ^)  0.961  0.070 0.017 ON  11.77 2.152  0  W  Ov  o  -O. ON  .  (aecsj  Average time i n t e r v a l (sees)  O N W v O O Vv H V v v D  0.301 0„827| 0.858 0.875  0.002 0.002 0.019  0  P - M - I O  O  TO V i vO W v n ^ j  Time i:itt*rvnl M  w w  o -  W  -0  o  o  ON O  o  p-  M  o  r  a a . . . W W Vl. M W COW O -O P-N M *M V PO Vi a » a  QN ON tv>pa a W V I W  V i W v O W CO ' W O W W a  o  COV£> Q N O V M  a  W  W  0.983  v M M  O.58O  0  0.017  »  11.98 2.233 0.238 0.259  S  0 160 0.179 0  O H ONVi  o  M  -0  W  0.C70 0.017i  O O  0.385 9.66 1.475  6.56 0.667 0.072 0.083 0  COM O ^ )  0.857 0.889 0.906 0.017  -  0.173  0.073 4.26 0.282 0.028 0.035  0  p-p-  o  ON ON M(a a W V W  O 0 & V D O < n v f ; W CO M (A vd O - W O > V « V i O  o  VO  Q  0.319 1.000 0.000  0.317 0.005  0.603 0.626 0.638 0.012  0.301 0.312  0.150 0.002 0  0.048 0.012  0.002  0.022 0.005  0.010 0.148  0.142 0  +>W COCO O * -  .  .  r-  W v* O -O vO vO O OW a a a  H  O  C  o  a  w  CO -O  W O v v O Q v P" v£i  v  o  o  w  O M  H vQ O  N / i v . H Hw w  * - ^ " N O N O O O  w  O W  p  o  a W  O  Q  o  O  tow  W 10  W v J OvO p--0  W  O  -O-J-J  0 0* W p a a W V i W  o  O  H M M n  O  Q  V l O  4T-+T-WWWW  H M W  O H  W  o  O  ->i-jco<»ww  O  O  Q  f - f - f I r w W  oo  N  o  W W I O I O W W  yivflvnyrWH u .- a a a a a » . a ^- w W W W p.pw -o, V .v i v o. O^W O N N C CO O O N Wv oW O O- O t a n •  cr. y  o  H NO  H  vO O  w  H O I vO CO P" CO  W  o  M  Q Q  W ON -!>  O O  J  o  H v i O  w  O O l CO CO W W  W  H  -P"  O O  M -  o  Weight of water (lbs) froza M.snain p i p e ; Upright l e g ; L l e f t leg  I- W X  M  VI NO O O  w  O W W CO O-O  o  IO O  O  o  j--4~-*~ww  ONON iO-Pa a W V I W  >  O  o  f S J S  3  M  p - ^ - W W W W O O O  to  co p- co  M  M '^J  0.358  0.092  0.408  oxz-o  '  N W W  ON  -  O  w  W  O  W v O  o  GN-"N fO-Ca * W V i  W  M O  o  g  O  H VM I O G NCO O N VW O  o  W  Q  IO M 0> . . . . v i W  o i  O  W  Co CO  ( W W a u . W  >o  ONON W-P" a a W v i W  O  oow'-;ww  l l .ON iOw l  I N OON O •  ;o  l  t  O  -w  I  ONON W.pa a W V I W  w tO ON  W M  O  O  ww  1 O e . W  i.O  V a  o I  1  t  O  v i w w w w w  -  OTZ'O  I  v  o o o WoW  ww  (-•• M  vi ONQ\ M v . a W W  1  o o o WoW  H O  OTZ'O  O  v- . H j) >£> I Q O  OTZ'O  I  o  W W C O  t  ':  M  V l O  O r i f i c e No,  IO  OTZ'O  1  c  W W  M  Vt 1 O  f  ^TZ'O  O  O 1 O  J*J  W  OTZ'O  g o  H O O  M  —J O  V.  M  M  OTZ'O  "vl 1 O  .  H vO  O  V e l o c i t y i n main pipe  (ft/sec)  V e l o c i t y head i n main pipe ( f t )  to V e l o c i t y in right or l e f t l e g (ft/sec)  H*  l\) V e l o c i t y head i n right or . ro l e f t l e g ( f t ) ro Wye l o s s ( f t ) ro Wye l o s s c o e f f i c i e n t  Collecting pipes  Wooden trough for l e f t branch pipe  Wye  Left hand flumi  Main pipe  Fig. 1.  General arrangement.  53  Branch pipes  Velocity traverse s t a t i Piezometer ring  13.25' 5-J" ID Lucite main pipe  Reducer  Flow  Straightener Section at AA of straightener 5" standard s t e e l  Reducer  Flow Straightener k" standard s t e e l pipe Controlling valve  F i g . 2. Details of main pipe from controlling valve to wye.  5<V  F i g . 3. Model lay out and manometric arrangement.  90 Large spherical wye  F i g . k.  Details of wyes.  Q  90 Small spherical  wye  56  57  P l a s t i c piping  F i g . 6. Pressure  tap.  5,8.  Orifice  ring  End piece  7  3.75"  Branch pipe  • D"  r-r-r  L  6*!L  Numerical designation of o r i f i c e 1* 1  External diameter (inches) 3.720  2 3 5 6 7 8 x  F i g . 7.  Orifice  arrangement.  Internal diameter (inches) 3,622 1 3.300 J 3.375 2.913 2.^90 2.000 1.3-+2 0.8-+0 0.53-*  Remarks Rounded orifices  no o r i f i c e  59  F i g . 8.  Velocity traverse across main pipe near wye preliminary investigations.  during  F i g , 9, Velocity traverse across main pipe near wye after modifications i n the main pipe section.  61  Left branch side  Rig  h t  branch s i d  15" C< >ntre ljLne c • f main pip< i  1. 1  10" Velocity head  !  5"  L5 12  11  io  9  8"  i i i i 1 7  "6 .  5  k  3 2:  1  \  Fig 1 0 . Velocity traverse with one l e g flow with discharge o 0.92 cfs.  0)  CO  N  F i g . 11  F r i c t i o n losses i n main  63  End piece Piezometric ring  LLJ 3.75" ID branch pipe, section A 9't.) 3.75" ID branch! pipe, section Cj  Piezometric  ring  ---41 B.!  -x.  Reducer  5.25" ID main pipe  t  Supply-  F i g . 12, Experimental set up for measurement of f r i c t i o n losses i n branch pipes.  B E S T - P R INTKK CO. LOOARITBMIC: 1 S/l By '  7  8  9  1  ' W-1NCK CYCLIS.  5  6  7  8  90.1  I..TU.  VALUES OF (VD) FOR WATER AT 60°F (VELOCITY IN FT/SEC » DIAMETER IN INCHES) -  0.2  J).4  0.6 0.6 I  2  4  6  8 10  20  40  60 80100  200  400 600 8001000  2000  8000 4000 6000 110,000  aoloool I  .000,01 8  Branch Pipes  Q Main Pipe  Friction  Factors  vs. Reynold A/vm&erj For Main & Brarix.  .000,005 ON  ON  67  1.1  l.o  (ft  Open l e g  0.9  0.8  Wye loss coefficien  -  K . . 0.7  0.6  Symraetr i c a l flow •—-°  f  Closed l e g  0.5  OA 0.2  OA  0.6  0.8  1.0  1.2  1A  Discharge (cfs) F i g . 16. 90  Large spherical wye,symmetrical & one leg flow.  1.5  1.0  F i g . 17.  Discharge r a t i o 90* Large s p h e r i c a l wye, unsymmetrical flow  0.9  69  Open jleg  0.8  0.7  0.6  Closed. leg 1  0.5 Wye loss coefficient K OA  Symmetrical  0.3  flow  0.2  0.1  07T  -crA-  0.6  jfng  -Q  1(  1.2  TA  Discharge (cfs) F i g . l8 . 90* Small spherical wye, symmetrical and one l e g flow  1.5  0.3  0.2  0.1  0  0  0.2  OA  0.6  0."8  l.C  Discharge r a t i o F i g . 19. 90 Small spherical wye, unsymraetrical flow.  71  0.7  0.2  OA  0.6  678 Discharge (cfs)  F i g . 20. 90°Tapered wye,  i.o  1.2  symmetrical and one l e g flow.  TA  1.5  72  0.7  0.6  73  0.6  Closed legN  0.5  Open leg  0.4  Vjye loss coefficient K 0.3  0.2  Syramet r i c a l flow  0.1  0.2  0.4  0.6  1.0  0.8  Discharge  1.2  1.4  (cfs)  F i g . 22. 60 Tapered wye (A), symmetrical and one leg  flow.  1.5  74  75  0.7  0.6  0.5  Closed  cO p l e g  0.4 Wye loss coefficien K 0.5  0.2  0.1  ^Symmetr: caT~flow  0.2  "074  0.6  0.8  ~  Discharge (cfs)  1.0  1.2  Fig. 24. 60° Tapered <wye(B),syrrunetrical and one leg flow.  1A  1.5  t  0  Y [Jnsymmetric a l  . 0.2  flow  0.4 0.6 Discharge r a t i o  0.8  F i g . 25. 60* Tapered wye <B.,unsymraetrical flow.  1.0  77  0.6  0.5 90 Large spherical  wy<i  OA Wye loss coefficient K 90 Small spherical  0.3  wye  0.2  0.1  0  0.2  oA~  "oTo"  60° Tapere 3 wye  (A)  60° Tapere 2 wye  (B)  578  T7o~  1.2  1A1.5  Discharge (cfs) F i g . 26. Wye  loss c o e f f i c i e n t s for a l l wyes, symmetrical flow.  1.0  78  0.9  0.8  0.7 ffye lose coefficient K 0.6  90 Taper)sd wye  .0.5  60* Tapered wye  (A)  9*Tapered wye  (B)  O.k  0.3  0.2  0.1  0.2  O.h  Fig. 27. Wye  0.6 0.8 Discharge (cfs)  1.0  1.2  loss coefficients for a l l wyes,one leg flow (open branch).  79  0.8  Wye loss coefficient E  0.2  0.1  OA  0.6  0.8  1.0  Discharge (cfs) Fig. 28, Wye  loss coefficients for a l l wyes,one l e g flow(cloeed branch).  1.0 8o  Discharge F i g . 29. Wye  0.6  loss coefficients  ' . ratio  0.8  f o r a l l wyes, u n s y m m e t r i c a l  flow.  Plate 1. Manometric board with gage tanks  82  Plate 2. Manometric  board  o3  Plate 3. Lay out of model looking downstream  85  Plate 5. Control valve  • Plate 7 . 90 tapered and 90 small spherical 0  wye.  88  89  P l a t e 9» O r i f i c e s and end piece  

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