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Head losses resulting from flow through wyes and manifolds 1967

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HEAD LOSSES RESULTING FROM FLOW THROUGH WYES AND MANIFOLDS by HUA WANG B.S., Taiwan Cheng Kung Uni v e r s i t y , 1964 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF APPLIED SCIENCE i n the Department of C i v i l Engineering We accept this thesis as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA September, 1967 In p r e s e n t i n g t h i s t h e s i s i n p a r t i a l f u l f i l m e n t o f t h e r e q u i r e m e n t s f o r an a d v a n c e d d e g r e e a t t h e U n i v e r s i t y o f B r i t i s h C o l u m b i a , I a g r e e t h a t t h e L i b r a r y s h a l l make i t f r e e l y a v a i l a b l e f o r r e f e r e n c e and S t u d y . I f u r t h e r a g r e e t h a t p e r m i s s i o n f o r e x t e n s i v e c o p y i n g o f t h i s t h e s i s f o r s c h o l a r l y p u r p o s e s may be g r a n t e d by t h e Head o f my Depar tment o r by h i-;: r e p r e s e n t a t i v e s . It i s u n d e r s t o o d t h a t c o p y i n g o r p u b l i c a t i o n o f t h i s t h e s i s f o r f i n a n c i a l g a i n s h a l l n o t be a l l o w e d w i t h o u t my w r i t t e n p e r m i s s i o n . D e p a r t m e n t o f 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 C o l u m b i a V a n c o u v e r 8, Canada September 1967. i ABSTRACT Laboratory tests were conducted to determine the head losses i n wyes and manifolds of conventional type, both with and without an i n t e r n a l t i e - r o d at the t h e o r e t i c a l centre of the wye. These wyes and manifolds, having 45°, 60° and 90° subtending angles of the wyes, were symmetrical about the longi t u d i n a l axis of the main pipe. The apparatus and method of testing used i n the tests are described. The experiment spans a range of Reynold's numbers from 85,000 to 420,000 i n the i n f l u e n t main pipe. The analysis of experimental data i s based on the energy equation of B e r n o u l l i for the one-dimensional condition. The r e s u l t s of the tests are given i n both tabular and graphical form. I t appears that the c o e f f i c i e n t of the form loss (the r a t i o of the form loss of a wye or manifold to the v e l o c i t y head i n the main pipe) i s a function of the proportional flow of water through the branches, the size of the t i e - r o d used and the subtending angle of the wye. i i TABLE OF CONTENTS PAGE ABSTRACT TABLE OF CONTENTS LIST OF TABLES LIST OF FIGURES LIST OF PLATES NOMENCLATURE ACKNOWLEDGMENT INTRODUCTION PREVIOUS RESEARCH CHAPTER I DESCRIPTION OF EXPERIMENT 5 1.1 Layout 5 1.2 Model 7 1.3 Instrumentation 14 1.4 Experimental Measurements 15 CHAPTER I I BASIC CONCEPTS RELATING TO HEAD LOSSES 18 2.1 Form Losses of Wyes 19 2.2 Form Losses of Manifolds 20 2.3 Hydraulic Power Losses i n Wye and Manifold 20 Arrangements CHAPTER I I I EXPERIMENTAL INVESTIGATIONS 22 3.1 Preliminary Investigation 22 3.2 Flow Patterns 23 i i i i v v i ix x x i i 1 3 i i i PAGE CHAPTER IV EXPERIMENTAL PROCEDURES 24 4.1 Determination of F r i c t i o n Losses i n Main Pipe and Branch Pipes 24 4.2 Sequence of Experiment 26 CHAPTER V RESULTS AND CONCLUSIONS 27 5.1 Results 27 5.2 Conclusions 29 APPENDIX HEAD LOSSES IN ELBOWS 31 BIBLIOGRAPHY 33 i v LIST OF TABLES TABLE NO. TITLE PAGE I -1 Areas of Main, Branch and I n l e t Pipes 36 I -2 O r i f i c e Arrangement 36 I I - l Distance from T h e o r e t i c a l Center of Wyes to 37 Piezometric Rings on Main and Branch Pipes (For Wye Arrangement) II -2 Distance from T h e o r e t i c a l Center of Wyes to 37 Piezometric Rings on Main and Branch Pipes (For M a n i f o l d Arrangement) IV-1 Data of S k i n F r i c t i o n Loss i n Main Pipe f o r 38 Length SS± (3.375 f t . ) IV-2 Data of S k i n F r i c t i o n Losses i n Branch Pipes 39 f o r Length BB^ (9.0 f t . ) V -1 Form Loss Data for 9 0 ° Wye without T i e - r o d 40 V -2 Form Loss Data f o r 9 0 ° Wye with TR1 T i e - r o d 42 V -3 Form Loss Data f o r 9 0 ° Wye with TR2 T i e - r o d 44 V -4 Form Loss Data for 9 0 ° Wye with TR3 T i e - r o d 46 V -5 Form Loss Data for 9 0 ° Wye with TR4 T i e - r o d 48 V -6 Form Loss Data for 6 0 ° Wye without T i e - r o d 50 V -7 Form Loss Data for 6 0 ° Wye with TR2 T i e - r o d 52 V -8 Form Loss Data for 6 0 ° Wye with TR3 T i e - r o d 54 V -9 Form Loss Data for 6 0 ° Wye with TR4 T i e - r o d 56 V -10 Form Loss Data for 4 5 ° Wye without T i e - r o d 58 V LIST OF TABLES - - (Continued) TABLE NO. TITLE PAGE V -11 Form Loss Data for 9 0 ° Manifold without T i e - r o d 60 V -12 Form Loss Data f o r 9 0 ° Manifold with TR3 T i e - r o d 62 V -13 Form Loss Data for 6 0 ° M a n i f o l d without T i e - r o d 64 V -14 Form Loss Data f o r 6 0 ° M a n i f o l d with TR3 T i e - r o d 66 V -15 Form Loss Data for 4 5 ° M a n i f o l d without T i e - r o d 68 V -16 Data of H y d r a u l i c Power Losses i n Wye Arrangements 70 V -17 Data of H y d r a u l i c Power Losses i n M a n i f o l d 73 Arrangements A -1 Distance from T h e o r e t i c a l Center of Elbows to 76 Piezometric Rings on S t r a i g h t Pipe A -2 Head Loss Data for 4 5 ° Elbows 77 A -3 Head Loss Data f o r 3 0 ° Elbows 78 A -4 Head Loss Data f o r 22%° Elbows 79 v i LIST OF FIGURES FIGURE NO. TITLE PAGE I - l D e t a i l s of General Arrangement 80 1-2 D e t a i l s of Wye Arrangement 81 1-3 Model Layout and Manometric Locations f o r 82 Wye Arrangement 1-4 D e t a i l s of M a n i f o l d Arrangement 83 1-5 Model Layout and Manometric Locations for 84 M a n i f o l d Arrangement 1-6 D e t a i l s of Main Pipe from C o n t r o l Valve to Wye 85 1-7 Geometrical D e t a i l s of 9 0 ° Tapered Wye 86 1-8 D e t a i l s of Wyes 87 1-9 D e t a i l s of Manifolds 88 I-10 D e t a i l s of Elbows 89 1-11 D e t a i l s of Pressure Tap 90 I I - l H y d r a u l i c & Energy Gradient Lines for Wye 91 II-2 H y d r a u l i c & Energy Gradient Lines for M a n i f o l d 92 I I I - l Flow Patterns "in Manifolds without T i e - r o d 93 I I I -2 Flow Patterns i n Manifolds wi th T i e - r o d 94 IV-1 S k i n F r i c t i o n Loss i n Main Pipe 95 IV-2 Experimental Set-up for Measuring S k i n F r i c t i o n 96 Losses i n Branch Pipes IV-3 Skin F r i c t i o n Loss i n Right Branch Pipe 97 IV-4 S k i n F r i c t i o n Loss i n L e f t Branch Pipe 98 v i i LIST OF FIGURES - - (Continued) FIGURE NO. TITLE PAGE V - l Form Loss C o e f f i c i e n t s f o r 9 0 ° Wye 99 (Symmetrical Flow) V-2 Form Loss C o e f f i c i e n t s for 9 0 ° Wye 100 (One-leg Flow) V-3 Form Loss C o e f f i c i e n t s f o r 9 0 ° Wye 101 (Unsymmetrical Flow) V-4 Form Loss C o e f f i c i e n t s for 6 0 ° Wye 102 (Symmetrical Flow) V-5 Form Loss C o e f f i c i e n t s for 6 0 ° Wye 103 (One-leg Flow) V-6 Form Loss C o e f f i c i e n t s f o r 6 0 ° Wye 104 (Unsymmetrical Flow) V-7 Form Loss C o e f f i c i e n t s for 4 5 ° Wye 105 (Symmetrical & One-leg Flows) V-8 Form Loss C o e f f i c i e n t s for 4 5 ° Wye 106 (Unsymmetrical Flow) V-9 Comparison of Form Loss C o e f f i c i e n t s for Wyes 107 (Unsymmetrical Flow) V-10 Form Loss C o e f f i c i e n t s for Manifolds 108 (Symmetrical Flow) V - l l Form Loss C o e f f i c i e n t s f o r Manifolds 109 (One-leg Flow) v i i i LIST OF FIGURES -- (Continued) FIGURE NO. TITLE PAGE V-12 Form Loss C o e f f i c i e n t s for Manifolds 110 (Unsymmetrical Flow) V-13 Comparison of Form Loss C o e f f i c i e n t s for Wyes 111 & Manifolds without Tie-rod V-14 Comparison of Form Loss C o e f f i c i e n t s for Wyes 112 & Manifolds with TR3 Tie-rod V-15 Hydraulic Power Losses i n Wye Arrangements 113 V-16 Hydraulic Power Losses i n Manifold Arrangements 114 A - l Experimental Set-up for Measuring Head Losses 115 i n Elbows A-2 Hydraulic & Energy Gradient Lines for Elbow 116 Testing Set-up A-3 Elbow Loss C o e f f i c i e n t s 117 ix LIST OF PLATES PLATE NO. TITLE PAGE 1 Model Layout for Wye Arrangement Looking 6 Downstream 2 Model Layout for M a n i f o l d Arrangement Looking 6 Upstream 3 Tapered Wyes i n V e r t i c a l View 10 4 Tapered Wyes i n H o r i z o n t a l View 10 5 Elbows 10 6 O r i f i c e s and T i e - r o d s 12 7 Top View of Wye i n Place 12 8 Top View of M a n i f o l d i n Place 13 9 Manometric Board wi th Gauge Tanks 13 X NOMENCLATURE The following symbols are used i n this thesis: A = Average i n t e r n a l cross-sectional area, i n sq. f t ; D = Average i n t e r n a l diameter, i n inches; 2 g = Acceleration of gravity, i n f t / s e c ; h^' = Skin f r i c t i o n loss of pipe, i n f t ; hp = Pressure head i n piezometric ring, i n f t ; h^ = V e l o c i t y head, i n f t ; ^ h = Form loss of wye or manifold, i n f t ; A hg = Elbow loss, i n f t ; Ah - Difference of pressure heads i n piezometric rings between P main pipe and one of branch pipes, i n f t ; k = Form loss c o e f f i c i e n t of wye or manifold; kg = Elbow loss c o e f f i c i e n t ; L = Length of pipe, i n f t ; N = Froude number; r p = Hydraulic power loss i n dimensionless expression; P^ = Hydraulic power loss, i n f t - l b / s e c ; P = Hydraulic power i n main pipe, i n f t - l b / s e c ; m Q = Discharge i n pipe, i n c f s ; Re = Reynold's number t = Time i n t e r v a l , i n sec; V = Mean v e l o c i t y i n pipe, i n fps; Js = Kinematic v i s c o s i t y , i n f t / s e c ; X L NOMENCLATURE -- (Continued) w = Unit weight of water, i n l b / c u . f t ; W = Weight of water, i n lbs; Subscripts: m = Occurrence i n main pipe; b = Occurrence i n branch pipe; r = Occurrence i n r i g h t branch pipe; 1 = Occurrence i n l e f t branch pipe; i = Occurrence i n i n l e t pipe. x i i ACKNOWLEDGMENT The author i s indebted to h i s supervisor , D r . E . Ruus, f o r h i s constant encouragement and invaluable guidance throughout the preparat ion of the work. He wishes to express h i s a p p r e c i a t i o n to Professor J . F . Muir f o r suggestions and c r i t i c i s m i n preparing t h i s t h e s i s , to the s t a f f of the C i v i l Engineering Instrument Shop f o r t h e i r ass is tance i n the c o n s t r u c t i o n of the models, and to the N a t i o n a l Research C o u n c i l of Canada for f i n a n c i a l support given through grants i n a i d of t h i s r e s e a r c h . 1 INTRODUCTION In recent h y d r o - e l e c t r i c development, a power plant of high capacity i s often proposed with a large diameter penstock to convey water from the overhead res e r v o i r to the powerhouse. A de t a i l e d study of the head loss i n the penstock becomes necessary for an economic design of the penstock. A major portion of the t o t a l head loss i n the penstock r e s u l t s from the flow through branched pipe junctions . Research i n hydraulics i s required to determine the exact amount of the head losses at these pipe junctions and to study the various parameters governing such head l o s s e s . The author deals s p e c i f i c a l l y with those investigations that concerned the head losses at wyes and manifolds. The study described i n this thesis was made to determine the head losses f o r various flow conditions at symmetrically branched pipe junctions having d i f f e r e n t subtending angles of the wyes. I t i s p r i m a r i l y concerned with the form losses r e s u l t i n g from the flows through wyes and manifolds. D e f i n i t i o n of Terms A wye (or a bifur c a t i o n ) i s a branched f i t t i n g used to connect an i n f l u e n t main pipe to two e f f l u e n t branch pipes . (See Figure 1-8) . When a branched f i t t i n g i s used to connect an i n - f l u e n t main pipe to three e f f l u e n t branch pipes, i t i s c a l l e d a t r i f u r c a t i o n . A manifold i s a branched f i t t i n g wherein the e f f l u e n t branch pipes are brought back p a r a l l e l to the i n f l u e n t main pipe by the 2 connection of elbows to each limb of a wye. The subtending angle of a manifold is considered to be the angle between the limbs of the wye. (See Figure 1-9). For example, a 45° manifold consists of a 45° wye followed by two 22-1/2° elbows connected to the downstream limbs of the wye. The form loss is the head loss arising from turbulence in a branched pipe system excluding the skin f r i c t i o n loss of head in the system. The form loss coefficient is the ratio between the form loss of a wye or manifold and the velocity head in the main pipe. When the experimental results are adopted to estimate the head losses in geometrically similar prototypes, the application of Froude law (N„ = V / / gD ) as the criterion for dynamic similarity F in interpreting the hydraulic models w i l l lead to reliable prediction of prototype performance. 3 PREVIOUS RESEARCH The e a r l i e s t important experimental i n v e s t i g a t i o n of the head (1)* losses i n branched pipe systems was undertaken i n 1928 by Vogel , (2) who dealt only with pipe tees. Later i n 1929, Petermann made a de t a i l e d study of the head losses i n piping b i f u r c a t i o n s with a main pipe that continued s t r a i g h t a f t e r the junction, a branch of which subtended at an angle of 45° to the l o n g i t u d i n a l axis of the main pipe. Since 1957, numerous t h e o r e t i c a l and experimental investigations of hydraulic behaviour i n branched pipe systems have been undertaken (3) i n many countries. In Switzerland, Cardel made tests to determine the head losses produced i n several types of wye branches where the main pipe 150 mm i n diameter was joined by branch pipes ranging from 60 mm to 150 mm, the angles between the branches varying from 45° to 135°. In I t a l y , Marchetti and N o s e d a ^ investigated the hydraulic behaviour of f i v e symmetrical b i f u r c a t i o n s with the angles between the branches varying from 60° to 180°. In Norway, F r i t j o f S a l v e s e n ^ conducted model tests on a 60° wye using i n turn four d i f f e r e n t i n t e r n a l r i b s i n the fork of the wye to f i n d which r i b provided the lowest head l o s s . In Canada, at the Un i v e r s i t y of B r i t i s h Columbia, (6) Ahmed conducted a series of head loss tests on f i v e symmetrical wyes of conventional and spherical types having the angles of 90° and 60° between the branches. In the United States, several basic studies of the mechanism of i n s t a b i l i t y of flow through a symmetrically * Numbers i n parentheses r e f e r to the Bibliography. branched pipe system were made at the University of Kansas Hydraulic model studies to determine the head loss i n a manifold co n s i s t i n g of a 45° wye followed by two 22-1/2° elbows were conducted by s t a f f members at Colorado State U n i v e r s i t y . A series of model tests was made by Gladwell, Tinney and K r e u z e r ^ ' ' at Washington State University on a large penstock t r i f u r c a t i o n to determine flow patterns, s t a t i c and dynamic pressures, energy losses and the shed v o r t i c i t y from a cen t r a l t i e - b a r . 5 CHAPTER I DESCRIPTION OF EXPERIMENT 1.1 LAYOUT The experimental i n v e s t i g a t i o n was conducted i n the Hydraulic Laboratory at the University of B r i t i s h Columbia i n 1966-67. The water was pumped from a sump into an overhead tank with a surface l e v e l about 55 f t . above ground and holding about 1760 cubic fe e t of water. Through a control valve this supply led to the test s e c t i o n . The pipes and f i t t i n g s of the model rested upon a wooden frame, the tightness of a l l j o i n t s being under observation. The model area extended from the control valve to the outlets of the branch pipes. From the outlets of the branch pipes ran two troughs which enabled the flow through each branch pipe to be guided into a weighing tank or the sump as required i n the experiment. The general arrangement of the model i n elevation i s shown i n Figure I - l . The plan views of a wye arrangement are shown i n Figures 1-2 and 1-3, and Plate 1. The plan views of a manifold arrangement are shown i n Figures 1-4 and 1-5, and Plate 2. Due to the existence of many elbows and tees on the l i n e p r i o r to entering the model area, a great amount of turbulence-induced pressure fluctuations occurred. Two flow straighteners each 2 f t . long were provided i n the upstream main pipe to dampen these f l u c t u a - tions as well as to obtain a symmetrical v e l o c i t y d i s t r i b u t i o n i n the entrance section of a wye or manifold. These flow straighteners were made of t h i n aluminum tubes varying from one to two inches i n diameter. PLATE 1 Model Layout for Wye Arrangement Looking Downstream PLATE 2 Model Layout for M a n i f o l d Arrangement Looking Upstream 7 The f i r s t one was located downstream from the bend below the control valve, and the other downstream from the f i r s t reducer, as shown i n Figure 1-6. 1.2 MODEL The model was made of l u c i t e except for the portion upstream from the second reducer to the control valve where s t e e l pipes were used. (See Figure 1-1). This set-up had the advantages of (1) en- abling the d i f f e r e n t parts of the model to be replaced e a s i l y , (2) permitting the hydraulic behaviour throughout the model area to be observed c l e a r l y , and (3) showing any entrapment of a i r which would a f f e c t the piezometric heads. A. Main Pipe and Branch Pipes The main pipe, of l u c i t e , comprised of three sections of equal length, had an i n t e r n a l diameter of 5.25 inch and a t o t a l length of 13.5 f t . I t was f i t t e d on both ends of the sections with l u c i t e flanges which connected the pipes to each other and to the upstream face of a wye or manifold. Each flange was glued to one end of a section with the face perpendicular to the p i p e l i n e . Two piezometric rings were f i t t e d on the downstream section of the main pipe close to i t s ends. A v e l o c i t y traverse s t a t i o n was set up at 6 inches from the downstream end of the main pipe. Details of the main pipe from the control valve to a wye are shown i n Figure 1-6. Four sections of the branch pipes, designated as A, B, C and D, having an i n t e r n a l diameter of approximately 3.75 inch and a length of 4.5 f t . , were f i t t e d with l u c i t e flanges and piezometric rings to from the r i g h t and l e f t branches. Throughout the experiment, 8 sections A and C formed the l e f t branch, and sections B and D the r i g h t branch. The length of the main pipe from the downstream end of the f i r s t reducer to the upstream end of a wye was 33 f t . , the length- diameter r a t i o being 75. The length-diameter r a t i o was equal to 30 fo r each of the branch pipes . This r a t i o was considered adequate to obtain a reasonably uniform v e l o c i t y d i s t r i b u t i o n , and to achieve accurate pressure head measurements at the downstream piezometric rings at the branch pipes. An i n l e t pipe was used to determine the skin f r i c t i o n losses i n the branch pipes and the head losses i n the elbows. (See Figures IV-2 and A - l ) . B. Wyes Three symmetrically tapered wyes with subtending angles 45°, 60° and 90° r e s p e c t i v e l y were investigated. De t a i l s of the outlines and dimensions of the wyes are: i l l u s t r a t e d i n Figures 1-7 and 1-8, and Plates 3 and 4. These c a r e f u l l y constructed models were symmet- r i c a l about the l o n g i t u d i n a l axis of the main pipe. In preparing each wye, the outer faces were f i r s t machined. The t h e o r e t i c a l centre and the length from the t h e o r e t i c a l centre to the points of i n l e t and outlets were determined. The conical water passages were turned on a lathe; the inner surface of the wye was polished by emery paper, then by crocus paper, and f i n a l l y by p o l i s h - i n g . l i q u i d to make the inner surface of the wye as smooth as possible fo r the purpose of decreasing skin f r i c t i o n l o s s . For a l l wyes, the diameter of the i n l e t was 5.25 inch and of both outlets 3.75 inch; the tapering was done at an angle of 10°. 9 C. Manifolds Three symmetrical manifolds with 45°, 60° and 90° subtending angles of the wyes were investigated. The 45° manifold consisted of a 45° wye followed by a 22-1/2° elbow, which was b u i l t up from a 15° and a 7-1/2° elbow, connected to each downstream limb of the wye. A s i m i l a r set-up was made for the 90° manifold, replacing the 45° wye with the 90° wye and the elbows with 15° and 30° elbows. For the 60° manifold, 30° elbows, one on each limb of the 60° wye, were used. Det a i l s of the outlines and dimensions of the manifolds are i l l u s - t rated i n Figure 1-9. These elbows, of constant diameter, consisted of a series of small-angle mitre bends joined together without any rounding at the planes of i n t e r s e c t i o n . Each elbow was designed according to the (12) recommendation of Bier , with bend radius (15 inch) equal to four times the diameter of the mitre bend (3.75 inch) and a d e f l e c t i o n angle of 7-1/2° between segments. Details of the outlines of the elbows are shown i n Figure 1-9 and Plate 5 . Since the segments of the elbows were glued together, f i n a l machining of the flanges at the ends of each elbow was necessary i n order to achieve accurate alignment. ( I t i s e s s e n t i a l that the main pipe and the branch pipes are p a r a l l e l and l i e i n the same horizontal plane.) When two elbows were connected to form a required d e f l e c t i o n angle f o r a manifold, two l o c a t i n g pins were i n s t a l l e d on each side of the elbow flanges to eliminate any d i s t o r t i o n i n the horizontal plane and to f i x the combined elbow into f i n a l p o s i t i o n . PLATE 5 Elbows 1 1 . D. Tie-rods Four tie-rods designated as TR1, TR2, TR3, and TR4 having diameters 0.187, 0.380, 0.562 and 0.754 inches r e s p e c t i v e l y were used i n the i n v e s t i g a t i o n of the head losses i n wyes and manifolds. A l l of them were made of l u c i t e except the TR1 t i e - r o d which was made of brass . Each of the four tie-rods was placed i n turn at the t h e o r e t i c a l centre of a wye, and screwed t i g h t to i t s inner surface. E. O r i f i c e s The v a r i a t i o n of discharges was c o n t r o l l e d at the i n l e t by the control valve and at the two outlets by o r i f i c e s . Table 1-2 and Plate 6 show the d e t a i l s of the o r i f i c e s . These o r i f i c e s were placed, one at a time, at the downstream end of the branch pipe. Each o r i f i c e was machined on one side to obtain a clean and sharp edge free from burrs. Throughout the experiments, the o r i f i c e s were placed i n such a way that the sharp edges were facing the flow with the centerlines of the o r i f i c e s at the same elevation. F . Set-up of Model (1) For wye arrangements: A wye was f i r s t bolted to the branch pipes. The j o i n t s were checked by hand to ensure a proper alignment. The connection of the wye to the main pipe (see Plate 7) was made with the help of two l o c a t i n g pins i n s t a l l e d i n the downstream flange of the main pipe to eliminate any o f f s e t between the wye and the main pipe. (2) For manifold arrangements: Elbows were f i r s t bolted to the branch pipes, then to a wye (see Plate 8). PLATE 7 Top View of Wye i n Place PLATE 9 Manometric Board with Gauge Tanks 14 For the f i n a l set-up of the whole system, the main pipe was aligned by means of a theodolite, and the pipes were leveled accurately with a carpenter's l e v e l . Leather be l t s were used on the main pipe and at places close to the outlets of the branch pipes to prevent v i b r a t i o n . 1.3 INSTRUMENTATION The following instrumentation was used to measure pressure heads, and determine discharges. A. Pressure Taps A t y p i c a l pressure tap with an opening of 1/8 inch, as shown i n Figure I-11, was used i n the experiment. The brass tube was held i n p o s i t i o n by a 1/8 inch National Taper Pipe threaded screw (NTP) i n a 7/8 inch l u c i t e tube. The NTP i n turn was connected to a 3/16 Imperial threaded nut with rubber r i n g at the junction to e l i m i - nate p o s s i b i l i t y of any leakage. The opening of the pressure tap should be small enough to prevent any disturbance i n the flow along the pipe w a l l . I t must be normal to the wall and free from any burrs. Any i n c l i n a t i o n of the opening, e i t h e r towards or away from the flow, may cause f a l s e manometer readings. B. Piezometric Connections The pressure taps on the piezometric rings were connected to manometers and gauge tanks by f l e x i b l e , transparent tubing. The manometers were i n s t a l l e d i n groups and connected to the gauge tanks as shown i n Plate 9. Figures 1-3 and 1-5 show the connections of the 15 manometer tubes and gauge tanks to the piezometric rings on the main pipe, and the l e f t and r i g h t branch pipes for both wye and manifold arrangements. C. Gauge Tanks, Hook Gauges and Verniers In s p i t e of e f f o r t s to minimize the turbulence-induced pressure f l u c t u a t i o n s by providing the flow straighteners, small o s c i l l a t i o n s of the water l e v e l s i n the manometers were observed. The water l e v e l s i n three gauge tanks corresponding to the average l e v e l s i n the manometers were used to measure the pressure heads i n each of the piezometric rings i n order to achieve a s a t i s f a c t o r y degree of accuracy. The pressure f l u c t u a t i o n s i n the manometers were automatically smoothed out i n these tanks. In this series of t e s t s , three gauge tanks, each of diameter 5.5 inches, connected with four corresponding manometers on the main and branch pipes, were f i t t e d with hook gauges and verniers to i n d i - cate the average pressure heads i n the r e l a t e d piezometric r i n g s . Each pressure head was measured to one thousandth of a foot. By the use of extension rods f i t t e d to the hook gauges when required, the range of difference i n pressure heads would be increased from 2 f t . to 3 f t . ( i . e . , 6 inch a d d i t i o n a l at the top and 6 inch at the bottom) using the same v e r n i e r s . The vernier i n the upstream gauge tank was set an a r b i t r a r y 0.210 f t . higher than those i n the central and down- stream gauge tanks to f a c i l i t a t e measuring. 1.4 EXPERIMENTAL MEASUREMENTS A. Measurement of Weight of Water A weighing tank with maximum capacity of 20,000 l b s . was 16 used to measure the weight of water. The scales of the weighing tank were checked and found correct before s t a r t i n g the experiment. B. Measurement of Time The time i n t e r v a l f o r a p a r t i c u l a r weight of water, which was c o l l e c t e d i n the weighing tank, was recorded by an e l e c t r i c clock to 0.1 second. C. Measurement of Temperature For each t e s t , the temperature of water was read by thermo- meter and the density and the kinematic v i s c o s i t y were determined f o r the purpose of c a l c u l a t i n g discharges and Reynold's numbers (Re = V D lis ) i n the corresponding main and branch pipes. D. Measurement of Pressure Head The pressure head was measured from the water l e v e l s of three gauge tanks under the assumption that the flow was i n the steady state condition, and that the water l e v e l s i n the gauge tanks were constant. Since the area r a t i o of a manometer tube (1/4 inch i n diameter) to a gauge tank (5.5 inchc; i n diameter) was approximately 1 : 480, a period of not less than 2 hours was considered necessary to adjust the water l e v e l s i n the gauge tanks to the steady state condition. In measuring the pressure heads, the presence of a i r bubbles i n the f l e x i b l e tubing connected to the piezometric points w i l l g reatly a f f e c t the accuracy. Great care was taken to ensure that a l l a i r bubbles were removed p r i o r to taking any readings. E. Discharge Determination The discharge was determined from the weight of water d i s - charged within a c e r t a i n time i n t e r v a l , Duiring the experiment, discrepancies were found i n measuring the weight of water unless a s u f f i c i e n t l y long time i n t e r v a l was adopted. For a l l t e s t s , a time i n t e r v a l of approximately 300 seconds was required i n order to achieve an accurate discharge determination. The discharge and the v e l o c i t y head i n each pipe was obtained from the formulas as follows: i n which Q = discharge, i n c f s ; W = weight of water, i n l b s ; t = time 3 i n t e r v a l , i n sees; w = u n i t weight of water, i n l b s / f t ; V = mean v e l o c i t y i n pipe, i n fps; h = v e l o c i t y head, i n f t ; and g = a c c e l - 2 eration of gravity, i n f t / s e c . Q = W / (t x w) (1) h = v (2) 18 CHAPTER II BASIC CONCEPTS RELATING TO HEAD LOSSES When water flows through a c losed conduit , c e r t a i n res is tances are created which oppose the motion, and depend upon the geometrical form of the c o n d u i t . They are caused by f r i c t i o n , changes i n flow d i r e c t i o n and cross s e c t i o n , merging and d i v i d i n g of flows and from other causes. K i n e t i c energy i s converted i n t o heat energy through the a c t i o n of turbulence . As far as the head losses at the junct ions f o r d i v i d e d flows i n branched pipe systems are concerned, the c o n t i n u i t y , momentum, and energy equations, and the f r e e - s t r e a m l i n e theory have been a p p l i e d to evaluate the approximate head losses for flow through b i f u r c a t i o n s and t r i f u r c a t i o n s ' (^), (16)^ Accurate determination of such head losses , i f r e q u i r e d , can only be obtained by model t e s t s . In t h i s study, the model tests of the head losses r e s u l t i n g from the flow through both a wye and a manifold were based on the energy equation of B e r n o u l l i for the one-dimensional c o n d i t i o n . These losses were c a l c u l a t e d under the f o l l o w i n g assumptions: (1) the mean v e l o c i t y at each c r o s s - s e c t i o n i s representat ive of the flow at that s e c t i o n . (2) the flow passing through the c r o s s - s e c t i o n where the measure- ment of pressure head was made i s i n steady and i r r o t a t i o n a l motion. (3) the l o n g i t u d i n a l axis of the whole system is h o r i z o n t a l . 19 2.1 FORM LOSSES OF WYES The energy equation of Be r n o u l l i f o r the one-dimensional con- d i t i o n states that the t o t a l head -- consisting of the sum of the v e l o c i t y head, pressure head and geometric head of the f l u i d -- above an a r b i t r a r y horizontal reference plane must be equal to that above the same reference plane at any successive section, plus the i n t e r - vening head losses . For a horizontal wye arrangement as shown i n Figure 1-3, the energy gradient l i n e s are extrapolated to the theo- r e t i c a l centre of the wye on the basis of a sudden t r a n s i t i o n at that point. (See Figure I I - l ) . The form loss of the wye i s determined as the difference between the energy gradient l i n e s upstream and down- stream of the wye measured at i t s centre. This form l o s s , ^ h , can be expressed from the energy equation as follows: h + h = h , + h L + d h + L + L , --- (3) pm vm pb vb fm fb or - h - - h p + <hvm " hvb> " ( h f m + V - — - ( 4 ) i n which h , h and h_ = piezometric head, v e l o c i t y head and skin pm vm rm f r i c t i o n loss of head i n the main pipe, i n f t ; *Vb an^ ^fb = piezometric head, v e l o c i t y head and skin f r i c t i o n loss of head i n one of the branch pipes, i n f t ; and ̂ h = h - h , = difference of r r ' ' p pm pb piezometric heads, i n f t . The wye loss c o e f f i c i e n t , k, based on the v e l o c i t y head i n the main pipe can be expressed as vm 20 When the v e l o c i t y , the skin f r i c t i o n loss and the pressure head at the piezometric r i n g on each pipe for a p a r t i c u l a r discharge are known, the form loss of a wye can be obtained from Equation (4). The loss c o e f f i c i e n t of the wye i s determined from Equation (5). The distance from the t h e o r e t i c a l centre of each wye to the piezometric rings on the main and branch pipes i s tabulated i n Table I I - l . The skin f r i c t i o n losses f o r the p a r t i c u l a r lengths from S to T i n the main pipe and from T to or i n the branch pipes are determined i n Section 4.1. The pressure heads at the piezometric rings are obtained from the steady water l e v e l s of the three gauge tanks connected to the manometers. The v e l o c i t y heads are obtained from Equation (2) . 2.2 FORM LOSSES OF MANIFOLDS For a manifold as shown i n Figure II-2, the energy equation can be derived i n the same way as Equation (3) where ^ h i s the form loss of a manifold instead of a wye. From Equation (4), the form loss of a manifold i s obtained. The manifold loss c o e f f i c i e n t , k, based on the v e l o c i t y head i n the main pipe i s obtained from Equation (5). The distance from the t h e o r e t i c a l centre of each wye to the piezometric rings on the main and branch pipes f o r manifold arrange- ment i s given i n Table II-2. 2.3 HYDRAULIC POWER LOSSES IN WYE AND MANIFOLD ARRANGEMENTS In most instances, the determination of the hydraulic power loss r e s u l t i n g from the passing of flow from the main pipe into the branch pipes i s necessary. This study was made to ascertain the 21 relationship between the hydraulic power loss and the proportional flow of water through the branches of the wye and manifold arrange- ments . The hydraulic power loss in a branched pipe system can be expressed as P = w (Q ^h (6) v r r u 1 in which P^ = hydraulic power loss, in ft-lb/sec; and = dis- charges in the right and l e f t branches respectively, in cfs; and ^h^ and h^ = form losses of wye or manifold resulting from the flow passing through the wye or manifold into the right and l e f t branches respectively, in f t . The above equation can be made more useful for direct applica- tion by reducing a l l the terms of i t into a dimensionless expression. The hydraulic power in the main pipe, P , is expressed as P = w Q h (7) m m vm Then Equation (6) can be converted into a dimensionless form as p = k r Qr_+ k i 5i_ (8) m̂ % i m̂ in which p = hydraulic power loss in dimensionless form; = dis- charge in the main pipe, in cfs; and and k^ = the coefficient of -^h^, and of ^ h^ based on the velocity head in the main pipe. 22 CHAPTER III EXPERIMENTAL INVESTIGATIONS 3.1 PRELIMINARY INVESTIGATION In the i n i t i a l stage of the study an experimental model was set up and subsequently modified to meet c e r t a i n proposed hydraulic requirements as follows: A. Symmetrical V e l o c i t y - D i s t r i b u t i o n i n Main Pipe Close to Wye Horizontal v e l o c i t y traverse tests were performed across the main pipe at a section about 6 inches upstream from the wye. These tests were made by Ahmed who provided maximum discharge of 0.92 cfs i n one branch with the other branch completely closed. A f t e r the length of the i n f l u e n t main pipe was increased to 75 pipe- diameters and two flow straighteners i n s t a l l e d i n the upstream main pipe, the t e s t showed that a symmetrical v e l o c i t y - d i s t r i b u t i o n about the l o n g i t u d i n a l axis of the main pipe across the t e s t section was achieved. Since the symmetrical v e l o c i t y - d i s t r i b u t i o n was demonstrated, the flow patterns for a symmetrical flow condition i n each of the branch pipes would have to be i d e n t i c a l . B. C h a r a c t e r i s t i c V e l o c i t y - D i s t r i b u t i o n at Piezometric Stations at Branch Pipes The disturbance a r i s i n g from the flow passing through a wye or manifold can influence pressure readings f o r some distance down- stream of the wye or manifold. Experience has shown that a minimum distance of 25 pipe-diameters i s necessary for gradual modification of the v e l o c i t y d i s t r i b u t i o n to a c h a r a c t e r i s t i c form through the remainder of the st r a i g h t pipe. Therefore, a piezometric r i n g was provided at the downstream end of each branch pipe, r e s u l t i n g i n a length-diameter r a t i o of approximately 30. C. Condition of Discharges into Free Atmosphere at Outlets Large troughs were provided at the outlets of the branch pipes to ensure atmospheric pressure at the o r i f i c e s . 3.2 FLOW PATTERNS A few of many possible flow patterns under d i f f e r e n t flow con- d i t i o n s , i . e . , symmetrical, unsymmetrical and one-leg flows, are shown i n Figures I I I - l and III-2. I t was observed that the region of the eddies formed i n a wye or manifold was influenced d i r e c t l y by the discharge, the v e l o c i t y , the size of the t i e - r o d , the subtending angle of the wye and the proportional flow of water through the branches. 24 CHAPTER IV EXPERIMENTAL PROCEDURES 4.1 DETERMINATION OF SKIN FRICTION LOSSES IN MAIN PIPE AND BRANCH PIPES The form loss of a wye or manifold was obtained from Equation (4) with the skin f r i c t i o n losses i n the main and branch pipes determined i n advance. For any given lengths, the skin f r i c t i o n losses i n e i t h e r the main pipe or each branch pipe under various d i s - charges were determined by i n t e r p o l a t i o n and by proportion from the empirical equations as derived below. A. Skin F r i c t i o n Loss In Main Pipe The i n s t a l l a t i o n , as shown i n Firuge 1-3, was used to determine the skin f r i c t i o n loss i n the main pipe for length SS^ (3.375 f t . ) . Two of the gauge tanks were connected to the piezometric rings at the cross-sections of S and S^. (See Figure 1-3). As the v e l o c i t y heads at these sections were equal, no velocity-head cor- r e c t i o n was required, therefore the difference of pressure heads between these two sections indicated the skin f r i c t i o n l o s s . The main pipe was tested with various discharges ranging from 0.32 to 1.50 cfs and the r e s u l t s tabulated i n Table IV-1. When the r e s u l t s were p l o t t e d on a log-log scale as shown i n Figure IV-1, a l i n e a r r e l a t i o n between the skin f r i c t i o n loss and the corresponding discharge was detected. Hence, by using the method of l e a s t squares f o r curve f i t t i n g , the following empirical equation was obtained. 25 h f ( S S l ) = ° ' 0 8 2 5 Q 1 , 7 8 9 ( 9 ) i n which h , x = skin f r i c t i o n loss i n the main pipe f o r length t (,bb̂ / S S 1 } i n f t . B. Skin F r i c t i o n Losses i n Branch Pipes The experimental set-up f o r the determination of the skin f r i c t i o n l o s s , f o r length BB^ (9.0 f t . ) , i n each of the branch pipes i s shown i n Figure IV-2. The tests were conducted s i m i l a r l y to those which determined the skin f r i c t i o n loss i n the main pipe. Correction f o r v e l o c i t y head between the upstream piezometric r i n g of the i n l e t pipe and the downstream piezometric r i n g of the branch pipe was made in the computations. Each branch pipe was tested with various discharges ranging from 0.32 to 0.75 cfs and the r e s u l t s tabulated i n Table IV-2. When the r e s u l t s were p l o t t e d on log-log graph papers as shown i n Figures IV-3 and IV-4, s i m i l a r l i n e a r r e l a t i o n s h i p s for each branch pipe as for the main pipe were found. By using l e a s t squares curve f i t t i n g , the empirical equations f o r the f r i c t i o n loss i n each branch pipe were obtained as follows: (1) For the r i g h t branch pipe (Sections B and D) h f r = 1.0696 Q 1 , 8 2 1 (10) (2) For the l e f t branch pipe (Sections A and C) h £ 1 = 1.0667 Q 1 , 8 1 1 (11) i n which h.. and h ~ = skin f r i c t i o n losses i n the r i g h t and l e f t f r f 1 branches pipe r e s p e c t i v e l y f or length B.. Bj (9.0 f t . ) , i n f t . 26 4.2 SEQUENCE OF EXPERIMENT In each t e s t i n g arrangement, a ser ies of head loss tests was made to determine the losses i n the wye or manifold under d i f f e r e n t f low c o n d i t i o n s . The tests were s t a r t e d with symmetrical f low c o n d i t i o n . O r i - f i c e s of equal s i z e were placed at the o u t l e t s of the branch pipes and the c o n t r o l va lve was then adjusted to the required discharge . For each tes t the discharge i n the main pipe was set at approximately 1.50, 1.10, 0.92, 0.75, 0.50 and 0.32 c fs i n t u r n . When the water l e v e l s i n the gauge tanks became constant , the measurement of combined discharge , r i g h t and l e f t branch discharges , the measurement of pressure head from the gauge readings and the measurement of water temperature were taken. The tests of unsymmetrical flow condi t ions were c a r r i e d out n e x t . O r i f i c e s of d i f f e r e n t s i z e s were placed to c o n t r o l the propor- t i o n a l flow of water through each of the branches . The r a t i o of branch discharge to the main pipe discharge v a r i e d from 0 to 100%. For the purpose of comparing the form losses of wyes and manifo lds , a constant discharge i n the main pipe was maintained at 0.75 cfs f o r the t e s t i n g arrangements with the subtending angles .of 9 0 ° and 6 0 ° , and 0.92 c f s f o r that with the subtending angle of 4 5 ° . Measurements were then taken as i n the foregoing paragraph. The tests of one- leg flow c o n d i t i o n s , where one branch was com- p l e t e l y blocked o f f and an o r i f i c e of appropriate s i z e was placed at the o u t l e t of the other branch, were f i n a l l y conducted. The discharge i n the open branch v a r i e d from 0.32 to 0.92 c f s . 27 CHAPTER V RESULTS AND CONCLUSIONS 5.1 RESULTS A. Form Losses of Wyes Tables V - l to V-10 give the hydraulic computations of the form losses and loss c o e f f i c i e n t s f o r the 90°, 60° and 45° wyes i n the wye arrangements: Tables V - l to V-5 give the computations f o r the 90° wye without any t i e - r o d , and with the TR1, TR2, TR3 and TR4 tie-rods placed i n turn at the t h e o r e t i c a l centre of the wye r e s p e c t i v e l y . Tables V-6 to V-9 give the computations f o r the 60° wye without any t i e - r o d , and with the TR2, TR3. and TR4 t i e - rods r e s p e c t i v e l y . Table V-10 gives the computation f o r the 45° wye without any t i e - r o d . The r e s u l t s of the above computations are plo t t e d i n Figures V - l to V-9: Figures V - l , V-4 and V-7 show the form loss c o e f f i c i e n t vs. discharge under symmetrical flow conditions f o r the 90°, 60° and 45° wyes re s p e c t i v e l y . Figures V-2, V-5 and V-7 show the form loss c o e f f i c i e n t vs. discharge under one-leg flow conditions f o r the 90°, 60° and 45° wyes re s p e c t i v e l y . 28 Figures V-3, V-6 and V-8 show the form loss c o e f f i c i e n t vs. the r a t i o of branch discharge to the main discharge under unsymmetrical flow conditions f o r the 90°, 60° and 45° wyes res p e c t i v e l y . Figure V-9 shows the comparisons of the form loss c o e f f i c - ients (a) among the three wyes without any t i e - r o d , and (b) between the 90° and 60° wyes with the TR3 t i e - r o d , under unsymmetrical flow conditions. B. Form Losses of Manifolds Tables V - l l to V-15 give the hydraulic computations of the form losses and loss c o e f f i c i e n t s f o r the 90°, 60° and 45° manifolds i n the manifold arrangements: Tables V - l l , V-13 and V-15 give the computations for the 90°, 60° and 45° manifolds res p e c t i v e l y without any t i e - r o d . Tables V-12 and V-14 give the computations f o r the 90° and 60° manifolds r e s p e c t i v e l y with the TR3 t i e - r o d . The r e s u l t s of the above computations are p l o t t e d i n Figures V-10 to V-14 under symmetrical, one-leg and unsymmetrical flow conditions r e s p e c t i v e l y . Figures V-13 and V-14 show the comparisons of wye and mani- f o l d loss c o e f f i c i e n t s without any t i e - r o d , and with the TR3 t i e - r o d under unsymmetrical flow conditions r e s p e c t i v e l y . The same coordinate systems f o r p l o t t i n g have been adopted as i n Section 5.1.A. 29 C. Hydraulic Power Losses i n Wye and Manifold Arrangements Tables V-16 and V-17 give the computation of the hydraulic power losses f o r the wye and manifold arrangements r e s p e c t i v e l y . Figures V-15 and V-16 show the hydraulic power loss vs. the r a t i o of branch discharge to the main discharge f o r both arrangements r e s p e c t i v e l y . 5.2 CONCLUSIONS (1) The form loss c o e f f i c i e n t of a wye or manifold i s a function of the proportional flow of water through the branches, the si z e of the t i e - r o d used and the subtending angle of the wye. (2) Separate head loss tests f o r wyes, manifolds and elbows indicated that the form loss of a manifold -- co n s i s t i n g of a wye and two elbows -- i s less than the sum of the i n d i v i d u a l form losses of the wye and elbows. (3) An i n t e r n a l t i e - r o d placed at the t h e o r e t i c a l centre of a wye tends to create considerable pressure f l u c t u a t i o n s and disturbance i n the downstream branched flow, as well as increasing the form l o s s . (4) The form loss c o e f f i c i e n t of a wye or manifold i s not n e c e s s a r i l y a minimum f o r a symmetrical flow condition. (5) For a symmetrical flow condition, the form loss c o e f f i c i e n t of a wye or manifold i s not greatly affected by the amount of d i s - charge. The form loss c o e f f i c i e n t increases as the subtending angle of the wye and the si z e of the t i e - r o d are increased. The system without any t i e - r o d i n either the 45° wye or the 45° manifold had the lowest form loss c o e f f i c i e n t . 30 (6) For a one-leg flow condition, due to the turbulence assoc- iated with eddies in the closed branch of a wye or manifold, the head loss in the closed branch is generally greater than the head loss in the open branch. (7) A l l the tests indicate that a one-leg flow condition is the most inefficient. (8) For an unsymmetrical flow condition, the form loss coeffic- ient of a wye or manifold is greatly affected by the proportional flow of water through the branches and the size of the tie-rod. For any fixed ratio of branch discharge to the main discharge, the form loss coefficient increases as the size of the tie-rod is increased. (9) For an unsymmetrical flow condition in a wye or manifold without any tie-rod, the form loss coefficient is a minimum when the ratio of branch discharge to the main discharge is approximately 0.6. Under the same flow condition with a tie-rod, the form loss coeffic- ient is a minimum when the ratio of branch discharge to the main discharge is approximately 0.4. (10) Referring to Figures V-13 and V-14, the curves of form loss coefficient vs. discharge ratio obtained for both a wye and a manifold are similar under the conditions that (1) no tie-rod is used in either the wye or manifold; (2) i f a tie-rod be used, i t shall be identical in both arrangements; and (3) there shall be an identical subtending angle of the wye. 31 APPENDIX HEAD LOSSES IN ELBOWS The head loss i n an elbow i s considered herein to be the loss i n excess of that i n a s t r a i g h t pipe of equal length. I t i s prim- a r i l y caused by the induced s p i r a l motions of flow i n the elbow which are probably independent of i t s length and create a considerable disturbance downstream. The motion around the elbow tends to take on the c h a r a c t e r i s t i c s of a free vortex having a larger v e l o c i t y at the ins i d e of the elbow than that at the outside. Correspondingly, the pressure at the inside i s less than that at the outside. At the downstream end of the elbow, the v e l o c i t y d i s t r i b u t i o n depends on the flow i n the elbow. This d i s t r i b u t i o n changes gradually i n the downstream s t r a i g h t pipe u n t i l i t assumes the c h a r a c t e r i s t i c form of that i n a s t r a i g h t pipe. This study i s mainly concerned with the head losses of the elbows which are used to construct the manifolds. The purpose of the study i s to determine the head losses i n the elbows alone. From the set-up shown i n Figure A-2, f o r horizontal piping, the l o c a l i z e d elbow loss can be expressed from the energy equation as follows: h + h v i . = h, + h , + Ah + h_. + h 1 b vb E f i fb (12) or ^h. = A h + (h . - h ) - (h_. + h _ ) E p v i vb f i fb (13) in which A L = head loss in an elbow, in f t ; h ., h . and h... = E p i ' v i f i piezometric head, velocity head and skin f r i c t i o n loss of head in the upstream inlet pipe, in f t ; and hp^j n v ^ a n c* = piezometric head, velocity head and skin f r i c t i o n loss of head in the downstream straight pipe, in f t . The elbow loss coefficient, k^, based on the mean velocity head in the upstream pipe is thus expressed by A h "E - — 5 — (14) V ^ / 2g in which « velocity in the upstream pipe. Table A-l gives the distance from the theoretical centre of each elbow to both upstream and downstream piezometric rings. The downstream piezometric ring has a distance of approximately 30 pipe- diameters downstream of the elbow. The results of the tests are tabulated in Tables A-2, A-3 and A-4 for 45 , 30 and 22-1/2 elbows respectively. The loss coeffic- ients of the elbows versus discharges are plotted in Figure A-3. 33 BIBLIOGRAPHY Vogel, G., "UNTERSUCHUNGEN UBER DEN VERLUST IN RECHTWINKLIGEN ROHRVERZWEIGUNGEN", Mitt, des Hydr. I n s t i t u t s der Technischen Hochschule, Munchen, No. 2, 1928. (Investigations of the Losses i n Right Angle Piping B i f u r c a - tions .) Thoma, D. and Collaborator, "Transactions of the Munich Hydraulic I n s t i t u t e " , B u l l e t i n 3, Translated by A.S.M.E., 1935. Cardel, A., "LES PERTES DE CHARGE DANS LES ECOULEMENTS AU TRAVERS DE BRANCHEMENTS EN TE", B u l l e t i n Techique de l a Suisse Romanda, Nos. 9 & 10, 1957. (The Loss of Head i n the Flow through Tee Branches.) Marchetti, M. and Noseda, G., "PERDITE DI CARICO NELLE BIFOR- CAZIONI SIMMETRICHE A DIAMETRO CONSTANTE, DELLE CONDOTTE FORZATE", L1ENERGIA ELLETTRICA NO. 4, 1960. (Loss of Head i n Symmetrical Bifurcations of Constant Diameter i n a Penstock Conduit.) F r i t j o f Salvesen, "Hydraulic Losses i n Branchpipes", The Water Power Laboratory, The Technical University of Norway, Oct. 1962. Ahmed, S., "Head Loss i n Symmetrical B i f u r c a t i o n s " , Master's Thesis, University of B r i t i s h Columbia, 1965. Herakovich, Carl T., and Otts, J.V., " C h a r a c t e r i s t i c s of Flow through Symmetrical L a t e r a l s " , Report No. 13, Studies i n Engrg. Mechanics, Center for Research i n Engrg. Science, Univ. of Kansas (Laurence), 1962. (8) Karake, S. and Ruff, T.F., " F i n a l Report of Hydraulic Model Studies for Diversion, Power and I r r i g a t i o n Tunnels", C i v i l Engineering Dept., Colorado State Univ., Jan. 1965. (9) Gladwell, J.S. and Tinney, E.R., "Hydraulic Studies of Large Penstock T r i f u r c a t i o n " , Journal of the Power D i v i s i o n , ASCE, V o l . 91, No. P01, 1965. (10) Gladwell, J.S. and Tinney, E.R., "Round Butte Penstock T r i - f u r c a t i o n " , B u l l e t i n 260, Washington State I n s t i t u t e of Tech- nology, Div. of I n d u s t r i a l Research, Washington State Univ., 1962. (11) Gladwell, J.S., Tinney, E.R. and Kreuzer, H., "The Round Butte Penstock T r i f u r c a t i o n Tie-Bar", Research Report No. 63/9-80, Washington State Univ., 1963. (12) Bier , P.J., "Welded Steel Penstocks, Design and Construction", Engineering Monography No. 3, U.S. Bureau of Reclamation. (13) Favre, H., "On the Law which Govern the Movement of Fluids i n Conduits having L a t e r a l Abductions", Rev. Univ. Minnes., 1937. (14) McNown, J.S., "Mechanics of Manifold Flow", Transactions of ASCE, V o l . 119, 1954. (15) McNown, J.S. and Hsu, E.Y., "Application of Conformal Mapping to Divided Flow", Proceedings, Midwestern Conference on F l u i d Dynamics (ed. by J.W. Edwards), Michigan, 1951. (16) Lakshmana Rao, N.S., Syamala Rao, B.C. and Ramaswamy, R.I., "Pressure Losses at T r i f u r c a t i o n s i n Closed Conduits", Journal of the Hydraulics D i v i s i o n , ASCE, V o l . 93, No. HY3, May 1967. (17) Freeman, J.R., "The Flow of Water i n Pipes and Pipe F i t t i n g s " , Published by A.S.M.E., 1941. 35 (18) Y a r n e l l , D.L. and Nagler, F.A., "Flow of Water Around Bends i n Pipes", Transactions of ASCE, V o l . 100, 1935. (19) A.S.M.E., " F l u i d Meters", 4th ed., 1937. (20) Streeter, V.L., " F l u i d Mechanics", McGraw-Hill, 1962. (21) Jaeger, C , "Engineering F l u i d Mechanics", McGraw-Hill, 1962. (22) Rouse, H., "Advanced Mechanics of F l u i d s " , John Wiley, 1959. (23) King, H.W. and Brater, E.F., "Handbook of Hydraulics", 4th ed., McGraw-Hill, 1954. (24) Bakhmetefv, B.A., "The Mechanics of Turbulent Flow", Princeton Univ. Press, 1941. 36 TABLE 1-1 Areas of Main, Branch and I n l e t Pipes D e s c r i p t i o n Mean Diameter (inch) Mean Area ( s q . f t . ) Diameter at Piezometric Ring (inch) Area at Piezometric Ring ( s q . f t . ) Main Pipe 5.252 0.1503 5.251 0.1503 Right Branch 3.746 0.0764 3.750 0.0766 L e f t Branch 3.750 0.0766 3.748 0.0766 I n l e t Pipe 3.734 0.0759 TABLE 1-2 O r i f i c e Arrangement Numerical D e s i g - n a t i o n of o r i f i c e External Diameter (inch) In ternal Diameter (inch) Remark X 3.720 3.622 ) Rounded edge 1 3.720 3.300 ) o r i f i c e s 2 3.720 3.175 3 3.720 2.913 4 3.720 2.749 5 3.720 2.490 6 3.720 2.000 7 3.720 1.342 8 3.720 0.840 9 3.720 0.542 37 TABLE II-1 Distance from Theoretical Centre of Wyes to Piezometric Rings on Main and Branch Pipes * (For Wye Arrangement) P a r t i c u l a r s Distance Distance Distance Distance Distance Distance SS. S.T ST TS, or TS 0 S..D.. TD. or TD„ 4 4 1 2 1 1 1 2 or S 2D 2 ( f t ) ( f t ) ( f t ) ( f t ) ( f t ) ( f t ) 90° Wye 0.500 0.125 0.625 0.374 8.833 9.207 60° Wye 0.500 0.083 0.583 0.497 8.833 9.330 45° Wye 0.500 0.060 0.560 0.608 8.833 9.441 * See Figure I I - l TABLE II-2 Distance from Theoretical Centre of Wyes to Piezometric Rings on Main and Branch Pipes ** (For Manifold Arrangement) P a r t i c u l a r s Distance Distance Distance Distance Distance Distance ST TSj^ or TS 2 S 1 C 1 C 1 F 1 F D 1 1 T C 1 D 1 or S 2C 2 or C 2 F 2 or F 2 D 2 or TC 2D 2 ( f t ) ( f t ) ( f t ) ( f t ) ( f t ) ( f t ) 90° Manifold 0.625 0.374 0.641 0.500 8.833 10.348 60° Manifold 0.583 0.497 0.333 0.333 8.833 9.996 45° Manifold 0.560 0.608 0.370 0.238 8.833 10.049 ** See Figure II-2. OA Ul -P- O J to h-> h-» >-> I-1 I-1 O Ul VO VO VO Ui O O O O O O O o O O O O O o O O O O J O J Ul Ul Ul Ui O J O J ho ho O J O J ho ho o o O J O J ho ho oo oo hO hO vO vo vo vo ho O J I O w 4>4> Ui O J O J Ui UlUi OJ OJ OJ . ho t-1 Ul ho hO ho vO Ul I-1 o 00 VO hO ho i> Ul Ul Ul OA Ov OA OA OA OA OA N> - J K i ho OA h o - ^ j IO - J o • i — ' • o o • • . . OJ OOJ OOJ O O J U i OJUi hO N> hO O hO 0 O A O A ho - J OJ Ui hO O o o o o l-> 0J U l - J VO b U l OA OJ o U l to VO to VO o h- 1 00 VO oo H-1 o o I-1 o I-1 hO bo 00 vO h-> to VO -P- U l o VO vO o 00 o VO o i - 1 M to o I-1 i> b b o OJ OJ 00 vO to I-1 OJ o OA VO vO to o O o o o o o hO ho to to to hO vO I-1 I-1 I-1 o o o o o o o o o o o o . • • • . • I-1 o o o o o o o o o o o o o o o o o o o o o o o o o . • . • • I-1 o o o o o I-1 t-> IO •p- vO 00 to •p- VO ^ 1 o o 1—1 ho to to -p- . • . • h-1 VO OJ o -p- VO o to OJ vO o OA t-1 U l ho Test No. Weight of Water from Main Pipe (lbs .) Time Inte r v a l (sees) Ave. Time Interval (sees) Temp, i n °F & S p e c i f i c Wt. of Water ( l b / c u . f t . ) Discharge (cfs) Hook Gauge Reading i n Upstream Tank ( f t . ) Hook Gauge Reading i n Downstream Tank ( f t . ) Vernier Correction ( f t . ) V e l o c i t y Head Correction ( f t . ) F r i c t i o n Loss ( f t . ) Reynold's Number (xlO ) 8£ Left Branch -p- O N o o VO O O O ro o o o ui o o o OJ U l U l U l U ) u> u> U l U ) u> u> U l U ) U l •vl v j - J - J VO VO ro ro 00 oo U i U l vg v j ro ro ui U l ro ro oo 00 00 oo •p- U l -v i vO VO v j •p- -p- •P- O N to ro •P- •P- 00 o ro ro U l U l 00 00 w u> u> u> u> U ) U l u> - v l v l VO ro oo U l -v l ro u> ro 00 00 •P- VO • • • • • • • • •p- ro •P- VD ro U l oo O N ro o> • oo ui o ro O N ro O N . oo u> o ro O N O N ro oo U l U l M o O N ro O N • oo ui o ro o o o o o o o o • * • • • • • • U l -p - VJ I-1 •p- U i VJ vO oo oo U l VO o o U l 00 00 •p- U l I-1 -p - VJ -p - Right Branch O N o o V O o o o ro o o o U l o o o ON ON ON ON ON ON r o o > M O O r o o o M O N . 00 00 U l O U l U l W U l U l o r o M o i - 1 o r o r o I-1 i - 1 t - 1 r o i— 1 « • • • • • • • M v j o -vi vO o o oo -P- o o VD O N o VO o O N O N 00 -P- VO t~* O N U l r o o r o r o I-1 w «vl vO i > i - 1 b b o U l U l r o r o i - 1 o U) i-> h-» r o -p- 00 U l o o O o o o o o o • • * • • • • • r o r o r o r o r o ho r o r o t-> i - 1 i - 1 I-1 M o o o o o o o O o o o o o o o o b o o o o b o b o o o i-1 o o I-1 r o i-> U l oo VD r o oo U l O N o o o O o o o o o i - 1 r o U i o r o U l O N U l VD VD vO U i o O N o •P- vO u> •P- r o i - 1 o l - » i - 1 r o o M r o -vl oo •vj U l VO v j U l r o -P- r o r o I-1 •p- Ui U l O N 00 Description Weight of Water from Main Pipe (lbs.) Time Interval (sees) Ave. Time Interval (sees) Temp, in F & Specific Wt. of Water (lb/cu.ft.) Discharge (cfs) Hook Gauge Reading in Upstream Tank (ft.) Hook Gauge Reading in Downstream Tank (ft.) Vernier Correction (ft.) Velocity Head Correction (ft.) Friction Loss (ft.) Reynold's Number (xlO ) 6£ 1 * o. «. ... I - s : J ; J ; O r l f l c a to. 111 ! I I 1 1 i i I I I I 1 I I I i 1 I I I I I i I f r o i * * Hole rip.! mm s S S S s s • - i, i ^ mm i. b b b. c mm SISSIES* S S s s a s 0. b b 1- b b - t i l ~ S s *- '» 3 s S S - s - 5 5 s - s - 5 £ * ~ s a i n s s s c - - S £ s S o - 5 g s if - s *—<•"••> u S 2. £ u I £ t T » p . » C U r . In °F .ao Specif ic W . lsht of W. t . r ( l b . / c o . f t . ) 11I I 1 1 1 1 I i I I 111 I I I 111 I i 1 i 1 i 1 o s 1 Op.tt.«.*T.»k ( f t f ) r i 1 I i i I i 5 I i 5 I i I i I i I I I I I i I i I ~<-> i i i i i i i i I I I 5 1 I 11 11 or Hi La Pip* & U f t Broach I I I 1 I I 11 i I i i I I I i s P i p . for Uagch 5.J75 I t . i i i i I I I i I F r i c t i o n U i . ( f t . ) Io r k l o P i p . for UaBta ST I i II 11 I I I I I I I 3 11 11 P r l c t l o a U . . . ( f t . ) to I l . h t or U f t Broach for Uagtb 9.0 f t . I i 11 11 11 I I II I I 11 11 P r l c t l o a Loo. ( f c . ) l a Rl s hc or U f t Ironch for Uagch T O , . , ™ , 11 II 11 11 I I I I I I 11 J 1 T o t . l P r l c t l o a U i . ( f t . ) i i i I 5 I I Velocity l a PkUn P i p . ( f t / u c ) i I i 1 I I I i I y . l o c l c ; B u d l a rfclo P i p . ( fc . ) I I II I I 1 I II 11 i i 11 11 • V . U c t t y l a I t i h c or U f t Ir .aca ( f t / . . e ) i I I i I I 1 i. I I 11 I I 11 I 1 Voloclt? Boo. l a l l j h t or U f t Broach ( f t . ) I I I I 1 1 II I I II I I. ? ? § : II F o r . U . 0 ( f t . ) I i I I I I 11 111 H ! ? ? ? = I | 11 i For . U * . C M f f l c U a t i = ^ b S fc s° i fe 2 ? s i l l = 5 b fc fc fc 07 s • = s 5. z s - T e . t S o . I " * - i : S " * ; ¥ -o> r O r i f i c e Mo. o i l . i i o i 8 1 I o o o 1 i o S o s s s 8 8 8 I ! I I I I I I I - Weight o f Hater ( l b . . ) f r o n H . M»in P i p e ; R . R i g h t B r . a c h ; L . l e f t B t . n c h u « •» - » o . V i » • „ b o b b •M u ~ '» b SSS555 T i o e I n t . r v . l ( . . c s ) . s jg . § s *o> b. . S g , s s , ' s s s I s s 2 S g 3 s 2 5 = s - - s I 5 L. « i- - 5 * 5 *. s *. I * £ *. S p e c i f i c Weight of W . t e r ( l b . / c u . f t . ) 0 .2 9 1 0 .2 9 3 0 .0 0 0  111 1 11 1 s 1 111 111 i l l 111 5 1 1 D i s c h a r g e ( c f i ) |  0 .7 2 8 £ 1 I 1 § S i 1 - Kook Ceuge Reading In Upstream Tank ( f t . ) i s i 1 - Hook Cauge Reading In C e n t r a l tank ( f t . ) i £ o 3 o 5 5 1 s 1 Hook Cauge Reading i n 0 o v n s t r e a » Tank ( f t . ) s I 1 1 o 5 1 o 5 S I E V e r n i e r C o r r e c t i o n ( f t . 0 .3 0 6  -0 .0 2 5  A o 1 5 A _ 1 g Is- i ~ S S S i I 1 o o S 5 i i Pr«tt«re Heed D i f f e r e n c e ( f t . ) or Main Pipe ft L e f t Branch H I i i I i i Z D i s c h a r g e f U c i o (Discharge In Branch P i p e / D i s c h a r g e In KB In Pipe) 0 .0 0 9  I I ! I 1 I I i s P r t e t t o n Loss ( f e . ) In Main Pipe f o r Length 3.375 f t . o 1 I 1 1 o s 5 1 o § 1 ; F r i c t i o n U I I ( f c . ) In Main Pipe f o r Length ST 0 .1 1 4 0 .0 0 0  0 o 1 i 0 o 1 s I 1 I I 1I I g s: f r i c t i o n Loss ( f t . ) In R i g h t or L e f t Branch f o r Length 9 .0 f t . 0 .1 1 7 0 .0 0 0  |  I 1 I 1 i 5 0 o 1 5 11 1 1 11 5 m e t : t o n Loss ( f t . ) In Right o r l e f t Branch f o r Length T D j or TD^ 0.118 0 .0 0 2  0 a 1 5 o a § j i 1 I I • 1 s I I 11 S T o t a l F r i c t i o n Loss ( f t . ) 1 i 1 i *• i i ** s s V e l o c i t y In Main Pipe ( f t / s e c ) ° = s I I 5 1 i s V e l o c i t y Head In Main Pipe ( f t . l i 1 s I 5 i 2 1 5 5 2 8 3 2 5 V e l o c i t y In R i g h t or L e f t Branch ( f t / s e c ) o o 8 s 1 i 0 >- • 1 § I £ o © 2 S 1 s i I o o § 1 S V e l o c i t y Head In Right or L e f t Branch ( f t . ) 1 i I I o o o o s s o o 2 § 11 I I 2 P o m L o s . ( f t . ) I 1 1 1 11 1 5 5 s o o 5 I B (Average) ^ ^ ^ S S § 1 S 5 O M — 8 2 k O M ** 8 2 b O M M 8 S 5 s s '= K S S bis O W s s ; S R e y n o l d ' s Nuober ( x l O 5 ) :T17 42 ( t0I») "°»>« t . p i o u i . , * 3 2 2 !! s 5 s « » S 5 5 . = 8 *. 2 2 2 .. ~ o IS :• 2 5 2 2 au.ioijjoco (0 .1 7 *)  0. 17 7 , 0 .1 7 0 \\\ 1 s s (0.1 7 8 ) 0 .1 7 0 1 £ 3 e o o • !ss s s SS SS < J J ) . . o i U O J I I S s S 5 I s S! I s IS SS 3 S (•al) i p o . J J j | r i JO § s 2 S s s S1 !• S 5 I S ! 5 ! JO ml , ! 01 i j j o o i . i S i. s s M ll § s 3 s- I s s S S I S jj s s <• .SS SS SS s s S! ss S! ! ! •„ J. 'oi aoj i p o i j g . ajoq » S u l u Ol (-1J) f l O l OOJ331JJ IS \ \ s s s s ! ! IS SS S! S! •3) 0'6 «J»»»1 J o , w i X I JO i q t n o, < J J ) ••«! o o i i a u i S I . ss ss ss s s 11 IS S! SI IS vatD»i JO) »dlj = 1 ! s ! ! ! S ! ! •3; Sit'C JOJ aou ! I s ! ! ! ! S S s s S S s s = IS SS ss s s s s SS M < • - — I s s s s s S s s s J § ! s I S S n o" - i 5 1 ! I § s s - s S s s s ! \\\ 5 S I sss s s s IS S sss SSS SSI SSI <•>»•«>/•«> J»J»« JO 3l|»l»J| ' " l ^ S <• •» 3 • \ * 3 * 3 = 3 * 3 ^3 •«§ » s a 3 ill I I I = s? s s S s s , ; ; s s s -s s s s - -5 K § iii iSi - iiiiia ssSSSS mm sii i i i • ° =>-•-. -a S 5-588 °. -. s s s s s s 5555'i'I iiiiii IqoooJB anSii 't oi-H -H ~ J J CHI) i r o n jo J»t,.» - IIS I I I 111 1 1 1 I I I 1 1 1 I 1 1 I I § I H o« mjiJo : s : s : i : 2 •o» m i s 5 Ut z c o - Tett Ho. i - o r* ¥ -O f. X " o t- * » ¥ - ¥ " I - T " o» c- M Orifice No. * 7000 L 0 t- W X o § i H 11000 > 11000 L 0 ]  M 15000 1 R 15000 L 0 C* » X I H 15000 II 9000 L 6000 H 15000 R 10000 L 5000 t* n 3t M 15000 R 12000 L 3400 Height of Uticer (lbt) from H . H A I O Plpo; R.Right Branch; L.Lefc Branch 355.0 355.0 335.0 J55.0 314.9 .325.0 324.9 325.0 318.2 318.3 318.2 316.3 • O O O O sO sO >A vO 321.0 311.0 308.5 308.5 336.2 336.3 320.7 320.7 325.8 326 .0 313.3 313.3 320.8 ' 320.8 335.3 335.3 295.8 296.0 320.7 320.7 317.9 317.9 328.6 328.7 320.3 320.4 324.0 323.9 366.4 348.2 *- Time Intirvsl («ec») 355.0 355.0 324.95 324.93 318.25 318.25 320.9 320.9 321.0 308.3 336.25 320.7 325.9 313.3 320.8 335.3 295.9 320.7 317.9 328.65 a. w o **' 3 ii. - Average Time Interval (aect) o» fr « o M 0 o w o o OJ »o 5 **b 62.29 o> is M° Os Temperature In °F and Specific Weight of Water (lba/cujl) 0.317 0.317 0.000 0.445 0.445 0.000 0.555 0.555 0.000 0.750  i 0.750 0.000 o o o U* *- o o o b fr U 2 w 0.751 0.479 0.271 0.751 0.556 0.195 0.752 0.595 0.157 Discharge (cfi) b 8 8 fr 1.717 1.060 b s o oo fr OB Hook Gauge Reading In Upstream Tank (ft) o* V- ie o 1.863 i 1.277 2.216 fr a. sO Hook Gauge Reading In Central Tank (ft) o OJ o 1.212 0.370 2.092 | fr o< | 0.686 1.210 -0.067 5 Hook Gauge Reading in Downatream Tank (ft) 0.210 0.210 0.210 0.210 0.210 1 0.210 0.210 0.210 0.210 = Vernier Correction (ft) o o 2 8 a o o o» sO iS 1.062 -0.093 1.904 -0.167 0.375 0.127 o o 8 5 fr o o o 0.684 -0.122 1.061 -0.154 (Si Preaaure Head Difference (ft) between Main Pipe & Right Branch or Main Pipe & Left Branch 0.555 0.445 0.591 0.409 0.639 0.361 o o o> o o 0.792 0.208 = Discharge Ratio (Discharge In Branch Pipe/ Discharge in Main Pipe ) 0.011 | 1 © o 0.029 o 8 sO a 8 sO 0.049 o 8 •o o 8 0.050 Friction' Loss (ft), in Main Pipe for Length 3.375 ft. 0.002 0.004 O.OOS ; 0 .0 0 9  0.009 o 1 0.009 0.009 0.009 = Friction Loss (ft). In Main Pipe for Length ST 0.132 0.000 o o 8 S o a b '** 8 s o o O o» 5 4> 0.217 0.147 o o ro 4> o> u» 0.280 0.100 0.367 0.055 o o s z Friction Loss (ft). In Right or Left Branch for Length 9.0 ft. 0.133 0.000 0 o 1 o 0.375 0.000 o o 3 S S sO 0.222 ' 0.150 O O 10 sO 0.286 0.103 0.375 0.057 0.425 0.038 = Friction Loss (ft). In Right or Left Branch for Length TDj or TDj o o s = 0 o 1 X 0.360 O.OOS 0.658 0.009 0.231 0.159 O O X 3 0.295 0.112 o o ° a? o~< fr o .o 5 fr 0B Total Friction Loss (ft) o SO 0» o JO SO *> sO sO «> sO s fr b 3.001 sO Velocity in Main Pipe (ft/sec) 0.069 o O* 0.212 0.387 0.387 0.388 O 0.368 o o Velocity Head la Main Pipe (ft) a *> 5.807 0.000 7.246 0.000 9.795 0.000 u» *•> *• cr c- 2 3 6.251 3.561 7.252 2.551 OS Ul s Velocity In Right or Left Branch (ft/sec) 1 j 0.265 : 0.000 a o % t> 0.B1S 0.000 1.490 0.000 o o io " t > o o o o 0.607 0.195 0.817 0.101 o o B Velocity Head In Right or Left Branch (ft) 0.031 0.036 0.053 O.OTJ 0.078 0.113 o o — «- 0.072 0.059 0.069 0.063 0.069 0.074 0.071 0.099 0.080 0.122 3 Form Loss (ft) o . o S C o o 1> SO O "-J o o o> o 0.371 0.545 o o Ut CD 0.179 0.163 0.179 0.190 o o u? 5 fr M o o S s (Aversge) Form Loss Coefficient o — o b *v* >o 1.30 1.82 0.00 1.61 2.25 0.00 § s s !fc> C* •> i> H b b *— o a. o 2.11 2.19 0.77 s k •: S Reynold's Number ( nlO^ ) - - t . i t lb. 5 " 5 " Orifice No. i l l . I I i I I I i 1 I I I i i i I 1 I I I I 'i i i - W.l,ht of U.t.r (lb.) f r o . M. Main Pip.; «.»l,ht Br.nch; L.UfC Br.nch mm 552*5* v.bb v.. nun SSSSgg gggsss - M> O » ao u> SSggSS - Tl« Interval (.et.) ni 2 g g £ 5 5 b s - 5 5 5 s * ; 5 s g • is 5 5 S 5 - = s Ill 5 g 5 - 5 - - = % s ? ». o s s ? ? s "o s ? ? - Sp«ifle WetjJie of U«t«r (Ib./cu.ft.) i n I IS 1 s 1 1 1 1 i 11 'i i 1 ? ? p 5 £ ; ? p .-5 S I ? ? .-2 g s 5 s i 5 9 s ? 2 i p I 1 - .- I i i i 1 'i ? s I - p s i i 'i i 1 ! ? s 1 Oovn.tr.L T.nk'(lt) I I i 1 i 1 ? s i ? 5 = p .- 3 s s = i i I 1 9 9 E £ ? ° 11 11 Z 11 n z (Dl.ch.rje In Br.nch Pip./ I I i I I ? % I 1 ? s i Friction Lo.i ( f t ) . In ».ln Pip. for Length 3.375 f t . I i i 1 1 1 1 1 1 ; Prlctlon l o . . ( f t ) . In U l n Pip. 11 11 1 1 11 ? p i s 11 11 11 Friction lo.< ( f t ) . In «lght or L»ft Br.nch for Ungth 4.0 f t . I 1 15 i i 1 1 1 1 ? ? i i 11 11 11 = Friction Lo>. ( f t ) . In tight or U f t 15' 11 n 11 1 1 ? p 8 5 11 11 11 • Iot.1 Prlc t l o n l o t . (ft) •> ! *> s .*• 3 £ £ i I 1 v . l o c l t r In Main Pip. (ft/a.c) 1 1 1 I i 1 p 3 1 £ s Velocltr Bea4 In Main Pip. (ft) i t 1 § 1 5 i i s S i 1 S 3 i i 1 i lo'llght or Laft Jr.nth (fc/a.c) I § 1 £ i i 11 p ? 2 S 1 1 ? ? £ 5 1 1 I I 2 In llgbt or U f t Iranch (fc) 0.120 1 1 1 1 11 1 1 i s ? P t i i •; 1 1 S For. l o . . (It) l i 11 3 S. H i H i j i l u s ? p ? 1g1 111 s For. U>II Co.fflcl.ot ? ~ ~ = 3 3 5 = 5 p ? r a 3 8 9 9 r s * s r r » s a S 5 S i : 8 * 5 C- z O Teat Ho. s : sr : t r- x -» 2> «- t> JO wt l- t " w« r- + O r i f i c e No. r w ac o i i r* •• ae f » S o I i r * at o I I r* s> X «, 1 1 l - "D I 1- •» X 1 1 i r »• x *• — ut 1 1 § (- » X 11 i - WelfthE of Water (iba) froai H. Halo Pipe; 1.Right Branch; L . L c f t Branch . a* o <• 'o <0 O -0 O •> -S« •> <rf" *> *• TLtw Interval (aces) . « ? • g § * 2 . ? 5 WON s s s " O w " ? ? - Average Tlow Interval (ICCI) 1* ° s o o 0 » t> u> ° Z St - Temperatura In P and S p e c i f i c Weight of Water (lba/cu.ft) 0.364 0.364 0.000 o o o o o o § S 5 0 O O 1 £ £ o o o § S 5 0 0 0 — 5 ~* 0 0 0 U> «- -4 0 *• *• — 0 a> 0 0 0 3 u" S *• — t- 0 0 0 i s J Discharge (cfa) O o #- in o I p io - Hook Caugr Reading In Upatrean Tank (fc) i 5 o o s • 0 00 0 Hook Gauge Reading In Central Tank ( f t ) s> 's » o ? p b 5 0 Hook Caugf? Reading In O o v n i t r c u Tank ( f t ) o o O o o o o o o o 0 0 p 5 0 0 p 5 5 Vernier Correction ( f t ) 0 o 1 £ e> o o -» -4 XI a — 8 S p _— o •> 9 r* 5 ? p p 0 0 8 £ — <0 0 p '— a> : « 5 8 = Pressure Read Difference ( f t ) between Main Pipe & Right Branch or Main Pipe 6, U f t Branch 0 0 £ 2 O O M S P 0 0 0 p p S £ = Dteeharge Ratio (Dlschscge In Branch Pipe/ Discharge In Kaln Pipe ) p b o 3 o o b a> o I o 1 1 O 0 5 0 b F r i c t i o n toss ( f t ) In Kaln Pipe for Langch 3.375 f t . a 8 o 8 o 8 o 1 o b 0 9 a S 1 0 9 = F r i c t i o n Loss ( f t ) . In Kaln Pipe for Length ST 0.170 0.000 o o § S 0 o 1 5 o o § s o o § I 0 0 4> — » -J 0 0 S 0 b U» 0 0 s i F r i c t i o n Loss ( f c ) . In Right or Le f t Branch f o r Length 9.0ft. 0.174 0 o 1 a o o 8 * 3 o o o § I o o § s O O % M p 0 >» •> 0 0 g s 0 0 b «j = F r i c t i o n Loss ( f t ) , i n Right or Left Branch f o r Length TDj or TD 2 0.177 0.003 o o ? 2 o o 8 S 0 o 1 5 o o O "> •M X) O O 0 p 0 0 0 0 1 5 = Total F r i c t i o n Loss ( f t ) !* s | «• o •> •> « •> b 0 <o V e l o c i t y In Main Pipe (ft/aec) o 1 p p O p o o O p s 0 0 0 V e l o c i t y Head tn Main Pipe ( f t ) § s § S § S § .i o — u> O »• WM O JJ *2 0 S io V e l o c i t y i n Right or Left Branch (ft/aec) o o § 5 o o § 5 0 o 1 s © — § i 0 — 1 I 0 p O O O W 0 0 3 S 0 0 8 * - V e l o c i t y Head in Right or Le f t Branch ( f t ) a o s '» a a 1 2 o o = 3 — a 9 9 p p 0 a 8 S O O a - 0 O 1 1 O O s i Fara Loss ( f t ) p p o> - i 9 9 w o> o o' a t o o» • 9 9 s * p p S 8 0 O 1 S 0 0 3 8 O O a <> .° ? w O (Average) Fara Loss C o e f f i c i e n t o - o 8 a is o — — 3 S S o « — 8 3 5 O r * " 8 * 5 O w *• 8 0 S '*t a- O •~t O v 2 io * 0 >o — S 8 iS 0 M ^ ^ *> w s Reynold's Number ( xlO^ ) S*7 46 - s 3 5 3 :• : : 2 5 : :• •• • 2 2 2 !• i 1 - ' ~ d s 11 1 ! § 3 |33 13 3 |33 ! 3 3 3 3 3 33 (>J> •• •>! B ; i o d 2 2 6 d 2 2 e d ! ! ! 3 33 33 2 E 6 6 = • 2 d d Oj) V . » . J I q ) n J O J H » I . 01 p . . H i ^ O O I . j S 5 3 _• 3 3 33 2 2 d d ! ! I! 3 ! !•!• 33 K 5 § I! 5 i. 3 3 3 3 ! 3 . S 9 > d 3 ! 3 ! (JJ> - d l ^ o i w "I s ! s o' 3 c 2 S o" 3 3 3 3 ( o o i / l j ) « l d oiwH o i '3I0O1.J s i. 2 i 3 3 S i § 2 IS 3-3 2 S d d 5 3 3 3 ! ! II 3 ! Ii- S"°W)" "2 = 3 3 33' s * e d 3! 3 3 3 ! 3 ! 3 ! i l ' J ) 0-1 H J » u » l JOJ q o o » J i j j n J O j o i n O ] () j) » o i O O I U J J J . 2 13 3 3 § § d d 3 3 3 3 ! ! 3 3 3 ! . 3 ! IB t )3to» l J O J •did " I H "1 ' (JJ) « o i oououi 2 5 I ! I I ! ! ! 3 t •« s a c U J » U « I J O J ? ? 3 3 3 3 8 3 3 3 2 3 3 3 1 3 ! 3 3 2 5 1 3 ! 33 s s d d ! ! H S 5 33 < » > ~ ™ = 3 3 3 3 3 • 3 3 3 3 3 ! 3 d i. 3 3 3 1 - 3 3 3 s d 5. 2 s - ! ! 5 d 5 _S ? ' ! 1 - 333 s 3 I o' e d 0.74 9  0 .3 7 4 333 0.34 5  0 .1 7 1 0 .1 7 4 3 3 ! 3 3 3 ' 3 3 ! 333 s 2 S ii s : s - s ? - * H 5 111 5 i i S _ „ 8 S S 2 S S s s s § I i ». s. S S » s HI 2 0 3 .0  2 0 4 .9  3 2 2 .5  3 2 2 .4  3 2 4 .2  1 3 2 4 .2  hiiii siiiii S s 11 i I 320.4  3 2 0 .4  3 0 9 .8  3 1 0 .0  3 4 7 .6  3 4 7 .7  isssss uou.jo, JJ»T1 !<|3i»jg qulll'l : » d i d " 1 W - H « o J J (.01) J « J . H j o J I I » I . B - ! ! ! I 1 I s n I I I 1 I 1 I I * 1 j * I I ! H I o|| .01J1J0 i s : i ; s ; i •oo - - - - - - - •> 47 s 8 S = 1 = J » « " 8 « S 1 !, Jl £ 3 ? •1 V5 - 1 5 ! 2 ! '-™-<3. J . : ; , ss SS ss SS ss ss SS SS ! ! (•a,) u o i ! 3 S! s s SS ss S3 SS •5 3 3 3 <3J> O O T J , j o 3 1 « T 1 Dl P » " H *31*>1»A I 5 S S ss ss s s ! I S s 3 5 33 (D. ./ -3J) t p n . i t 3 J » 1 u 3HITI o i * a i o o i . A s " ? S! s s ? s 5. 8 s ° 6 ? » o s s 35 •5 3 g S « * o S s s o s o S ! ( M . / - 3 » » 1 * » > toWA s s * s 5 3. ! ? s ! s S! SS S 5 o o ss s ? o o S! S3 S! •3 3 -« » ,•_ J O J caiii 3 j r j JO s SS H S O D 0 2 46  1 0 .1 3 O  ss ! ! SI S S S! 3 3 ' I 0 6 <0 « » » I J O J 0OO . J I 3J.7. J O 3q>T| m C J ) " O ! n o i J . l J J 2 .! S ss ss 5 1 6 o 5 1 o o 3 3 3 3 Si IS o j t o n J O J »dTd °T*H TI C J ) « ° 1 u i » U J 2 ! i o i o ! I S i e i s o •3j « r t m»tt»i J O J . d , j ° J " H » 1 C J ) t . o i o o , j = , i . S i I . o ! ! s ? o i o 3 ! ( . d l l o i w <r, . t jnro .w / • d i d n o o . j , o, . 1 J . q o . M ) 3 ! S ss o O S! qomijj j j n , . d j j o in* J O qoO*> t i n t n , . d i j irtm o . w o . 2 s s ss a s o o 33 s J M = 5 3? < 3 J , » ™ , . , O J . 4 2 s o 3 s s s 3 S 3 ! 3 S ? 5 5 o I 5 C J ) T » J . J . J 3 0 . J ni 8"1P » »1 . l n ^ ) joes - S 1 I s. S n I n - s s 3 5 i 3 ( . , . ) . S J . O O . U - 2 3 ? M i * I a M l S 2 i M l S H 35 3 ( • 3 j n . / . q i ) J . j . f t jo 3iffT*n o i j i . a d s T i 2 s 2 s s . » 2 S -.2 ^3 - s a s 5 s S s « - 5 s s 32 1 .3  1 3 2 7 .6  3 1 2 .3  = 8 - 5 I * S S ' « "! 5 5 ' 5 3 • a » S 5 ' i i • - 32 2. 1 3 2 2 .0  : 31 9. 1 3 1 9 .2  1  33 0. 1 33 0 .0  3 2 1 .3  ! 3 2 1 .2  3 3 6 .8  3 3 7 .0  3 3 2 .8  33 2. 8 3 2 1 .6  32 1. 4 i 3 2 7 .J  j 3 2 7 .3  ! 3 1 2 .3  31 2. 3 =.° - • * 5555' i i i i - •..d„ „ » J , (-.0.1) J . j . f l J O , , » , . , , - I H I 1 I 1 I I I I I I I " I 1 - 1 1 ° i r 11 ° •o. . o „ ) J 0 : s ; S : s : ! — 2 5 2 2 s s s s T..t»o. s : i - s ; 5 ', 5 ' I I I i i I i I i § i i % i I i i I 11 i I I I i i I - ».ltht of Hour (lo..) 1. UfC Braach mm i. ~ u » b i. mm -SSSSS SSssss - - • ~ ̂ * SSSS5S 205.0 203.1 324.2 324 .4 323.9 323.8 * T l - L,,.™, <.....) m Ill H I 8 2 : S s - III s 1 i SSI III S s s a - 3 - E - £ s - S t i r ™ I I I H i H i o o o 3 i S I I I o o o 5 S g I I I in H i - i i 1 I i I £ - ^Si.'r.S'ci?)1" 1 i i i o 5 I I 4 5 I - o I I s £ I I i A ! I S Donucr.m Took (It.) I i o g o 8 I I o g I I S f i = i i i s i 5 i 2 S i i s i 5 i Z Pr...ur. a... Dlff . r.oc. (ft.) or Hot. Pip. & Loft Broach i i I i I i Z IM.ch.fi. lo ' S r - M . Pip./ I I I •I I I 1 I I Friction Lo.. ( f t . ) ^ l a nolo. I o 1 o i I I I I I I = Hpo'for Uogth'si' ^ II II II II II i l II I I II Prlctloo Lo.. (ft.) lo Il|bc ot L.tt Brooch for L m t h LO f t . II I i I i 1I- I I o o s i 11 I I II o r ^ - f t ^ r o o c l / f o r ' l° L ~ " h TOl " ™l 11 I i o o § S i i 0 o 1 I II 11 II I I = t o u t m o t t o . L . . . (ft.) i I i i S i » 8 l> I V.,^B... l»H.Lo, Ip.(ft /..o, 1 I I I o 5 I I 0 e i » II i i II I I I 5 11 I i = 1 I I L . fT»rL^h ( f f / . M . ) i i I: i i I i i i II II i i I I « 1Uft ' « r l o c» l(ftT ' I i II i I i I II ' 11 i I i I I I Pora Lo.. (ft.) i i - i l II I I I I I I = 0 8 8 5 3 111 I 1  » i 5 * = S 5 i, i i i •. * S B 8 S 3 . « s * 3 s i i s a s 3 s s s s c E s T e s t No . 1 " i : I - O r i f i c e No. o I ! . I I . I I . I I i i ' l i I I H  15000  R 10000  I I I I i i I f r o n H . . M a i n P i p e ; E . B i g h t Branch; L . L e f t Branch. • i f ! ! .SSsS 3 2 2 .6 3 2 2 .3 3 2 2 .6 3 2 2 .3 • S8SS 321.3 321.3 3 0 9 .3 3 0 9 .3  335 .0 3 3 3 .0 3 2 1 .3 321.3 3 2 7 .7 3 2 7 .6 3 1 1 .7 3 1 1 .3 3 2 1 .6 321.7 319.2 319.1 3 2 9 .0 329.1 3 2 0 .9  3 2 0 .9 324 T  3 2 4 .6 3 5 7 .7 3 5 7 .5 *> Time I n t e r v a l • 8 ! . 5 5 S 5 . 5 S a s •n S S s b v. u S 5 S - a - s 5 S s S 5 5 S 5 8 s e 5 s 3 • 3 • - Average Time I n t e r v a l (sees) s s s » . IK g * 5 ̂  S 3 is • g *° g g ' Temperature l a ° P . and S p e c i f i c Weight of Water ( I b a . / e u . f t ) § S 5 i i i 1 !ES i . « 8 S i s i s 5 S 3 5 8 i s s i - 01 •charge (cfa) o 2 i i i £ i i i o S - Hook Cauge Reading l n Uputream Tank ( f c . ) § i i i i i Rook Gauge Reading l a C e n t r a l Tank ( f t . ) 0 .7 7 4  i i o 3 i 1 1 i 5 Hook Cauge Reading l n Dovnatreaa Tank ( f t . ) o g ? g o g o g o g o g o g o g S V e r n i e r C o r r e c t i o n ( f t . ) 0 .3 6 9  •0 .0 1 2  A s i s A - 1 1 A - 5 1 Q O S s a o S S 0 .7 0 2  0 .0 3 7  11 1.112 -0.114 C Preaeure Head D i f f e r e n c e ( f t . ) between Main Pipe & Right Branch or Main Pipe & L e f t Branch Q O a s 11 0 © 1 i 11 o o s 2 C Dlacharge R a t i o (Discharge In Branch P i p e / Dlacharge l n Mala P i p * ) 0 .0 10  o * 1 o ! I I I 1 o 1 P r l c t l o n Loaa ( f t . ) l n Main Pipe f o r Length 3.373 f t . 10 0 '0  o i O o 8 o 8 o 8 o I o I o 8 P r l c t l o n Loaa ( f t . ) In K a l a P l p « f o r Length ST. 0 .1 2 S  O O O 'O  £9 1 0  0 .157 I 1 11 0.241 0 127 0.277 11 o o § S P r l c t l o n Loaa ( f t . ) In Right or L e f t Branch f o r Length 9.0 f t . 0 .131 0 .0 0 0  0 .2 4 9 0 .0 0 0  I I 0 .6 4 9  0 .0 0 0  1 1 § l i 1 11 11 F r i c t i o n Lose ( f t . ) Ln Right or L e f t Branch f o r Length TD^ or TD^ 0 .1 3 1 0 .0 0 2  0 .2 3 3 0 .0 0 4  0 o 1 3 I I 1 1 i l 5 3 0 o 1 » 0.431 0.047 s T o t a l F r i c t i o n Loea ( f t . ) i i i 4> s i I f I *> i IS- T e l o c i t y In Main Pipe ( f t / s e c ) o 1 1 1 o •> ? S O* o o 8 s cl V e l o c i t y Head l o Main Pipe ( f t ) l i I 5 11 1 1 i i 1 2 i 1 £ £ i £ S V e l o c i t y In Right or L e f t Branch ( f t . / s e c ) i 1 0.321 0.000 11 1 i i i 11 11 . i 1 11 K V e l o c i t y Head In Right or L e f t Branch ( f t . ) 11 i i 11. 1 1 0.173 0.206 |  0 .1 9 6 0 .1 3 1 p ? s 5 s Fona Loaa ( f t . ) 11 0 o 1 s o o S S 1 1 o o S £ 1 1 l i l l 11 (Average) F o r * Loea C o e f f i c i e n t O .M  1 .1 6 0 .0 0  1 .1 4 0 .0 0  8 3 a 8 S S s S 8 5 * iS 8 3 S s s s I k 5 R e y n o l d ' a Bhanbar (xlO*) 6^ 50 3 : 2 2 2 5 5 2 2 2 5 2 2 1.39 0.98 0.96 s * a o o o 2 2 2 5 2 3 2 2 S' i»i>!W«s ""ji « J O I S i n S 3 ! H i I I I 1 3 ! I I I 3 3 33 33 5 3i 31 3 ! 33 3 ! 3 3 33 3.3 3 3 S 1 ! 3.3 33 33 3 ! ! ! ! 3 31 33 J . O l 0,0.'oA. s 11 3 ! 3 3 3.3 3 3 33 3 3 ! ! s ! ! 8 o 3 3 3 3 3 3 s- § 3 3 3 3 3 ! ! s 33 s * e o 33 s's e © i ? o © i ? e o 3 ! 3 ! 3 ! 'ox J . '01 J O J I J O O O J I aj» i » ><<9l «1 ( J J ) oool O O J J . J J J s 3 1 3 3 33 3 3 ! ! 3 3 3 3- 31 3 ! jo"q?TI S (•3j)°"2l~lJij»i s 33 33 o o 33 ! I ! ! i! 31 3 ! IS q i t a l J O , odu O I W 01 CD) 0 . O ! O O T J O T I J a i o s o s ! ! 3 ! ! ! s s o 3 3 * o 3 ! ! ! ! • .OTj 0,0,1 o, olj.qo.ra / . d W . . . . J l o, otĵ ooM) 2 i i o e 3 ! 5 3 q o o i J l JJ»1 o o4,J o,tH jo 2 3 ! 3 3 3 3 3 3 i % o o 3 J 3 3 3 5 s 3 1 3 3 \ 3 ! 8 o 3 01 «0)P»o« .«n̂,*5ôJ 2 3 J ! 3 5 s 2 © oi'«oip»o, ««»oo V*V - 3 o a S a 1 a * ! s 8 5 s « 3 < — - 1.4(2  0. 74 1 0. 74 4 3 S S © © a ? s o o o 3 3 ! \ 3 2 O O o 333 333 3 3 ! 3 3 ! J » " » i° sq»i»« « * 3 •«3 il * 3 - 2 5 5 ^ s s S 5 s S * 5 3 2 1 5 § S s - - 5 = a 1 9 9 3*3 5 5 s 3 - -5 5 = Hi - 205 .9  20 5. 9 32 4. 6 32 5. 0 32 3. 6 32 3. 6 27 3. 7 27 3. 7 31 4. 6 31 4. 7 | 31 7. 7 j 31 7. 8 32 1. 2 1 3 21 .1  1 32 0. 6 I 32 0. 6 32 1. 8 I 32 1. 8 SSsSSS » 9 » - 23**** isii l i Ssilii siissi ! « H "TH K ~ J J (•.„) j » q . „ jo , ^ , . B - I I I I I I i i i i l l 1 11 I 1 s I I 8 H ' i s : s : i : s : s ... s Ul S o Tmmt Ho. S " s : S " f -u> r* ui r» M M o» r- + os r O r i f i c e No. r » x o> t> o i § r* P» ac o o o § 8 r* •» X o § i r •» ar r M x •o o> u> § 11 f Tm X f » X fr j" ^ r JO x Veighe of Weter (Ibe) f r o n M. Hein Pipe; R.Right Branch; L . L e f t Branch U| Ul U l w . .s.3.3.3 u> wt u> ut W ui u> U> Ul u> ut u> . rrrr -j co ~J a 0> 0» 0> 0ft r- i — V * U 2 so a< a M u >. cs Q O rtJ M M S U> Ul b K» '•- fr Tlae I n t e r v a l (aeca) Ul u» 5 fr O s s S 8 B 8 Average Tine I n t e r v a l (aeca) M M O <• M ° o> o sO Is* N° so " o 0> <si ls» 0 sO °*0 OS <o sO Temperature In °F and S p e c i f i c Weight of Water (Iba/cu.ft) 0.337 O O O o o» o o o 8 s o o o as e> o o o Ul w at S o o b « j ao u! •- o o o o o s ui » o o o ^ OS 1st Dlacharge (cfa) w o o» 8 o b O b OP sO o - Hook Gauge Reading In Up«Cream Tank ( f t ) 8 sO V* M fr fr OS g » o o> fr o Book Gauge Reading i n Ce n t r a l Tank ( f t ) I O sO Ul Wt p o O s0 , M o o s o b fr O Hook Gauge Reading In Downstream Tank ( f t ) O o o o p o o o O o p o p o p o 5 V e r n i e r C o r r e c t i o n ( f t ) p p b V 3 8 Q O 3 "S -J o p ? s o •*» S S Ul O 0 o 01 o> o o 8 * o p i— Oft w fr o* •- b OS K> Pressure Head D i f f e r e n c e ( f t ) between Kaln Pipe & Right Branch or Kaln Pipe & L e f t Branch 0 a 1 i o o o o o o 5 fr 0B M o p = Discharge Ratio (Discharge In Branch Pipe/ Dlacharge In Main Pipe) p O o 3 o '8 o '8 a fr sO o g o fr sO o b o fr F r i c t i o n Lose ( f t ) , i n Main Pipe f o r Length 3.375 f t . o o 1 o '! o o o 3 o § o 1 o 3 = F r i c t i o n Loss ( f t ) , i n Main Pipe f o r Length ST 0 o 1 s 0 o 1 5 o o § 8 o o § s o o fr I-i p p 8 2 o p b w Ui OS o p b o> F r i c t i o n Lose ( f t ) . In Right or L e f t Branch f o r Length 9.0ft. 0 .0 0 0  0 o 1 s 0 o 1 5 0 o 1 5 p o o K o p 5 £ p p O w o o b sO Ul = F r i c t i o n Loss ( f t ) , i n Right or L e f t Branch f o r Length TD^ or TDj 0 o 1 = o o 9 3 0 o 1 S a o O » a o p p 5 8 o o 8 S o o 8 S 0B T o t a l F r i c t i o n Loss ( f t ) M fr *•> sO J? f fr sO sO fr sO o i = V e l o c i t y In Halo Pipe ( f t / s a c ) O b o OJ u> o o» o s p ao p p o o V e l o c i t y Head In Main Pipe ( f t ) o *• ! S O 0" § I § 3 O i - § 1 fr u. U fr * sc 2 s S Oft V e l o c i t y In Right o r L e f t Branch ( f t / s e e ) 0.301 0 .0 0 0  o o § 2 o — § 1 0 - 1 2 a o M <£ o o — s>\ S 3 p p f Oft o ^ o o 2 S V e l o c i t y Head In Right or L e f t Branch ( f t ) o o 8 8 W • o o a g p p p o <* » p p b b o o fr 2 ^ o o o s g 0 o 1 8 = Porn Lost ( f t ) O O s s o p Ul " ui S - p p Ul ft* * s p p ui is) « s a o 8 8 o o 5 S o o b Ss p p a* S p— o> fr (Average) Pora Loss C o e f f i c i e n t o — o 8 s s O M — '8 3 5 o ** ** 8 !S '= O <-* M 8 S S 3 3 3 8 5 3 O KI M 3 5 3 O NI IS* 2 E 3 u> Reynold's Nuafaer ( z l O 3 } G IS - 0» - T . i t No. i : 5 " s ; • •s " s ; I I I 8 i I 8 i 1 g I i I I I i I I I I I I l l I i i Weight of U.c.r (lb.) f r c M. Main Pipe; R.Right Bench; L . U f t Branch 3J1.» 322.0 327.4 321.2 399.7 39B.5 S S 3 S 3 3 323.5 323.5 321.0 320.9 326.2 326.3 55SSSS » V ~ V. V L> 313.9 313.8 313.3 313.3 3)4.2 314.2 276.9 276.8 320.5 320.5 320.6 320.5 201.3 201.5 254.5 254 .5 254.4 254 .5 III j= ? .8 I I l 379.33 378.5 380.2 Ul 5 5 5 - » s 313.85 313.3 314.2 1 1 1 201.4 254.5 254.45 - Average Tine Interval (a.ce) I * i I - S t i f l e WelghC of Water (lb./cu.fc) 1 1 1 0.748 0.716 0.032 ] 1 0.748 0.736 0.012 ? p p s 5 = 0.496 0.250 0.246 0.750 0.375 0.375 0.920 0.461 0.459 ? ? r S s 2 j  1.5U 0.757 0. 757 0 l .ch.rg. (cfa) £ * £ £ ? S £ I ? = i - 3 i £ i 1 1 1 ? 5 1 •? s 1 J r i £ ? 3 £ ? 5 "£ 5 I I ' I £ 1 £ I £ £ ~ i i 1.711 -0.155 11 0.122 0.112 £1 11 11 i i or Haln Pip. 6 [ e f t Br.nch 1 1 i i i 1 S DlacherS. lo haln Pip.')' i i i i £ £ i 5 .° 5 » for Length 3.375 f t . " i 1 1 1 I 1 £ | 5 xrxgz(,c) **• i i 1 1 1 1 1 1 i i s 5 11 11 £ £ ; P r l c t l o n Lo.. (ft) lo Right or Left Branch for Length 9.0 f t . i i I 1 11 i i £ £ p ? S i £1 11 11 z Prlctlon Loaa ( f t ) , i n Right or L. f t Br.nch for Length TO, or T0 2 i i 11 11 £ 1 11 p ? s I 11 11 £1 s Total P r l c t l o o L o a . ( f t , "i i i .~ 5 £ 'i £ £ s Velocity lo Kalo Pip. (ft/.ec) 1 1 1 £ ? i £ P s 1 r 3 s 1* tu'o'Flp^Cft) ? .» 1 s I 1 1 I - £ £ £ 1 s s £ £ i i £ 1 2 E'EiS o t L . f r . r a n c h , , , . . . , i i i £ I £ £ £ ? ? 8 5 £1 £ 1 1 i £ £ S In'Sliht ot*L.ft Branch (ft) ? .° S 8 11 5 s 1 £ 1 £ 1£ I 5 ? ? s 5 i i s i i . 11 11 i l l P P p S i I ? ? ? 5 5 I ? ? P 5 5 I (0.171) 0.171 0.170 (0.167) 0.163 0.169 B Wa.Co.fflcl.ot ? - .» 2 3 5 t.n  0.19 a '5 I % % l ? ? r S S S s * •= 2.16 l.Sl 1.51 5 S - f -3 3 S 5 ^ . . ^ . r , W , u* *> s •O. O •*< . : TtiC Ko. i : i : i : S " f • ui r* ui r" v - M Orifice No . » o> o § § r » I r w * ts> »*» c § § f P X o i i P H I § I i P" >B X § ̂  If t- jo X i ^ ̂ - Weight o f Water (lbs) from M. Haln Pipe; a.Right Branch; L.Left. Branch W U* u » w IS* M M M •> *• ' bob b V* U l U l Ui o o o o U U O O N N « >0 <3 4) M rg Ul Ul Ul Ul u> W - 0> » M N fO N) *> *» •- P- U l Ul U l U l U l U l N N N M M N SO SO O O N Ul ui <H oa CO so o » Time Interval (feet) w ui tU M «> 4> o o VI Ui U * Ul U l u » Ui U l M Is* o o u i ui u> U l Ul U l »— ON K) hJ *> — S O is* Ui Average Time Interval (tecs) » OS M 0» * o u» U> OH OS K» 0S 0 W U l OS o" M OS 0 u> u> o\ ,j •s* V 0 or. to \jl ON O O *j Kt U l M U l OP o K* VI IS* Ul OS 0 OS Temperature in °F and Specific Weight of Water (lbs/cu.ft) o o o § 2 S O o o Q #> #> 8 S E O O O O U i U l Q u> u> •5 so -o o o o § iS X O O O U) *> M Ul 0B o o o U> g - J S a so o o o r - Ui - J . ui o* - Discharge (cfa) N 5 •> SO OS KJ NJ c* 09 09 Hook Gauge Reading in Upstream Tank (ft) IS* O 0* Ul *» is* os a 00 •o a>' IS) OS OS SO Hook Gauge Reading in Central Tank (ft) 00 s s b p u> SO <o u> Ui OS o O Hook Gauge Reading in Downstream Tank (ft) p IS* O p 1st O p s O o o o o ro O o o = Vernier Correction (ft) O O 8 is p O "o *»* U» SO '8 1 o «• p U l K> •— oa p o •sj oa O O p O SO -J = Pressure Head Difference (ft) between Haln Pipe & Right Branch or Haln Pipe & Left Branch p p *«" U l t: S o p e» ui o o o o OS C* U l Discharge Ratio (Discharge ln Branch Pipe/ Discharge In Haln Pipe ) O b os o 3 2 p C O O 8 o « o SO «• Friction Loss ( f t ) . Ln Main Pipe for Length 3.375 f t . o § o 8 o 8 u» o O 8 o 1 O 8 SO 5 Friction Losa ( f t ) , in Haln Pipe for Length ST O Cf § 1 o o § s O O § 5 o o o o> 8 O O p o o O O b "u> Ul OS Ul OS Friction Loss ( f t ) . In Right or Left Branch for Length 9 . 0 f t . 0.105 0.000 o o § S o o o u> Q os o o c o 8 S o p o 2 p p p— ro »— vO O O b i-* Friction Loss ( f t ) , in Right or Left Branch for Length TD^ or TDj o o g i o o 8 's o o § 5 0 o 1 I O O •-• ro U l >-* 09 U o o p o OS 09 OS ' J CD Total Friction Loss (ft) M OS W O* ui b u i ui a» U l 8 *• *• s sO OS U l <C Velocity in Main Pipe (ft/sec) o 8 p *• o» o ** 8 p p s o CO o> O 00 o Velocity Head Ln Haln Pipe (ft) O w> § S o » § 2 o § I o * § 5 *• U l w V *> U l 3 ? ui O B Velocity in Right or Left Branch (ft/aec) o b § £ o o § s o o § 2 o — o *• 5 o O ui p p 4 Ui p p is* U i Ui •— M U» p o o o Velocity Head tn Right or Left Branch ( f t ) . o o 3 S o o *S 3 o • p p £ o U l i— O O KJ r— M U> •o u» O O 8 2 O O o o 8 1 Form Loss ( f t ) . O O ie is °*. w p p o> U a 3 o o p p 3 $ p p W •» p p i - r-» 8 = p p ro r* ISl *• (Average) Foro Loss Coefficient 8 t 2 8 3 2 b « V O o> o 8 3 S W >l N »J - O i- U l 0B is* is* O -* O Reynold's Number ( mto' ) 9 T..C no. i ^ s ; s : * » - i ; O r l f l c . Ho. i f i 1 I 1 i l l I I I I I I i i i I I I I I I I I I - U.l jht of W.t.r (Ik.) f r o o H . K . ' n P i . . ; I . t l . h t Br.nch; L . L . f c Br.nch mm 321.9 322.0 327.3 397.3 397.3 ssSSSs 5 5 5 5 5 5 mm. 200.5 200.4 316.0 316.9 316.9 * m 3 5 5 > s b 338.13 337.75 338.* 111 ? ? 5 S 5 5 s 3 b 1i1 ? 5 3 * 3 J -u s *• £ 1 - Specific V . l j h t of W.t.r (Ib./cu.ft) £11 l i l I I I I I I H i 0.750 0.375 0.375 0.940 0.471 0.469 H E l i s i .-2 £ i £ 1 r * £ l i -£ i i i .-2 £ £ - C""rrS W t > " * - ? i 1 ? 3 £ i i r g i £ 1 £ P S £ £ £ £ £ £ 5 ? .- 5 s ? .- 5 2 l l 11 = = £ £ i i | 0.413 ! 1 | 0.407 | £1 i ! S or K i l n P ip . T u f t BrSnch'™ ° i i I £ i i c 1 ! £ £ 1 i i i ? a for Length 3.375 f t . * I p § . £ i - £ £ £ i I s f o r C U o » t h ° " T f f e ) 1 K * ' n F t P * IS 11 £ 1 £1 i i ? ? 2 3 11 11 11 Prlctlon Lots ( f t ) , in l ight or U f t Branch Cor Length 9.0 f t SB. 11 £1 £ 1 i i ? ? 5 1 11 1 £ 11 Prlctlon Loaa ( f t ) , in tight or U f t 1 £ £1 i i . 11 £ 1 ? P i i 11 1 £ p p % it Tot. . Prlct lon . . . . ( f t , £ £ £ £ £ £ £ ? 5 s o . l o c l t ; In M i n Plo . ( f t / . . c ) £ 1 1 i ? i £ 1 s £ 3 in H i l n ' p i o . (ft) i I £ £ i i £ £ 1 £ £ i 5 s r r s s \ I l J ' J l i h t or U f t Br.nch ( f t / . . c ) \\ i £ i i ? ? I s 11 1 £ p ? § i i'i K. In I l tht or U f t Br.nch (ft) ? ? S s £ 1 £ 1 5 £ £ i i i ? ? s 1 ? ? S 5 1 £ S £1 l i £ £ (0.2S1) 0.252 0.250 i U S i l l I I I 5. i l £11 S s » = I - = % 5 b P ? .- s s z p ? r S S S b S = .- .- r* 3 3 s « « b b b = s - p o o , , . U4 *• O Tai t Ho . I 'r s : u> r u* » ut r- OS r K> O r i f i c e N o . - . V m at - I I o ^ ^ t- v at KI to o § § r" H X V* u> o I 1 f m • 3E p* w as i§ vf ^ i r w x § H If U* W e l g h C o f W a t e r (Lb«) f r e e M . Me I D P i p e ; R . R i g h t B r a n c h ; L . L e f t B r a n c h . 3 2 7 .5  3 2 7 .3 3 2 7 .3  io %0 •»! u w u u Ul i> iff «• w u u u N N M N O) <o o> <o u> u> ui u> ui u* U U M H N N < O i f l W W > « > M s l i - i - O i s , U* Ul u> u> u* U* OS A Ul U* ts* is* Os OS O O Ul Ul OS t » KI I— c> CD Ul W Ul U> Ul Ul •si Ul W M N sO CO >j -si sO SO «• T i m e I n t e r v a l ( a e c a ) Ut Ul tst M *• > S £ on o> Ul Ui u> u» Ul U* K» K> b> CD w* w u» u> u* U> «— IS* sO Ul O ^4 *** OS Ut Ul Ul U) OS u K> OS O Ul Ul P M m Ul Ul Ul Ul f is* -J Ul IS* CD ~j so U> A v e r a g e T i m e I n t e r v a l ( a e c a ) «> ~i Is* »- io u» <o a K» o ct OS -J IS* f* 0 s o> -J •si C*> o K» OS -4 is* m io ut OX o O* -J (St U< k> ut o> 0 OS -4 KI J> K> Ul -1 o o> T e m p e r a t u r e l a ° F a n d S p e c i f i c W e i g h t o f W a t e r ( l b a / c u . f t ) 0 .3 9 2  0 .3 9 2  0 .0 0 0  o o o B •*> *• g 9> <r> O fo M o o o o m u» 8 £ £ O O O O sO SO O O O ut *» -1 Ui 4> » - O K) o o o U» *- -J 3 co f o o o K* Ul » ° ** D i s c h a r g e ( c f a ) IS* b o IS* so IS> b Ui S K> CD OS Ul u> co Ul CD Hook Gauge R e a d i n g i n ( U p a C r e a m T a n k ( f t . ) IS* ro * M i» ut IS* IS* sO U» OS S IS* k> m CD Kt Cjs OS OS SO S0 Hook Gauge R e a d i n g I n C e n t r a l T a n k ( f t . ) 8 g ** SO 6 Ut vO KI so K> Ul CD Ul O CD Ul OB O Hook Gauge R e a d i n g I n D o v n a c r e a m T a n k ( f t . ) O M o O is* O O K> O o K> O o IS* O. O IS* O o K> o - V e r n i e r C o r r e c t i o n ( f t . ) & o b v> ut s»l «*. © o o o Ut os i-> u> 4 ~ o o *• is* 6 - vO W UJ OS OS o o u* S I- OS O O b ut 13 8 4 o b » S ts> P r e a a u r e Head D i f f e r e n c e ( f t ) b e t w e e n M a i n P i p e & R i g h t B r m o c h o r M a i n P i p e & L e f t B r a n c h o o *• Ut £» ut W o o j> Ul I-* CO IS* CD o o U) os I- CD CD K> U> D i s c h a r g e R a t i o . ( D l a c h a r g e i n B r a n c h P i p e / D l a c h a r g e i n M a i n P i p e ) o b m o b ts> o b K» 09 O b so o o b ** SO o ? sO ** F r i c t i o n L o a e ( f t . ) i n M a i n P i p e f o r L e n g t h 3,375 f t . o 8 ut O o 8 Ut o i o 8 SO o 8 sO o 8" sO Ui F r i c t i o n L o s a ( f t ) i n M a i n P i p e f o r L e n g t h S T o o § 5 a o § z O O Q ui O 0D .° ° b os S w o o i— is* I: P o o i - is* K) U> OS CD o o O U> SO KI o» F r i c t i o n L o a a ( f t ) i n R i g h t o r L e f t B r a n c h f o r L e n g t h 9 .0 f t . 0 .2 0 2  0 .0 0 0  o o 8. 3 O O § 3 p o a v i o m 9 ° i— Is* *s I- sO sO o o i— IS) v* «> O OS O O O u> CD K) KJ X> f F r i c t i o n L o a a ( f t ) i n R i g h t o r L e f t B r a n c h f o r L e n g t h T D . o r ! 0 .2 0 4  0 .0 0 3  0 o 1 S o o 8 is Ul o> O O Q OS S o> CD W O O i - is» » M p o »— K> Ul Ul so Ui o o O Ul 5 T o t a l F r i c t i o n L o a a ( f t ) N o> o b u» <JS •*> o» J> so 0D *• vO Ul CD 4> SO Ut KI *• SO OS so V e l o c i t y i n M a i n P i p e ( f t / a e c ) o o *> o> o is* O o* o Ul C0 u> o Ul SO o Ul CB o Ul CO Ul KI O ' V e l o c i t y H e a d i n M a i n P i p e ( f t ) O v» § 5 o 0» § § o -* § 5 o o § is O NO § "5 «• u> Ul Ul K> U> i— CD *• m 8 3 Ut OS Ut OS §.# - K> V e l o c i t y i n R i g h t o r L e f t B r a n c h ( f t / a e c ) o o § 5 o o § J i i o o S 1. o o ' SO —1 o o i - C* *• CD so m K> KI V e l o c i t y Head I n R i g h t o r L e f t B r a n c h ( f t ) o o 8 ! o o b b SO —I (si e* o o M O o> 0> o o KI I— f* Ul o o b i-» OS KI J— 0 o 1 5 O O S 5 sO K> KI W F o r n L o s a ( f t ) o o ? 8 o o 5 f o o o* U M KI 0 * K» O O b> V KI U* o o H* PS* o o I-" w Ul f KI M o o 1— KI s s KI •> ( A v e r a g e ) F o r n L o a e C o e f f i c i e n t 8 if S 8 9 8 8 » £ 8 5 B Ul o» o> CP *J K» CD i -•«* 1- sO SO O — K> UJ t a y n o l d ' s * a a b « r ( a l O 5 ) 1 " i ", s : I « . t I k . O r l f l c . H a . I fI ill i l l i i I i l l i l l 1 I I i i i 11 i - H . K . l n H p . ; B . ' l l i i t ' . rTncb ; L . U f t B e n c h mm SSS55S 321.B 111.I 127.1 197.2 197.0 111.2 111.2 334 .0 ill .a 112.9 132.9 •» ~ u t , u 333.3 333.2 331.8 331.9 332.4 332.2 298.3 298.3 313.8 313.8 313 .4 313.2 mn *> in n j S ! » - is - I! S 111 I I I 5 a s w • » 111 -S =• I z s fc Z 2 fc - u«ltf>t o f H . t . r ( l t a / « ! ! f t ) < l C i n £ £ £ £ £ £ £ £ £ £11 111 £ £ I £ £ £ £ £ 1 - i £ 1 1 £ 1 i £ 5 - Book Gauge leadIng In £ 1 1 £ i £ £ £ <*> Book Gauge leading In £ £ { . £ I £ £ £ £ s s a w I 1 £ I £ £ £ £ s ' « » < « > i§ £ £ i i I i £ £ £ £ i £ £1 £ 1 s or Haln Pipe & Left Branch ; i £ £ i i s SSTss W i £ £ £ £ £ £ £ £ for U n . t h 3.373 ft. i I £ £ £ £ £ £ £ s 11 1 £ £ £ I i I £ i i i i £ I £ £ £ P r l e t l o o L o . . ( f t ) , l o U | M or U f t Br .nch for U n « t h 9.0 ( t . I £ I £ i l 11 £ I ? ? 5 5 i £ i i £ £ 5 P r l e t l o o L o . . ( f t ) . lo P. l i«t o r I £ £ 1 £ £ 11 i i £ £ i i £ £ I £ S T o f l P r l c t . o o L o . . < « > 1 £ £ £ £ £ £ s v . l o c t t , to H . l o P i p . ( « / . . . ) £ £ £ £ £ £ £ £ £ s ln'lfcln'pip^ft) 11 i £ £ £ £ 1 £ £ £ £ I i i i £ £ s 1 £ I i i i £ £ £ I £ £ £ £ £ £ s Ufr.rLcolft ) * * * ' " £ £ £ i £ i 11 £ £ £1 1 £ £ £ £ £ s F o r . L o u (ft) l i £ I i i £11 111 i l l i l l £ £j £ £ £ s 5 fc fc S 5 b s , fc 5 S t s . 1 s S b i ; i s s : s fc ̂ s 95 . B 5 B s E S c s • s: ! : 5 : J : J : - . I f o i i . 11 . I I I i I § i I i 11 i l l ! 11 - f r a M . Hot. H o i ; \. Eight Br.ocb; L. U f t Brooch -mi . S555 - ̂  u •„ .SSSS b ~ b ~ •mi mm ssssss • 11 . 5 5 • 1I - l l s s 2 s s a Ill t i . j ! I III «- Ik £ *. £=. £ =0 - Tnp«racurc to °F and S p e c i f i c W.liht of tet.r ( l b e / e i i . f t ) . i i i I i i I i i I i i i i i i i i i i i i i i i i i § 5 i i S i 1 i 1 i i. i i i i •i S 1 1 I i 1 i I •i i 1 S i i i S I i i " " ' - — • • « ' > i i t g i i n i i i i i i i i h b«Cvcto Main Plp« & ll Bht f8r»nch or Kaln Pipe & U f t Branch i i i i i i i i i i I I i i i I i i I F r i c t i o n Looo (ft), to Kolo P i p . for U n gth 3.375 f t . I i i i I i I 1 I for U n g t h ST ' I i I i I i I i i i i i I i I i I i F r i c t i o n Lo.. ( f t ) . In l i g h t ot L e f t Bronco for Length 9.0 f t . 1 1 I i I i I i . i i i i i i i i I i F r i c t i o n Looo ( f t ) . In Right o r TD^or'Sj I i I i 1 i I i i i i i i l i i i i Totol F r i c t i o n Lo.. ( f t ) i i !' i *> s ** 2 i i B V e l o c i t y i n Hold F l p . (ft/o.c) 1 i i i i i i • V e l o c i t y Hood In Holn Moo ( f t ) I i I i I i I i 'i i i £ i £ i fe i fe- V e l o c i t y In Right or U f t Bronch (f t / . e c ) I i 1 1 I i I 1 i i i i i i i 1 i i V e l o c i t y Hood In Bight or U f t Bronch ( f t ) i i I i 5 -5 i i i i I i I i ° ? § 5 0.110 0.143 For. Lo.. ( f t ) i I i i i i 0.410 0.190 i i i i i i S i • M e C o . f f l c l . o t 1 s s s ; : s fc k * = s S 3 S * i = i i s i •= s k i s loyn.ld'o ftafcor ( » 1 0 S ) 58 » 2 2 5 2 2 2 2 3 2 5 2 2 2 2 2 :• 2 5 2 2 2 2 1 2 2 2 3tl»T31I3*CO MO? lUOi 111 Ui l l ! I H 133 33 53 33 3.3 ! 8 13 ! i ! ! I i 33 33 13 ! 5 (Jl) n 5 0.il i i r ] a. l o l r l o) 1 § II 33 3 3 3 3 3 3 ?! ! 1 3 ! (.../Jl) qoo.ao i i r ] 3 8 33 5 8 3 3 3 3 33 33 33 (11) oo'M̂ n.H o, ! ! 3 8 3 3 3 3 3- ( . . . / l l ) . d u aim of <I,.o,o. 3 3 3 3 3 3 ! 3 . •(Jl) . . . 1 o . l l o , a . , . 1 0 1 1 ! 13 13 3 3 3! 3 ! ! ! 1 ! 33 loz ao ,01 ^ q i t o r , ao] uou.ifl J , ^ I 13 33 3 3 3 3 !! I i 3 3 ! ! 3 3 •1) 0 6 . H u r l a.i uoooa. , i n ao J u l , , (i|) aoo-, o o u o i a i ! 1 3 3 3 3 33 3 3 I i 31 1 ! 3 3 ^ IS m«u^i aoi 5 1 ! ! 3 ! 3 1 3 U HCC 11«»ei aoi ..,« » ™ o, • („) „.„.,>! 3 3 I ! 3 3 ! I 3 3 3 3 3 3 ! 3 3 S i 3 3 3 3 33 3! H 2 3 3? 15 1 3 3 3 3 1 3 1 3 2 3 5 3 ! 3 J J 3 ! - 3 f 5 5 3 3 3 3 - 3 I 3 ! 3 3 3 3 3 ! 3 3 3 3 3 ! ! ! 333 333 1 1 ! 311 3 3 3 3-3 5 - £ i ]?3 • *3 "»3 * 3 * 3 *3 * 3 - 8 S S i l l 2  ? " 3 S S III ill s s. -. 5 5 3 i i i i i i I i i ,....) , - a . J . , „ u - mm s s I S s * mm ssasii silii'I mm lo.o.ao. l » l n - i !«l,a n,^ - H « a , (•11) Hon 1 . ! . » , . » - 1 I I 111 I I 1 I ! I I I I I I s I I I I I i i n OH » m » : s : * : s : i •o« J I U - - - - •> f , 1st - o - Test No. o r o rr 7 * o r* *> c * • s* r * Orifice No. r* sa ac o» o» <-* u> o 8 8 r* so ac - § § CJ o o t- » X 8 8 o o o r- » 36 sO y£> o o a o © o o r* » x » J <o o o o o o 55 r » at p o o 8 8 3 Ul Weight of Water (lbs) from M.Maln Pipe; R.Right Branch; L.Left Branch 307.0 306.9 307.0 306.9 i s s s> s 'v \t* Li w i - u> *- • - N r J W W w m ~j O O t> »< N p- k* Ul o o •«* © o *• V- }> b> w> j . *> line Interval (sees) ' f ? is is u> w 9 O {> Ui ui p ^ o 5 b ** t> Li Average Time Interval (aeca) so OS •s> O so OS is* O SO OS is) O OS Kl 2 ° Os is ~ O* Temperature In °F and Specific Weight of Water (Iba/cu.ft) © o o 8 «• «• S o © o o o o *• *> O f* • 6- o o o 8 S £ © © © i l l © © © OB *> rSl W O Ul © © © i> on u> Discharge (cfs) u> >0 OS o OS b o rs> o> o> Hook Cauge Reading ln Upstream Tank (ft) o> ? K> kO «• CD M a> OS u> is* SO Hook Cauge Reading In Central Tank (ft) u» o w CD o OS o CD «• OS o Hook Cauge Reading ln Downstream Tank (ft) o IS* o o •s* O o 3 a o a © © O = Vernier Correction (ft) e o o «• ui u> •*4 IS* O r - so sn • <o o o a *s> 2 OS Os OS o o O SW o o S CD VJl vO Pressure Head Difference (ft) between Main Pipe & Right Branch or Haln Pipe & Left Branch o o O © ui o> o> ui = Discharge Ratio (Discharge In Branch Pipe/ ' Discharge In Haln Pipe) o b O b 03 o s SO o 1 o b o b Friction Loss (ft), ln Main Pipe for Length 3.375 f t . o o b o o 1 o b o o b 1st o b Friction Loss ( f t ) , in Main Pipe for Length ST 0.150 i 0 .0 0 0  o o O Ul 8 S o o O OS 8 B o o o © CD ** O CD o © r- "*> 4> O OS -J OS Friction Lose ( f t ) . Ln Right or Left Branch for Length 9 . 0 f t . 0.157 0 .0 0 0  o o ^ OS © © O OS 8 5 © o o a> O ** o o O O p- it> Friction Loss ( f t ) . In Right or Left Branch for Length TDĵ  or TD2 0.159 0 .0 0 2  o o 8 S o o 8 S O is» o o a a> — Ul O *• © o o © Ss !o CD Total Friction Loss (ft) OS 8 f> sO OS OS 4> OS © sD Velocity in Haln Pipe (ft/sec) o b sO ' O o o CD OS o *4> sO o o CD O CD O Velocity Head In Haln Pipe (ft) O *> o **• 5 oo o — o o 8 S © -o § s o u> o — o o 8 S * - - J *> -~l Ul OS OS Velocity In Right or Left Branch (ft/aec ) o o 8 O o o o — b *• 8 * O i - 8 5 o o U» CD -J - O O Velocity Head in Right or Left Branch (ft) o o ? ? o 0» o o § o o o S ce o o ui -• © O S2 2 OS o o b o B Form Loss (ft) o o © S •O •si- o o Ul «• o o o o W CD o © b b CD S> o o *p- b O w (Average) Form Loaa Coefficient tS - © 8 5 S O f» — 8 b is o ^ - O Ul M o <•* O *•* ^ s b is N W « 5 Reynold's Number ( xlO* ) TABU Y~il *•*» L M * °*ta for 9 0 ° H a a l f o l d without T U - r r d y a M • J tj s flu B So J w • £ C O M « IT i i -* 3 c e c ** • M m •2 •2 ° u •t S •3 t M "* "u « d) */ •5 • +J • B • c • • • o B A B ^ 0 5 rS.3 « -* "u ** 2s 2* *• "* £ U »> ->< a M •O *. "° £ w 3 -2" "So . o » * w w 1. ° .5 iu s •3 a -S SM at ° w C B « ^ • H • Si 1 * "Z 1 o • 1 . J H ' . S o u **2 3 til! 31 G c p U 0 • 0 rS S ^» m 3 • i • Z*X a M m •»< s U n- U i 3 j ss . tJ c c 3 * -J fail o " 3 .3 Xs 1- g 2 H -* m u £ $ ii £ I ••3 •0 | f j n M u Jl B i s i ; O 4i U t i 3 3 . B " J I 0 ; • 1 a £ H 5 4 o 8 !. m ±T O l 8 | EC <5 S £ J S o o a 3 o *u %. h O I . » • H £ i i 1 s . 1. > 0 S £ i 2 3 4 5 6 7 8 9 1 0 u il 13 IS 13 16 17 IB 19 20 2 1 22 13 24 15 i • L 1 + 1 M 19000 R 19000 L UOOO 207.5 207.6 306.4 306.3 304.0 304 . 1 207.55 306.45 304.05 6 9 ° 62.31 1.469 0.733 0.739 1.910 0.310 0.336 0.110 0.901 0.930 0.164 0.030 0.608 0.617 0.699 0.709 0.729 0.740 9.775 1 .484 9.372 9.647 1.623 1.445 0.136 0.119 (0.156) 0.158 0.154 3.97 2.78 2.80 i 1 L 1 + 1 H 19000 R 11000 L 1 1 0 0 0 276.6 276.3 321.5 321.6 316.9 276.55 321.35 31B.B3 6 9 ° 62.31 1 .103 0.549 0.554 0.174 -0.171 -0.147 0 .2,10 0.531 0.355 0.098 0.018 0.939 0.366 0.611 0.420 0.431 0.439 7.336 0.836 7.167 7.228 0.798 0.811 0.138 0.141 (0.167) 0.165 0.168 2.98 2.08 2 . I O > L 3+3 K 1B0O0 R 9000 L 9000 313.3 313.2 3 1 3 . 1 313.1 312.8 312.9 313.23 313.1 312.83 6 8 ° 62.32 0.922 0 .461 0.4(2 1.852 1.667 1.670 0.110 0.391 0.395 0.071 0.013 0.161 0.163 0.101 0.303 0.314 0.316 6.135 0.584 6.021 6.026 0.563 0.564 0.10O 0.100 (0.171) 0.170 0.171 2.46 1.72 1.73 * 1 L 3+3 M 13000 R 7300 L 7300 320.3 320.4 321 . 1 321 . 1 320 . 1 320.0 320.45 321 . 1 320.03 6 8 ° 62.31 0.751 0.373 0.376 0.898 0.634 0.836 0 .110 0.171 0.174 0.049 0.009 0.179 0.161 0.206 0.209 0.115 0.216 4.997 0.388 4.893 4 .909 0.372 0.374 0.073 0.070 ( . .184) 0.188 0.1B0 2.01 1.40 1.41 R L 3+3 H 10000 R 3000 L 3000 318.9 316.6 316.0 317.9 320.3 320.3 316.85 311.93 320.3 6 6 ° 61.32 0.503 0.232 0.230 0.867 0.947 0.941 0.710 0.116 0.130 0.014 0.004 0.087 0.087 0.100 0.100 0.105 0.104 3.348 0.174 3.294 3.268 0.169 0.166 0.037 0.034 (0.203) 0.211 0.193 1.B4 0.94 0.94 6 R I M 7000 R 3300 L 3900 321.3 321.3 322.8 322.8 320.6 320.8 311.3 322.8 320.7 6 7 ° 62.32 0.330 0.176 0.175 1.652 1 .392 1.393 0.110 0.069 0.070 0.013 0.001 0.044 0.045 0.051 0.052 0.051 0.055 1.316 0.084 2.271 2.286 0.080 0.081 0.010 0.018 (0.225) 0.234 0.217 0.92 0.6* 0.65 7 R L (+9 H 13000 R 13000 I 300 320.B 320.6 323.7 323.6 im 320.8 325.75 387.0 6 7 ° 62.32 0.750 0.739 0.012 1 .297 1.678 -0.393 0.110 1.900 -0.171 0.984 0.016 0.049 0.009 0.617 0.000 0.709 0.000 0.718 o.olo 4 .992 0.387 9.646 0.162 1.445 0.000 0.114 0.106 0.320 0.332 1 .98 2.73 0.03 > R L I+B H 13000 R 13000 L 600 320.9 321.0 334.3 334.4 333.6 334.0 320.95 334.33 333.8 . 7 . 5 ° 62.32 0.750 0.720 0.029 1.170 1.331 -0.411 0.110 1.791 - 0 . 1 ) 2 0.961 0.038 0.049 0.009 0.568 0.001 0.676 0.002 0.686 0.011 4.990 0.387 9.398 0.377 1.371 0.001 0.111 0.101 0.313 6.511 1 .99 1.68 0.11 • > L 1+7 II 13000 1 uooo l 2000 320.9 320.9 334.4 334.9 404 .1 403 .0 320.9 334.43 •04.9 6 7 . 5 ° 62.32 0.750 0 . 6 ) 2 0 .079 1 .412 1.794 0.118 0 .110 1.904 -0 .172 0.893 0 .103 0 .049 0 .009 0 .319 0 .011 0.597 0.012 0.606 0.011 4 .990 0.367 8.76f 1.039 1.194 0.017 0.091 0.177 0.133 0.437 1.99 1.90 0.19 s 5 s s S c s s - s : i : i : s ; s : * * - O r t f t e . «V>. , § i . I I . I I . I I i i I i l l I i I i l l ! I I - « . l t h t of w . c . r ( l b . ) f r o . H . H . l o P i p . ; » . , l t f l t I r . o c h ; l . U f t b u t •mi . •S5SS V - V u 121.1 121.1 321.1 321.1 • s 320.9 321.0 1 3 0 7 .8  | 3 3 8 .9  { SSssss 3 2 0 .9  3 2 1 .1 3 0 2 .1 3 0 2 .2  124  .4  | 3 2 0 .6  3 2 0 .6  ! 3 1 8 .0  3 1 8 .0  3 2 6 .6  325 !o 3 2 0 .1  3 2 0 .2  1 2 4 .2  3 2 4 .1  3 2 3 .5  1 2 1 .7 • -ll . s % s is • ! 1 • I I s s s s - is E S I 5 s 5 s c « I I I 5 s s ' S S - g * IK fU IK - Specific U e t » h t of v . t . r - ; o i ' c . ( l b . / c . f t ) I i i £ £ 1 £ £ £ £ £ £ £ £ i £ £ £ 11 £ £ 1 £ £ £ £ 1 1 £ £ •i £ I - 1 £ S 1 1 i £ £ £ £ 1 i i - i £ 1 £ £ £ £ £ £ £ ~ ' « > £1 £ £ £1 £ 1 £ £ £ £ i i £ £ £ £ 1 i £ £ £ £ i £ £ •1 £ £ £ i S * P r l c t l o n L o . . ( f e ) . lo K i l o H p . f o r U n j t h 1 . 1 7 5 f c . i I £ 1 £ £ £ £ £ = P i p . f o r U n g t h S t 1 M * 1 " i i S I £ £ i £ 1 £ i £ £ £ £-1 £ £ P r l e t l o o L o . . ( f t ) . In « l , h t or U f t B r . n c h f o r L . n t t h 9 . 0 f t . i i £ £ I £ £ £ £ £ £ £ £ £ £ £ P r l e t l o o U i . ( f t ) . In Right or U f t Branch f o r U n g t h ID, or t D , i i I i £ £ £ £ J £ £ £ 11 I £ £ £ £ £ •> 2 £ £ £ 1 2 1 V . l o c l t , i n M.IO P i p . ( f t / . , c ) S ? = £ £ £ 1 £ 1 £ v . i o c i t r a . . d i n W i n P i p . ( f t ) i i £ £ 1 £ 11 £ £ £ £ £ £ £ £ V . l o c l t y l n Bight or U f t Br .nch ( f t / . . e > i i £ £ £ i i i 1 £ 1 £ £ £ £ I £ I V . l o c l t y Hood l n l i t h e or U f t B e n c h ( f t ) £ £ 1 i £ £ £ £ i £ i I i I 1 £ 1 1 • P o r . L o . . ( f t ) £ £ £ £ £ £ i 1 , £ 1. £ £ £ £ £ 1 £ £ -i 5 . « i « s i; -s S i 'i ~ b b s s b s b b b b b a farnolo". K n u r ( « 1 0 5 ) T9 62 3.9 2 2.7 3 2.7 5 11 2 s * » 8 3 S s ? ? ? ? 2 *• ~ 3 2 2 2 2 2 2 10070711.03 8 S 8 0 0 0 |88 1 8 ! 18 8 S88 188 8 8 8 8 8! (•11) n i l •«< i 8 8 8 8 8 8 8 1 ! 33 . 8 8 s 5 88 (1J) nra.li n r » i q « T l 07 P'»H Jiioc-l*' : 8 8. S 0 0 8 0 0 3 8 0 0 S1 8 ! 81 8! i i e i i° iqtTt 5 l i lool . i s « 8 8 ! ! 38 8 8 8 8 8 8 '5-S 31 (•31) K l l 0 ™ «, pni i i , » o , e . ! 3 8 8 8 i 0 8 8 3 (=••/!») o*U " I * "I fclooie. 2 8 s 8 8 . i i s «' (U) ..<n 00,3.111 i n o i 9 3 ! 38 88 8 8 88 i l 31 8! 33 ««, 1. t « ^ 1 - , 1 . , qoo.1, 1! 0.41 2 0.4 18  8 8 8 8 3 3 II 13 81 81 •31 0 6 qitool-loj qonit " i » ntn =1 (u) «.<n ooii.m 2 88 88 8 8 88 i « 0 0 s i 8 ! 81 8 ! ..,1 H i * oj (11) S ^ o . ; , . " } 8 0 3 8 ! 3 ! i ! 3 • « , . non •n,(ii)C.toi'c«,3.5i. 8 8 3 ! 1 3 3 1 ! 1 « 8. 0 0 88 * s 0 0 qoo»H 9 eo,i t r r o s> qn . i t i i i l n , . 0 , . o^«3«| 9 S3 13 81 S « 0 ' 0 88 5. ? 8-5 H 1.1*7  -0 .1 13  (1J) ooiiooiioo i . r m.i s. s. 0 8 8 8 8 8 8. e 3 2 8 J 5. 1 8 I 8 8 J ^(JJ) T » I i n o » o - § § 1 I 8 j? . <3I> u m i ^ n o o o - 8 s 0 „• 8. ? 1 ! 3 3 S. 3 3 •1 0 0 888 s. s. s 0 0 0 8 8 8 888 881 3 3 3 188 ( i j -ro/.q,) i.im jo iqt,^, j j j i ^ l i ,§ * 3 = 3 S3 * 3 S3 - = s - S. 5 S a «s ». S 3 § 833 s • " S 5 = 3 33 333 I I i 31 i 113 - Ii«§3 277. 2 27 7. 3 ! 321 .9 i 322 .1 320 .1  ! 32 0. 0 329 .3  329 .3  313 .2 | 313 .3 i 311 .6 31 1.7  i  32 0.6  i  320 .7  321 .3 | 321 .7 319 .7 ! 31 9.6  j 1 3 18 .4  JIB .3 317 .3 319 .4  1 31 9. 3 316 .1 314 .0  32 0. 3 320 .6  317 .1 317 .0  1°.-. S s s S s s « f l » t7>PV i l f f i (•qi) 101m 10 1<0,W - i 11 I II I I I l I I I I I 1 1 I I I 5 i i 1 H i i 2 i s i s : s : 1 : 1 - - - » 6»> s c z c B s T e i t K o . I " I I i ; s • 0 r l f l c « N o . . 1 1 .11 . I 1 . i i i i I i i § I I I I I I W e i g h t o f U . t e r ( l b a . ) f r o m H . H a l o P i p s ; R. R i g h t B r a n c h ; L . U f t B r a n c h •m '<- *u <- u 321.0 321.1 321.0 321.1 •SIS 321.2 321.2 307.9 307.6 337.6 337.7 321.0 321.0 327.5 327.6 311.8 311.9 L . " M ^ ' , > « o . 321.1 321.2 318.8 318.9 *- T t M I n t e r v a l ( a e c a ) 323.13 323.13 • n , 5 5 "S 8 . s s a a 3 2 1 .2  3 0 7 .8 5  3 3 7 .6 5  | 3 2 1 .0  3 2 7 .5 5  3 1 1 .8 3  S 5 S b 3 8 3 2 1 .1 5  3 1 8 .8 5  3 2 7 .8 5  \f A v e r a g e T i n e I n t e r v a l ( a e c a ) ! * t i i 5 - T e m p e r a t u r e Ln ° P and S p e c i f i c W e i g h t o f Water ( l b . / c u . f t . ) § i i § 8 s i s s = S I s i § 2 5 § i 2 g l.M » i i § I i i £ Hook Gauge R e a d i n g l n O p a t r e a n Tank ( f t . ) r 8 i 5 ro g I 5 SO Book Cauge R e a d i n g l n C e n t r a l l a n k ( f t . ) 1 O S o * s I £ o s i s Hook Cauge R e a d i n g l n I o i O i 1 o ii o o g B V e r n i e r C o r r e c t i o n ( f t . ) i i i i : 5 5 0 o 1 i o o S = I i i o 3 3 E P r e a a u r e Bead D i f f e r e n c e ( f t . ) between H a l n P i p e 6> R i g h t B r a n c h o r M a i n P i p e 6. L e f t B r a n c h il i i I i o o S 5 C ( D l a c h a r g e l n B r a n c h P i p e / D i s c h a r g e l n H a l n P i p e ) i o i o I o i o I I o i i F r i c t i o n L o a a ( f t ) i n H a l n P i p e f o r U n g t h 3.375 f t . i I I 3 1 I I o 1 C f r i c t i o n L o a a ( f t ) I n H a l n P i p e f o r U n g t h ST : : ii § S i i s s i i * 3 . § s F r i c t i o n U a a ( f t ) l n R i g h t o r Left B r a n c h f o r . L e n g t h 9 . 0 f c . 0.186 0 .0 0 0  1 i 0 o 1 ii i i o e •i i i i i i o o 5 8 = F r i c t i o n L o a a ( f t ) l n R i g h t o r L e f t S t a n c h f o r L e n g t h TD^ o r TDg I i 0 o 1 H 0 o 1 3 11 i I i i o o E 8 i 1 s T o t a l F r i c t i o n L o a a ( f t . ) i 5 2 i ** 3 4> ii ** S V e l o c i t y I n H a l n P i n e ( f t / a e c ) i o s o i o £ i 5 o 5 o i 3 T e l o c i t y Bend In f a i n P i p e ( f t . ) O O O 'O  C 0 9 '»  § 3 o s § s i i § 3 S 5 i s T e l o c i t y l n R i g h t o r U f t B r a n c h ( f t / . . c ) i l I i § § i 3 s s 5 S is s T e l o c i t y B e a d l n R i g h t o r U f t B r a n c h ( f t . ) 8 1 i i 3 3 1 s - 5 i 5 £ B F o r . U a . ( f t . ) i i I • i § i § i i 5 S S S S Form L o t a C o e f f i c i e n t 0 .9 4  1.32 0.00 8 3 U » 'i • 8 s b s a s 5 5 8 S 5 8 K R e y n o l d 1 a Number ( x l O S ) 64 2 2 5 2 2 2 5 5 5 3 2 : 5.5 2 2 2 3 2 2 § 2 2 2 2 2 s * S n S i ! I I I 1 3 ! 1 3 3 3 3 3 3 3 3 3 3 ( « ) . . 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I 3' 3 3 3 I 3 ! ! 3 3 3 3 3 3 q s u . i g . o » « H U,«M J O s 33 3 3 3 3 3 3 3 3 M M IJ 3 3 3 3 3 3 3 3 3 s 3 ! 3 i 3 3 3 ! 3 . , , o l , « ^ - § Ct 5 5 3 3 3 § 5 3 - 1 o ! 3 3 H 3 3 3 §33 !• 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 ! 3 • * 3 1.3 * s t i - S i ! s - , S * » i s £ H I S S 3 a S s Iii ii i a 3 s <-~- - mm asiiSa mm iaaaia •prog 1W\ 8 51 111 1 1 I I 1 « I I 1 111 I 1 * I I i 1 1 i - : s : s : s - s C c o - T « « t H o . i ; i : i : I I * -u i r * » KI O r i f i c e H o . r m x _ t> o ° 8 8 M  10 0 0 0  L  0  r w X ° I 1 0 1  0 0 0 9 1  8  0 0 0 9 1  H  r wt x CO Ul 111 r » X o> s C § i § r m x U . SO C s i § U l W e i g h t o f W a t e r ( l f a i ) . f r o m M . K a l n P i p e ; R. R i g h t B r a n c h ; L . L e f t B r a n c h 1 w w u w w u u w KJ N M N l o o o o m t> m » 3 2 0 .9  3 2 0 .9  3 2 0 .9  3 2 0 .9  3 3 7 .0  3 3 7 .0  3 3 7 .0  3 3 7 .0  u u u u w w O i - 4> w *• 3 2 0 .5  3 2 0 .6  3 2 5 .7  3 2 5 .7  3 13 .8  3 13 .8  w w w w w u a « *° M KI (-> - J CH U) KI *> Time I n t e r v a l ( a e c a ) t * m U» W t u» u> ut m ut ut KI Kt 1 O O Ui U l U» u» K> M 1 O O 3 3 7 .0  3 3 7 .0  S 5 S O u» ut m u> w 3 2 0 .3 5  3 2 5 .7  3 13 .8  | 3 2 1 .2 5  3 1 8 .6 5  3 2 6 .1 3  1 U l A v e r a g e T i m e I n t e r v a l ( a e c a ) rM OR I* ° M K> 0B I . ° KI 9 Kt M 00 a w M KI —• Ut U> KI O . o KI 0B KI CK T e m p e r a t u r e i n ° ? a n d S p e c i f i c W e i g h t o f W a t e r ( I b a / c u . f t ) o o o § £ S 0 .5 0 1  0 .5 0 1  , 0 .0 0 0  0 .7 3 0  0 .7 5 0  0 .0 0 0  0 .8 5 7  0 .8 5 7  0 ,0 0 0  o o o Ut *• - J S S> SO 0 .7 3 1 0 .4 4 3  0 .3 0 7  0 .7 4 9  0 .4 7 8  0 .2 7 1  D l a c h a r g e ( c f a ) « w *> S0 Kt 8 b M O Kt 5* o* 00 w b 0B Rook Gauge R e a d i n g i n U p f t r e a m T a n k ( f t ) | 1 . 1 7 2  CD Kt 1 N KI Kt c* 0B s U l K> U l SO SO Hook Gauge R e a d i n g i n C e n t r a l Tank ( f t ) 0 .7 S 1  o KI o o ut U l Uf -0 .2 5 0  K> b i o VM o Hook Gauge R e a d i n g I n D o m e t r e a t s Tank ( f t ) 0 .2 1 0  o K» o O Kt o o Kt o o Kt o o KI o a KI o V e r n i e r C o r r e c t i o n ( f t ) 0 .3 6 *  -0 .0 2 7  0 .6 8 9  -0 .0 7 3  i r 1— sO ON Kt -J ** O Kt N P- CD S 0 .3 5 2  ' 0 .1 0 3  o o ? u> 0B Ul 4 o b 0* KI t> KI KI KI F r e a a u r e Head D i f f e r e n c e ( f t ) b e t w e e n M a i n P i p e & R i g h t B r a n c h o r K a l n P i p e & L e f t B r a n c h O O * £ V " i> u i i — so o o S is O O k s KI 0B U l D l a c h a r g e R a t i o ( D l a c h a r g e I n B r a n c h P i p e / D l a c h a r g e I n K a l n P i p e ) o b o o b K» * - o 8 <o o 8 Ut O so o 8 SO o ? <o *> F r i c t i o n L o u ( f t ) . I n M a i n P i p e f o r U n g t h 3 . 3 7 5 f t . 0 .0 0 2  o 1 o 8 O b o 8 so o i o 8 so U l F r i c t i o n L o a a ( f t ) , i n K a l n P i p e f o r L e n g t h S T 0 .1 3 0  0 0 0 *0  S O T O  1 0 .6 3 4  0 .0 0 7  0 .2 2 0  o o f KI Kt *- *• U» 0 .2 8 1  CK F r i c t i o n L o i a ( f t ) . i n R i g h t o r L e f t B r a n c h f o r L e n g t h 9 . 0 f t . 0 .1 6 3  0 .0 0 0  0 .3 3 8  0 .0 0 0  o o § I 0 .8 9 6  0 .0 0 0  o o 3 S 0 .2 7 2  0 .13 8  o o O M 5 F r i c t i o n L o a a ( f t ) , i n R i g h t o r L e f t B r a n c h f o r L e n g t h TD^ o r TD^ 0 .14 6  | 0 .0 0 2  o o 8 I 0 .7 1 2  0 .0 0 9  0 .9 0 7  0 .0 1 1  o o C* w» —1 K» 0 .2 8 0  0 .14 7 o o *~ Kt OB O s T o t a l F r i c t i o n L o a a ( f t ) . 2 .0 8 2  M W '•o s U l O Kt P- •» >o vo *> sO CD Ul sO V e l o c i t y I n K a l n P i p e ( f t / a e c ) 0 .0 6 7  O M o u> OB o is U l o U l O" o U l CD CD O k » Kt o . V e l o c i t y H e a d I n K a l n P i p e ( f t ) O O O 'O  9 8 0 '1  6 .5 3 5  0 .0 0 0  9 .7 9 2  0 .0 0 0  1 1 .1 8 9  0 .0 0 0  *> U l ut o- N UJ *> U l 8 3 Ut QS m KI u> *• u i u i KI V e l o c i t y i n R i g h t o r L e f t B r a n c h ( f t / a e c ) 0 .2 3 9  0 .0 0 0  0 .6 6 3  0 .0 0 0  O t - § i S ? o o CO 5 SO Kt o o KI <J* *> K> to O , o O KI K* V e l o c i t y Head i n R i g h t o r L e f t B r a n c h ( f t ) 0 .0 2 6  0 .0 3 9  0 .0 5 6  0 .0 9 5  0 .1 1 0  0 .2 1 1  | 0 .13 4  0 .2 7 6  ^  o o b b Ut KI w *> 0 .0 2 0  1  0 .0 4 0  0 .0 2 2  0 .0 5 2  KI Ut F o r m L o a a ( f t ) o o Mi W 0 .3 2 3  0 .5 5 2  o o o o t S 0 .0 6 1  0 .0 8 6  0 .0 5 2  | 0 .1 0 3 j o o KI *• ( A v e r a g e ) F o r n L o a a C o e f f i c i e n t 0 .8 4  1 .1 7  . 0 .0 0  8 5 IS 2 .0 0  2 .8 1  0 .0 0  2 .2 9  3 .2 1 0 .0 0  KI Ul SO u> m so C> S 8 2 3 8 KI U l R e y n o l d ' s Humber ( x i o ' ) 66 2 2 :• 5 2 2 2 5 5 2 2 2 2 S 2 l.ot 2.76 0.11 2 2 3 2 2 3 2 2 2 lu 1 3 3 1 3 3 1 1 3 1 3 3 3 3 3 3 ! 3 . 3 3 ())) • u o i 3 3 3 ! 3 3 ! 3 5 3 3 3 •3 3 3 3 3 3 - ^ , J ) u o o . i . ^ l r ] 10 » 3 3 1 3 3 3 3 3 3 3 3 3 3 3 3 3 3 ! s 3 3 : 3 3 ! ! !• 2 3 3 3 3 3 ?• 3 3 2 «!« o i w 01 p«. H i j i o o t o a s s 3 3 3 3 3 3 3 3 = s. 3 ! 3 ! ! ! = I ! 3 3 3 3 3 3 ! 3 3 3 3 ! 3 ! 3 ! l o ^ ^ r u - d s 33 1 3 3 3 3 3 . I i 3 3 3 ! 3 3 1 1 •»l 0-.« 01»o»i J O J ooooil a m '» M » 1 I -1 C H ) "<"1 O M J O H 1 33 3 3 3 3 3 3 3 ! 3 1 ! 3 3 5 = 3 3 i 3 i. o 3 ! 3 ! 3 3 3 ! ! ! ! ! ! 3 ! 3 ! 3 3 3 3 2 3 ! 3 3 1 3 3 ! 3 3 ! J M 3 5 < » > ~ — 3 3 3 3 3 3 3 3 2 5 3 3 ! 3 3 5 3 • 3 J 1 3 3 2 3 3 •3 - 1 3 5 3 3 ? ! 3 3 ' C o ) . - - p . , . 3 3 3 ! 3 3 3 3 3 3 3 3 1 3 3 3 3 3 3 3 ! 3 3 3 3 3 3 - * 3 * \ v 3 s\ %\ • 3 *3 «3 * 3 - i l l \\\ : i s I 5 i » i a a a ill a a s s S i i l l - liaSli ii'ssss iasgli 321.1  32 1, 1 32 1. 0 32 1. 0 31 9. 6 Ssasaa mm mm iiiiii mm H I I I I 1 I I I 1 1 III ! 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L e f t B r a n c h 4 4 5 .5  4 4 5 .7  4 4 5 .5  4 4 5 .7  4 2 9 .3  4 2 9 .3  4 2 9 .3  4 2 9 .3  3 2 1 .1 3 2 1 .0  3 2 1 .1  3 2 1 .0  3 6 0 .2  3 6 0 .3  3 6 0 .2  3 6 0 .3  4 0 7 .3  4 0 7 .3  4 2 4 .7  , 4 2 4 .7  4 3 5 .3  4 3 5 .3  4 0 6 .7  4 0 6 .7  5 0 5 .1  5 0 5 .0  4 6 7 .9  6 6 8 .0  *• Time I n t e r v a l ( s e c a ) t s W» Ui '<* "o «• »• •o >o 3 2 1 .0 5  3 2 1 .0 5  - 3 6 0 .2 5  3 6 0 .2 5  4 0 7 .3  4 2 4 .7  4 3 5 .3  4 0 6 .7  5 0 5 .0 5  6 6 7 .9 3  A v e r a g e Time I n t e r v a l ( a e c a ) •> -o u o 7 0 ° 6 2 .3 0  o 7 0 ° 6 2 .3 0  ~ 3 o Ul o OH T e m p e r a t u r e i n ° F and S p e c i f i c W e i g h t o f Water ( l b s / c u . f t ) . 0 .3 6 0 1 0 .3 6 0  0 .5 6 1  0 .5 6 1  0 .0 0 0  0 .7 5 0  0 .7 5 0  0 .8 4 7  0 .8 4 7  0 . 74 9  0 .4 1 6  0 .3 3 2  0 .7 5 0  0 .4 7 7  0 .2 7 4  D i s c h a r g e ( c f s ) 1 .5 3 1  N ? M M 2 .0 3 8  2 .1 8 5  1 .0 8 0  a Hook Gauge R e a d i n g i n U p s t r e a m Tank ( f t ) 1 .7 7 1  u» o K> **» co ' *» M 2 .2 7 0  1.3 0 2  >e Hook Cauge R e a d i n g l n C e n t r a l Tank ( f t ) 1 .2 5 6  1 .2 1 5  O u> u> te -0 .2 6 8  1 .9 5 5  o £ o Hook Gauge R e a d i n g I n Downstream Tank ( f t ) 0 .2 1 0  0 .2 1 0  0 .2 1 0  0 .2 1 0  0 .2 1 0  0 .2 1 0  5 V e r n i e r C o r r e c t i o n ( f t ) 0 .4 8 5  -0 .0 3 0  1 .1 3 9  -0 .0 7 6  1 .9 9 3  -0 .1 3 6  2 .3 16  - 0 .1 7 5  o o M *> Ut O o o 2 | ro P r e s s u r e Head D i f f e r e n c e ( f t ) , between H a l n P i p e & R i g h t B r a n c h o r M a i n P i p e & L e f t B r a n c h 0 .5 5 7  0 .4 4 3  ? ? ui o» » Ul Lr> Ul u> D i s c h a r g e R a t i o ( D i s c h a r g e i n B r a n c h P i p e / ' D i s c h a r g e i n M a i n P i p e ) . 0 .0 1 3  o *o 0 .0 4 9  1  0 .0 6 1  j o O **> s P r l c t l o n L o s * ( f t ) , i n H a l n P i p e f o r L e n g t h 3 . 3 7 5 f c . 0 .0 0 2  0 .0 0 5  6 0 0 *0  0 .0 1 1  | 0 .0 0 9  o I F r i c t i o n L o s s ( f t ) , i n M a i n P i p e f o r L e n g t h S T 0 .1 6 8  0 .0 0 0  0 .3 7 4  0 .0 0 0  0 .6 3 4  0 .0 0 0  0 .7 8 9  | 0 .0 0 0  o o •> a 0 .2 7 9  0 .1 0 2  F r i c t i o n L o s s ( f t ) , l n R i g h t o r L e f t B r a n c h f o r L e n g t h 9 . 0 f t . 0 .1 8 6  o.ooo o o s S o» 0 .7 0 4  0 .0 0 0  1 0 .8 7 6  ! o.ooo 1 1 0 .2 4 2  0 .1 5 9  j 0 .1 1 0  0 .1 1 3  | = F r i c t i o n L o s s ( f t ) . i n R i g h t o r L e f t B r a n c h f o r L e n g t h TD^ o r TD^ 0 .1 8 9  0 .0 0 2  0 .4 2 1  0 .0 0 5  1 0 .7 1 2  0 .0 0 9  • 0 .8 8 7  0 .0 1 1  1 0 .2 5 0  0 .1 6 8  0 .3 18  0 .1 2 1 a T o t a l F r i c t i o n L o s s ( f t ) 2 .3 9 7  3 .7 3 1 5 .6 3 3  *• vO CD *>o a> V e l o c i t y l n H a l n P i p e ( f t / s e c ) 6 8 0  0  0 .2 1 6  0 .3 8 7  | 0 .4 9 3  o Ul CO Ul 0 .3 8 7  ro O V e l o c i t y Head I n M a i n P i p e ( f t ) 4 .7 0 3  0 .0 0 0  7 .3 2 2  0 .0 0 0  9 .7 9 0  0 .0 0 0  1 1 .0 5 2  0 .0 0 0  *• ui U O* aa . J M * - s V e l o c i t y I n R i g h t o r L e f t B r a n c h ( f t / s e c ) O O O 'O  tw o 0.8 3 1  o — O *" Q ce O CD 1.8 9 7 0 .0 0 0  o o •O **» j£ 4̂ 0 .6 0 1  ro V e l o c i t y Head i n R i g h t o r L e f t B r a n c h ( f t ) o . o 8 8 0 .1 0 2  0 .1 3 3  O O M «e 0 .2 2 5  0 .3 0 7  0 .1 1 8  0 .0 5 1  0 .1 1 5  0 .0 5 4  ro Ul F o r m L o a a ( f t ) 0 .4 7 1  0 .6 3 8  0 .4 7 2  0 .6 2 3  J 0 .4 6 3  0 .6 2 6  p a 0.3 0 6  1  0 .1 3 2  0 .2  9 7 0 .1 4 0  ( A v e r a g e ) Form L o s e C o e f f i c i e n t 0 .9 9  1 .3 9  0 .0 0  1 .5 4  2 .1 6  0 .0 0  2 .0 6  2 .8 9  0 .0 0  2 .3 2  3 .2 6  0 .0 0  s s a 2 .0 6  1 .8 3  1 .0 6  R e y n o l d ' s Number ( x l O ^ ) S 68 s a c « ~ « 8 2 = n ' ~ ~ 5 5 :• 3 3 : S * i - d o' 2 2 2 2 :• 3 R S B ~ ~ d 2 2 I a l l ! S 3 ! !!I 1 3 3 • 33 '53 3 2 12 (aj) .«n .ao* ! ! 1! II 3 ! i 5 3 3 3 2 22 3 5 <aa> u.oo.a. aj»a jo auSia 01 P.-U <a , o o , . 4 K 2 2 2 I 3 3 3 3 ! 5 o' d 31 ! ! s I -' d 3 5 (=»•/»» 0 O « . a . aj»l Jo J o l « 01 i a i o o i . j s 5. 5 o. o. i 5 !3 33 S 3 = ° 1 s 2 - 2 2 2! (JI) . o H o , W o , •am <al»oi. A 2 ! i 3 3 2 o' 2 2 2 5 ( 3 . . / 5 j ) . d M « J « H « 1 i a i o o t . j 3 s ! 3 3 5 • 5 .' 3 S 2 2 13 3 3 3 3 1! 3 ! ! ! 2! 22 2 1 3 i 3 3 3 3 5 3 5 5 ! ! ! ! 22 •33 0 '6 H 3 » u » l JOJ 33*1 JO SIJIITH u i -.(a.)) aao*i u o n a i J i s 22 3 3 3 3 s s o' d 3 3 5 3 3 ! ! 2 3 3' IS l i * " * ! JO; 2 i 3 5 !• 5 3 2 3 3 S s o § d S 3 3 I !• I ! uauMa »1 »lj»u3 » ia ) 2 2! ! 2 2! 2 5 ipuMfl. aj»i «j wlia ni*N Jo . s i 3 3 3 3 2.2 5 3 M M \ M i 3 3 3 3 3 3 3 5 2 2 5 ?• ! 3 5 J J 2 2 5 «? 3 5 3 2 3 3 - a o' 3 s _.' 3 5 d I 3 3 2 - 3 5 5 !22 3 3 ! 3 3 3 1 3 3 3-5 3 ! ! ! 222 222 <3)"«.»/"<n) « 3 » f l t° 3 M « T " n 3T3T3»«li pu* i o u i » j i .3 «J »dn» l - * 3 s 3 >. > 5 s 3 * ^3 * § • - i 3 i 5 5 3 c , S s 1 s i i i i i i i I i 2 *• °-s 2 * 1 !l I » -S s s i l i i i i s s i i i 1 i i i i i i S'S55sS 343.9  3* 4  . 0  3 5 7 .3  3 5 7 .3  4 2 3 .3  4 2 3 .9  i i i i i i R S S R S K Uou.ag I j a V T ! u o a « J « au»T. ' 1 !»diJ. - I I I I I I I I § a s s I I I § | | 1 I I l i s I I I 1 1 i 'on . o i l f a o - ; s « * •on a . . i - - •> 5 Ul z 5 o T c i t Mo. i : s ; I " x n & f t " Ul f- O r i f i c e Ho. r tm x o § i t- • ae . I i «- >• ac o i i r> » x ve vo o § § •r* et X § § § t- » X 09 0. VO 1 § 1 - Weight of Wecer ( l b i ) f r c a H . Halo f l p e ; R.Right Branch; L . L e f t Branch 345.0 343.1 343.0 343.1 u w w u « - b i - b •>(•<»« -o o* -a o> •> i> o> <£ o o « M M b b *• Tine I n t e r v a l (eece) Ui Ui o o * « •e <« b b e> at CM- Ok 04 0> ui o> •e vo n at o> o 2 ? 5 "o> M o Average T 1 M l o t e r v a l (aeca) M * ui la M O o> o> M » t> 0> UT- Ui to o 0> 04 M -O O 0> 0> 1**, 0̂ tvt o> Tenperature l a °P and S p e c i f i c Weight of Water ( l b e / c u . f t ) O O O S " " O M N o o o o o o o o o | s s o o o Ul Ul vB 4* X K o o o Oteeharfje (cfa) Ul 0* M 2 M o to b 0> i to b o> Book Gauge Reedla 3 l o Opetreen Tank ( f t ) 8 § CB ve 8 U> vO Book Gauge Reading l a C e n t r a l Tack ( f t ) M o o ut ut o 0V b » o Book Gauge Reading i n Dovmitreata Tank ( f t ) O . o © o o o p o p o o o = V e r n i e r C o r r e c t i o n ( f t ) ~ o o ? S M 9> o «- o »- vO <> o> vo Ul O «• M Ui <o ut o o 8 i o o s s U> M Pre M u r e Bead D i f f e r e n c e ( f t ) between Main Pipe & Right Branch or Main Pipe & L e f t Branch o o 5 i p p u> o> 04 ut K I Ct> = Dlacharge Ratio (Dlacharge i n Branch Pipe/ Dlacharge i n HeIn Pipe ) O b a> o '8 o D 8 vO O 8 o b o b - F r i c t i o n Loaa ( f t ) . In K a l n Pipe f o r U n g t h 3.37S f t . o § o 8 Ui O i O b o p b o b to = F r i c t i o n U a a ( f t ) . In Main Pipe f o r U n g t h ST 0.17« O.OOO o o § 2 o a § 5 o o § 3 o o 5 5 p p V •* o F r i c t i o n U a a ( f t ) , l o t i g h t or U f t Branch f o r U n g t h 9.0 f t . 00 0* 0 MI 'O  o o § S o o fi vO S 0> o o § g P o M UJ S 5 p p s i - P r l c t l o a Loae ( f t ) . In Right o r U f t Branch f o r U n g t h TD^ o r TD^ 0.201 0.002 o o 8 'S ui e> o o p o b *o» O M p p ve o p •> V at T o t a l F r i c t i o n U a a ( f t ) Ul » e» 1 Ui Ok 5 to 0* <o V e l o c i t y In Main Pipe ( f t / e e c ) o 3 Ui p OJ p <M o o Ul o s O k o V e l o c i t y Bead i n Main Pipe ( f t ) o •*- § 5 O -* § * O vB § 8 0 E 1 8 U> «-J b o <o ui 0> u> » V 0> ss V e l o c i t y In Right or U f t Branch ( f t / a e c ) OO O' O m co  0 o 1 1 o 1 5 o O vO 8 8 p o vB 3» a ui p p to <o «o j-^ V e l o c i t y Heed i n Right o r U f t Branch ( f t ) 0.034 0.031 p p o> p p o o o o s s 0V 1— o o 'S i3 O Form Loaa ( f t ) o o 5 5 o o . U> Ul M ve o o * 2 o o o o '8 8 o o 8 ? 0" Ul (Average) Forn Loaa C o e f f i c i e n t o •- o 8 t i S 8 S S 8 a * 8 5 Ul M S ui C C S s Reynold'a Number ( a l o ' ) Si 7 TABLE V-16 Data of Hydraul ic Power Losses i n Wye Arrangements A. 9 0 ° Wye Without T i e - r o d Q (cfs) Qb Qm K P Q (cfs) Qb Qm K P M 0.748 M 0.747 R 0.748 1.000 0.322 0 .322 R 0.552 0.740 0 .149 0 .173 L 0.000 0.000 0.526 L 0.195 0.260 0 .243 M 0.752 M 0.753 R 0.740 0.984 0.290 0 .294 R 0.479 0.638 0 .148 0 .158 L 0.012 0.016 0 .521 L 0.273 0.362 0 .175 M 0.748 M 0.753 R 0.717 0.957 0.264 0 .274 R 0.444 0.591 0 .126 0 .138 L 0.032 0.043 0.493 L 0.308 0.409 0 .155 M 0.751 M 0.751 R 0.674 0.895 0.210 0 .233 R 0.416 0.555 0 .134 0 .137 L 0.078 0.105 0.429 L 0.334 0.445 0 .140 M 0.752 M 0.749 R 0.595 0.791 0.166 0 .193 R 0.374 0.499 0 .146 0 .134 L 0.157 0.209 0.296 L 0.375 0.501 0 .123 B. 90 Wye with TR3 T i e - r o d Q (cfs) M 0. 7*8 R 0.748 L 0.000 M 0.752 R 0.739 L 0.012 M 0.748 R 0.716 L 0.032 Qb Qm K 1.000 0.530 0.530 0.000 0.582 0.984 0.486 0.487 0.016 0.578 0.957 0.469 0.473 0.043 0.556 Q (cfs) Qb Qm K M 0.747 R 0.553 L 0.194 M 0.749 R 0.476 L 0.273 M 0.749 R 0.441 L 0.308 0.740 0.279 0.287 0.260 0.309 0.636 0.366 0.320 0.364 0.240 0.588 0.399 0.331 0.412 0.234 71 TABLE V-16 - - (Continued) Q (cfs) Qb Qm K P Q (cfs) Qb Qm K P M 0.751 M 0.748 R 0.673 0.895 0.390 0.401 R 0.414 0.553 0.358 0 .307 L 0.078 0 .105 0.496 L .0.334 0.447 0.244 M 0.748 M 0.749 R 0.592 0 .791 0.307 0.320 R 0.375 0.501 0.323 0 .317 L 0.156 0 .209 0.367 L 0.374 0.499 0.312 C. 6 0 ° Wye without T i e -•rod Q (cfs) Qb Qm K P Q (cfs) Qb Qm K P M 0.750 M 0.749 R 0.750 1 .000 0.292 0.292 R 0.555 0.742 0.060 0 .100 L 0.000 0 .000 0.554 L 0.195 0.258 0.213 M 0.749 M 0.750 R 0.737 0 .984 0.274 0.278 R 0.480 0.640 0.052 0 .077 L 0.012 0 .016 0.548 L 0.271 0.360 0.121 M 0.749 M 0.749 R 0.717 0 .958 0.194 0.207 R 0.416 0.556 0.057 0 .069 L 0.034 0 .042 0.518 L 0.332 0.444 0.084 M 0.750 M 0.750 R 0.673 0 .897 0.135 0.166 R 0.376 0.501 0.073 0 .069 L 0.079 0 .103 0.434 L 0.374 0.499 0.065 M 0.752 R 0.596 0 .793 0.086 0.126 L 0.157 0 .207 0.281 72 TABLE V-16 -- (Continued) D. 60° Wye with TR3 Tie--rod E. 45° Wye without Tie-•rod Q (cfs) Qb Qm K P Q (cfs) Qb Qm K P M 0.749 M 0.844 R 0.749 1.000 0.454 0.454 R 0.844 1.000 0.484 0.484 L 0.000 0.000 0.625 L 0.000 0.000 0.538 M 0.748 M 0.898 R 0.736 0.984 0.426 0.428 R 0.863 0.960 0.390 0.394 L 0.012 0.016 0.612 L 0.035 0.040 0.499 M 0.745 M 0.922 R 0.712 0.957 0.402 0.409 R 0.836 0.906 0.270 0.284 L 0.032 0.043 0.590 L 0.086 0.094 0.424 M 0.747 M 0.923 R 0.669 0.896 0.333 0.351 R 0.729 0.789 0.130 0.152 L 0.078 0.104 0.509 L 0.193 0.211 0.236 M 0.746 M 0.922 R 0.509 0.682 0.268 0.240 R 0.646 0.700 0.063 0.088 L 0.238 0.318 0.180 L 0.275 0.300 0.146 M 0.744 M 0.923 R 0.438 0.588 0.311 0.237 R 0.588 0.637 0.035 0.059 L 0.307 0.412 0.132 L 0.334 0.363 0.102 M 0.742 M 0.923 R 0.411 0.553 0.294 0.236 R 0.540 0.585 0.028 0.050 L 0.331 0.447 0.164 L 0.382 0.415 0.081 M 0.750 M 0.923 R 0.375 0.500 0.232 0.230 R 0.462 0.501 0.041 0.046 L 0.375 0.500 0.227 L 0.460 0.499 0.051 TABLE V-l7 Data of Hydraulic Power Losses i n Manifold Arrangements A. 90° Manifold without Tie-rod Q (cfs) Qb Qm K P Q (cfs) Qb Qm K P M 0.750 M 0.751 R 0.750 1.000 0.348 0.348 R 0.555 0.736 0 .177 0.206 L 0.000 0.000 0.541 L 0.197 0.264 0 .286 M 0.750 M 0.750 R 0.739 0.984 0.320 0.323 R 0.478 0.637 0 .170 0.193 L 0.012 0.016 0.532 L 0.272 0.363 0 .234 M 0.750 M 0.751 R 0.720 0.962 0.315 0.323 R 0.442 0.590 0 .175 0.192 L 0.029 0.038 0.521 L 0.308 0.410 0 .216 M 0.750 M 0.750 R 0.672 0.895 0.235 0.258 R 0.417 0.557 0 .182 0.203 L 0.079 0.105 0.457 L 0.332 0.443 0 .207 M 0.752 M 0.751 R 0.594 0.788 0.190 0.221 R 0.375 0.499 0 .188 0.184 L 0.159 0.212 0.339 L 0.376 0.501 0 .180 B. 90° Manifold with TR3 Tie-rod Q (cfs) qb Qm K P Q (cfs) Ob Qm K P M 0.750 M 0.750 R 0.750 1.000 0.500 0.500 R 0.447 0.636 0 .383 0.349 L 0.000 0.000 0.588 L 0.273 0.364 0 .289 M 0.750 M 0.750 R 0.718 0.956 0.445 0.450 R 0.441 0.588 0 .405 0.353 L 0.033 0.044 0.562 L 0.309 0.412 0 .280 M 0.749 M 0.750 R 0.671 0.895 0.376 0.390 R 0.417 0.556 0 .370 0.333 L 0.079 0.105 0.514 L 0.333 0.444 0.286 74 TABLE V-17 -- (Continued) Q (cfs) Ob Qm K P Q (cfs) Qb Qm K P M 0.751 M 0.751 R 0.592 0.789 0.320 0.337 R 0.374 0.499 0.318 0.315 L 0.158 0.211 0.403 L 0.376 0.501 0.313 M 0.750 R 0.554 0.739 0.301 0.314 L 0.196 0.261 0.351 C. 60° Manifold without Tie-rod Q (cfs) Qb Qm K P Q (cfs) Qb Qm K P M 0.750 M 0.749 R 0.750 1.000 0.283 0.283 R 0.478 0.638 0.057 0.085 L 0.000 0.000 0.546 L 0.271 0.362 0.134 M 0.750 M 0.751 R 0.718 0.956 0.207 0.220 R 0.443 0.591 0.052 0.072 L 0.033 0.044 0.514 L 0.307 0.409 0.102 M 0.749 M 0.749 R 0.672 0.895 0.144 0.175 R 0.418 0.559 0.061 0.072 L 0.078 0.105 0.445 L 0.330 0.441 0.086 M 0.751 M 0.750 R 0.593 0.788 0.057 0.107 R 0.375 0.499 0.055 0.060 L 0.159 0.212 0.294 L 0.376 0.501 0.065 M 0.749 R 0.554 0.739 0.063 0.104 L 0.196 0.261 0.221 75 TABLE V-l7 — (Continued) D. 60° Manifold with TR3 Tie-rod E, . 45° Manifold without Tie-rod Q (cfs) Qb Qm K P Q (cfs) Qb Qm K P M 0.750 M 0.847 R 0.750 1.000 0.463 0 .463 R 0.847 1.000 0.516 0.516 L 0.000 0.000 0.626 L 0.000 0.000 0.536 M 0.751 M 0.887 R 0.718 0.955 0.419 0 .427 R 0.853 0.962 0.382 0.386 L 0.034 0.045 0.595 L 0.034 0.038 0.499 M 0.750 M 0.922 R 0.671 0.893 0.347 0 .365 R 0.836 0.906 0.272 0 .286 L 0.080 0.107 0.518 L 0.086 0.094 0.426 M 0.750 M 0.922 R 0.592 0.788 0.284 0 .299 R 0.728 0.790 0.118 0.143 L 0.159 0.212 0.354 L 0.1.94 0.210 0.236 M 0.750 M 0.922 R 0.555 0.739 0.264 0 .266 R 0.646 0.700 0.057 0.080 L 0.196 0.261 0.274 L 0.276 0.300 0.135 M 0.750 M 0.921 R 0.477 0.635 0.297 0 .239 R 0.587 0.638 0.045 0.060 L 0.274 0.365 0.140 L 0.334 0.362 0.086 M 0.749 M 0.922 R 0.416 0.557 0.306 0 .229 R 0.538 0.584 0.036 0.046 L 0.332 0.443 0.132 L 0.384 0.416 0.061 M 0.750 M 0.921 R 0.375 0.499 0.201 0 .218 R 0.459 0.499 0.031 0.037 L 0.376 0.501 0.236 L 0.461 0.501 0.041 76 TABLE A - l Distance from T h e o r e t i c a l Center of Elbows to Piezometric Rings on S t r a i g h t Pipe * P a r t i c u l a r s Distance SS* f t . Distance s'c f t . Distance CF f t . Distance FD f t . Distance SD f t . 4 5 ° elbows 0.167 0.641 . 0.5 8.833 10.141 3 0 ° elbows 0.167 0.333 0.333 8.833 9.666 22%° elbows 0.167 0.370 0.238 8.833 9.608 Note: the average radius of each elbow i s 15 i n c h e s . •* See Figure A-2 L e f t Elbow Right Elbow I—1 t - 1 i - 1 1—1 (—1 t—' I-1 O N o O N vo O N o U i VO U i o o O U l o o o o o o O o o o o NJ o o o o o o o o OJ u> OJ OJ OJ OJ 0J OJ 00 OJ OJ OJ OJ 0J OJ OJ u> OJ •P- -P- OJ OJ OJ OJ I-1 I-* I-1 I-1 OJ OJ U l U l '—1 ~J (—1 H-1 o o 4> -P- O N O N vO vo -p- •p- OJ •P" -P - - J ^1 OJ OJ •p~ OJ -p- -p- OJ OJ l - » I-* OJ OJ OJ OJ OJ OJ OJ OJ OJ OJ OJ -p- OJ OJ OJ U l o -p- O N VO •p- •p- j > - J OJ OJ OJ OJ U l O N O N O N O N O N O N O N O N O N O N O N N J « - J NJ NJ «~4 NJ vo NJ vo NJ VO NJ O N • o • O . o • o VO U l o OJ O OJ o OJ o OJ U i OJ U l OJ U l OJ o o O o o h-» O I-1 o I-1 o I-1 o O o o O o o o OJ U i VO OJ U l vO O N I-1 O U i OJ o U i I-1 OJ O N •P- •p- NJ « J .p- NJ h-1 o o o r-* o o o -~J vO o o - J 00 vO b o O N o o NJ o o o O o o vO O N t-o 00 OJ NJ •P- ~J •p- I-1 o o 1 o I-1 o o 1 o 00 OJ NJ 00 b o 0J NJ 00 OJ U i o NJ U i o •p- o NJ O N U l •p- N > o O o I-1 o o o I-1 • • • • • • • • OJ I-1 I-1 OJ I-1 vo O N CO o o OJ O N vO VO NJ O N OJ o OJ O N O O o o o o I-1 I-1 OJ b h- 1 OJ b -P- •P- M •p- •P* U l NJ I-1 o U l VO 00 o O N NJ NJ co o o O o o o o o b b b b b b b b 1—1 o r-» NJ •p- o M NJ •p- I-1 U i NJ 00 N i •P- OJ 00 o O O o o o o o b b b (-* b b b l-> (—1 -p- vo OJ NJ U l VO OJ NJ NJ VO vO NJ h- 1 VO vO O o o o O o o o b b b b b b b b I-1 CO O N 00 ^1 O N O N OJ 1 U i OJ U l NJ O N U l O N OJ Description Weight of Water from Main Pipe (lbs) Time In t e r v a l (sees) Ave. Time Interval (sees) Temp, i n F & S p e c i f i c Wt. of Water (lb/c u . f t . ) Discharge (cfs) Hook Gauge Reading i n Upstream Tank ( f t ) Hook Gauge Reading i n Downstream Tank ( f t ) Pressure Head Difference ( f t ) (Vernier Correc- t i o n 0.210 f t . ) Total F r i c t i o n Loss ( f t ) V e l o c i t y Head Correction ( f t ) Elbow Loss ( f t ) Elbow Loss C o e f f i c i e n t LL Left Elbow Right Elbow 1—1 r-1 I-1 I-1 I-1 O U i VO Ov o U l vO o O o U l o o O to o o O o o o o O o o O o o o o O LO LO Lo LO LO LO LO LO Lo LO LO LO LO Lo LO LO LO U> r-> M r-» h- 1 to to to to r-> !-• i - » r-» to to to ro « J - J vO VD as as 00 00 00 00 U l U l 00 00 LO oo oo •P- •P- to to as oo - ^ i •~J ON Ov Ov VO oo LO LO LO LO LO LO LO LO LO r-1 r -» to to r-1 h- 1 to to VO as co 00 U i 00 •P-• • • • • • • * 00 •P- to as as OV oo U l U i U l U l as as ON as OV Ov as as OV OV OV as to as to as to as to Ov to vO to VO to vo to vO • VO • vO • VO • vO U i u> o LO o Lo o LO O LO U i LO U l LO U i LO U l 1—1 l - 1 I—1 I-* o H* O M O o o o o O o o O o • • • • • • • 00 U i VO Lo U l VO as r-> o U i LO r—1 o as to LO ON •p- LO ^1 •p- LO ~J O o O I-1 o o o • • • • • • • • 00 U l U l 00 U l LO ON U l as ^ 1 •p- VO U l ON to o •̂ J U i 00 r-> 1—* o o i o I- 1 o o 1 o . • t> • • • « • to to as to to 00 VO r-1 LO VO LO o as VO •P- •P- t-1 LO o to to VO O O O r-> o o o • • • • • • • • LO O h-1 LO o vO U l U l to U i U l -p- as to 00 VO o U i U l ON o o O o o o O o • • • • • • • • r—1 LO as O I-1 LO vO o -p- LO oo •P- LO o vO o LO h-1 LO to VO o O o o O O o O • • . • • • • • r-> o O o o o o o o I-1 o (-> to -p- o I-1 to -p- U i to oo w U i LO oo LO o o o o o O o O • • • • • • • . r—1 o o o r-1 o o o r—1 to t-> LO O h-1 LO O ^1 ~J o r-» ~J LO LO o O o O O O o O . • • • • • • • 1—' o o o O o o o O LO as U l •P- •P- as U l -p- •P--p- U l ON -P- Lo U l U l Description Weight of Water from Main Pipe (lbs) Time Interval (sees) Ave. Time Interval (sees) Temp, in F & Specific Wt. of Water (lb/cu.ft.) Discharge (cfs) Hook Gauge Reading in Upstream Tank (ft) Hook Gauge Reading in Downstream Tank (ft) Pressure Head Difference (ft) (Vernier Correc- tion 0.210 ft.) Total Friction Loss (ft) Velocity Head Correction (ft) Elbow Loss (ft) Elbow Loss Coefficient i LO fD P O. O CO co a P rt H i O l i LO O O m I—1 a1 o si CO Left Elbow Right Elbow I-1 h-» 1—1 h-1 t - 1 I-1 H-* CN O U i VO O N o U i VO o O o O o o o O NJ o O o O o o o O o O o O o o o O Lo LO LO LO LO LO L o LO LO LO LO LO LO LO L o LO NJ NJ I-1 l-> NJ NJ NJ NJ NJ NJ NJ NJ I-1 l - 1 L0 LO NJ NJ oo 00 I-1 h-* l-> K-* O N O N O O h- 1 l-> LO Ln -P- CN O l-> LO NJ LO -P- O N ~J U i U l I-1 M (jJ LO LO LO LO LO LO LO NJ NJ NJ NJ NJ I-1 LO NJ oo 1—1 O N O I-1 •P-• • • • • • • • •P- CN o NJ Lo O N U l >-* L n U i U i U l U l U l O N O N O N O N O N O N O N O N O N O N O N NJ CN NJ CN NJ O N NJ vo NJ VO NJ vo NJ O N NJ O N • VO • VO • vO • • • • • • . VO • vo U l Lo O LO O LO O LO U l Lo U l LO U l LO O LO O r-> I-1 (—* o o I-1 o l - » I—1 O O o o o o O O • • • • B a • • NJ U l VO NJ U l vO O N vO o U l NJ VO o O N NJ VO -P" o I-1 U i I-1 o NJ I-1 o o O J—1 o o O • • • # • • • a VO oo O N •P- vo 00 O N LO •P" o -P- I-1 LO •P- O NJ NJ NJ -P- LO -~J o o O I-1 o o 1 o • • • • • • • • CN 00 L o U i LO 00 O o O U l 00 NJ O N LO LO NJ NJ U l NJ O O o l-> O O O 1—1 • * « • • • • • Lo O I-1 LO o VO LO •P- NJ LO •P- NJ I-1 -̂ 1 vO o •P- LO NJ NJ VO O O o O O O O o • • • • • • • • I-1 I-1 LO O N VO LO O N VO o NJ NJ - J 00 NJ NJ VO CO 00 VO O N o U l U l NJ LO O O o o O O O O • . • • • • • • o O o o O O o o I-1 o I-* NJ •p- o t-> NJ •p- •p- LO - J l - 1 U l NJ 00 NJ o O O o o O O O • « a • • • • • I—1 o O o o o O o o NJ I-* Lo O N 00 I—* NJ U l -p- LO r-> U l NJ vo oo 00 o O o o O O o o • • • • • • • • h- 1 o O o o o o o o LO U l •P- •P- LO U l •p- LO LO 00 vO 00 •p- •p- oo U i Description Weight of Water from Main Pipe (lbs) Time Interval (sees) Ave. Time Interval (sees) Temp, in F & Specific Wt. of Water (lb/cu.ft.) Discharge (cfs) Hook Gauge Reading in Upstream Tank (ft) Hook Gauge Reading in Downstream Tank (ft) Pressure Head Difference (ft) (Vernier Correc- tion 0.210 ft.) Total Friction Loss (ft) Velocity Head Correction (ft) Elbow Loss (ft) Elbow Loss Coefficient 6L GRAVITY SUPPLY fPOM TH£ OVERHEAD TSMK 1 £M> P/£CE STAT/OA/ I—f/RST/?£&UCE# E C E V A T / O f V FIGURE 1-1 Details of General Arrangement 81 82 MAM P'PZ FIGURE 1-3 Model Layout and Manometric Locations f o r Wye Arrangement TROUGHS P/p£S eLBOWS mi* PIPE \ I t COlieCT/NG P'P£ 705UMP> .: i i i — C0UECTM6 P<P£ ro W£/GH/rt6 TANK G/)U6£ TANA'S BOARD FIGURE 1-4 Details of Manifold Arrangement Pt£Z<yf£77?/C- L£fT JBP/tfJCAf p/Ezoifm/c. AWN P/P£ P/£ZQAt£r/ftC- Af///G AlAlN PIPE PVEZOAfETP/C KING MPT BAMMCM p/p& DOWA/STPEAM GAU6E TANK C£U77?A1L GA(/6& TANA 6 MAN0META7JC TUBES 7 o UPSHREA)M GQUGE FIGURE 1-5 Model Layout and Manometric Locations f o r Arrangement 85 3%d "IO £l/C/T£ smrro// P/£ZOMEZRIC P/A/GS 5/* ID me/re AfAJN P/P£ S~Sr/)A/£MPD &0W ST/V)/&HT£H£P P/PST p£DUC£R ST££L P/A£ i • — i i J i i 05 5 06 CP05S S£CT/W OD rsr/?/)/6//r£A/£P) FIGURE 1-6 D e t a i l s of Main Pipe from Control Valve to Wye FIGURE 1-7 Geometrical Details of 90° Tapered Wye  FIGURE 1-9 Details of Manifolds  /=£/)Sr/CP/P/A/G 3//6" DMM£T£P &/9/ISS/°/P£ 3P6* JMPWPM THREAD 7//6"D//W£T££t i Pi/BBEP 3/9" #//)M£T£R f/8" //rp F*P£ IVfiLL FIGURE I-11 Details of Pressure Tap 91 P L A N FIGURE II -2 Hydraulic & Energy Gradient Lines f o r Manifold 93 94 Q», FIGURE III - 2 Flow Patterns i n Manifold with T i e - r o d 95 FIGURE IV-1 Skin Friction Loss in Main Pipe 96 &JD PIECE P/EZOMETP/C PW6 BRANCH PIPE TO BE TESTED P/J=ZOM£TP/C PING . J ' IA/ZET P/PE REDUC£P A1AW P/P£ SUPPLY FIGURE IV-2 Experimental Set-up for Measuring Skin F r i c t i o n Losses i n Branch Pipes   <>7i . • I 1 - | ;—I p 1 1 1™ A 90" wy£ w/mouT vs-ffoo o 90' wy£ MTH TR/ T/£-/?0[> at, — . 90'W/£ WtTH Tft2 T/£*lOO • x 90cW/£W/r// TR3 T/Ei?0O GJ 90' W/£ W/TH Tft4 r/£S?OD as ; 1 — - | — ' o./ 3 I i • ' ' i i i i i i I i 03 <X4 a6 a& f.O 12 S.4 /5 /1AW D/SCHARGE SCES) FIGURE V - l Form Loss Coefficients for 90° Wye (Symmetrical Flow) 100 CL7 0-6 05 I OA "•si 0.3 02 01 as — OPEN BRANCH — CLOSED BPfANCH A. 9 0 ' WVE w/rnour 7 7 E - & O D o 90' WYE MTH TR/ T/£-#OD • Jo'wyE w/rp z r/p-poo x 90'y/yE W/W 7793 T/E-POO a 90' WVE H W W T/E-POD _L *4 o.s o.6 . a.7 SfP/A/ O/SCP/jPGE: <CPS) ae4 FIGURE V -2 Form Loss Coefficients for 90° Wye (One-leg Flow) AO FIGURE V-3 Form Loss C o e f f i c i e n t s f o r 90° Wye (Unsymmetrical Flow) 102 07 Q6 0.5 1 03 cu. - 1 1 A 60' WE ® 60' WE 1 | i WITHOUT T/E-POO WITH TjRZ T/E-POO 1 - - • • • €0' WE WITH 7H3 T/E-&OD o 60* WYE WITH TR4 77E-RQD - - - i i - — « • - - 9 - 1 I 1 1 1 - ai 0-6 0.8 AO /.2 MA/N D/5CHPR6E (CPS) /.<* /.5 FIGURE V-4 Form Loss C o e f f i c i e n t s f o r 60° Wye (Symmetrical Flow) 103 0.6 X OS 1 1 « si I at OPEN BPA/VCH — — CLOSED BPA#CP 1 A €0* WYE MTHOUT © 60' WYE WW TP.2T/E-POO • 60' WYE MM TR3 77Z-POQ B 60' WYE MTP 77=t4 77£-/fOO Q3 0.4- O.B 0.6 /YAM D/SO/PP6E YCPSJ « 7 FIGURE V-5 Form Loss C o e f f i c i e n t s f o r 60° Wye (One-leg Flow) FIGURE V-6 Form Loss C o e f f i c i e n t s for 60° Wye ^ s y m m e t r i c a l Flow) 105 - 1 1 1 1 | 1 | 45°WYEMrH0UT 77E-RQQ. A SYMMETlR/CftL FLOW © RJOW M OPENBRANCH m PWW/N OOSED B&WCH - - n "• o - - • - - . j • - — • - 1 1 1 1 1 •—-A a.3 a4~ OS O.B AO MAIN DISCHPR6E (CPS) J.2. AA /-5 FIGURE V-7 Form Loss Coefficients for 45° Wye (Symmetrical & One-leg Flows)  0.7 0~2 o-3 out 0.5 o.e 0.7 FIGURE V-9 Comparison of Form Loss C o e f f i c i e n t s for Wyes (Unsynimetr.ie.al Flow) « 9 t.o 108 & 90' MWFOW tV/m TP3 7?f-P0O O 40'M/W/FOLD MntOl/T T7S-P0O • GO'/VM/FOW MM TP 3 77F-POO * 60°/fM/F0U> W/rHOt/T 77£-POD a 4£'A/MiFOW MrPOUT T/E-POO O.A OS /.o /J2. MAM £>/LSCP/)P6E (CPS) / 4 /3 FIGURE V-10 Form Loss Coefficients for Manifolds.(Symmetrical Flow) 109 OPEN BAMGH CLOSED BPAMCti A WMAWFOLD T&3 PE-POD © 90' AW/PO/0 ?//J7/0£/r 7/E-POD &0 " PAAVfdlD H/tTA/ 7P3 77E-POO ' 6 0 ' M Q M P O L D wrmour PE-POD s 45' L tPOCO MAHOUT PE-POD _ l L I 03 0.4- 0.5 0.6 <\7 MA/A/ D/SCPPP67E fCFS) a 86 FIGURE V - l l Form Loss Coefficients for Manifolds (One-leg Flow) T 1 1 [ I j I 1 1 j 1 1 r I I I I • I 1 I I I I 1 I I I I I I I I I O a/ az as A 5 ae 0.7 0.8 0.9 /-o FIGURE V - 1 2 Form Loss C o e f f i c i e n t s f o r ̂ lanifolds (Unsymmetrical Flow) c 0.4 0.-5 P.6 Q.7 . D/SCH/IR6E XAT/O Oi/Offi FIGURE V-13 Comparison of Form Loss C o e f f i c i e n t s f o r W y e s M a n i f o l d s without Tie-rod 0.6 k ° 5 \ g 04 £ 0.3 1 1 • i 1 • GO" A 90' MAN/FOLD A 60'A4AN/F0LD 1 1 1 1 UNsyi 1 WETRICA 1 L FLOW - \ - • Ay- - \ *k \ V \ ^ \ \ X \ A c XN N . N - ^ / / ?• - - . - \ \ A ^ / - — . - 1 • 1 1 1 l 1 1 1 1 1 0.2 04. 0.5 O.S D/SCHA&GE A3AT/0 A/ O.2. 0.3 FIGURE V-14 Comparison of Form Loss C o e f f i c i e n t s for Wyes & Manifolds with TR3 Tie-rod 0.7 <St,/<Sm 0.8 0.9 /o 113 *• v> • . » n - * <» a-7 i | r—| 1 1 1 A 90'/VM/rOLD fr/TH T#3 W£-FO£> e> 9O°A//W/F4!J> H//7HOUT. VE-AToO • eo'tfAMFOLO W/TH 7P3 T/E-A?OD * €0*AfAMFOW iV/THOUr 77£-POO " a 45' A4W/P0LD WATPOL/r 77S-POO 06 U/VSyMMETRICAL fiDW OJ a* 0.5 «.« o-T 0.9 AO FIGURE V-16 Hydraulic Power Losses in Manifold Arrangements END PIECE PIEZOMETRIC BPfiMCH P/PE ELBOW PlEZOtfErplC PlN& /NLET P/PE flMN PIPE SUPPLY 1 F I G U R E A - l Experimental Set-up for Measuring Head Losses i n Elbows 116 FIGURE A-2 Hydraulic & Energy Gradient Lines f or Elbow Tes t i n g Set-up ao3o\ i i 1 i 1 L__ L I _|_ I 1 l I ! aa os 0.6 o.r oa t-r D/SCHAGGB (CPS) FIGURE A-3 Elbow Loss Coefficients

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