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Head loss in symmetrical bifurcations 1965

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HEAD LOSS IN SYMMETRICAL BIFURCATIONS BY Sirajuddin Ahmed B.A., B.E., University of Hyderabad, 1943 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGRISE OF MASTER OF APPLIED SCIENCE IN THE DEPARTMENT OF CIVIL ENGINEERING We accept t h i s t h e s i s as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA 1965 In presenting th i s thes i s in p a r t i a l f u l f i lmen t of the requirements for an advanced degree at the Un ivers i ty of B r i t i s h Columbia, I agree that the L ibrary sha l l make i t f r ee l y a v a i l a b l e for reference and study. I fur ther agree that per- mission for extensive copying of t h i s thes i s for scho la r l y purposes may be granted by the Head of my Department or by his representat ives v . It is understood that copying or p u b l i - cat ion of t h i s thes i s for f i n a n c i a l gain sha l l not be allowed without my wr i t ten permiss ion. Department of C i v i l Engineering, The Un ivers i ty of B r i t i s h Columbia Vancouver 8, Canada Date September 29, 1965 . ABSTRACT Five symmetrical wye branches of conventional and spherical types were tested f o r hydraulic losses under symmetrical and unsymmetrical flow conditions. Results are presented g r a p h i c a l l y . A wide v a r i a t i o n i n l o s s factor was observed depending on the type of wye and on flow condition. For a given wye the minimum wye loss c o e f f i c i e n t does not necessarily occur under conditions of symmetrical flow. i i TABLE OF CONTENTS Page Noo ABSTRACT 1 TABLE OF CONTENTS i i ACKNOWLEDGEMENT i x INTRODUCTION 1 PREVIOUS RESEARCH 3 CHAPTER I. INSTRUMENTATION AND APPARATUS 5 1 . 1 Lay Out 5 1 0 2 Apparatus 6 1 0 3 Instrumentation 9 CHAPTER I I . BASIC CONCEPTS RELATING TO HYDRAULIC 1 5 LOSSES IN WYE 2 . 1 Theory 1 5 CHAPTER I I I . PRELIMINARY INVESTIGATIONS 1 9 3 . 1 Preliminary experiments and re s u i t s 1 9 3 - 2 Investigations 1 9 • 3 * 3 . Modifications 2 0 CHAPTER IV. EXPERIMENTAL PROCEDURE 2 3 4 . 1 F r i c t i o n losses 2 3 4 . 2 Areas of main and branch pipes 2 5 4 * 3 Discharge and pressure measurements 2 6 4 * 4 Experimental procedure 2 6 i i i TABLE OF CONTENTS (Cont'd) CHAPTER V. RESULTS AND CONCLUSIONS 30 501 Results of experiments 30 502 Conclusions and discussion 30 BIBLIOGRAPHY 33 APPENDIX NOTATION 35 i v TABLES Page Table 1 Areas, main and branch pipes 38 Table 2 Distance from t h e o r e t i c a l centre of wye to piezometric ring, main and branch pipes 38 Table 3 Veloci t y traverse: Symmetrical flow, preliminary investigations 39 Table 4 Ve l o c i t y traverse: Symmetrical flow, f i n a l test set up 39 Table 5 Ve l o c i t y traverse: One l e g flow, f i n a l t e s t set up 40 Table 6 F r i c t i o n losses i n main pipe 40 Table 7 F r i c t i o n losses i n branch pipe (Sections A & C) 41 Table 8 F r i c t i o n losses i n branch pipe (Sections B & D) 41 Table 9 Reynolds' numbers and f r i c t i o n f actors, main and branch pipes 41 Table 10 Wye loss c o e f f i c i e n t s f o r 90° large spherical wye (symmetrical flow) 42 Table 10 (cont'd) Wye l o s s c o e f f i c i e n t s f o r 90° large spherical wye (unsymmetrical and one leg flow) 43 Table 11 Wye loss c o e f f i c i e n t s f o r 90° small spherical wye (symmetrical flow) 44 Table 11 (cont'd) Wye l o s s c o e f f i c i e n t s f o r 90° small spherical wye (unsymmetrical and one leg flow) 45 TABLES (cont'd) Table 12 Wye loss c o e f f i c i e n t s f o r 90° tapered wye (symmetrical flow) Table 12 (cont'd) Wye loss c o e f f i c i e n t s f o r 90° tapered wye (unsymmetrical and one leg flow) Table 13 Wye loss c o e f f i c i e n t s f o r 60° tapered wye (A), (symmetrical flow) Table 13 (cont'd) Wye loss c o e f f i c i e n t s f o r 60° tapered wye (A), (unsymmetrical and one leg flow) Table 14 V/ye l o s s c o e f f i c i e n t s f o r 60° tapered wye (B), (symmetrical flow) Table 14 (cont'd) Wye loss c o e f f i c i e n t s f o r 60° tapered wye (B), (unsymmetrical and one l e g flow) v i FIGURES Page Figure 1 General arrangement 52 Figure 2 D e t a i l s of main pipe from c o n t r o l l i n g valve to wye 53 Figure 3 Model lay out and manometric arrangement 54 Figure 4 D e t a i l s of wyes 55 Figure 5 Geometric d e t a i l s of 90° tapered wye 56 Figure 6 Pressure tap 57 Figure 7 O r i f i c e arrangement 58 Figure 8 . V e l o c i t y traverse across the main pipe near wye during preliminary i n v e s t i g a t i o n 59 Figure 9 V e l o c i t y traverse across main pipe near wye a f t e r modification i n the main pipe section 60 Figure 10 V e l o c i t y traverse f o r one leg flow with discharge of 0.92 cfso 61 Figure 11 F r i c t i o n losses i n main pipe 62 Figure 12 Experimental set up f o r measurement of f r i c t i o n losses i n branch pipes 63 Figure 13 F r i c t i o n losses i n branch pipe (Sections A and C) 64 Figure 14 F r i c t i o n losses i n branch pipe (Sections B and D) 65 Figure 15 F r i c t i o n factors versus Reynolds numbers fo r main and branch pipes 66 v i i .FIGURES (cont'd) Page Figure 16 90° large spherical wye, symmetrical and one leg flow 67 Figure 17 90° large spherical wye, unsymmetrical flow 68 Figure 18 90° small spherical wye, symmetrical and one leg flow 69 Figure 19 90° small spherical wye, unsymmetrical flow 70 Figure 20 90° tapered wye, symmetrical and one leg flow 71 Figure 21 90° tapered wye, unsymmetrical flow 72 Figure 22 60° tapered wye (A), symmetrical and one leg flow 73 Figure 23 60° tapered wye (A), unsymmetrical flow 74 Figure 24 60° tapered wye (B), symmetrical and one leg flow 75 Figure 25 60° tapered wye (B), unsymmetrical flow 76 Figure 26 Wye loss coefficients for a l l wyes, symmetrical flow 77 Figure 27 Wye loss coefficients for a l l wyes, one leg flow (open branch) 78 Figure 28 Wye loss coefficients for a l l wyes, one leg flow (closed branch) 79 Figure 29 Wye loss coefficients for a l l wyes, unsymmetrical flow 80 v i i i PLATES Page Plate 1 Manometric board with gage tanks 81 Plate 2 Manometric board 82 Plate 3 Lay out of model looking downstream 83 Plate 4 Main pipe and control valve 84 Plate 5 Control valve 85 Plate 6 Wye in place 86 Plate 7 90° small spherical and 60° tapered wye (B) 87 Plate 8 90° small spherical and 60° tapered wye (B) ' 88 Plate 9 Orifices and end piece 89 i x ACKNOWLEDGEMENT The author i s deeply g r a t e f u l to his Supervisor, Dr« Eo Ruus who, i n spite of his multifarious a c t i v i t i e s , was always accessible and available to discuss the problems during the period involving the research and writing of t h i s t h e s i s from June 1964 to September I965• He i s also g r a t e f u l to the Colombo Plan Authorities and the Department of External Aid, Government of Canada, f o r the f i n a n c i a l assistance during the period of hi s stay at the University of B r i t i s h Columbia© 1 1 INTRODUCTION In several recent hydro-electric power plants units of capacity up to 300,000 HP have been i n s t a l l e d . S t i l l larger units are proposed f o r future projects. In the penstocks which serve these plants both the diameter and water v e l o c i t y have been increased beyond previous l i m i t s to match the increase i n turbine discharge capacity. A major portion of the t o t a l f r i c t i o n l o s s i n penstocks of large diameter carrying water at high v e l o c i t y i s due to bends, outlets, wyes and valves. An accurate determination of hydraulic losses i n these devices i s necessary for an economical design of the penstock. This thesis describes a model te s t program to determine hydraulic losses i n large symmetrical wye branches. In three conventional type of wyes tested the influence of the magnitude of the angle between the branches of the wye was investigated. In two spherical wyes tested, the influences of the size of the sphere and the rounded pipe intersections were studied. The i n v e s t i g a t i o n was primarily concerned with the hydraulic losses r e s u l t i n g from wyes. Therefore f r i c t i o n losses i n the i n d i v i d u a l pipes were deducted from the t o t a l l o s s to obtain the form loss of the wye. 2 The flow i n general was well within the turbulent range, the Reynolds number varying from 50,000 to 3 7 5 , 0 0 0 . When the r e s u l t s of the experiments are applied to estimate the losses i n a geometrically s i m i l a r prototype, the Froude number i s used as the c r i t e r i o n f o r dynamical s i m i l a r i t y . For convenience the wye loss c o e f f i c i e n t s K are related to the v e l o c i t y head i n the main pipe. 3 PREVIOUS -RESEARCH Considerable research has been undertaken for the computation of hydraulic loss in bends, elbows, tees, branch outlets and symmetrical bifurcations, but most of i t i s confined to small pipes as part of losses in pipe f i t t i n g s . Hinds, Thoma, Shoder, Weisbach and others^) have shown in graphical form head loss in bends for various radius-diameter ratios. Model tests have been made on small tees and branch outlets at the Munich Hydraulic Institute. (2) Gardel(3) describes tests on water flow through eight tees with main pipe diameter of 150 mm joined by pipes ranging from 60 to 150 mm at angles ranging from 45° to 135°». The theoretical basis has been developed by F a v r e ^ and McNown(5) for lateral bifurcations only. The character- i s t i c s of flow and pressure pulsations in la t e r a l bifurcations have also been a subject of study at the University of Kansas (6), (7), (8). Marchetti and Noseda (9) have made experiments on five bifurcations constructed by welding 70 mm diameter pipes with included angles between the downstream branches varying from 60° to 180°. The laboratory results were presented for different conditions of flow in graphical form enabling deter- mination of hydraulic losses. For symmetrical bifurcations, the value of wye loss coefficient K varied from 0.27 for a 60° bifurcation to O.96 for a 180 bifurcationo The Reynolds 4 numbers varied from 97000 to 322000 for these experiments. Gladwell and Tinney^ 1 0^ conducted investigations on a t r i f u r c a t i o n , the tests including measurement of head loss for d i f f e r e n t conditions of flow. With the centre pipe closed and flow equally divided, the value of K f o r a given discharge was 0.73 and 0 .94 f o r r i g h t and l e f t l e g respect- i v e l y . The large difference appears to be due to the bend upstream of the t r i f u r c a t i o n . 5 CHAPTER I. INSTRUMENTATION AND APPARATUS 1.1. LAYOUT: The research project was conducted i n the / —————— Hydraulic Laboratory as shown i n Figure 1 and Plate 3o The supply i s from an overhead tank and hence no dynamic pressure f l u c t u a t i o n s are introduced into the feeding system. During the period i n which the experiments were under way care was taken to ensure that there were no with- drawals at any other point i n the laboratory and, thus, f o r each experiment a stable £low condition under constant head was established. The general arrangement of the model i s shown i n Figures 2 and 3 and Plate 3» The supply to the model could be diverted to one or both of the branch pipes leading to l e f t and ri g h t flumes (Figure 1) according to the requirements of the experiment. The turbulence induced pressure f l u c t u a t i o n s , i n t r o - i duced into the system due to the many elbows and tees between the overhead tank and the valve c o n t r o l l i n g flow to the wye, were dampened by providing two flow straighteners each 2 f t . long as shown i n Figure 2. The f i r s t one was located down- stream from the bend below the control valve, and the other downstream from the reducer near the f i r s t straightener. The straighteners consisted of t h i n aluminium tubing varying i n 6 diameter from one to two inches. The length of the main pipe on the upstream side of the wye, comprised of s t e e l and l u c i t e sections, was 33 f t . , the,length-diameter r a t i o being 75- The length-diameter r a t i o equalled 30 f o r the branch pipes, which was considered adequate to eliminate flow disturbances caused by passage of water through the wye and thus assure observation of correct pressure heads at piezometric points on the branch pipes. 1.2.• APPARATUS: Lucite was used throughout f o r a l l the wyes, a portion of the main pipe and the branch pipes. This set up allowed: (i ) to replace the d i f f e r e n t parts ( i i ) to observe v i s u a l l y the portion i n which hydraulic losses occurred, and ( i i i ) to see that there was no entrapment of a i r i n any part which might a f f e c t the piezometric heads. , DESCRIPTION OF WYES: A t o t a l of f i v e wyes, a l l of them symmetrical, were used f o r conducting the experiments. Three were 90° wyes and the remaining two were 60° wyeso The 90° wyes have been designated as (i) Large Spherical Wye, ( i i ) Small Spherical Wye and ( i i i ) Tapered Wye; the 60° Wyes as ( i ) Tapered Wye (A) and ( i i ) Tapered Wye (B). For a l l wyes, the connecting main pipe and branch pipes had diameters of 5*25 and 3*75 inches respectively. The d i f f e r e n t wyes are shown 7 i n Figure 4 and Plates 6, 7 and 8 . Although dimensions of the wyes were chosen a r b i t r a r i l y , the shapes follow a certain geometrical pattern as indicated i n Figure 5« 90° Large Spherical Wye: As shown i n Figure 4»(a), the sphere had a diameter of 7.5 inches equivalent to twice the diameter of the branch pipes. On the outlet side the int e r s e c t i o n of sphere and pipe was rounded at a radius of 3/8 inch. 90° Small Spherical Wye: As shown i n Figure 4»(b), the sphere had a diameter of 5*85 inches. The inters e c t i o n s were sharp. 90° Tapered Wye: As shown i n Figures 4 and 5 the cone angle f o r the tapered wye was kept at 20°. 60° Tapered Wye (A): As shown i n Figure 4.(d), the tapering was done at an angle of 10°• 60° Tapered Wye (B): As shown i n Figure 4«(e),. t h i s wye contained a 3 inch long tapered portion. Otherwise i t i s sim i l a r to the 60° tapered wye (A) i n a l l respects. The t h e o r e t i c a l centres of the wyes are shown i n figure 4* Distances from the t h e o r e t i c a l centres to the points of i n l e t and outlet of the wyes are given i n Table 2. Preparation of Wyes: In order to obtain dependable and accurate r e s u l t s , great care was taken i n preparation of the models. Accuracy was carried to one-thousandth of an inch and i n t e r n a l surface of the wyes was made as smooth as possible. 3 During preparation of a wye, the faces were machined and the t h e o r e t i c a l centre, angle of symmetrical b i f u r c a t i o n , length from the t h e o r e t i c a l centre; to points of i n l e t and outlet, and position of holes f o r connection with main and branch pipes were l a i d out. After turning the conical and c y l i n d r i c a l water passages on a m i l l i n g machine, p o l i s h i n g of inner surface of wyes was done by emery paper f i r s t and then by crocus paper. F i n a l p o l i s h i n g was done by p o l i s h i n g l i q u i d . ..Two l o c a t i n g pins were i n s t a l l e d on the main pipe to eliminate any o f f s e t between the wye and the main pipe. Main and Branch Pipes: As shown i n Figure 3» the Lucite section of the main pipe, approximately 13 f t . long, comprised of three sections. Flanges made from Lucite were f i t t e d on both ends of each section of the main and branch pipes to connect the d i f f e r e n t sections of the main and branch pipes or the pipes with the wye. Each flange, with the end face machined and smoothened was then glued, to the pipe with the face perpendicular to centre l i n e of pipe. To stop •leakage, annular rings 1/8 inch wide were machined on the connecting faces i n which rubber rings l/8 inch diameter were placed. Setting: up of Apparatus: For the f i n a l t e s t setup the main pipe was aligned by means of a theodolite." The main pipe, branches and wye were l e v e l l e d accurately with a carpenter's levelo Measures were also adopted to eliminate 9 d i s c o n t i n u i t y at a l l j o i n t s on the main and branch pipes, and p a r t i c u l a r l y at j o i n t s with the wye. 1.3o INSTRUMENTATION: Primarily i t consisted of means to measure pressure, discharge, temperature, and time. Pressure Taps: The standard requirement f o r pressure taps i s that the openings should be f l u s h with the conduit wall and free from burrs, while the axis of the piezometric tube should be perpendicular to the centre l i n e of pipe. .The tap should be free from leakage. The pressure tap used i n these experiments i s shown i n Figure 6. The piezome'ter had an opening of 1/8 inch. The brass tube was held i n p o s i t i o n by a 1/8 inch NTP threaded screw i n a 7/8 inch Lucite cube. The NTP i n turn was connected to a 3/l6 imperial threaded nut, with rubber r i n g at the junction to eliminate p o s s i b i l i t y of any leakage. Piezometric Connections: Piezometers were i n s t a l l e d i n groups (Figure 3 and Plates 1 and 2) and connected to gage tanks. This arrangement was suitable because the water l e v e l i n the manometric tubes could be observed simultaneously and any single pressure reading which appeared out of l i n e could be checked immediately. The pressure taps were connected to manometers by f l e x i b l e tubing with provision f o r removal of a i r bubbles trapped i n the system. Numbers i n Figure 3 indicate these connections on the piezometric rings, manometer 10 tubes and gage tanks to main, l e f t and ri g h t branch pipes respectively. The gage tanks 5.5 inches i n diameter were f i t t e d with hook gage rods and verniers to obtain reading of water surfaces. There were three gage tanks, (i) the upstream tank connected to the four pressure taps forming the piez- ometric r i n g and the corresponding manometers on the main pipe, ( i i ) the central tank connected to corresponding manometers and piezometric r i n g on the l e f t branch pipe and ( i i i ) the downstream gage tank connected to the manometers and piez- ometric r i n g on the r i g h t branch pipe. The board containing the manometer tubes along with the d i f f e r e n t gage tanks i s shown i n Plates 1 and 2. The gage vernier i n the upstream tank was set 0.210 f t . higher than the^gage verniers i n the centre and downstream tanks. The range of pressure heads that could normally be observed by the gage rods was only 2 f t . and height of gage tanks was also about the same. With the aid of extension rods to the gage points i t was possible to measure pressure head differences up to 3 f t . of water. O r i f i c e s f o r v a r i a t i o n of discharge through Main and Branch Pipes: The experiments were conducted f o r d i f f e r e n t conditions of flow; symmetrical, unsymmetrical and-one leg, as explained subsequently i n more d e t a i l . For symmetrical flow the t o t a l discharges used varied from 0.32 to 1.5 c f s ; 11 f o r unsymmetrical flow, the t o t a l discharge was 0.75 and 0.92 c f s , whereas the discharge r a t i o i n the two branches varied from zero to 1.0. For one leg flow the discharge v a r i a t i o n was from 0.32 to 0.92 c f s . The v a r i a t i o n of discharge through the main pipe was accomplished p a r t l y by operating the control valve shown i n Figure 1. For a p a r t i c u l a r experiment i t was, at the same time, necessary to create conditions so that pressure differences could be obtained by observation of water l e v e l s i n a l l the three gage tanks simultaneously. For t h i s purpose o r i f i c e s of d i f f e r e n t sizes, which are shown i n Figure 7 and Plate 9, were placed i n end pieces attached to the branch pipes. These o r i f i c e s had d i f f e r e n t diameters and, depending on the desired p a r t i c u l a r discharge i n each branch, o r i f i c e s of certain diameters were placed i n the end pieces attached to the branch-pipes. I f f o r a p a r t i c u l a r wye and a p a r t i c u l a r flow condition, water l e v e l i n the gage tanks could not be observed simultaneously due to manomotric l e v e l s being lower or higher than the l i m i t s of observation imposed by the hook gages, diameter of the o r i f i c e s i n one or both the branches was changed u n t i l the desired r e s u l t was achieved. These o r i f i c e s were machined from one side to obtain a clean and sharp edge free from any burrs. In a l l experiments the o r i f i c e s were placed i n such a way that the sharp, undamaged edges of the o r i f i c e s were facing the flow. 12 Measurement of Time: A degree of accuracy up to 0.1 second was obtained f o r determining time i n t e r v a l s i n which a p a r t i c u l a r weight of water was co l l e c t e d i n the weighing tank. For t h i s purpose an e l e c t r i c clock reading d i r e c t l y up to 0.1 second was used. Measurement of Temperature: To determine Reynolds' numbers f o r the corresponding f r i c t i o n l o s s c o e f f i c i e n t s i n the main and branch pipes, temperatures were recorded by using a thermometer, and readings obtained to the nearest h a l f degree of Fahrenheit. Measurement of Weight of Water: This was done by means of a weighing tank having a maximum capacity of 20,000 l b s . , the scales of which were tested and found correct before s t a r t i n g the experiments. Pressure Measurements: In spite of the fac t that supply was from an overhead tank under constant head conditions i n which no dynamic pressure f l u c t u a t i o n s could have been possible, and that two sets of straighteners were provided at the upstream end of a long straight main pipe, some pressure f l u c t u a t i o n s were observed i n the manometric tubes connected to the d i f f e r e n t piezometric r i n g s . , I t could be d e f i n i t e l y established by process of elimination that these were turbulence induced pressure f l u c t u a t i o n s . I t was observed that maximum fl u c t u a t i o n i n water l e v e l was of the order of 0.05 f t . The 13 pressure f l u c t u a t i o n s , as observed v i s u a l l y , were i n the neighbourhood of 30 cycles per minute. The corrective measure adopted f o r obtaining pressure differences to the required degree of accuracy was to adjust the water l e v e l s i n the d i f f e r e n t gage tanks corresponding to average l e v e l s i n the manometric tubes, the area r a t i o of the tube (diameter, £ inch) to the gage tank (diameter, 5 i inches) being approximately 1:480 and then allow 2 to 3 hours to elapse. By t h i s procedure i t was observed that water surfaces i n the tanks assumed constant l e v e l s , automatically averaging out pressure fluctuations i n the manometric tubes. Discharge Measurements: As the degree of accuracy i n obtaining v e l o c i t y heads at points of piezometric rings was d i r e c t l y related to discharge, i t was necessary to measure the d i f f e r e n t discharges accurately. Combined discharge through the main pipe was obtained by allowing both the branch pipes to discharge into the weighing tank simultaneously. The discharge from each of the. branch pipes was then obtained separately. I t was observed that discrepancies occurred i n measurement of discharges 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 provided. For combined * r Note: This measure was adopted to reduce the period required f o r the water l e v e l s to become steady i n the gage tanks. Water was either poured into or taken out from the tank u n t i l i t s l e v e l approximated the average water l e v e l indicated in the manometric tubes. 14 discharge and f o r the discharge from the r i g h t branch pipe the necessary time i n t e r v a l was found to be about 300 seconds, whereas f o r the l e f t branch pipe the required time i n t e r v a l was,500 seconds. For a l l the experiments conducted, the time i n t e r v a l s mentioned above were adhered to, and Column 3 of Tables 10 to 14 show that the maximum difference i n time i n t e r v a l s f o r weighing a p a r t i c u l a r quantity of water from the main, r i g h t , or l e f t branch pipe did not exceed about 0.1%. The v e l o c i t y head calculated on the basis of discharge so obtained was thus correct up to a thousandth of a foot, the degree of accuracy required. 15 CHAPTER I I . BASIC CONCEPTS RELATING TO HYDRAULIC LOSSES IN WYE 2.1. THEORY: It i s assumed that the measurement of piez- ometric heads has been made a f t e r stable flow conditions have been established and a f t e r the water l e v e l s i n the d i f f e r e n t gage tanks were steady. For a horizontal piping, the energy losses can be. expressed from the energy equation of B e r n o u l l i as follows: hpm + hvm 1 h p r + h v r * A h + hfmt + h f r . ••••• A hpm + hvm = h p l + h v l + A h + hfm + h f l < 1 } B (See Page 16). Defining Q as discharge; A, area; hp, pressure head; h v, v e l o c i t y head; hf, loss of head due to f r i c t i o n ; Vj, mean v e l o c i t y i n the pipe; V"2> v e l o c i t y at piezometric r i n g and designating subscripts m, r and 1 to main pipe, right and. l e f t branch r e s p e c t i v e l y the following equations can be obtained. Continuity i s given by: Q m = Q r -t- Qi . . o . . (2) Average v e l o c i t y i n the main pipe i s given by: V m l " A Î . . . . . (3) Similar expressions are v a l i d f o r average v e l o c i t y i n the r i g h t or l e f t branch; Qr, Qi, A r i , An being known. Ve l o c i t y at the piezometric r i n g S on the main pipe i s given by: 1 6 Elevation. 17 vm2 ~ Aj^2 • <•.<>. (4) Similar expressions f o r v e l o c i t y at the piezometric rings DQ_ or D2 o n "the r i g h t or l e f t branch can be obtained i n terms of Qr»-'Ql> A r2 and Ai2» Equations (3) and (4) are required to d i s t i n g u i s h the average v e l o c i t y related to f r i c t i o n losses, and the average v e l o c i t y at the piezometric rings which are related to v e l o c i t y heads at these rings. V e l o c i t y heads h y m , h v r , h v i i n the main, ri g h t and l e f t branch pipes can be determined once v e l o c i t i e s are obtained from equation (4)» The l o c a l i z e d l o s s of wye can be expressed as: A h r = (hpm ~ h p r ) -• ( hfm + h f r ) + (Km " h v r ) A h r = A P R _ ( h f m + h f r ) + ( h v m - h v r ) . 0 . . . ( 5 ) S i m i l a r l y * h l = ( h p m - h p l ) - ( h f m + h f l ) + (hvm - hvl)» A h ! = Ap]_ - ( h f m + h f i ) + (hym - h v l ) " ( 6 ) F i n a l l y wye l o s s c o e f f i c i e n t fK' f o r the r i g h t or l e f t branch pipe i s given by: K = lot ' ',0*, (7) 2g Equations ( 5 ) and ( 6 ) have been used to determine l o c a l i z e d wye l o s s at T, the t h e o r e t i c a l centre of wye, and equation ( 7 ) f o r determination of K f o r the following flow conditions: 18 (a) Symmetrical Flow: The discharge i n the main pipe i s divided equally between the right and l e f t branch pipes. (b) Unsymmetrical flow: The discharge i s divided unequally i n the two branches with the discharge r a t i o S ranging from 0 to 1. (c) One Leg Flow: The discharge i s wholly diverted to the r i g h t or l e f t branch. In the figure the hydraulic grade l i n e s and the t o t a l energy grade l i n e s have been shown from S to Di, D2, assuming that a l l wye losses are l o c a l i z e d at the t h e o r e t i c a l centre T. In addition to these l o c a l i z e d wye losses, piezometric and v e l o c i t y heads and loss of head due to f r i c t i o n at locations S, T, Di, D2 are also indicated. The discharge passing from the main pipe through the wye into the branch pipes causes formation of vortices and turbulence i n the wye. Mixing i s carried a considerable distance and extinguished slowly while proceeding i n the branch pipes. The e f f e c t of v o r t i c e s and turbulence i n the wye i s extended into the main pipe f o r a very short distance only. The distance of S from T has, therefore, been kept much shorter than the distance of and D£ from T. 19 CHAPTER I I I . PRELIMINARY INVESTIGATIONS 3 . 1 . PRELIMINARY EXPERIMENTS AND RESULTS: A complete set of experiments f o r symmetrical, unsymmetrical and one l e g flow was conducted f o r the 9 0 ° small spherical wye and the r e s u l t s tabulated i n the way as shown i n Tables 10 to 14. On exam- inat i o n of the r e s u l t s so obtained, i t was found that ( i ) the head loss i n the wye was . d i f f e r e n t f o r the two branches, ( i i ) the piezometric readings of the central and downstream gage tanks d i f f e r e d considerably, ( i i i ) there was v a r i a t i o n i n consecutive time i n t e r v a l s when a p a r t i c u l a r discharge was measured, (iv) discharge from the l e f t branch pipe was consistently l a r g e r than that from the r i g h t branch pipe and (v) there was considerable turbulence induced pressure f l u c t u a t i o n (about 0.100 f t . ) i n the manometric tubes. 3.2.. INVESTIGATIONS: These were undertaken with a view to determine the causes and to ef f e c t changes i n the apparatus u n t i l the discrepancies were removed. A number of t e s t runs were conducted to f i n d f a c t o r s responsible f o r the discrep- ancies observed. While a p a r t i c u l a r experiment was i n progress, i t was found that a i r was trapped i n the f l e x i b l e tubing connected 20 to the uppermost piezometric points on the d i f f e r e n t pipes and hence the top piezometric connections were pinched o f f to eliminate the source of t h i s e r r or. By observation i t was found that a r e l a t i v e l y large quantity of a i r was necessary to obtain the condition "discharge into free atmosphere11 and, hence, large wooden troughs were provided f o r both branch pipes. I t was also noticed that the maximum v a r i a t i o n occurred i n measurement of discharge from the r i g h t branch pipe due to surge waves i n the c o l l e c t i n g system. When the wooden trough carrying water from the r i g h t branch pipe was extended so as to discharge i n the r i g h t hand flume (Figure 1) an immediate improvement was found. V e l o c i t y traverse: An unsymmetrical v e l o c i t y d i s t r i b u t i o n was found when a v e l o c i t y traverse was made across the main pipe about 6 inches from the wye, the traverse station being shown i n Figure 3« The r e s u l t i n g flow d i s t r i b - ution i s shown i n Figure &M>ased on observations recorded i n Table 3 which conclusively proved that the v e l o c i t y d i s t r i b - ution was not symmetrical about the axis of the main pipe. 3 . 3 . MODIFICATIONS: To improve the pattern of flow the following modifications were ca r r i e d out i n the main pipe section: (i) The 4 inch standard s t e e l pipe was replaced by a new section of 5 inch standard s t e e l pipe (Figure 2). 21 ( i i ) Two sets of flow straighteners each 2 f t . long were provided i n positions shown i n Figure 2, ( i i i ) The c o n t r o l l i n g valve was rotated and made symmetrical with the d i r e c t i o n of flow. These modifications were proposed not only to improve the flow conditions i n order to eliminate the discrepancy i n discharge i n the two branches but also to provide the maximum straight portion of the main pipe with a lar g e r length- diameter r a t i o of approximately 75 to dampen turbulence induced pressure f l u c t u a t i o n s . Afte r incorporating the changes i n the main pipe section, the r e s u l t s of the v e l o c i t y traverse, made at the same point at which the previous traverse was made, and shown in Table 4 and Figure 9, indicated an e n t i r e l y symmetrical v e l o c i t y d i s t r i b u t i o n about the axis of the main pipe with the maximum v e l o c i t y occurring at the centre. Branch Pipes: Because the length of the branch pipes was only about 3.75 f t . , g i v i n g a length-diameter r a t i o of about 12, i t was considered necessary to increase the length so that most of the vor t i c e s and turbulence created i n the wye would be extinguished by the time water reached the piezometric rings on the branch pipes. At the same time too large an increase i n length of branch pipes would have resulted i n magnifying the e f f e c t of f r i c t i o n losses, and 22 thus •would have .reduced the degree of accuracy i n obtaining the wye losseso The branch pipes were consequently replaced by two sections of pipe as shown i n Figure 3» The length- diameter r a t i o was thus increased from 12 to approximately 3 0 . Location of Piezometric Ring on the Main Pipe: Some doubt was f e l t about the proximity and influence of the wye on the readings of the piezometers on the main pipe because of turbulence and formation of vo r t i c e s i n the wye. In order to check t h i s s i t u a t i o n , a v e l o c i t y traverse was made under extreme conditions of maximum discharge of 0.92 cfs i n the r i g h t branch with the l e f t branch completely shut-off. The v e l o c i t y p r o f i l e so obtained, shown i n Table 5 and Figure 10, indicates p r a c t i c a l l y symmetrical flow about the axis of the main pipe, proving that the lo c a t i o n point of the piezo- metric r i n g on the main pipe was outside the influence of the wye • F r i c t i o n Losses i n Branch Pipes: As a re s u l t of preliminary investigations, i t was also decided to measure f r i c t i o n losses at more or l e s s a constant temperature which, i n the present case, was 65° F and to keep the water temperature during the subsequent schedule of experiments on a l l the wyes close to t h i s temperature. By adopting t h i s procedure, f r i c t i o n losses i n the branch pipes could be determined with a greater degree of accuracy. 2 3 CHAPTER IV. EXPERIMENTAL PROCEDURE The preliminary investigations having determined the pattern on which the experimental work was to be carried out, the procedure as described below was adopted with a view to obtain graphical representation of wye l o s s c o e f f i c i e n t s K f o r each of the f i v e wyes f o r the cases of symmetrical, unsymmetrical and one l e g flow. 4 . 1 o FRICTION LOSSES: To obtain the d i f f e r e n t wye losses as per equations ( 5 ) and ( 6 ) , i t was f i r s t necessary to determine f r i c t i o n losses i n the main pipe f o r the length S to T (Figure 3 ) and from T to Dj' and D 2 i n the branch pipes. F r i c t i o n Losses i n the Main Pipe: To obtain f r i c t i o n losses i n the main pipe, two of the gage tanks were connected to piezometric rings at S and as shown i n Figure 3 * F r i c t i o n losses were determined f o r d i f f e r e n t discharges ranging from 0 . 3 2 to 1 . 5 c f s and r e s u l t s thus obtained (Table 6 ) were plotted on log-log scale as shown i n Figure 1 1 . These f r i c t i o n losses are f o r the length SSi (Figure 3 ) which was 3 . 3 7 5 f t o For the length ST the f r i c t i o n l o s s that corresponded to any p a r t i c u l a r discharge was determined from the graph i n Figure 1 1 . The lengths SS^ and ST f o r the d i f f e r e n t wyes are shown i n Table 2 . 24 Friction Losses in the Branch Pipes: The experimental set up for determination of f r i c t i o n losses in the branch pipes i s shown in Figure 12o Four sections of pipes, designated with A, B, C, D, each having 3 • 7 5 inches nominal ID and 4 * 5 f t . long, were duly f i t t e d with flanges and piezometric rings to form the right and l e f t branches. Different combinations were tried so that f r i c t i o n losses for a l l discharges for these two legs would be equal. It was found that the two branch pipes could be formed by putting Sections A, G and B, D together which then would have almost identical f r i c t i o n losses. For the 90° wyes sections A and C formed the right branch pipe and B, D the l e f t branch pipe. For 60° wyes i t was found that more symmetrical discharges and pressure elevations were obtained by having Sections A,. C as the l e f t branch pipe and B, D as the right branch pipe. Friction losses were determined for length B1B2 (- 9 ft.) for Sections A, C and B, D (Figure 12) as in the case of the main pipe for different discharges ranging from 0 .32 to 0 .75 cfs., and the results thus obtained (Tables 7 & 8) were plotted on log-log scale as shown in Figures 13 and 1 4 . It may be seen from the two graphs that for high dis- charges, f r i c t i o n losses are almost the same; but for low discharges, the branch pipe formed by Sections A, C had somewhat less f r i c t i o n losses than the branch pipe formed by Sections B, D. 25 F r i c t i o n losses from T to D]_, D 2 (Figure 3) f o r the two branch pipes were obtained i n a s i m i l a r way to that of the main pipe. The lengths S 2D 2, S3D1, TDi and TD 2 (Figure 3) f o r the d i f f e r e n t wyes being the same fo r the two branch pipes, are shown in Table 2. Reynolds Numbers and F r i c t i o n Factors f o r Main & Branch Pipes: For the d i f f e r e n t discharges f o r which f r i c t i o n losses were determined f o r the main and branch pipes, Reynold's numbers and the corresponding f r i c t i o n f a c t o r s were determined (Table 9) and plotted on Moody's diagram i n Figure 1 5 . I t may be observed that the points thus obtained f o r the branch pipes adhere very c l o s e l y to the curve f o r smooth pipes. Some of the points on the main pipe are s l i g h t l y s h i f t e d . 4.2. DETERMINATION OF AREAS OF MAIN AND BRANCH PIPES: Both f o r the main and branch pipes the following data were deter- mined separately: (a) Mean area of the pipe f o r c o r r e l a t i o n of f r i c t i o n l o s s to the mean v e l o c i t y i n the pipe, (b) Area at piezometric rings to calculate'the v e l o c i t y heads used i n equations (5) and ( 6 ) . For the main pipe the area was determined by measuring the diameter near the centre and at each end i n four d i f f e r e n t p o s itions and then taking the average of the 12 values. The nominal ID of the pipe was 5*25 inches but the mean diameter 26 was found to be 5*252 inches. The same value of the diameter was also found at the piezometric r i n g . For the branch pipes, the required areas were found by measuring diameters at both ends of each section i n four d i f f e r e n t positions and taking the mean of the 16 values thus obtained. Table 1 indicates the mean diameters and mean areas and areas at piezometric rings f o r the main and branch pipes. 4.3. DISCHARGE AND PRESSURE MEASUREMENTS: Discharge was determined by measuring the time and weight of water. Care was taken to ensure that a steady condition was reached a f t e r any change i n control valve p o s i t i o n . The extent of pressure f l u c t u a t i o n s i n the mano- metric tubes connected to the main and branch pipes was observed c l o s e l y and water l e v e l s i n respective gage tanks were adjusted to represent average pressure at each of the 3 piezometric r i n g s . A period of not le s s than 2 hours was considered s u f f i c i e n t f o r the water l e v e l i n the gage tanks to' assume positions representing the actual pressures and only thengage readings were taken. 4.4. EXPERIMENTAL PROCEDURE: For each of the f i v e wyes tested, hydraulic losses had to be obtained f o r three d i f f e r e n t conditions of flow, (i) symmetrical flow, ( i i ) unsymmetrical flow and ( i i i ) one l e g flow. For each wye, therefore, there 2 7 were three ser i e s with a t o t a l number of twelve experiments to be performed. Again, f o r each condition of flow, losses had to be evaluated f o r s p e c i f i c discharges f o r comparison of r e s u l t s . For symmetrical flow, discharges f o r which observations were taken were 0 . 3 2 , 0 . 5 , 0 . 7 5 , 0 . 9 2 , 1 . 1 and 1 . 5 c f s : f o r one leg flow these discharges were 0 . 3 2 , 0 o 5 , 0 . 7 5 and 0 . 9 2 c f s . In the case of unsymmetrical flow, as already explained, with combined discharge maintained at 0 . 7 5 cfs f o r 9 0 ° wyes and 0 . 9 2 c f s f o r 6 0 ° wyes, the discharge r a t i o between the branch pipes was varied from 0 to 1 0 0 % by placing o r i f i c e s of d i f f e r e n t sizes into the two branch pipes. 4.4. EXPERIMENTAL PROCEDURE: The sequence of experiments with a p a r t i c u l a r wye was as follows: (i) The wye was f i r s t ^ b o l t e d to the branch pipes. Connection between the wye and the branch pipes were checked by hand so that the j o i n t s were without o f f s e t s as f a r as possible. The connection of the wye was then made to the main pipe with the help of the l o c a t i n g pins. ( i i ) S t a r t i n g with symmetrical flow conditions, a f t e r placing o r i f i c e No. 1 i n both the branches, the opening of the control valve was adjusted by t r i a l and error so that the discharge was as near 1 . 5 c f s as possible. Afte r observing each piezometric tube, water l e v e l s i n the gage tanks were adjusted and the necessary time allowed f o r the water l e v e l s 28 become constant. Observations were then made separately f o r combined discharge, discharge from r i g h t and l e f t branch and f o r gage readings of water l e v e l s i n tanks connected to the..-main and branch pipes. The control valve was then closed and No. 1 o r i f i c e s i n the branch pipes were replaced by No. 2 o r i f i c e s and the whole procedure repeated f o r discharge of 1.1 c f s . This procedure was continued u n t i l a l l the experiments under t h i s flow condition were completed f o r the discharges 1 .5 , 1 .1 , 0 . 9 2 , 0 . 7 5 , 0.5 and 0 .32 c f s . ( i i i ) The experiment f o r unsymmetrical flow condition was carri e d out next, a f t e r placing d i f f e r e n t o r i f i c e s i n the branch pipes and repeating the procedure, the series was completed f o r a v a r i a t i o n of discharge r a t i o from 0 to 100%. (iv) For one leg flow, one branch pipe was completely blocked and o r i f i c e numbers 1, 2 and 3 were placed one a f t e r the other to obtain discharges of 0 . 9 2 , 0 . 7 5 , 0.5 and 0 .32 c f s . Similar observations as i n the previous flow conditions were then made. (v) After completing experiments on one wye another wye was tested and a s i m i l a r procedure adopted to carry out the experiments. The tabulation of r e s u l t s and graphical represent- ation of points, d e t a i l s of which have been given i n the 29 following chapter, were proceeded with simultaneously. Any discrepancy i n wye loss c o e f f i c i e n t or di s c o n t i n u i t y of curve joining the points on the graph was corrected immediately by repeating the experiment or by applying other remedial measures i f required. In p a r t i c u l a r , when i t was found that f o r un- symmetrical flow, the curve was not well-defined f o r discharge r a t i o around zero, a d d i t i o n a l points were obtained i n the v i c i n i t y by using o r i f i c e s 7 and 8 i n the branch pipe. 30 CHAPTER V. RESULTS AND CONCLUSIONS 5 . 1 . RESULTS OF EXPERIMENTS: The wye losses and wye loss c o e f f i c i e n t s have been obtained f o r a l l experiments on each of the f i v e wyes. These have been shown from Tables 10 to 14 . Results of experiments conducted on the d i f f e r e n t wyes are shown graphically on Figures 16 to 2 9 . Two graphs have been drawn f o r each of the wye models. The f i r s t graph shows wye loss c o e f f i c i e n t K against discharge i n the main pipe. The second graph shows the wye lo s s c o e f f i c i e n t K versus discharge r a t i o ' between the branch pipe and the main pipe. Again, the f i r s t graph com- pr i s e s 3 curves f o r (i) symmetrical flow, ( i i ) open branch pipe and ( i i i ) closed branch pipe. 5 . 2 . CONCLUSIONS AND DISCUSSION: Symmetrical Flow:' For symmetrical flow (Figure 2 6 ) , the wye ..loss c o e f f i c i e n t s f o r a l l the wyes show s l i g h t l y l a r g e r values f o r low discharges. For high discharges the value becomes more or l e s s constant as given below: 31 Particulars of wye Value of K 90° large spherical 0,44 90° small spherical 0 .30 90° tapered 0.16 60° tapered wye (A) 0.088 60° tapered wye (B) 0.080 The considerable variation in the value of K between the different wyes may be observed. K. for Open Branch: In the case of 90° wyes the value of K f a l l s with increase in discharge as shown in Figure 27, whereas for 60° wyes the value increases with increase in discharge, but for a l l wyes the values seem to become constant for high discharges. The value of K for large discharges for the differentJwyes i s given below: Particulars of wye Value of K 90° large spherical 0.92 90° small spherical 0.86 i 90° tapered 0.47 60° tapered (A) 0.41 60° tapered (B) 0.41 For this condition of flow also there i s a large variation in value of K for the different types of wyes. K for Closed Branch: For the closed branch there i s l i t t l e change in the value of K for a l l wyes as seen from 32 Figure 28, the smallest value of K being 0.45 and the largest value, 0.60. Unsymmetrical Flow: Figure 29 gives corresponding values of K for different discharge ratios for each of the five wyes. A significant fact that emerges for unsymmetrical flow i s that the minimum value of K need not necessarily occur for £ =• 0.5, i.e., when flow i s equally divided between the two branches. The minimum value of K and the correspond- ing discharge ratio for each wye i s given below: Particulars of Wye ^ Minimum value Corresponding of K discharge ratio 90° large spherical 0 .41 0.14 90° small spherical 0 .26 O.38 90° tapered 0.17 0.50 60° tapered (A) O.O85 0 .54 60° tapered (B) 0.080 0.50 1 33 BIBLIOGRAPHY (1) Engineering Monographs No. 3 , Bureau of Reclamation, "Welded Steel Penstocks, design and construction" by P.J. Bier, I 9 6 0 . (2) Thoma, D. and Collaborators, "Hydraulic Losses i n Pipe F i t t i n g s " , Transactions of the Munich Hydraulic I n s t i t u t e , B u l l e t i n No. 3 . Translated A.S.M.E., 1934. (3) Gardel, A. B u l l e t i n Techn. Suisse Rom. 83, 9 , pp. 123-30 and 10, pp. 143-8, A p r i l and May 1957. (4) Favre, H. 1937. On the laws which govern the movement of f l u i d s i n conduits having l a t e r a l abductions. Rev. Univ. Mines. (5) McNown, J.S. "Mechanics of Manifold Flow". Trans. ASCE,' Vol. 119, 1954. pp. 1103-18. (6) Herakovich, C T . 1962. " C h a r a c t e r i s t i c s of Flow at D i v i s i o n into Symmetrical L a t e r a l s " . M.S. Thesis, University of Kansas. (7) Otts, J.V. 1962. "A Study of Pressure Pulsations and Mass-Flow Fluctuations through Symmetrical La t e r a l s . " M.S. Thesis, University of Kansas. (8) McVickar, D.B. 1963. "An Experimental Study of Flow at D i v i s i o n into Symmetrical Laterals with C i r c u l a r Section." M.S. Thesis, University of Kansas. (9) Marchetti, M. and Noseda, G. i 9 6 0 . "Loss of Head i n Symmetrical Bifurcations of Constant Diameter In a Pressure Conduit", L'Energia E l e t t r i c a No. 4 , PP» 289-301. (10) 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 Di v i s i o n , ASCE, V o l . 91 No. P01 , May 1965. (11) " F l u i d Mechanics" by Streeter, V.L. McGraw-Hill. 1962. (12) "The Mechanics of Turbulent Flow." by Baklmeteff, B.A. Princeton University Press, 1941. 34 (13) "Modern Developments i n F l u i d Mechanics", by Goldstein, S. Oxford University Press, 1938. (14) "Advanced Mechanics of F l u i d s " , by Hunter Rouse, Wiley, 1 9 5 9 . (15) "Momentum Transfer i n F l u i d s " by Corcoran, W.H. and Others. Academic Press I n s t i t u t e Publishers, New York, 1956. 1 35 Appendix Notation: The following symbols have been used; Ami ~ i n t e r n a l average cross-sectional area of the main pipe i n sq. f t . j A r i = i n t e r n a l average cross-sectional area of the r i g h t branch i n sq. f t . ; A3, = i n t e r n a l average cross-sectional area of the l e f t branch pipe i n sq. f t . ; Am2 = i n t e r n a l area of the main pipe at piezometric r i n g i n sq. f t . ; A r2 = i n t e r n a l area of the r i g h t branch pipe at piezometric ri n g i n sq. f t . ; A12 = i n t e r n a l area of the l e f t branch pipe at piezometric r i n g i n sq. f t . ; Lni = length of the main pipe i n f t . from S to T, the t h e o r e t i c a l centre of Wye, (Fig. 3 ) ; L r • = length of the r i g h t branch pipe i n f t . from T to Di, ( F i g . 3 ) ; Li - length of the l e f t branch pipe i n f t . from T to D , ( F i g . 3 ) ; Qui = discharge i n the main pipe i n c f s ; Q r = discharge i n the r i g h t branch pipe i n c f s ; Ql = discharge i n the l e f t branch pipe i n cfs;. = r a t i o of discharge i n the right or l e f t branch pipe to discharge i n the main pipe; vml = average v e l o c i t y i n the main pipe i n fps; V r i = average v e l o c i t y i n the right branch pipe i n fps; average v e l o c i t y i n the l e f t branch pipe i n fps; v e l o c i t y i n the main pipe i n fps at the piezometric r i n g S, (Fig. 3 ) ; v e l o c i t y i n the r i g h t branch pipe i n fps at the piezometric ri n g Di, (Fig. 3 ) ; v e l o c i t y i n the l e f t branch pipe i n fps at the piezometric r i n g D 2, (Fig. 3 ) ; piezometric head i n the main pipe i n f t . at S, ( F i g v . 3 ) ; piezometric head i n the r i g h t branch pipe i n f t . at D l f (Fig. 3 ) ; piezometric head i n the l e f t branch pipe i n f t . at D 2, (Fig. 3 ) ; v e l o c i t y head i n the main pipe i n f t . at S, (Fig. 3 ) ; v e l o c i t y head i n the right branch pipe i n f t o at Di, ( F i g . 3 ) ; v e l o c i t y head i n the l e f t branch pipe i n f t . at D 2, (Fig. 3 ) ; f r i c t i o n losses i n the main pipe i n f t . from S to T, ( F i g . 3 ) ; f r i c t i o n losses i n the r i g h t branch pipe i n f t . from T to Di, (Fig. 3 ) ; f r i c t i o n losses i n the l e f t branch pipe i n f t . from T to D 2, (Fig. 3 ) ; difference of piezometric heads i n f t . at S and Di, ( F i g . 3) ; difference of piezometric heads i n f t . at S and D 2, (Fig. 3 ) ; 37 A , - l o c a l i z e d loss of head of wye at T between S and D^, ( F i g . 3 ) ; n x - l o c a l i z e d l o s s of head of wye at T between S and D2, ( F i g . 3 ) ; K = Wye loss c o e f f i c i e n t . 38 Table 1 Areas, Main and Branch Pipes, Description Mean diameter (inches) Main pipe 5 . 2 5 2 Branch pipe 3*746 (Sections A,C) Branch pipe 3*750 (Sections B,D) Mean area (sq.ft.) 0 . 1 5 0 3 0 . 0 7 6 4 6 . O 7 6 6 Diameter at Area at Piezometric Piezometric r i n g (inches) rings (sq.ft.) 2 . 2 5 1 3 * 7 5 0 3 * 7 4 8 O o l 5 0 3 0 . 0 7 6 6 0 . 0 7 6 6 Table 2 Distance from Theoretical Centre of Wye to Piezometric Ring?* Main and Branch Pipes P a r t i c u l a r s Distance Distance Distance Distance Distance Distance of Wye from S from to point point of of i n l e t i n l e t M f t . ) to T - ( f t . ) 9 0 ° large spherical 9 0 ° small spherical 9 0 ° tapered tapered ST from T from TD 1,TD 2 ( f t . ) to point point of ( f t . ) of(s a,Sjf outlets,.^ outlet to Di.D 2 . ( f t . ) ( f t . ) 6 0 ° (A) 6 0 ° IB) tapered 0 . 5 0 0 0 . 2 4 3 0 . 7 4 3 0 . 3 5 5 8 . 8 3 3 9 . 1 8 8 0 . 5 0 0 0 . 2 4 0 0 o 7 4 0 O.36O 8 . 8 3 3 9 . 1 9 3 0 . 5 0 0 0 . 5 0 0 0 . 1 2 5 0 . 0 8 3 0 . 6 2 5 . 0 . 5 8 3 0 . 3 7 4 0 . 4 9 7 8 . 8 3 3 8 . 8 3 3 9 . 2 0 7 9 . 3 3 0 0 . 5 0 0 . 0 . 3 1 8 0 . 8 1 8 0 . 4 9 7 8 . 8 3 3 9 . 3 3 0 *• See F i g . 3 3 9 Table 3 Velocity Traverse, Symmetrical Flow, Preliminary Investigations. Discharge I0IO7 cfs Temperature 7 0 ° F Station Calliper Distance Manometer Velocity No. reading from readings head (inches) Station 1 (inches) (inches) (inches) 1 0 . 4 0 7 0 5 . 0 0 + 1 . 0 6 6 . 0 6 2 0 . 6 5 7 0 . 2 5 0 8 . 9 0 + 1 .75 1 0 . 6 5 3 l o l 5 7 0 . 7 5 0 1 1 . 3 0 + 2 . 1 5 1 3 . 4 5 4 1 . 6 5 7 1 . 2 5 0 1 2 . 6 0 + 2 . 5 5 1 5 . 1 5 5 2 . 1 5 7 l o 7 5 0 1 3 . 4 0 + 2 . 9 0 1 6 . 3 0 6 2 . 6 5 7 2 . 2 5 0 13 . 7 5 + 3 . 2 5 1 7 . 0 0 7 3 . 1 5 7 2 . 7 5 0 1 3 . 5 0 + 2 . 9 0 I6.4O 8 v 3 . 6 5 7 3 . 2 5 0 12.75 + 2 . 6 0 15 . 3 5 9 4 o l 5 7 3 o 7 5 0 1 1 . 8 0 + 2 . 4 0 1 4 . 2 0 1 0 4 . 6 5 7 4o250 1 0 . 6 0 + 2 . 2 0 1 2 . 8 0 1 1 5 d 5 7 4 . 7 5 0 8 . 8 0 + 1 . 6 0 1 0 . 4 0 . 1 2 5 . 3 8 0 4 . 9 7 3 7 . 7 0 + 1 . 1 0 8 . 8 0 13 5 . 6 3 0 5 . 2 2 3 4 . 6 0 + . 1 . 0 0 5 . 6 0 Table 4 Velocity Traverse, Symmetrical flow, Final Test Set Up. Discharge 1 . 1 0 cfs Temperature 6 5 0 F Station Calliper Distance Manometer Velocity Noo reading from readings head (inches) Station 1 (inches) (inches) (inches) 1 5 . 6 1 1 0 o 0 0 4 . 7 0 + 0 . 9 5 5.65 2 5 o 3 6 l 0 . 2 5 0 7 . 8 0 + 1 . 2 0 9 . 0 0 3 4 . 8 6 1 0 . 7 5 0 1 0 . 0 0 + 1.85 11 . 8 5 4 4 o 3 6 l 1 . 2 5 0 1 1 . 3 5 + 2 . 2 5 1 3 . 6 0 5 3 086I l o 7 5 0 1 2 . 4 0 + 2 . 5 0 1 4 . 9 0 6 3 o 3 6 l 2 . 2 5 0 1 3 . 2 0 + 2 . 8 0 I60 0 0 7 2 0861 2 . 7 5 0 1 3 . 7 0 + 3 . 1 5 •16 .85 8 2 . 3 6 1 3 . 2 5 0 1 3 . 6 5 + 3 . 3 0 16 . 9 5 9 I086I 3 . 7 5 0 1 3 . 0 5 + 2 .85 1 5 . 9 0 1 0 1 . 3 6 1 4 . 2 5 0 1 1 . 9 5 + 2 . 4 0 14.35 1 1 O086I 4 . 7 5 0 , 1 0 . 1 5 + 2 . 1 0 1 2 . 2 5 1 2 O06II 5 . 0 0 0 8 . 8 0 + 1 . 8 0 1 0 . 6 0 1 3 . 0o420 5 . 1 9 1 5 . 1 0 + 1 . 0 0 6 . 1 0 40 Table 5 Velocity Traverse, One Leg Flow, Final Test Set Up. Discharge 0.917 cfs Temperature 6 5 ° F Station No. 1 2 3 4 5 6 7 8 9 10 11 12 13 Calliper reading (inches) 0.410 0 . 6 6 0 1 . 1 6 0 1.660 2 . 1 6 0 2 . 6 6 0 3 . 1 6 0 3.660 4 . 1 6 0 4 . 6 6 0 5 . 1 6 0 5 . 4 1 0 5.620 Distance from Station 1 (inches) 0 . 0 0 0 . 2 5 0 . 7 5 1 . 2 5 1 . 7 5 2 . 2 5 2 . 7 5 3 o 2 5 3 . 7 5 4 . 2 5 4 . 7 5 5 . 0 0 5 o 2 0 Manometer readings (inches) 5 . 4 5 7 . 7 5 9 o 2 5 1 0 . 3 0 1 0 . 9 5 1 1 . 3 0 1 1 . 3 0 1 0 . 9 5 1 0 . 3 5 9 . 4 5 8 . 1 5 7 . 2 0 5 . 1 5 - 1 . 2 5 - 0 . 8 5 - 0 . 5 5 - 0 . 4 5 - 0 . 2 5 - 0 . 1 2 - 0 . 1 0 - 0 . 1 0 - 0 . 2 0 - 0 . 2 5 - 0 . 5 5 -. 0 . 9 0 - 0 . 9 5 Velocity head (inches) 4 . 2 0 6 . 9 0 8 .70 9.85 10.70 11.18 11.20 10.85 10.15 9 . 2 0 7 . 6 0 6 . 3 0 4 . 2 0 Table 6 Friction Losses, ~ Main Pipe. Discharge (cfs) i ' 1 . 4 8 1 . 1 1 0 . 7 4 8 0 . 4 9 8 0 . 3 2 2 Temperature (*F) 65 6 4 . 5 . 6 6 65 6 4 Length Area Friction (ft.) (sq.ft.) (ft.) 3 . 3 7 5 ' 0 . 1 5 0 3 0 . 1 7 0 3 . 3 7 5 0 . 1 5 0 3 0 . 0 9 8 3 . 3 7 5 0 . 1 5 0 3 O.O48 3 . 3 7 5 0 . 1 5 0 3 0 . 0 2 2 3 . 3 7 5 0 . 1 5 0 3 0 . 0 1 0 41 Table 7 Friction Losses, Branch pipe, Sections A and C. Discharge- (cfs) 0.744 0.501 0.321 0.200 Temperature (*F) 64.5 64 64 64.5 Length (ft.) 9.00 9 . 0 0 9 .00 9 . 0 0 Area (sq.ft.) 0 . 0 7 6 4 O .O764 0 . 0 7 6 4 0 . 0 7 6 4 Friction Loss (ft.) 0.604 0.300 0.136 - 0.059 Table 8 Friction Losses ~ Branch pipe, Sections B and D. Discharge (cfs) 0.746 0.499 0.321 0.198 Temperature ( F) 65 65.5 64 63.5 Length (ft.) 9.00 9.00 9.00 9.00 Area (sq.ft.) 0 . 0 7 6 6 0 . 0 7 6 6 0 . 0 7 6 6 0 . 0 7 6 6 Friction Loss (ft.) 0 . 6 0 2 0 . 2 9 7 0 . 1 3 8 0 . 0 6 2 Table 9 Friction Factors and Reynold Number Main and Branch Pipes Particulars Branch Pipe (Sections A-C) Branch Pipe (Sections B-D) 11 ti Main Pipe n tt tt n n Discharge (cfs) 0.744 0 .501 0.321 0.200 0 .746 0.499 0.321 0.198 1.480 l o l l O 0 .756 0.498 0.324 0.201 Velocity head (ft.) 1 . 4 7 3 0 . 6 7 0 0 . 2 7 5 0 . 1 0 7 1 . 4 7 3 ; 0 . 6 5 7 0 . 2 7 3 0 . 1 0 3 1 . 5 0 8 0 . 8 4 9 0 . 3 9 2 0 . 1 7 0 0 . 0 7 2 0 o 0 2 9 Length diameter 28.7 28.7 28.7 28.7 28.7 28.7 28.7 28.7 7.71 7.71 7.71 7.71 7.71 7.71 Friction factor .0142 .0155 .0172 .0193 .0142 .0156 .0174 .0207 .0146 .0150 • .0167 .0168 £0180 .0230 Reynold' Numbers (xl05) 2.71 1.79 1.14 0 .72 2.72 1.81 1.14 0.72 3.78 2.90 1.94 1.27 0.83 0 .50 Vn .f- U J rO H Vn .p- U J N H + * •*• *• * vn f U J rO H H ro Test No. Or i f i ce No. f w K t-1 » 3 tr" jo K t-< so 3 f W S ( - " ( - • H M H H H H M J ? - \ j J - s l - v J V J l O O -0 vn vn O vo vo vn vo vjn vn O Vn O O O vn O O Q 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 O O O O O O O O O U J Weight of water ( l b sF from M,main pipe; R,right l eg ; L , l e f t leg 4?- .p- vo U J u> U J f-j^uwuvjo J^- -p- ui u> U J U J P--p-ro ro ro ro p- p- U J U J ro ro J>-*-*-1-J?-t- -a~3rorororo rorororonro wu^>o>i>j O O H H O O vn vn oa a* O^j OO^WWOO y i m O O v O O CvOvOOCTvOv vnvnvOvororo H C>U H>0 M -p-^lVovOp-p- * - » 0 ^ - > ] 0 OK»p- O O P " C* p--vl-P" 0»-0-vl Time in terva l (sees) w \ J p- U J U J p- U J U J p- ro ro -p- U J ro ^- p- p- -j ro ro ro ro H u» vo O H O vn 00. ̂0 Ov U J O vn O vO Ov O 0v vn vo ro . • . • • • • . « • • ' • . . . •p- ro M c* c* p- o> » M I a» ov vn ov -a vn Average time in terva l (sees) O * CJv OvC* O*. O*. Ov 0 s OvOv • rovn rovn rovn ro J?- M P -• • • • • • • vo vo U J vn vo vn vo vo U J U J U J Ov Temperature i n c F and spec i f i c weight of water ( lbs /cu. f t . ) O O O O O O O O O O O H O O H • . « • • • • » . « • ' • • • • H H U J ro ro vn vo U J 3̂ »C H -0 ^] vn Ov Ov ro vn .p- O vn if. vn 0 vn vn O I O H U J U ) O » H ov vn ro 5 ** w H ro -p-u> w ov O CO vn vn -0 Discharge (cfs) H O H O H H 0» O Ott vn H oa ro vo o» •p- H O vo 01 Hook gage reading in upstream tank ( f t ) H O O O O • • .« • • ro vo co U J U J P - H U J o O-O O H O - O vO Hook gage reading in centra l tank ( ft) H O O o o ro vo co. ro U J p- H U J vO <J< o ro vn -0 H O Hook eage reading in downstream tank ( f t ) o o o o o • • • • . ro ro ro ro ro H H H H H o O O O O H H Vernier correct ion ( ft) O O O O O O O O H H • • • . • • . • » . . O O H H U J vo o i o a -p- p-o a o a o> oa - v o o a O O vo p- P - P - . ^ ] H O v O o v n r o r o H ro Pressure head di f ference ( ft) between main pipe and r ight leg or main pipe and l e f t leg H U J Discharge r a t i o , Discharee in branch Discharge in main pipe O o o o o • • • • • O O O O H H ro P - vo ~o O ro oo oo U J H •F- Fr i c t i on loss ( f t ) in main pipe f o r length 3 . 3 7 5 ' o o o o o . • » • . o o o o o: o o H ro U J ro vn H ro ca H vn F r i c t i on loss (ft) in main • pipe f o r length ST 0 .6 1 1  0 .6 0 5  O .3 5 8  0 .3 5 6  0 .1 7 9  0 .1 8 0  0 .0 8 6  0 .0 8 8  0 .0 4 0  0 .0 4 0  H Ov F r i c t i o n loss ( ft) in r ight or l e f t leg, for length 9 . 0 ' 0 .6 2 3  0 .6 1 9  O .3 6 6  0 .3 6 3  O .1 8 3  0 .1 8 4  0 .0 8 8  0 .0 9 0  0 .0 4 1  0 .0 4 1  H Fr i c t i on loss ( f t ) , in r ight or l e f t leg , for length TD-L or T D 2 0 .6 6 1  0 .6 5 7  0 .3 8 8  O .3 8 5  0 .1 9 4  0 .1 9 5  0 .0 9 3  0 .0 9 5  0 .0 4 3  0 .0 4 3  H Total f r i c t i o n loss ( ft) H ro U J vn 0 . . . . . . H U J O U J O vn U J . H P - ro H vO Veloc i ty in main pipe (ft/sec) O O O O H . . . . . . O H U ) oa vn ->j ~j vo U J vn ro u> 0 ON *o ro 0 Veloc i ty head in main pipe (ft) K M . p- p- ~0 -J vOv O « • . « » • • * H H vo ro vo vo r o r o oaoa M H O v n W H O H H U J ro H Velocity in r ight or l e f t leg (ft/sec) O O O O O O O O H H . . « • • » O O H H U J U J 01 00 * - v n - O C * 0"> Ov - O O O vo O O v O v O - J ON P - vn ^] Ov ro ro ro Velocity head in r ight or l e f t leg (ft) O O O O O O O O O O • • • • • • O O 0 0 r o w co- cu •p- *- \0 vO O H vo vo UJ p- O * - v O H O O O O ro U J Wye loss ( ft) 0 .5 3 7  0 .5 3 7  0 .5 3 4  0 .5 3 4  0 .5 4 1  0 .5 3 6  0 .5 4 2  0 .5 5 5  0 .6 1 1  0 .5 9 7  ro •t- Wye loss coef f i c ient 0 0 0 0 0 1 . • . . J£ vn vn vn vn v> .f- vo vo vo • P \0 vO' p- -s] ro vn Average wye loss coef f i c ient W ( O H V t * - W l \ 3 H H |Teat No. w w r o w H so w c - 1 H t-< *- r* v« tr1 + • + + + + + + + . xt -* x r * xtr* oo w -o. w- ow w po ropo ro Orifice No. M 15000 R 14500 L 5000 H 15000 R 9500 L 8000 M  10000 R 2000 L 19000 K  15000  R 1 0 0 0  L 19000 H  15000  R 5 0 0  L 19000  M 15000 R 15000  M 10000  R 10000  L M 10250 R 10250  jL - w Weight of water (lbs) from M.maln pipe; R,right leg; • L.left leg V1V* W W W W f -pyiwww *-*-*-*-ww *-*-wwww *-*-wwww *-*-*-*-ww HH *-*- . ro ro HHOO*roro rorocaoaroro vi vi\o*£r ro ro MH*-*-roro vtvioororo t i ro ro i i coco i i H H f w c o ^ H H C3NC3-*OC*MH (>ff>wuiHH roro^\OHH r o H * - * - o o c»*- .*-*- . ro ro *Ov<rooo^3c» H vi~o ooro c* C7*O*0*-o*- , viorow^jco OOO* -HM *- •Time interval (sees) 320.2  404.2  451.8 321.8 349-2  412.7 321.2 395-7 456.3 321.4 486.8 426-3 321.8 569-0 415.2 1321-2 348.4 512.6 VI Average time interval (sees) 65.5 62.33  65 6 2 .33 65 62.33 65 62.33 65 62.33 65.5 62.33 65.5 62.33 65-5 6 2 .33 0 1 Temperature in F° and specific 'weight of water (lbs/cu.ft.) .. 0.751 0.575 0.177 0.749 0.081 0.668 0.749 0.081 0.668  0.748 0.033 0.715 0.748 6.O I4  0.734 0.749 O .46O  O .321 3̂ •Discharge (cfs) 1.365 1 .822 1.563 1.928 2 .085 2.357 2.228 1.772 ca t [Hook gage reading in upstream : tank (ft) r o r o r o o o O H H 0 -0 ro • ro H ca • H O W v£3 V< W W vt *- 0 * - vi 0 w r - * o i*3 • Hook gage reading in central ' tank' [ft) H H O r o r o H H O v » o * - * - w * o * - w ~J H co v> 0 0 1 r o s o O * O O ^ 3 V I * - H O H O : Hook gage reading in downstream • tank (ft) 0.210 0 .210 0.210 0.210 0.210 0.210 0.210 0 .210 H H Vernier correction (ft) 1 .185 0.084 0.611  0 .207 •0.181 1.640 •0.167 1.893 •0.162 2.000 2.087 •0.167 0.819 •0.062 0.412 L0.O 32 H ro ] Pressure head difference (ft) : between main pipe and right leg or main pipe and l e f t leg O M O O O O O O O O O O o b " o b " o b co H * - vi ro "0 O O co H v i * - \o 0 H co w r > H *c cr* * - ro c» CJ* * - -0 w H W Discharge ratio, •Discharee in branch Dincharee in main Dioe O O O O O O O O 0 a <D 0 a 0 a h H H * - * - * - * - * - * -o ^ o c o c o c o c o c o c o H * - Friction loss (ft) in^main Friction loss (ft), in main pipe for length ST 0.011  0.011  0.011  0.011 0.011 0.011  0.004 ! 0.002| H VI O .38O  0 .044 0.237 0.128 0.012 0.494 0.002  0.556 0.001 0.583 0.607  0.256 0.137 H Friction loss (ft) in right or left leg, for length 9.0' 0 0 O 0 0 0 0 0 0 0 0 0 0 I H i r o 1 0 v i o vi 0 v i o H ro o w *- ro \0 0 0 0 O H w *= *- \o 0 H 0 vi H -0 ro *- ro H r o vi 0 H 3̂ Friction loss (ft), in right or left leg, for length TD-, or TD, 0.401 0 .0 5 6  0 .253 0.142 0.023 0.515 0.013 0 .578 0.012 0 .606 0 .6 3 1  0.011  0.265  0.004  0.142 0.002  H OO H Total friction loss (ft) r o r o * - * - * - * - * - v i w o c o c o c o c o c o o Velocity in main pipe (ft/sec) 0 0 • 0 o - o 0 0 0 O H W W W W w w ^ w o j c o c o c o c o c a H s£) CJ* Vi vi O V i c» 8 , Velocity head in main pipe (ft) 7.51 2.32 5.70 4.06 1.06 8.72 0.44 9-33 0.19 9-58 9-78 6.01 4.19 ro H Velocity in right or left leg (ft/sec) 0.876  O .O 84 0.505 0.257 0.019 1.182  0 .003 1.355 0.001 1.428 1.485 0.562 0 .274 ro ro Velocity head in right or left leg (ft) 0.296  0.164 0 .2 3 8  0.193 O .I6 3  0.329  0 .202 0.345 0 .210: 0.351 0.357 0 .208 0 .1 3 1 1  0.073  Jo.072 J0.037 to w Wye loss (ft) O H O O O O O O O O O O O O O O VI O V v O V l \ 0 vOVl CO VI 0 3 * - *- o> *-H H r o * - w r o H * - v c r o vt ro 03 H ro 0 \0 co ui M \o * - w cr* vi w w r o 0 co w w ro *r Wye loss coefficient wi J?- UJ 10 H H Test No . VI f UJ IO M •»- • • + + wi UJ ro H ro O r i f i c e No. M  19 0 0 0  R  10 0 0 0  L 19000  M  19 0 0 0  R  10 0 0 0  L 15000  M  15 0 0 0  R  7500  L 10500  M  10 0 0 0  R  5000  L  750 0  M  7500  R  3 75 0  L 5000  UJ Weight of water (lbs) from M, main pipe; R,right leg ; L , l e f t leg U J U J U J U J UJUJUJU ) f j>-wuwu t-J?-ro ro ro ro *-*-ro ro ro ro > © \ O - 0 - J ^ J - 0 --j~j 10 to ro ro * - * - ro ro H H UJUJVOVO^J^J O C I J P O O ^ • O U ^ - v n u i . O ^ O ^ U J U J O O VI O O 0 \ G vO f - y i o o v j i w O O O H O O . . . . . . . . . . . . . . . . . . . . . . . . • • » • • • f - C S O O O O * - 0 " O O ^ O W i . \ O U J O O > U J I O vO H ro 0**wi 0** 'wiwi O a O f O *- Time in terva l (sees) .r- UJ UJ j?- UJ UJ UJ UJ r N M *- ro ro V O - J - J - j ro ro * - ro H U J V D ^ J O H O O* UJ wi O UJ O O ^ O v O wi O wt O O O • . . • . • • . • . » . • • • O oa O ro *- ro H ->J wi 0 wi wi 0 ro O O WI O O WI Wl Average time in terva l (sees) rowi rowi rowi rowi rowi • • • • . UJ 0 W W ! UJ O UJ 0 UJ 0 UJ UJ UJ UJ UJ 0^ Temperature in F ° and spec i f i c weight of water ( l b s / c u . f t . ) ' 1.5 2 2  0 .7 6 0  0 .76 1 1.10 7 0 .5 5 2  0 .5 5 3  0 .7 5 3  0 .3 7 5 : 0 .3 7 7 5  0 .50 1 0 .2 4 8  0 .2 5 3  0 .3 2 1 0 .161 0 .16 1 - J Discharge (cfs) M O O O M . . . . . O or* NO 0 ro 0» u j H >0 Cf< wi a> *- ro ro oa Hook gage reading in upstream tank ( f t ) M 0 O 0 O . . . . . M OJ CO UJ w * ro 0 ca O sO - UJ \0 NO Hook gage reading in centra l tank ( f t ) 0 .3 7 4  0 .2 9 7  0 .8 2 9  0 .9 0 3  1.2 3 2  H O Hook gage reading in downstream tank ( f t ) 0 .2 10  0 .2 10  0 .2 10  0 .2 10  0 .2 10  H H Vernier correction ( f t ) 1.0 9 8  1.0 8 3  0 .6 0 5  0 .5 9 9  0 .2 9 5  0 .2 9 8  0.133  0.147  0 .0 6 3  0 .0 6 5  H IO Pressure head di f ference (ft) . between main pipe and r ight leg or main pipe and l e f t leg H UJ Discharge r a t i o , Discharge in branch Discharge in main pipe 0.177  0 .0 9 8  O .O 4 8  0 .0 2 2  0 .0 10  H *- F r i c t i o n loss ( ft) i n main pipe for length 3 .375' 0 .0 3 9  0 .0 2 1 0 .0 11 0 .0 0 5  0 .0 0 2  H WI Fr i c t i on loss ( f t ) , in main pipe for length ST 0 .6 15  0 .616  0 .3 5 7  0 .3 5 8  0.182  0.183  0 .0 8 6  0 .0 9 2  0 .0 4 0  0 .0 4 2  H Fr i c t i on loss ( ft) i n r ight or l e f t leg , for length 9 - 0 ' 0 0 0 0 0 0 0 0 0 0 . . . . . . . . . . O O Q O H H U J U J O O <o oa 00,00. O O ro ro UJ M J ? - o » -0 ~ J O- wi \0 oa H Fr i c t i on loss ( f t ) , in r ight or l e f t leg, f o r length TDi or TD 2 O O O O O O O O O O . . . • . . . . O ' O O O H ' H UJ UJ O O f j * r - \0 >0 \ O v O CO CKJ O 0^ wi uj V O U J oa oa - 0 0 * oa H oa Total f r i c t i o n loss ( ft) H ro UJ wi - j 0 . . . . . H UJ O UJ H UJ UJ r-1 0^ UJ H 0 Veloc i ty in main pipe ( f t /sec) O O O O H . . . . . O l-i UJ o» WI -0 ->} O vO H UJ 0 ro u> ro O Velocity head in main pipe ( f t ) 9 .9 4  7.2 2  7.2 2  4 .9 0  4 .9 2  3.23  3.3 0  - 2 .10  2 .11 ro H Velocity in r ight or l e f t leg (ft/sec) 1.5 3 2  1.5 3 7 0.811  0 .8 10  0 .3 7 4  0 .3 7 7  0 .16 3  0 .16 9  0 .0 6 8  0 .0 6 9  ro ro Velocity head in r ight or l e f t leg (ft) 0 0 0 0 0 0 0 0 0 0 . . > « » . . « . O O O O H H r o r o r o r o wi wi H H 4> wi -0 vO ro UJ ro 0 W I U J * - 0 H I O ro UJ Wye loss ( f t ) 0 .3 0 9  0 .2 9 5  0 .2 9 7  0 .2 9 0  0 .2 9 0  0 .2 9 5  0 .2 8 9  0 .3 0 1 0 .3 2 4  0 .3 10  ro •r- Wye loss coef f i c ient 0 .3 0 2  0 .2 9 4  i 0 .2 9 3  0 .2 9 0  0 .3 0 7  ro Wl Average wye loss coef f i c ient W M H Vt *- w N H H Test No. w W r o w w w w f w r r - o tr* *- r u i H R P M f c a w «o w H W w w r o w N Orifice No. t - w K r » E r> • » K e w x • w » H W K f W K t - w R H H H H H H H H H H H H H H • s i - N j Q Q i v / i v i \D u i v o r o v i r o v i u i oo. o v i u i r o v i • V i V i 1 © Q S f i 9 V J S Q Q O Q Q Q Q ro O u ; w O 88 88 88 8 8 8 8 8 8 8 8 8 8 o 8 8 8 8 W Weight of water (lbs) from M,main pipe; R,right leg; L,left leg w w w w f - f - u i u i w w * - * - i o i o w w J £ j > w w w w p - p - w w w w v n v n w w w w -o^s t o w MPOV<MOW M ( o > j - j w r o o o c £ g i r o r o M H - O ^ J M W o o * - * - r o r o 1 f H M 1 t CttsO r 1 H H f v t N O v O H K «OOicaiC-roro H M O O H H r o r o O i O i O O H N O O t O H \o\0 NO*- CMO • - o w c o o o i o a - ro oaovcoro*- *- io .p-caONio o i o - p - c a o o N O M O O > O *- Time interval (sees) 320.8 349-0 5 0 1.6 320.0 3 7 6.6 412.3 321.8 360.6 401.7 3 2 2.3 9 7 9.2 427.0 321-7 569-4 415-0 3 2 1.8 319-2 371.9 Oi Average time interval (sees) 65-0 6 2.33 66.0 6 2.33 65.0 6 2.33 65.O 62.33 65-5 62.33 65.O 6 2.33 65.O 6 2.33 65.O 6 2.33 c* Temperature in F° and. specific weight of water (lbs/cu.ft.) 0 .7 5 0  0.574 0.176 0 .7 5 2  0.437 0.312 O .7 4 8  0 .6 6 7  0.079 0 .7 4 6  0 .0 3 3  0.713 0 .7 4 8  0.014 0.734 0.745 O .5 O 2  0 .3 2 4  •< Discharge (cfs) 1.262 1.703 1.472 I .8 8 3  2.065 2.179 0 .8 5 3  0.588 03 Hook gage reading in upstream tank (ft) 1.610 1.796 1.874 0 .2 4 7  0.295 2.570 1.140 0.830 O Hook gage reading in central tank (ft) 0.394 1.409 0 .1 0 7  2 .2 7 2  2.457 0 .3 4 4  0 .1 0 3  0.384 c Hook gage reading in downstream tank Tft) 0.210 0.210 0.210 0.210 0 .2 1 0  0.210 0.210 0.210 t Vernier correction (ft) 1.078 -0 .1 3 2  0.504 0.117 1 .5 7 5  -0.192 -0.179 I .8 4 6  -0.172 1.968 2 .0 4 5  -0.181 O .9 6 O  -0 .0 7 7  0.414 -O .0 3 2  H ro Pressure head difference (ft) between main pipe and right leg or main pipe and left leg O H O O , O O O O O O O O Q . O * 0 O * 0 O H 0 » J r 01 to O O Cc- H u i * - Q -3 H O f t W O N 0 0 H v0 0 1 * * C> W ff«fO 01 01 H Discharge ratio, BnHsharKs in branch Discharge in main pipe O O O O O O O O b 0 b b b b b b o i o o a c a c o c o c o o Q - Friction loss (ft) in main pipe for length 3.375' 0.011 0.011 0.011 o .o u  0.011 0.011 0 .0 0 5  0 .0 0 2  H Friction loss (ft) in main pipe for length ST 0 .3 8 0  0 .0 4 9  0 .2 4 0  0.1 3 3  0 .4 9 9  0.011 0 .0 0 2  0 .5 6 2  0.001 0.583 0 .6 0 6  0.302 0 .1 3 7  Friction loss (ft) in right or left leg, for length 9.0' 0.387 0 .0 5 0  0.245 0.136 0.510 0 .0 1 1  0 .0 0 2  0.574 0 .0 0 1  0 .5 9 5  0.619 0 .3 0 9  0.140 H - J Friction loss (ft), in right or left leg, for length TDi or TDj 0 .3 9 8  0 .0 6 1  0 .2 5 6  0 .1 4 7  0 .5 2 1  0 .0 2 2  0 .0 1 3  0 .5 8 5  0.012 0.606 0.630 0 .0 1 1  0.314 0 .0 0 5  0.142 0 .0 0 2  t- C0| Total friction loss (ft) ro w - r - ' * - *- *- 01 H w \Q iO VO • '10 • O vQ •O Velocity In main pipe (ft/sec) O O O O O O O O Q H W W W W W W S - - o a i cn oa co \o o» r o p - r o o i w o i o - v j 8 Velocity head in main pipe (ft) *- Oi VO I O O v O O H t » * - o i 1 0 - 0 ro 01 "0 O I H W f - 0 - 0 O - o w o i w ov ro 0 0 . 0 a H K > * - H - O H O W ' ro H Velocity In right or left leg (ft/sec) 0.872 0.085 O .5 0 6  0.257 1.178 0 .0 1 7  0 .0 0 3  1.348 0 .0 0 1  1.428 1 .4 6 8  0.669 0.278 » Velocity head in right or left leg (ft) 0.1 0 9  0.1 3 2  0.103 0.261 0.154 0.188 O .2 9 6  0 .2 0 0  0.319 0.329 0.190 0 .1 5 1  0.086 O .O 6 5  0.038 ro Wye loss (ft) O .5 O 4  0 .2 8 2  0.338 0 .2 6 4  0 .6 7 8  0.40O 0.490 0 .7 7 3  0.519 0 .8 2 8  0.861 0.497 0 .8 6 6  0.495 0.917 0.528 Wye IOBS coefficient '• vn *- UJ ro H H Test No. vn *- V»J ro M , * + + • • » • • vn f U J ro t-J ro Or i f i ce No. f - o s t - w s t - w a s t - w s f w s H M H 1—' 1—' I—' H H H vn U J —3 VJI Q O ^ J v n O O vO N O vn N O O - N j v n vn O O O v n O O O O O O O O V J I 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 O O O U J Weight of water (lbs) from M,main pipe; R,right l e g ; L , l e f t leg * - * - U J U J U J U J * - * - U J U J U J U J * - * - U J U J U J U J ujuJUJUJUJUJ * - * - U J U J ro ro vOvo-o->a^j^ -o~o ro ro ro ro rorororororo H H H H O O O O W IM O O vn-^j;*-vnujuj -oo>vnf-HH caoaujuj ro ro oo-o-o o a H H caro I O U J * - H*-Orj.ro ov*- vnUJ H O V U J 0** O ^ U J O v f O *- 0 V N O * - U J N O W H H w r > o *• Time in terva l (sees) 2 0 3 .8  3 2 2 .2  4 0 7 .7  3 0 1.6  3 1 8 .1 5  318 .0  3 2 2 .2  3 2 3 .4 5  4 2 8 .3 5  3 2 1.4 5  3 2 4 .8 5  4 7 7 .9 0  3 7 3 .5  3 7 5 -0  4 9 7 .7  vn Average time in terva l (sees) O N O N 1 O V C J V 0**C7V 0"NC*N OvOv rot- 1 ro*- ro*- rouj rouj U J uj UJ UJvn UJVn *- *- *- *- *- ' O Temperature in F° and spec i f i c weight of water ( lbs /cu. f t . ) O O O O O O O O O H O O H . . . . . . . . . . . . . . . H H U J r o r o * - U J U J - O vn VJI 0 --J ~o * -O ON 1 0 U - I * - N O - 0 -vi *- O O H * - * - N O H 0 ro r---vjNO *- ro 0 - *- *- H o a ov - 0 U J U J : - - J Discharge (cfs) 0 .9 6 0  0 .2 0 3  0 .8 2 9  0 .8 0 0  1.0 6 1 1 i 00 Hook gage reading in upstream tank (ft) 0 .3 4 3  0 .114  0 .7 9 8  0 .8 9 0  1.2 16  NO Hook gage reading in centra l tank ( f t ) 0 .3 3 8  0 .112  0 .8 0 0  0 .8 9 5  1.215  H O Hook gage reading in downstream tank Tft) 0.210  0.210  0 .210  0 .210  0.210  H Vernier correct ion ( f t ) 0 .8 3 2  0 .8 2 7  0 .401  0 .3 9 9  0 .2 3 9  0 .241  0 .115  0.120  0 .0 5 6  0 .0 5 5  H ro Pressure head difference (ft) between main pipe and r ight leg or main pipe and l e f t leg H O J Discharge r a t i o , Discharge i n branch Discharge in main pipe 0 0 0 0 0 . . . . . O O O O H H ro * - 0 0 vn 0 ro o» ro 0 H *- Fr i c t i on loss (ft) in main pipe fo r length 3.375' 0 .0 2 8  0 .0 15  0 .0 0 9  0 .0 0 4  0 .0 0 2  H 0 1 Fr i c t i on loss ( f t ) , in main pipe fo r length ST 0 .601  O .3 O 6  0 .3 0 6  0.176  0 .178  O .O 8 5  0 .0 8 8  0 .0 4 0  0 .0 4 2  H 0 > Fr i c t i on loss (ft) in r ight or l e f t leg , f o r length 9 . 0 ' 0 .6 13  O .6 O 4  0 .313  0.313  0.180  0 .182  0 .0 8 7  0 .0 9 0  0 .041  0 .0 4 3  H F r i c t i o n loss ( f t ) , i n r ight or l e f t leg , for length TDi or TD 2 O .6 4 I 0 .6 3 2  0 .3 2 8  0 .3 2 8  0.189  0.191  0 .0 9 1 0 .0 9 4  0 .0 4 3  0 .0 4 5  0 0 Tota l f r i c t i o n loss ( f t ) ro U J * - ^ 3 N O . . . . . H UJ N O U> N O v/i ro - 0 ro vn H - 0 Veloc i ty in main pipe (ft/sec) 1.5 3 0  0 .8 3 3  0 .3 8 3  0.171  0 .0 7 2  ro 0 Veloc i ty head in main pipe (ft) r o r o U J U J * - * - O N O N N O . N O . . . . . . . . . . H H r o r o o a o a v n v n - 0 - 0 H O cq ro o a o v o a o a - 0 *- ro H Veloc i ty i n r ight or l e f t leg ( ft/sec) O O O O O O O O H H . . . « . ' . . . . . O O 4-> H UJ UJ O N ON *~ *-ONOV O N O V - 0 0 V O a ^ J N o o a - 0 ro H->o r o u j u j v n ro ro Veloc i ty head in r ight or l e f t leg (ft) 0 .2 4 6  0 .2 3 2  0 .13 3  0 .13 2  0 .0 6 6  0 .0 6 2  0 .0 3 2  0 .0 3 0  0 .0 17 0 .0 13  ro Wye loss (ft) 0 .16 1 0 .15 2  0 .160  0 .158  0 .172  0 .16 4  0 .187  0 .175  0 .2 3 6  0.181  ro F-Wye loss coef f i c ient O .I 5 6  0 .159  0 .16 8  0.181  0 .214  ro Average wye loss coef f i c ient W IO H V I *" W rO H H T e s t N o . w r* ro t* M H H H H t-i M R ) w w S ' p o S m S w c a w i » c« p £ H A r* ro O r i f i c e N o . c w se t-> w a c-> a & f w 3 H w 3 H w s f a s . t - w a M H H H H H H H H H H H H H H W W e i g h t o f w a t e r ( l b s ) f r o m M , m a i n p i p e ; R , r i g h t l e g L . l e f t l e g 3 2 0 .5  3 2 0 .4  3 4 7 .4  3 4 7 .2  4 4 1 .5  4 4 0 .7  3 2 5 .4  3 2 4 .9  3 7 0 .5  3 7 0 .1  5 2 3 .8  5 2 3 .4  3 2 2 .5  3 2 3 .0  3 5 1 .7  3 5 1 .4  4 5 5 .5  4 5 6 .1  3 2 0 .7  3 2 0 .3  6 0 1 .0  6 0 2 .2  4 2 3 .6  4 2 4 .O  3 2 1 .4 5  3 2 1 .0 0  5 7 8 .5 0  5 7 9 .3 0  4 1 4 .5 0  4 1 5 .0 0  3 2 4 .6  3 2 5 .0  4 8 2 .8  4 8 2 .0  - 497 .3  497 .0  *- T i n e i n t e r v a l ( s e e s ) 3 2 0 .7  3 4 7 .3  4 4 1 .2  3 2 5 .1 5  3 7 0 .3 0  5 2 3 .6 0  3 2 2 .7 5  3 5 1 .5 5  4 5 5 .8 0  3 2 0 .4  6 0 1 .6  4 2 3 .8  3 2 1 .2 2  5 7 8 .9 0  4 1 4 .7 5  3 2 4 .8  4 8 2 .4  4 9 7 .1 5  •J-l A v e r a g e t i m e i n t e r v a l ( s e e s ) O N O N cr* 0* cn ov crvov 0 * O N O N cr* ovo* rov*. ro*- row ro o\ W O N r o * - r o * - r o * - w w w i n w w w w w w * - * - w w * - * - * - cr T e m p e r a t u r e i n 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 s / c u . f t . ) 0 .7 5 0  0 .5 7 7  0 .1 7 3  0 .7 3 9  0 .4 3 3  0 .3 0 6  0 .7 4 6  0 .0 7 8  0 .6 6 8  0 .7 5 0 S  0 .0 3 2 | 0 .7 1 9  0 .7 4 9  0.0 1 3 9 ^  0 .7 3 5  0 .7 4 1  0 .4 9 8  0 .3 2 2  D i s c h a r g e ( c f s ) H H H O O H H H • • • • » . • • W V I ' H v / 1 - O . v O v O - J W v O - O v i • v i ca Q v i v i ro vo *- *" H 0 ro a Hook g a g e r e a d i n g i n u p s t r e a m t a n k ( f t ) O O O O O O H H . • . • • e • • w 0 w w r o H - 0 v i 3 • 3 « S S • .V $ 3 0 H o o k g a g e r e a d i n g i n c e n t r a l t a n k ( f t ) O H ro ro ro H H O • • • • • > • • S O w r o H - o w * : so W v>n *o W H -o Q O W - o \3 W C O H 0 H O H o o k g a g e r e a d i n g i n d o w n s t r e a m t a n k ( f t ) O O O O O O O O g (3 H H ' W H H O O O O . O O O O H V e r n i e r c o r r e c t i o n ( f t ) O O O O H O H O H O H O O O O O • • • * W Q W O G O H C O H - O H • * - H O *- H O P r e s s u r e h e a d 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 a n d r i g h t l e g o r m a i n p i p e a n d l e f t l e g H O O O O O O O 0 0 0 0 0 b \o 0 vo 0 p a n f - v i ro - 0 S S CO H V I * - vg O H O f . W O N O O H vo - 0 W V I V I * - 0 N H vo D i s c h a r g e r a t i o , BAasjiRrRs.in brans!., D i s c h a r g e i n m a i n p i p e O O O O O O O O t • . • • • . • • • O O O O O O O O H I O . * - * - * - * - * - * - O W - o O a o a o a Q n C O H P- 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 3 0 7 5 ' p p p O p 0 0 p 1̂  »§ *§ H 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 ST 0 .3 8 5  0 .0 4 7  0 .2 3 1  0 .1 2 8  0 .0 1 1  0 .4 8 8  0 .0 0 2  0 .5 6 4  0 .0 0 1  0 .5 8 5  0 .5 8 3  0 .2 9 7  0.139  Ol 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 l e g , f o r l e n g t h 9 . 0 * 0 .3 9 4  0 .0 4 8  O .2 3 6  0 .1 3 1  0 .0 1 1  0 .4 9 9  0 .0 0 2  0 .5 7 7  0 .0 0 1  0 .5 9 7  0 .5 9 7  0 .3 0 4  0 .1 4 2  H -J 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 l e g , f o r l e n g t h T D i o r T D 2 O .4 O 3  0 .0 5 7  0 .2 4 5  0 .1 4 0  0 .0 2 0  O .5 O 8  0 .0 1 1  O .5 8 6  0 .0 1 0  0 .6 0 6  0 .0 0 9  0 .6 0 6  0 .0 0 4  0 .3 0 8  0 .0 0 2  0.144  H C O T o t a l f r i c t i o n l o s s ( f t ) r o w * - * - * - - - * - * - H Co Co Co Co Co > vo C O ^ H w o o v o - o r o v o H -O V e l o c i t y I n m a i n p i p e ( f t / s e c ) o o o o o o o o . . . * * » • » • O H W W W W W W P P c a O N C a w o N - o ro 0 V e l o c i t y h e a d i n m a i n p i p e ( f t ) *- ns so vO O N 0 O O a H W v i r o - 0 • 1 • 1 . 1 . * * • • • • • ro v i O N , O H w*- - 0 0 vo O N r o v i O O - 0 . O cn cnN) r o r j v o v i ON W ro H V e l o c i t y i n r i g h t o r l e f t l e g ( f t / s e c ) O O H H O H O H O O O O O ro 1 O N 1 *- 1 *- b w b H O r o * - 0 » -o v i v i w o O N O . O O H * - V O s e n v i - 0 v> r o H s o w W O N cn 0 vo H V e l o c i t y h e a d i n r i g h t o r l e f t l e g ( f t ) O O O Q O O O O O O O Q O O O O * • • • . . . . * . O O O <? \ H N H W H W ' H H S O H Q w*- e n v o i 0 0 0 V I Q w o ro O N H v S V I W W O N \ W *- ro O N - v j w O N * - vo O N • o r o . ro VA> Wye l o s s ( f t ) O O 0 0 0 0 0 0 0 0 0 0 0 0 0 0 • « • f • » * t • • • * * - C h * - v i * - v i w v n W V I w *- H H r o w t3 s . n f 0 s ¥ a s a s £ & ** ^ Wye l o s s c o e f f i c i e n t vn * - vo to H >- Test No. * - vo vo ro (-• + + + • • «• *- vo vo ro M r\ O r i f i c e No. t« w K r w a B f j o S f so 55 f r o S S (_. M H t—• I—" t—• r-< H ~ J v n Q Q ^ I v n vn Q vO Q vO v O v n v O ^ 2 Q Q ^ Q O O O O O O O O Q O O Q Q O O O O Q O Q Q Q Q O O O O O O O O O O O O O O O O v. Weight of water (Ibis) from M,main pipe; R,right l e g ; L , l e f t leg * - * - vovovovo f - f - w u v J U J vnvnvovjjvovo vnvnrorororo *- *-vovororo o» oa (-1»-" i—' i—1 ro to ro ro to ro ro ro*-*-rovo torovOvo-j^i O O M M O O ro t - i ^ j - j N O v o -o^j o o o o i-'i-'-j-ovo o M ro ro ro vo*-vovo ro \~> . . . . . . . » . . » . . . . . . . . . . . . . . . . . . . O o>0*»oavjnvn *- ro MI-* ro 0 \ orov / ivOO oarovOvn'^jvn sOHvnOUtio *• Time in terva l (sees) 202.1  319.3  4 0 4 .0  2 7 7.6  2 9 2 .7  5 2 2 .0  3 3 0 .0  3 4 7 .3  521 .3  3 2 0 .2  3 2 0 .2  4 2 7 .3  319 -5  317.7 481.6  VI Average time in terva l (sees) OvOv OvOV OvOv OvOv OvCJ> rovn rovn ro*- ro*- rowi . . . . . . . VO v n vo vo vo v n vo vo vo vo vo 0 Temperature in F° and spec i f i c weight o f water ( Ibs/cu.ft.) O O O O O O p o O O O t - i O O . . . . . . . . . . . . r o r o v n vo vo *~ *- vo v n vn 0 -g. - 0 vn v n v n o s j >1 y i Cfl p ro vn *- \ 0 v n v n O O vo ro v A v n t - i >o jo * - O o a o a v n vo 00 v n vn O Discharge (cfs) O O H O O . . . . . oa oa - J * - oa O M +- Ca vO vo ro a Hook gage reading i n upstream tank (ft) O O r-> O O . . . . . vo oa Ov to vo vn Ov * - vn - 0 vo vo oa Ni Hook gage reading i n centra l tank ( f t ) O O \-> O O . . . . . vO oa ov ro vo O I-" v n Ov * - o> H ro vo oa 1- c Hook gage reading i n downstream tank ( f t ) 0.210  0.210  0.210  0.210  0.210  t Vernier correct ion ( f t ) 0 .7 3 9  0 .7 3 9  0 .4 2 3  0 .4 2 3  0 .3 0 1 0 .3 0 0  0.218  0 .2 12  0 .111 0.102  H t\ Pressure head di f ference (ft) between main pipe and r ight leg or main pipe and l e f t leg 1-V> Discharge r a t i o , Discharee in branch Discharge i n main pipe 0.174  0 .0 9 8  0 .0 7 0  0 .0 4 8  0 .0 2 2  i? F r i c t i o n loss ( f t ) i n main pipe f o r length 3.375* 0 .0 3 0  0.017  0.012  0 .0 2 2  0 .0 0 4  vn Fr i c t i on loss ( f t ) , i n main pipe fo r length ST 0 .6 0 3  0 .6 0 3  0 .3 5 0  0 .3 5 0  0 .2 5 8  0 .2 5 7  0.182  0.180  0.091  0 .0 8 7  O F r i c t i o n l o s 3 ( f t ) in r ight or l e f t l eg , f o r length 9 .0» 0 .6 2 5  0 .6 2 5  0 .3 6 3  0 .3 6 3  0 .2 6 8  0 .2 6 6  0.190  0.187  0 .0 9 4  0 .0 9 0  t- F r i c t i o n loss ( f t ) , in r ight or l e f t l eg , f o r length TD, or TD 2 0 .6 5 5  0 .6 5 5  O .3 8 O  O .3 8 O  0 .2 8 0  0 .2 7 8  0.198  0.195  0 .0 9 8  0 .0 9 4 } y- aj Tota l f r i c t i o n l o s s ( f t ) 1-0 vo vn OV O . . . . . vo 0 H 1 Vo O *- O vn 0 vo >- vC Veloc i ty in main pipe ( f t /sec) 1.5 6 4  0 .8 2 9  0 .5 9 6  0 .3 8 8  0.173  rv C Veloc i ty head i n main pipe (ft) W W p- O O * * - - O - O *0 "O • • • • • • • t • • i\> w V O N O 0 0 w w oa c» O O O O w w -o vi V i w ro 1- Veloc i ty in r ight or l e f t leg ( f t /sec) 0 0 0 0 O O O O W W • • • • W W w w vi o a - o V i V t Q\ sO W w O -f* JV) - J vO W rv ro Veloc i ty head i n r ight or l e f t leg ( f t ) 1 1 0 .14 5  0.139  0 .0 7 5  0 .0 7 0  0 .0 5 3  0 .0 5 2  0 .0 3 5  0 .0 3 2  0 .0 17 0 .0 15  IV v>. Wye loss (ft) 0 .0 9 3  O .O 8 9  0 .0 9 0  0 .0 8 5  0 .0 8 9  0 .0 8 7  0 .0 9 0  O .O 8 4  0 .110  0 .0 9 7  ro *- Wye loss coef f i c ient 0 .0 9 1 0 .0 8 8  0 .0 8 8  0 .0 8 8  0 .10 4  IV \j Average wye loss coe f f i c ien t *~ VO M _ M Vh JT- W W H H T e s t N o . WjO MJO P » M,W H » » H , " -T M *• W * M J p St - J t - x t - J i t - ^ i " M * t - u f » f M O r i f i c e No. t - S J K r - W t a t r - S J S r w K tr1 »> 3 t- W 3 r< W 3 tr> 3) S t - B J K , -0 -v) | O O vo vo IO VO 5 X 3 M VO VO M VO VO O vn VO - o vn vo I O O ' O O I O O I O O vn o o vn o o o o o o o o V 5 2 K o o o o o o o o o o o o o o o o o x x S o o S o S o o S o o o o o o o o o o o o O O O W W e i g h t o f w a t e r ( l b s ) f r o m M f ! n a i n p i p e ; R , r i g h t l e g ; L . l e f t l e e U O WW J^j^v VOW v n v n W W WOJ OvOvWVOWW W W W V o W W r , ^ t M > W U ^J^WWWW 1 | J^4r- H H O O NOVO D O W W O U v O ^ * - > W v O -o - ^ O - O v w W r O M ^ r - t j W ^ • ^ O ^ O ' V O V O 5 t i i i % i i , , MM MH-O-OPM f i pf - y j j M r^rfpp ?.°rr-p.° Y??'.PP. H v n cool b-P- rovn ^ O v v n ' o v o W H O M N M H covn »"W CO.O * - C < : N O H O v i W M W i O * - T i m e i n t a r v a l ( s e e s ) vo Vo r~ vo vn W  QV W W W W .p- w J T - V o v o - J C i j S O » M V . M O t " O p t - O M O O 1 1 u 1 1 n 1 ' w O ' J H * - O H ro ro vo M -o o W W OV vn A v e r a g e t i m e i n t e r v a l ( s e e s ) C o . over C .O. OCT- cnOv ovov p . Q . pvt> o>ov M o . tovn iv. 4-— ro-p- roo . tovn t o * - w r fOvn vo vo vovn w v n Co vo w v n vo w W W W W VO VO VO S~ W 0> T e m p e r a t u r e i n 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 s / c u . f t . ) O O O O O O O O O O o o o o o o p o p | | V O 1 t vn 1 I -*0 1 1 b v o v o O O a v O O , Q > v 0 w vn vO Ov vO M O ? H H O H W CO H < > » V O M ™ C K M °? K vo M vO O v M « v v n V O O t t V . O V H M H V O . v n ^ J M -O D i s c h a r g e ( c f s ) O O M W VO vo W H H v n ^ J O * - IO H -~J P" -O Ov Ov H Cl -J O O -O -O H P" -vl -p- O H *~ vO VO CO H o o k g a g e r e a d i n g i n u p s t r e a m t a n k ( f t ) O H M V O vo vo vo H W Co O * - Co -o vn H Ov H o vK o Sj w o tn to va l O O V o - o Ov °v ^ °^ vO H o o k g a g e r e a d i n g i n c e n t r a l t a n k Tft) O O O O  O p H O vo H w Cc OO O -0 O TO vO O -p- W 1—' Ca M CO H V O O M O o Ov - o Ov O H O H o o k g a g e r e a d i n g i n d o w n s t r e a n t a n k Tft) O O O O O o O P P M M M M M M fO M [0 H H l - J H H H H H H O O O O 5 O o o o H H V e r n i e r c o r r e c t i o n ( f t ) O O O O O H O M o . M 6 w O M P P P b w b c o M m "o^ j " o a . M vn M H £ vo^j -o-vj o m ovoa vn -o. vn M -0 CO Ov O vo vo H Co Ov P- Ovvn w p- o v o v n v n vn ^3 w w . p- w H M P r e s s u r e h e a d 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 a n d r i g h t l e g o r m a i n p i p e a n d l e f t l e g 0 .2 7 6  0 .5 8 6  0 .4 1 4  0 .9 0 8  0 .0 9 2  0 .9 6 2  0 .0 3 8  0 .9 8 3  0 .0 1 7  1 .0 0  0 .0 0  H w D i s c h a r g e r a t i o , D i s c h a r e e i n " b r a n c h D i s c h a r g e i n m a i n p i p e p o o p 0 0 0 0 0 b o o b b b b b b H M *~ -.j 0 - j 1̂ ^ , O W C O O O O O O O H -P- 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 3.375' p o p o 0 0 0 0 0 0 0 0 b b b b b b O O O H H H H H H M * > C o M M M M M M H vn 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 .4 9 2 |  0 .0 9 3  0 .3 4 3  0 .1 8 7  0 .7 2 8  0 .0 1 3  0 .8 0 2  0 .0 0 2  0 .8 3 2  0 .0 0 1  0 .8 5 5  0 .6 0 0  0 .3 0 1  0 .1 4 1  H Ov 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 l e g , f o r l e n g t h 9.0* i ? 1 ? i P i P P P P P P ° 0 0 0 0 £ V ° ^ 0 1 O C O O c o O ^ l H V O O v n *~ H M CO O O V O W H V n v O V . v O H Ov M M Ov H M M O W f - W Q V 0 > 0 H 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 l e g , f o r l e n g t h T D i o r T D ? 0 .5 2 2  0 .1 0 8  0 .3 6 8  0 .2 0 5  0 .7 6 8  0 .0 2 5  0 .8 4 2  0 .0 1 4  0 .8 7 4  0 .0 1 3  0 .8 9 8  0 .0 1 2  0 .6 3 0  0 .0 0 8  0 .3 1 6  0 .0 0 4  0 .1 4 8  0 .0 0 2  H CO T o t a l f r i c t i o n l o s s ( f t ) M V O . f - O v Ov O v O v Ov Ov H W V O H H H H H H V n * ~ C O O O O W -f- vo H vC V e l o c i t y i n m a i n p i p e ( f t / s e c ) O O O O 0 O O O O O . H w v i VT. vj. vn vn v . ^ J - O C O - O -0 ~0 VO vO vO M W v n ^ j vO vO W Ov jr- M 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 ) 8 .7 1  3 .3 2  7 .0 6  4 .9 9  1 0 .9 2  1 .1 0  1 1 .5 3  0 .4 6  1 1 .7 8  0 .2 1  1 1 .9 8  9 .7 7  6 .5 5  4 .2 2  M H V e l o c i t y i n r i g h t o r l e f t l e g ( f t / s e c ) ( p ( 0 ^ H ^ M O t O O M O H O O O H M Ov M O H O O O C O w " j H H -0 ov co w O C T - O O v H v n c o ^ l ^ I c o -0 Ov ^ H H O W O O v O W ^ 3 V n M M M M V e l o c i t y h e a d i n r i g h t o r l e f t l e g ( f t ) 0 .0 8 3  0 .1 1 0  0 .0 5 6  0 .0 6 7  0 .1 5 9  0 .2 7 4  0 .1 9 4  0 .3 0 7  0 .2 1 5  0 .3 0 8  0 .2 3 6  0 .3 0 2  0 .1 5 7  0 .2 0 3  0 .0 6 5  0 .0 9 3  0 .0 2 5  0 .0 3 9  M W W y e l o s s ( f t ) 0 .1 4 0  0 .1 8 5  0 .0 9 4  0 .1 1 2  0 . 2 6 8 . 0 .4 6 2  0 -3 3 5  1 0 .5 3 0  0 .3 7 1  0 .5 3 2  0 .4 1 0  O .5 2 2  0 .4 0 8  0 .5 2 7  0 .3 7 6  0 .5 3 7  0 .3 4 7  0 .5 4 2  M W y e l o s s c o e f f i c i e n t 6*i UJ N . r-1 Test No. •p- UJ . (O •, ML t—' + t- + + +- •t- uj ro ro h> ro O r i f i c e No. OO SZ . 1  00 05  H  00 S0 T W  OO OO T 1  00 08  H  O O O ST  W  • 00 06 T 1  OO OO T H  00 06 T W  00 06 T 1 00 5O T H  00 06 T W  00 06 T 1 00 05 T  H , 00 06 T W j  UJ Weight of water (lbs) from M,maln pipe; R,right leg ; L . l e f t l eg --- -p- uj uj uj uj *- .p- ui uj uj uj *_n \n uj uj uj uj uiu%w uj ro ro .p- .p- uj uj ro ro oubhmuvj ro ro-t-*-h I-1 h i- J*-*-ro ro p y o o - j - j o o r o r o o o on on 0000.-0-0 u u o o > ) - i ro h ro ro.p-*- hi-onon-o-o oo-oujuj.p-.f- oorONO-OH»o vflyi o o c a - J ro oa-o oo-o oo -ti«onoo.i-juj H v o O H w r o •F- Time in terva l (sees) 2 0 4 .3 323.1 408.0 2 7 7 .2 3 0 6 .7 521.8 324.8 3 4 2 .8 512.0 317.8 3 4 0 .0 4 2 3 .7 .3 3 7 .1 318.8 4 8 6 .5 vn Average time interva l (sees) 010* OvO"* ONON OnOn ro*- ro*- rout rov- rovn u> vn UJVn ui w UJ uj uj uj uj uj ON Temperature in F° and spec i f i c weight of water ( lbs /cu. f t . ) O O O O O O O O O O O H 1 O O H . . . . « . ' . . . . . * . . . r o r o * - uj uj -o .p- vo \j- nj- o --j. -o -f- f- y i vO -O. -0 vji -o on UJ \_n -p- vO *- -p- vO oo o no no oa -o o oo oa o no no -o in ro - J Discharge (cfs) o o o o o . . . • • - J oo. o *- 00. so u» -o oa v/i ro ro oa On 00. Hook gage reading in upstream tank Tft ) o . O no o o vo oo. vo ro u> O ro o -o. ro O u> -o o ro NO Hook gage reading in centra l tank (ft) , o O MO o o co- oa no ro uj no ro -o -o h-1 O \ - i \~*. uj y-1 I-1 0 Hook gage reading in downstream tank (ft) 0.210 0.210 0.210 0.210 0 .2 1 0 M }-• Vernier correct ion ( ft) 0.7 4 0  0 .7 3 9 0 .4 2 3 0 .4 2 6 0.317 0.321 0.217 0 .2 1 9 0.112 0.102 I-1 ro Pressure head di f ference (ft) between main pipe and r ight leg or main pipe and l e f t l eg UJ Discharge r a t i o , Discharee in branch Discharge in main pipe 0.1 7 1  0.098 0 .0 7 2 0.049 0 .0 2 2 t-» •F- F r i c t i o n loss (ft) in main pipe f o r length 3-375' 0 .0 4 2  0 .0 2 4  0.0 1 7  0 .0 1 2  0 .0 0 5 VI Fr i c t i on loss ( f t ) , in main pipe f o r length ST 0 .5 9 6 0 .5 9 9 0.3 5 2  0.3 5 4  0.267 0.267 0.184 0.1 8 2  0.091 0.0 8 6  H1 ON Fr i c t i on loss (ft) in r ight or l e f t l eg , f o r length 9-0' 0 .6 1 9  0 .6 2 2 0.3 6 5  0.3 6 7  0.2 7 7  0.2 7 7  0.1 9 1  0 .1 8 9  O .O 94 0 .0 8 9  •—' - J Fr i c t i on loss ( f t ) , i n r ight or l e f t leg , for length TDi or TD 2 0.661 0 .6 6 4 O .389 0 .3 9 1 0.2 9 4  0.2 9 4  0 .2 0 3 0.2 0 1  0.099 0.0 9 4  CO Tota l f r i c t i o n loss (ft) UJ lA On NO uj 0 ro uj vo ro -p- -p- 0 ro h-1 NO Veloc i ty in main pipe (ft/sec) 0 0 0 0 w • » . . . H* uj 0 00 m -0 no 0 ro uj O -F- NJ1 NO O ro 0 Veloc i ty head in main pipe (ft) 9.75 7 .1 7 7.1 8  6 .1 1  6 .1 3 4-93 4 .9 5 3.28 3.23 ro H 1 Veloc i ty in r ight or l e f t leg (ft/sec) O O O O O O O O M M . . • « « . . . . . t—1 H u j u j N j - u i oa -0 F- -P- ONON OO-O. 0000 O NO - J O N ro -0 0 0 0 -p- 0 h o o cono ro ro Veloc i ty head in r ight or l e f t l eg (ft) 0.140 0.127 0.067 0.065 0.0 4 8  O .O 48 0 .0 3 0 0 .0 3 2 0 .0 1 6 1  0.016 ro UJ Wye loss (ft) O .091 O .O 83 0.0 8 1  0.0 7 8  0 .0 7 9 0.0 7 9  0.076 0.0 8 1  0.0 9 4  0.0 9 4  ro •F- Wye loss coef f i c ient 0.0 8 7  0.0 8 0  0.0 7 9  0 .0 7 9 O .O 94 ro Average wye loss coef f i c ient * - W W M W * - W W . M M W fC iO W M W ' M . M W w W H * W M * PO V . J*J + 4 + -I- + + + • X Ir* M l - ' H f ; X tr* Co I - - o f O f w C-* W f 1 IO Or i f i ce No, f W X r w K t - S J ^ K . l - ' w S t - M 3 f S J S I- W X M H M M ': v - . H M H M M M H H M H H H "vl —J O O V t V l j ) >£> N O NO H ' ^ J IO V I NO v i Q vO NO V l vQ 1 O O 1 O O 1 O O I Q O v t O O O O O O O O O Q O O O O g o c o o o o o O Q O g o o o o o o o Q Q Q Q O O C O o o o o O O O O O O O O O O O O o o o VO Weight of water (lbs) froza M.snain pipe; Upright leg; L r l e f t leg W W W W W W W W v i w w w w w p - ^ - W W W W W W I O I O W W f - f - f I r w W 4 T - + T - W W W W (-•• M ww ww oow'-;ww j--4~-*~ww ->i-jco<»ww H M M n tow N / i v . H H w w 1 I 1 N O V O 1 1 O O t ( W W IO M 0> N to y i v f l v n y r W H -O-J-J O * - ^ " N O N O O O COV£> Q N O V M M • .« . . e . a u . . . . . . u .- a a a a a » . a a a . o . . 0 a a a . . . v t v . Kiro N O N O O O H V I O G N O N V O V . i v o O W O v o O O N N C O O N O W v O O O v O W C O W P O - P - M * - Time i:itt*rvnl (aecsj W i.O W W v i W W ^- w W W W W r- .p- W p- W W J> M - w w o w W p - .p- w -o, oo w M M W V l . M W •I- V O I I O l l . N l M CO W v . ^ W W - O CO M * - v O O V O N M I i a j | a • i o • . t a n • . a a a a » a v i ;o >o o co p- co cr. y o w o o t> o M o w w V i Average time interva l (sees) O N Q \ ONON ONON G N - " N ONON 0 0* ON ON QN ON 0 0 M v . W.p- W-P" fO-C- iO-P- W p - M(- tv>p- M(- a a a a a a * a a a a a a a a a a ' W W V I W v i W V i W V I W V i W V W V I W V ? W W W W W W W W V I Ov Temperature in F° and specif ic weight of water {lbs/cu \> f t •) o o o o o o o o o o o o o o o o o o o 1 I w l l V i t l ^ J *0 O v o vO O 0 & V D O < n v f ; V i W v O O N W v O tO O V i H M O M W CO M ( A v d W CO ' W O V v H ON W p 0 > O N O O N O - W O > V « V i O v O W W a - - V v v D Discharge (cfs) O O . W W W W W H M W ^ J O N O - 0 Ov -o * ~ -O. Co O w O O N O O CO ON w w o ON O - 0 v i p - p- 03- Hook gage reading in upstream tank (ft) O M W w w w w H . O CO O -P" W H ro O -vl W O v - l - ' - W ON M W CO - 0 M O O O -!> W 10 - O vo vO Hook gage reading in central tank (ft) 2.185  1.626  0.718  0 .2 8 0  0.301  0.319  0 .3 5 8  0 .0 9 2  0 .4 0 8  M O Hook gage reading in downstream tank (ft) oxz- o O T Z' O  O T Z' O  ^T Z' O  O T Z' O  O T Z 'O  O T Z 'O  O T Z' O  M H Vernier correction (ft) O O O O O H O W O W O W O W O O . ' M O O W O O l H O I W v J W O v TO V i W M 0 O M W W CO CO CO vO CO O v O v O Q v vO W M v O O O N O M O - O W W P" CO p - - 0 P " v£i v n ^ j —J ^ ) - > ] O i w M M W Pressure head difference (ft) between main pipe and right leg or main pipe and l e f t leg 0 .2 7 7  0 .7 2 3  0 .U 5  0 .5 8 5  0 .9 6 1  0 .0 3 9  0 .9 6 1  0 .0 3 9  0 .9 8 3  0.017  1.000  0 .0 0 0  w bischarge rat io , Discharge in main pipe 0 .0 7 0  0 .0 7 0  0 .0 7 0  0.070  0 .0 7 0  0 .C 7 0  0 .0 4 8  0 .0 2 2  0.010  M Fr ic t ion loss (ft) in main pipe for length 3*3751 0.017  0.017  0.017  0.017  0.017  0 .0 1 7 i 0.012  0 .0 0 5  0 .0 0 2  1—' \n Fr ic t ion loss ( f t ) , in main pipe for length ST 0 .0 9 2  0 .4 9 4  0 .1 8 8 |  0.341  0 .7 2 7 ! 0.013  0 .7 9 8  0.001  0„827| 0 .0 0 2  0 .8 5 7  0 .6 0 3  0 .3 0 1  0.142  H Fr ic t ion loss (ft) in right or l e f t leg, for length 9o0* 0 .0 9 6  0.512  0 .1 9 5  0 .3 5 4  0 .7 4 4  0.013  0 .8 2 7  0.001  0 .8 5 8  0 .0 0 2  0 .8 8 9  0 .6 2 6  0.312  0.148  I—1 - O Fr ic t ion loss ( f t ) , in right or l o f t leg, for length TDi or 0.115  0 .5 2 9  0 .2 1 2  0 .3 7 1  O .7 6 I 0 .0 3 0  0 .8 4 4  0.018  0 .8 7 5  0 .0 1 9  0 .9 0 6  0 .0 1 7  0 .6 3 8  0 .0 1 2  0 .3 1 7  0 .0 0 5  0 .1 5 0  0 .0 0 2  oa Total f r i c t i on loss (ft) W W p - O v ON ON ON ON ON M W v O M O M M M M - J W C » M vO M W -F- M H vO Velocity in main pipe (ft/sec) 0 .5 8 3  0 .5 8 6  0 .5 8 2  0 .5 8 0  0 .5 7 6  O .58O  0 .3 8 5  0.173  0 .0 7 3  O Velocity head in main pipe (ft) 3.32  8.67  5.00  7.04  1 0 .9 1  1.10  11.52  0.47  11.77  0 .2 1  11.98  9.66  6.56  4.26  to H * Velocity in right or l e f t leg (ft/sec) 0 .1 7 1  1 .1 6 8  0 .3 8 8  0 .7 7 0  1.849  0.019  2 .0 6 3  0 .0 0 3  2.152  0.001  2 .2 3 3  1.475  0 .6 6 7  0 .2 8 2  l\) ro Velocity head in right or . l e f t leg (ft) O .O 98  0.081  0 .0 5 4  0 .0 5 2  0.169  0.216  0.210  O .2 6 4  0.218  0 .2 6 2  0 .2 3 8  0 .2 5 9  0 S 1 6 0  0.179  0 .0 7 2  0 .0 8 3  0 .0 2 8  0 .0 3 5  ro Wye loss (ft) 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 + > W p-p- P - W P - W W W O O M M COCO C O M O H P - M V i - O w O v - O v O O O v Q W Q v O * - O ^ ) ONVi - I O V i v o V i W M O V O W v O C O ro Wye loss coeff ic ient Collecting pipes Wooden trough for l e f t branch pipe Wye Left hand flumi Main pipe Fig. 1 . General arrangement. 53 Branch pipes Velocity traverse stati Piezometer ring 13.25' 5-J" ID Lucite main pipe Reducer Flow Straightener 5" standard steel Reducer Flow Straightener k" standard steel pipe Controlling valve Section at AA of straightener Fig. 2. Details of main pipe from controlling valve to wye. 5<V Fig. 3. Model lay out and manometric arrangement. 90 Large spherical wye Q 90 Small spherical wye Fig. k. Details of wyes. 56 57 Plastic piping Fig. 6. Pressure tap. 5,8. Branch pipe End piece Orifice ring 3.75" L r-r-r • D" 7 6*!L Numerical designation of orifice 1* 1 2 3 5 6 7 8 x External diameter (inches) 3.720 Internal diameter (inches) 3,622 1 3.300 J 3.375 2.913 2.^90 2.000 1.3-+2 0.8-+0 0.53-* Remarks Rounded orifices no orifice Fig. 7. Orifice arrangement. 59 Fig. 8. Velocity traverse across main pipe near wye during preliminary investigations. Fig, 9, Velocity traverse across main pipe near wye after modifications in the main pipe section. 6 1 Left branch side R i g h t branch sid 1 5 " 1 0 " Velocity head 5" C< >ntre ljLne c i 1 . 1 • f main pip< ! i i i i L5 12 11 io 9 8" 1 7 "6 . 5 k 3 2 : 1 \ Fig 1 0 . Velocity traverse with one leg flow with discharge o 0 . 9 2 cfs. 0) CO N Fig. 11 Friction losses i n main End piece Piezometric ring LLJ 3.75" ID branch pipe, section A 3.75" ID branch! pipe, section Cj 9' t.) Piezometric ring - - - 4 1 -x. B . ! 63 Reducer 5.25" ID main pipe t Supply- Fig. 12, Experimental set up for measurement of friction losses in branch pipes.  LOOARITBMIC: 1 S/l By ' ' W-1NCK CYCLIS. B E S T - P R I N T K K C O . I..TU. 7 8 9 1 5 6 7 8 90.1 0.2 VALUES OF (VD-) FOR WATER AT 60°F (VELOCITY IN FT/SEC » DIAMETER IN INCHES) J).4 0.6 0.6 I 2 4 6 8 10 20 40 60 80100 200 400 600 8001000 2000 8000 4000 6000 110,000 aoloool I Branch Pipes Q Main Pipe Friction Factors vs. Reynold A/vm&erj For Main & Brarix. .000,01 8 .000,005 ON ON 67 1.1 l . o 0.9 0.8 Wye loss coefficien K . . 0.7 0.6 0.5 OA (ft Open leg - Symraetr i c a l flow •—-° f Closed leg 0.2 OA 0.6 0.8 1.0 Discharge (cfs) 1.2 1A 1.5 Fig. 16. 90 Large spherical wye,symmetrical & one leg flow. 1.0 Discharge ratio Fig. 17. 90* Large spherical wye, unsymmetrical flow 0.9 0.8 0.7 0.6 0.5 Wye loss coefficient K OA 0.3 0.2 0.1 07T Open jleg Closed. 1 leg Symmetrical -crA- flow 69 0.6 jfng 1(-Q Discharge (cfs) 1.2 TA 1.5 Fig. l8 . 90* Small spherical wye, symmetrical and one leg flow 0.3 0.2 0.1 0 0.2 OA 0.6 0."8 l.C Discharge ratio Fig . 19. 90 Small spherical wye, unsymraetrical flow. 0 71 0.7 0.2 OA 0.6 678 i.o Discharge (cfs) 1.2 TA 1.5 Fig. 20. 90°Tapered wye, symmetrical and one leg flow. 72 0.7 0.6 73 0.6 0.5 0.4 Vjye loss coefficient K 0.3 0.2 0.1 0.2 Closed legN Open leg Syramet r ica l flow 0.4 0.6 0.8 1.0 Discharge (cfs) 1.2 1.4 1.5 Fig . 22. 60 Tapered wye (A), symmetrical and one leg flow. 74 75 0.7 0.6 0.5 Closed c O p l e g 0.4 Wye loss coefficien K 0.5 0.2 0.1 ^Symmetr: caT~flow 0.2 "074 0.6 0.8 ~ 1.0 1.2 1A 1.5 Discharge (cfs) Fig. 24. 60° Tapered <wye(B),syrrunetrical and one leg flow. t Y [Jnsymmetric al flow 0 . 0.2 0.4 0.6 0.8 1.0 Discharge ratio Fig. 25. 60* Tapered wye <B.,unsymraetrical flow. 77 0.6 0.5 OA Wye loss coefficient K 0.3 0.2 0.1 0 0.2 oA~ 90 Large spherical wy<i 90 Small spherical wye 60° Tapere 3 wye (A) 60° Tapere 2 wye (B) "oTo" 578 T7o~ Discharge (cfs) 1.2 1A1.5 Fig. 26. Wye loss coefficients for a l l wyes, symmetrical flow. 1.0 0.9 0.8 0.7 ffye lose coefficient K 0.6 .0.5 O.k 0.3 0.2 0.1 0.2 90 Taper)sd wye 60* Tapered wye (A) 9*Tapered wye (B) O.h 0.6 0.8 Discharge (cfs) 1.0 78 1.2 Fig. 27. Wye loss coefficients for a l l wyes,one leg flow (open branch). 79 0.8 Wye loss coefficient E 0.2 0.1 OA 0.6 0.8 1.0 Discharge (cfs) Fig. 28, Wye loss coefficients for a l l wyes,one leg flow(cloeed branch). 1.0 8o Discharge 0.6 ' . 0.8 r a t i o F i g . 29. Wye l o s s c o e f f i c i e n t s f o r a l l wyes, unsymmetrical f l o w . Plate 1. Manometric board with gage tanks 82 Plate 2. Manometric board o3 Plate 3. Lay out of model looking downstream  85 Plate 5. Control valve  0 • Plate 7 . 90 tapered and 90 small spherical wye. 88 89 Plate 9» Orifices and end piece

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