‘c. .3 cw ‘u’ (a K 'd ' ha 4'? A C. L ,5 ”.2. \1 2n . ‘ K ”V C G ,A 5 «u -v ‘1'“ at: V. at if. . «a M V‘ a . 3L“ S “Mar 0? WLU 3 “It. a g “V (.0? «an. W‘M till ‘ ‘v 2 ”N. g? a "-w ' m 15:35.4 (f; kc :fi‘; Tc; '- I! ”\z a. “h- 1 .r0. 9. u . A f . - .P 99m 9.. .6: R a I“. v . , In In‘ “0‘“! 0.... “u ‘MSI. ‘5. :n o O 3'“ ~ V‘ (’2‘ . fl! 3L?!- ' iii . - I U {’1‘ L E p "t J "g a. “6 3;“ Ski ii 95 ' . ‘ “Q‘ ’ .‘. .: K" 3:2 51 a} ' It's; ‘ u .3 n ‘ \f ‘ 4” c .0. {an m... o 5 .23.... f‘x. \u/P.‘ “at-.5! ‘4 .. .TV' I I)“. H {0. I {LES " A 0 R K. I b i .a '3 i it 9 I; .o . to. 0- M." 1 what) «*1. an s. \. 1a»... “m I’l‘. \ \Wb. v.“ 53.1. 4 . o awn r‘u Him, a... V f. u...- u“.’_ «hm A ”41.0.! trio .134 I . o N [I Quirk Vi " ‘- «Az. WI» 1. a u H_3,3,i:;.,_E_,__:,,_:_E_;__,_, This is to certify that the thesis entitled “the Determination of the Friction factor J'or New 6-Inch Alumina Tubing and Road Loss in fibers and Sprinklerunl’ipe couplers' presented by Alberto Dakar has been accepted towards fulfillment of the requirements for J'_3°__ degree in Mural 336130011118 41mm W Major professor Date 3 €le ’5 I I 15-0 ‘1‘. THE DETERMINATION OF THE FRICTION FACTOR.FOR NEW 6-INCH ALUMINUM TUBING AND HEAD L088 IN ELBOWS AND SPRINKLERPPIPE COUPLERB By ALBERTO 251cm A THESIS Submitted to the School of Graduate Studies of Michigan State College of Agriculture and Applied Science in partial fulfillment of the requirements for the degree of EASTER OF SCIENCE Department of Agricultural Engineering 1950 “ft-11:5“: _ACKNOWLEDGMENTS The anther wishes to express his sincere appreciation of the kindly interest, valuable suggestions, and helpful advice received from Professor E. H. Kidder of the Agricul- tural Engineering Department during the course of this investigation. ‘ He also wishes to express his appreciation to the following: ’ Instructor P. E. Schleusener of the Agricultural Engineering Department for many suggestions. Instructor B. F. Cargill of the Agricultural Engineer- ing Department for the pictures taken. Perfection Sprinkler Company of Ann Arbor, Mich., for the use of their pipes and couplers in making this study. Gorman Rupp Company, Mansfield, Ohio, for the use of their engine and pump in this experiment. 244585 I. II. III. IV. V. VI. VII. TABLE OF CONTENTS INTRODUCTION 00.....0000000000000000000000000.0000. REVIEW OF LITERATURE co...000000..0.0.0..eo0.000000 1. 8. 3. 4. 5. Letter symbOIB 00000.00..0.....000..00.00.0..00 The Bernoulli Equation ........................ Head Lost by Pipe Friction .................... The Darcy-we13ba°h Formula eeeeeeeeeeeeeoeeeeee minor Losses 00.000.000.00...0..0.000000.000... “ETHDDS OF PROCEDURE 00.00000.00.000000000000000... 1. 2. 3. 4. ‘pparatus ..0.....000.0.00....OO....00..0..000. u‘terial Tested 000.0000..........000..00..0000 Experimental Procedure ........................ Sequence of Operation ......................... PRESENT‘TION or D‘TA 0.00.00000000.00.000.00.000... 1. 2. 3. 4. 5. 6. Evaluation of Exponents and Coefficients in the General Pipe Flow Equation ............. Pipe Without coupler 00.0.0.0...0000000000.0000 coupler Losses .00000000..0..0......0.0.000..0. Loss Coefficient for Couplers ................. Elba. 1103303 oeeoeooooeeeeoeoeoeeeoeeeeoeecoeee Loss Coefficient for Elbows ................... GONCLUBIONS 0000000000000.0.00000000000000000.00000 SUMMARY 0.00.00.00.00000000000000000000000.00000000 LITERATURE CITED 0000000....0000000000000...00.0000 39 46 47 49 49 52 55 58 I. II. III. IV. VI. VII. TABLE OF CONTENTS INTRODUCTION 00000000000000.00000000000000000.0000. REVIEW OF LITERATURE .............................. 10 Letter symbOIB 00.00.00.000000.0000000000.00... 2. The Bernoulli Equation ........................ 3. Head Lost by Pipe Friction .................... 4. The Darcy-Weisbach Formula .................... 50 Minor Losses 0000.00.00.00000000.00....00000000 “ETHDDS 0F PROCEDURE 00000.00000000000000000000.000 lo Apparatus eeeeeeoeoeoeooeooeeeoooooooeoeoeeeeee 2. Material Tested ............................... 3. Experimental Procedure ........................ 4. Sequence of Operation ......................... PRESENTATION OF DAT‘ 00.0.000000000000000000.000000 1. Evaluation of Exponents and Coefficients in the General Pipe Flow Equation ............. 20 Pipe Without coupler .00.....0..0.00000000.00.. 30 coupler Losses .00....00000...00.00000000000000 4. Loss Coefficient for Couplers ................. 50 Elbow LOBBBB 00.00.00.000.00.00.00.000000000000 6. Loss Coefficient for Elbows ................... CONCLUSIONS 000000000000.00.0000000000000000.0.0... SUMMARY 0.000000000.000..0000000.000000...0000000.0 LITERATURE CITED 000000...00000000000000.00.00000.0 '1. 2. 5. 4. 8. 9. 10. 11. 12. 15. 14. 15. 16. LIST OF FIGURES AND TABLES FIGURES: Friction loss in pipe ............................... General view of experimental installations .......... Discharge pipe into hydraulic channel ............... Use of hook the Cip01lettiwe1r 00000000000000.000000000000000 Water flowing over the Cipolletti weir .............. Close up of piezometer tube with stop cock and manometer tube attachment fittings ............... Carbon tetrachloride differential manometer and piezometer connections ........................... 90-degree elbow (piezometers 7 and 8) ............... lBO-degree elbow (piepometers 3 and 4) .............. Coupler set with pipes forming a 6-degree horizontal deflection 0000000000000000000000000000 Sketch of layout of experiment ...................... Friction loss vs. flow rate in 17.53' of tubing, and head loss vs. flow rate in 20.16' of tubing with one coupler correctly aligned with second section or tubing 00000000000000000000000000000000 Head loss vs. flow rate (20.16' length of tubing and one connecting coupler in position 1) ........ Head loss vs. flow rate (20.16' length of tubing and one connecting coupler in position 2) ........ Head loss vs. flow rate (20.16' length of tubing and one connecting coupler in position 5) ........ Head loss vs. flow rate (go-degree and 180- degree elbows) ................................... Page 4 11 12 15 14 15 17 18 18 20 21 4O 41 42 43 50 LIST OF FIGURES AND TABLES (Continued) HABLES: Page 1. General experimental data (Head loss in half inches as read on a 0014 differential manometer) ........ 23 2. General experimental data (Head loss given in feet or water and in p.801.) 0000000000.000000000000000 25 3. Experimental data on couplers in position 1 (Head loss in half inches as read on a 6014 differential manometer) 00000000000000000000000... 31 4. Experimental data on couplers in position 1 (Head loss given in feet of water and in p.s.i.) .- 32 5. Experimental data on couplers in position 2 (Head loss in half inches as read on a 0014 differential manometer) 00000000000000000000000... 34 6. Experimental data on couplers in position 2 (Head loss given in feet of water and in p.s.i.) . 35 7. Experimental data on couplers in position 3 (Head loss in half inches as read on a C01 differential manometer) ..................?....... 36 8. Experimental data on couplers in position 3 (Head loss given in feet of water and in p.s.i.) . 37 9. Loss of head per loo-foot length of six-inch a1uminum.tubing with and without couplers ........ 45 10. Comparison of equations ............................. 46 11. Loss of head and loss coefficient for couplers ...... 48 12. Loss of head and loss coefficient for elbows ........ 51 INTRODUCTION Although sprinkler-irrigation has been practiced in parts of the United States for about fifty years, it was not until about 1930 that light weight pipe with quick- coupling for portable sprinkler systems came into use (1, p. 5). Since 1942, when extruded aluminum tubing first be- came available, aluminum has been the dominant material used in manufacturing sprinkler-irrigation tubing and fit- tings (7, p. 5). That is the reason why the hydraulic char- acteristics of aluminum tubing, couplers, and bends is es- sential for the economic design of a portable-sprinkler sys- tem for the farm. In these studies the friction factor was determined for 6—inch diameter of new aluminum tubing and the head loss coefficient determined for 6-inch diameter of coupler when the longitudinal pipe alignment was straight in all planes. Since the head loss coefficient for couplers varies with varying degrees of poor alignment of connecting sec- tions of tubing through the coupler, three different posi- tions of connections were tested as follows: position 1 - coupler out of alignment in the vertical plane using the maximum amount of vertical displacement within the coupler; position 2 - tubing vertically displaced in the coupler as in position 1 and in addition a three (3) degree deflection. from true alignment through the coupler in the horizontal plane; position;3 -identical to position 2, except the an? gle of deflection.was increased to six (6) degrees, the maximum allowedLby the test coupling. This experiment includes also the determination of the head loss coefficient for 90 and 180 degree elbows. REVIEW OF LITERATURE Letter gzmbols To simplify the discussion and presentation of data, the following symbols will be used. They agree as closely as possible with those presented in hydraulic literature and are given in accordance with Le Conte (6, p. 11). Area of pipe, square feet General constant Diameter of pipe, feet Coefficient of friction (Darcy-leisbach) Acceleration of gravity (32.2 ft/secz) Head loss in couplers, feet Head loss in elbows, feet Head loss due to friction, feet Total head loss, feet Coefficient of proportionality Coefficient of prOportionality for aluminum pipe Loss coefficient for couplers Loss coefficient for elbows Loss coefficient in fittings Length of pipe, feet Exponential values Reynolds number Pressure, lbs/ing Q Rate of flow, cfs V Velocity, ft/sec w Unit weight, lbs/’ft3 2 Difference in elevation, feet Q Density, lb—secZ/ft4 ft Viscosity, lb-sec/ft2 The Bernoulli eguatign Head loss in straight pipe flow is illustrated graph- ically in Fig. 1. Two lines designated respectively the hy- draulic gradient and the energy gradient are shown (5, p.196). l Dang + Iig.1 Frictional loss in pipe. The Bernoulli equation between any two sections of a straight pipe (8, p. 181) as those shown in Fig. 1, is 2 2 h 21 z =E2 h Z-eeeeeeeeeee (1) 38+' + l 28+58+ f+2 Durand discusses total energy as being in the primary and secondary forms (7, p. 4). The three primary forms, shown diagrammatically in Fig. 1, are: 1. Pressure energy or pressure head (p/w) 2. Kinetic energy or velocity head (V2/2g) 3. Potential energy or gravity head (2) The two secondary forms of energy are: l. The internal energy or the kinetic energy of eddies and turbulence 2. Head energy The three primary forms may be converted into each other and also into either of the two secondary forms; how- ever, the secondary forms are not convertible into the prin- cipal forms of energy. The internal energy is inevitably converted into heat energy, which is dissipated and, there- fore, unavailable from a mechanical standpoint in pipe flow. This loss of energy is incidental with the transfer of fluid in a pipe (7, Po 5)- The head loss hf (See Fig. l) which occurs when an in- compressible fluid flows between two sections of a straight pipe of uniform diameter is due to the viscous shear between fluid particles (8, p. 180). Head lost by pipg friction Certain general laws based upon observation and experi- ment appear to govern fluid friction in pipes and are ex- pressed in all the generally accepted pipe formulae. These laws briefly stated are (5, p. 181): l. _Frictiona1 loss in turbulent flow generally in- creases with the roughness of the pipe 2. Frictional loss is directly proportional to the area of the wetted surface, or toZTdL 3. Frictional loss varies inversely as some power of the pipe diameter, or as l/dx 4. Frictional loss varies as some power of the velocity, or as Vm 5. Frictional loss varies as some power of the ratio of viscosity to density of the fluid, or as §a%5)P Combining these factors, a rational equation for head lost by pipe friction for any fluid can be written in the form: hf: Ktxrdel/dxxvm y/OV ..... (2) H' in the above formula is a combined roughness coef- ficient and proportionality factor. If n+1 is substituted for x, equation 2 can be written in the form: hf-[er/(u/fl)fl ébvm (3) The effect of viscosity and density of water on loss of head at usual flow velocities is so small that it can be easily included in a general coefficient (5, p. 181). K being substituted for the quantity in brackets in equation 3, the base formula for head loss in pipe flow can be written as: hf==K LIV“ .................. (4) dn Experiments show that the coefficient and exponents vary in value. For laminar flow, m is equal 1 and for turbup lent flow its value ranges from 1.70 for smooth pipe to 2.0 or more for a rough pipe. Likewise n has a value of 2 for laminar flow and varies from 1.0 to 1.3 for turbulent flow (8, p. 181). Unwin (9, p. 217) gives the following mean values for K, n, and m: Surface 1: g m Wrought iron .000351 1.210 1.75 Asphalted pipes .000395 1.12? 1.85 Riveted wrought iron .000405 1.390 1.87 New cast iron .000534 1.168 1.95 Cleaned cast iron .000378 1.168 2.00 Incrusted cast iron .000685 1.160 2.00 Many empirical formulae have been pr0posed to represent the friction factor for smooth tubes over all or part of the range of Reynolds' Numbers. Practically all have been of the form f==A.+B/Nfi , the constant A, B, and n being adjuted to fit various sets of experimental results (3, p. 94). Blassius (3, p. 94) published five such equations to cover the range of Reynolds Number from 2500 to 107. Freeman arrived at the equation 51 r a 0.5597/NR'2 as a result of his experiments on hydraulic smooth pipes. This is in agreement with the work of Blassius (3, p. 87) who pr0posed the equation r\= 0.3164/NR-25 from an analyses of experimental data reaching to about NR- 100,000. Weston (11, p. 1) in reviewing experimental results in pipes, considered lead and brass tubing as being very smooth pipes. He proposed a formula based on his experiment for these kind of tubing. For tubing having interior sides simi- lar to new cast iron pipes, he came to the conclusion that Darcy's formula was very well adapted. The investigation carried on by Gibson (4, p. 207) indicates that if roughness of the surface of a galvanized iron pipe is taken as a unity, that of other surfaces is ap- proximately as follows: New uncoated cast iron..................... 1.40 New asphalted cast iron.................... 3.55 New wood stave pipes....................... 5.65 Concrete pipe carefully hand-finished...... 1.50 COncrete pipe with ordinary finish......... 6.00 Rough concrete pipes....................... 18.50 Results of experiments on friction losses in pipes of various materials and diameters are commonly expressed by plotting the friction factor versus Reynolds Number. In the region of turbulent flow the results of this plot for hydrau- lically smooth pipe indicate that the pipe roughness when submerged in the boundary laminar film.has no effect on the friction factor. However, as the thickness of the boundary laminar film decreases When the Reynolds Number increases, pipe, which may be hydraulically smooth for low values of the Reynolds Number may become rough as the Reynolds Number increases (10, p. 160). The Darcy-Weisbach formula A determination of K, m, and n is necessary for prac- tical application of equation 4 to flow problems. Chezy stated that the head loss in the flow of water in conduits varied approximately as the square of the velocity. Darcy, Weisbach, and others, accepting Chezy's value of 2 for m, further modified equation 4 by pr0posing a value of 1 for n, and divided and multiplied by 2g (5, p. 182), so that - 2 hr -.(K" 2g) §V§§ By substituting a so-called "friction factor" f for K" 2g, the well-known pipe formula, called the Darcy- Weisbach formula, was obtained (5, p. 182): reusing. d 2g (5) This formula is of convenient form since it expresses - 10 - _ the loss of head in terms of the velocity head in the pipe. Moreover, it is dimensionally correct since f is a numerical factor, L/d is a ratio of lengths, and hi and Vz/Zg are both expressed in units of length (5, p. 182). Minor losses Whenever the velocity of a flowing stream is altered either in direction or in magnitude, such alteration sets up additional eddy currents and thus creates a loss of energy in excess of the usual pipe friction. The magnitude of this loss is pr0portiona1 to the abruptness of the velocity change. It is customary to refer to such losses as minor losses because in a pipe line of considerable length the pipe friction itself may be so large that the value of these other losses may be relatively insignificant (2, p. 214). It has been found that minor losses vary roughly as the square of the velocity, and they are commonly expressed by applying variable coefficients to the velocity head (5, p. 203). This led to the pr0posal of the basic equation: 2 hL=‘KL‘%E in which EL is the loss coefficient. Its value for a particu- lar fitting can be determined only by experiment. 2 11.- METHODS OF PROCEDURE apparatus A gasoline engine driven centrifugal pump unit was 0p- erated to produce the required rates of flow. The water was drawn from a reservoir on the basement floor level and passed through the pump into the irrigation pipe line, then up to the first floor level to a hydraulic flume where the rate of flow was measured by a Cipolletti weir. The flow on passing through the Cipolletti weir returned to the basement reservoir (Fig. 2, 3, 4, and 5). u. .f' -a-.-: g - § § fifijflyg Fig. 2 General view of experimental installations. - 13 - Fig. 3 Discharge pipe into hydraulic channel. - 13 - Fig. 4 Use of hook gage to determine the discharge over the Cipolletti weir. --14- Fig. 5 water flowing over the Cipolletti weir. The several rates of discharge were obtained by regu- lating both the throttle of the engine and the gate valve that was placed between the pump and the first section of aluminum tubing. The rate of discharge for the weir is ex— pressed by the equation Q==3.1025 Hl‘43 . The height was determined by the use of a hook gage at a point five feet upstream in the channel from the weir. The temperature of the water ranged between 60 and 65 degrees Fahrenheit. - 15 - Orifice Openings 3/16 inches in diameter were made near the ends of each of the four 20-foot sections of 6—inch diameter aluminum tubing. A piezometer connection was made at each of these orifices (Fig. 6). Fig. 6 Close-up of piezometer tube with st0p cock and manometer tube attachment fittings. Friction loss measurements in the tubing were replicated in triplicate for each rate of discharge. The head loss meas- urements through the couplers were duplicated for each rate of discharge. Single readings were made of the head loss _ 15 - through one quarter turn elbow ( 90 degrees ) and two quarter turn elbows that were paired to give a 180 degree change of direction of flow (Figs 8 and 9). St0p cocks were made a part of each piezometer so that the manometer connecting tubes could be coupled and uncoupled to a pair of piezometers at will (Fig. 6). A differential manometer filled with carbon tetra— chloride was used to determine pressure differences between two piezometers (Fig. 7). The specific gravity of carbon tetrachloride at 60 degrees Fahrenheit is 1.60. The dif- ference in elevation of the two manometer columnes in half inches was multiplied by the constant 0.025 to give the equivalent reading in feet of water. To obtain the pressure in pounds per square inch, the manometer reading in half inches was multiplied by the factor 0.010825. .Fig. 7 Carbon tetrachloride differential manometer and piezometer connections. .Material tested The materials tested were: new 20-foot length of ALCOA 63S-T6 extruded aluminum tubing, having a 6-inch outside diameter, 0.063 inch wall thickness, 5.874 inch inside diameter, and 0.1882 square foot cross sectional area; com- mon couplers as shown in Fig. 7; 90 degree elbow; and 180 degree elbow (Figs. 8 and 9). - 13 - Fig. 8 900 elbow (piezometers 7 and 8) ..19 - Egperimental procedure The purpose of the experiment was to determine the friction loss in pipe, the head loss in couplers, and the head loss in 90 and 180 degree elbows. The experiment was divided into two parts. The first part was the determination of the friction losses in the tubing and the head losses in couplers when the longitudinal pipe alignment was straight in all planes. The second part was the determination of the friction losses in couplers due to varying degrees of poor alignment of connecting sections of tubing through the coupling as fol- lows: position 1 - coupler out of alignment in the vertical plane using the maximum amount of vertical displacement with- in the coupler; position 2 - tubing vertically displaced as in the coupler of position 1 and in addition a 3-degree de- flection from true alignment through the coupler in the horizontal plane; position 3 - identical to position 2 ex- cept the angle of deflection was increased to 6 degrees, the maximum allowed by the test coupling (Fig. 10). Fig. 10 Coupler set with pipes forming a 6-dsgree horizontal deflection. For each test run, 11 manometer readings were made ac- cording to the following sequence (Fig. 11). 1st: 2nd: 3rd: 4th: 5th: 6th: Pies. 1-7 (Check) ' 1-2 (Head loss in 2.63' of tubing with coupler) u 1-3 ( s a 2-3 ( n n 3-4 ( w n 4.5 ( w I! 20.16' n ' " " ) 17.53' ' ' only) 180-degree elbow) 17.53' of tubing only) (a) -.' (7) -— (6) i. (5) -— (4) .1 “"7vEngine 4 P K~—’)> Fig. 11 (1) (3) __ (3) Pump ~4~vmv0ate valve Scale: 1 inch 5.5 feet . : Couplers - : Piezometers Note: Figures in parentmsis are piezometers numbers. Sketch of layout of experiment - 23 - 7th: Pies. 4-6 (Head loss in 20.16' of tubing with coupler) 8th: . 5-6 ( I - v 2.63‘ ' . n u ) 9th: " 5-7 ( ' n a 20.15: I w u u ) 10th: ' 6-7 ( " " " 17.53' “ " u n ) 11th: ' 7-8 ( ' " " 90-degree elbow) These data are shown in Tables 1 and 2. For the three different positions of tubing in the second part of the study, two manometer readings were made for each test run: between piezometers 1-2 and 5—6, to give the head loss in 2.63 feet of tubing and one coupler; and between piezometers 1-3 and 5-7 to give the head loss in 20.16 feet of tubing and one coupler (Tables 3, 4, 5, 6, 7, and 8). Sequence of Operation The pumping unit was started and as soon as the engine had warned up sufficiently to give a reasonably steady run- ning speed, and the rate of discharge through the Cipolletti weir had become reasonably constant the test data was col- lected in the following order: (1) measurement of rate of flow through the pipe system by means of the Cipolletti weir at the end of the hydraulic flume; (2) tabulation of the 11 manometer readings as indicated under Experimental Procedure; (3) redetermination of the rate of flow through the pipe system. .Table 1 General Experimental Data (Head loss in half inches as read on a CCl4 differential manometer. P: T-aT Height Disch 5:7 667 4: -4 4-5 *Piezometers: (1‘7 1-2 TI- (*1 Run: ONE (feet)(cfs) .145 .156 .175 .199 .221 .257 .285 .507 .186 .196 HNIOfl‘LD .448 .491 .519 .572 .652 0262 .275 .284 .504 .526 (OHV‘OCD Nt’DIOdifi' swarms) 0 0 0 0 0 020202020 (IJONDL‘O) 0 0 0 0 NNl‘Qt’Dd‘ #4050502 0 e e e OOOOH bflmwb 0 0 NNDK‘DNDV‘ (130202021‘ r4020202t0 dleGJNI-l (OdilOL‘O (Unfit-ll!) 0 0 020202010 fiOifl‘to NtOtOtOVF IDE‘OHIQ 0 0 0 OOHr-lr-l bmmma 0 0 0 0 0 omwwn HHHHN 8 42 6 40 55 11 12 15 14 15 .871 .948 .456 1.016 .469 1.058 .479 1.091 .412 .454 FDF‘OV‘O V“ 02t0H HNNDV'D 0202020202 24 - pamsfinomxm mo Macao “*v ana.a new. m.oe m.em m.me m.m o.ne n.mm = n.nm e.me m.m = ea we aaa.a mes. H.mm m.ma c.8e s.m m.oe m.am = H.mm m.oe e.m = on we mee.a mam. c.8m e.am m.an m.m a.mn a.on : H.Hm n.0m o.m = om He ema.a ems. m.mn m.on m.mn H.m m.mm 2.0m = a.om a.mm m.a = on oe moo.a one. m.en H.0m m.mm e.e «.mm 6.0m = 5.09 «.mm m.a = ma an Hmm.a mme. n.mn n.mm n.8m a.a m.am m.mm = 4.0m 0.0m e.a = an an mmm.a one. m.mn m.am m.en e.a p.08 e.mm = n.mm m.en e.a = ea an mmm.a was. o.mm n.8m N.en e.a H.nn n.©m = m.mm m.em m.a z an on mam.a boa. H.Hm n.mm e.mm a.e m.mm m.mm : o.em n.mn a.e : mm mm mme.a mam. n.0m m.nm n.0m m.o a.om a.nm = m.em o.an 8.8 = ma en mee.a can. o.mm m.mm m.mm e.m m.mm e.am = m.nm ©.mm m.m = mm mm aoe.a mam. 0.8m m.am 2.5m m.m H.8m m.om eeA m.mm m.am 2.2 g mm mm mmn.a amm. m.em m.om H.em m.e H.mm e.ma m.ne m.aa m.em m.e a on am mmm.a can. o.em a.om o.em m.e m.em H.0H n.ne e.ma o.em a.e : ma on eam.a cam. m.nm m.ma H.mm o.e m.mm n.mH m.ae «.ma n.mm e.e = am am oom.a «no. H.mm a.oa m.om H.e H.Hm a.aa n.mn n.6H 0.0m m.e = am am mmm.a mam. n.0H e.oa H.ma a.» m.ma a.ma m.mn m.ea m.ma 0.9 = am am oeH.H ewe. m.aa e.na 6.6H H.m a.oa a.na a.mn 9.6a m.oa o.n sex an em semen esxaom am-a ‘1e-e aim w-m -mwe m-e sum (mum n-H ”EH0? ”mampoEONWW% nemesaoaouv a eases muHxsqu, (asphmm. “emu: -25- 0000. 00000. 0000. 0H000. 0000. 00 0000. 00000. 0000. 00000. 0000. 00 0000. 00000. 0000. 00000. 0000. 00 00H0. H0000. 0000. 00000. 0000. 00 000H. 00H00. 0000. 00000. 0000. H0 000a. 000H0. 0000. 000H0. 0000. 00 000a. 000H0. 0000. 000H0. 0000. 0H 00HH. 000H0. 0000. 000H0. 0000. 0H 00HH. 000H0. 0000. 0HOH0. 0000. 0H 000H. 0HOH0. 0000. 000H0. 0000. 0H 0000. 000H0. 0000. 000H0. 0000. 0H 0000. 00000. 0000. 00HHO. 0000. 0H 0000. 00000. 00H0. 000H0. 0000. 0H 0000. 00000. 00H0. 00000. 00H0. NH 0000. 00000. 00H0. H0000. 00H0. HH 0000. 00000. 00H0. 00000. OOHO. 0000. 00000. 0000. 00000. 0000. 0000. 00000. 0000. 00000. 0000. 0000. 00000. 0000. 00000. 0000. 0000. 0H000. 0000. 00000. 0000. 0000. 0H000. 0000. 0H000. 0000. 0000. 00H00. 0000. 0H000. 0000. 0000. 0H000. 0000. 00H00. 0000. 00H0. 00H00. 0000. I I 00H0. 00H00. 0000. 00H00. 0000. riNlOVl'H-D (000052 poomv n0.m.a comma. fita.m.a peony Hanna. omen. meema. omom. momma. oeemfl. ooom. meema. oeom. ooeHH. ooeHH. omem. ooooa. ommm. oeaaa. omooa. ooom. meeoo. oomm. eaeoo. Homoo. mmam. ooemo. omow. Homoo. eeoeo. ooeH. Homeo. ooeH. Homeo. Haeoo. oomH. mmeoo. oooH. oeaoo. oeHoo. omefl. Hemeo. mafia. oeoeo. nmooo. mena. oeoeo. omHH. Heoeo. eoomo. mmmfi. omeeo. omoa. ooneo. eomoo. oooo. oooeo. mmoo. moeoo. onHoo. mmoo. omaoo. omeo. moono. mmomo. oeoo. Hammo. omoo. omemo. mommo. oooo. Hoomo. omoo. ooemo. mommo. oooo. meoao. ooeo. Hoomo. Hoomo. ommo. moeao. ooeo. nemmo. ooamo. oooo. oeoao. ooeo. oemmo. oeoao. ooeo. onHo. oono. ooamo. nmoao. memo. nmofio. oeoo. omomo. oamao. oooo. eoeHo. mmoo. onHo. eoeao. omno. ooHHo. memo. eoeao. oomHo. oooo. eeooo. ommo. ooaao. eeooo. mmmo. eeooo. ommo. mooao. eoeoo. oeao. oeooo. ooao. eoeoo. oomoo. oomo. noeoo. ooao. Heooo. ‘h0.m.a nooap ha.m.a omega wa.m.m ae-o .Noam o-e .Nmam mum .Noamv “mum .Nofim mua .uofima .oz Noowamoo oz. oaHQIMortnm.eH. .A.H.m.a GH 0cm aouma 00 #000 CH co>H0 I! MOHmdoo my“: omwmlmo .mmnm £50 mmOH 00000 0900 HmpsoEHanxm Hwacnow 0 mapma f 26.- 00000. 0000. 00000. 0000. 00000. 0000. H0000. 0000. H0000. 0000. 00 0H000. 0000. 00000. 0000. 00000. 0000. 00000. OOH0. 00000. 00H0. 00 00000. 0000. 00000. 0000. 00000. 0000. 00000. 0000. 00000. 0000. H0 H0000. 0000. 00H00. 0000. 00000. 0000. 00000. 0000. 00000. O00H. 00 00000. 0000. 00000. 0000. 00000. 0000. H0000. 000H. 00000. O00H. 00 H0000. 00H0. 00000. 0000. 000H0. 0000. 00000. 000H. 0000C. 000H. 00 00000. 0000. 00000. OOH0. 00000. 00H0. OHO0O. O00H. OHO0O. 000H. 00 00000. 0000. 00000. 0000. 00000. 0000. OHO0O. O00H. 00000. OO0H. 00 00000. 0000. 00000. 0000. 00000. 0000. 00000. 000H. 00000. 000H. 00 0HH00. 0000. 00000. 0000. 00H00. 0000. 0H00O. 000H. 00H0O. O00H. 00 H0000. 0000. 00H00. 0000. 00000. 0000. 00000. O00H. 00000. 000H. 00 00000. 0000. HOH00. 00H0. H0000. 0000. 00000. OO0H. 00000. 000H. 00 000H0. 0000. 00000. 0000. HO0H0. 0000. H0000. 00HH. 00H0O. OONH. H0 000HOH 0000. 00000. 0000. 000H0. 0000. 00H0O. OO0H. 00000. 00HH. 00 00000. 0000. 0O00H. 0000. HO00H. 0000. 00000. O0HH. 00000. OOHH. 00 0000H. 0000” OHO0HH 0000. 0000H. 0000. 00000. 00OH. 00000. 000H. 00 0000H. OOH0. 0000H. 0000“ H000H. 0000. 00000. 0000. H0000. 0000. 00 0O00H 0000 0000H 0000 0HO0H. 0000. 00000. 0000. 00000. 0000. 00 A.H.m.m pmowv H.H.m.m‘ poomp fi.H.m.m\ peony R.H.m.milpmouv R.H.m.m nooflv .o oNOiHmv b.“ ONOHP N-H Guam, 2 \hmoH Soc 020 o H0Hmwl000.0a noHQSOO Spar ogHm mo _mmnm dam moosnfiunoov m .Hnga ZV—fiB - 000.H 000.H 0H0.H 000. H50. 000. 005. 005. H05. 600. H00. 050. 0H0. H00. 000. 00¢. 00¢. Haw. 000. 000. mon. wmm. 00m. mmm. 00H. 05¢. 00¢. 00%. 00¢. 0H0. 000. 000. 000. 003. [(0 000. 0N0. 000. 000. 05m. 000. 000. 500. H00. 000. 000. 00a. 00H. 05H. 00H. 00H. 005a. 550a. $00H. 50¢H. H50H. 0H00. 0050. 0050. 0H50. 5H00. 0H00. 0000. 0000. 0000. H000. 0000. mwwo. WOH0. 00H0. 0HHO. c000. #000. 0000. 0000. 0000. 0000. 0500. 0550. 0000. 0500. 050a. 055a. 050a. 000a. 00¢H. 000a. 000A. 0000. 0550. 0000. 0000. 0500. 0000. 0500. 0500. 0000. 00H0. 0NHO. 00H0. 0500. 5000. H000. 0050. 0000. 00am. HO0H. 005a. 000a. 000a. HO0H. 000a. 0550. 5000. 5000. 0000. 0000. 0000. H000. 00H0. m0H0. 0NHO. 0HHO. 00H0. 5000. 5000. 0005. 0005. 0000. 0000. 000w. 000w. 00aw. 0000. 0000. 0500. 0000. 000a. 00¢H. 00HH. 0000. 0000. 0000. 0000. 0000. 0500. 0000. 0500. 0000. 0000. 0000. $00H. 0HOH. mafia. 000a. 00HH. 0000. 0000. 0050. 0H50. H000. 0000. 0000. 5000. 0H00. 0000. H000. 0000. 0000. 0000. 00H0. HOH0. owao. 0HHO. e000. 5000. 0550. 0000. 0500. 0500. 0500. 00HN. 0000. 005a. 000a. 050a. 000a. 0000. 0000. 0050. 0050. 0000. 0000. 0000. 0500. 0500. 0000. 0000. 0500. 0000. 0mm . mama. wooa. anna. omaa. wwaa. 0000. #000. 0050. 5000. #000. 0000. ammo. 0000. anno. 0000. 0000. 0000. 0H00. 0H00. 00H0. Noao. owao. 00H0. 0000. #000. 0050. 05¢0. 0500. 0050. 0500. 00am. 000a. 000A. 00¢H. 000a. 05HH. 0000. 0000. 0550. 0500. 0000. 0000. 0000. 0000. 0000. 0500. 0000. 0000. 0000. 00H0. 0H5H. 05¢H. 000A. 000a. 000a. 0000. 0050. 0000. 0000. $030. 5000. 0000. 0000. #000. 0000. apmo. Obmo. ammo. m¢mo. ”mac. 05H0. HQHQ. 00H0. 0000. 0000. 0000. 0000. 0000. 0000. 0000. comm. abba. mmma. oooa. omna. 00HH. 0000. 0000. 0050. 0000. 0000. 0000. 0000. 0500. 0000. 0300. 0000. 0000. DDQO. rt (u C 00H0. D x .0500 r-INLQVI‘I) HWMOV apmmm0 “a.m.mwuommp “gamma pguammp mm-» .NmHH .am oh. AH.m.mwpomw0 W%.m.m,pmm0v.ww.m.mwpm000 film .wam, Abum .Nmfim o-¢ .NmaH maonam anmdoo Spas mflmm‘mO 00mg mHnom “H.m.m\pomm, .00 a .NmaV My m H ,0 22m AdeSapqoov m mange 29-30 amm.a moo. Hmnw. moo.a = = opmw. omo.a ¢o@¢. opo.a mmm¢. ooo.a n¢ muo.a owe. «ma¢. ammo. = : wmmw. mao.a Hmmw. noo.a oa¢w. omo.a m mwo.a mam. Hmmm. omam. : = monw. comm. nmm¢. mumm. wmm¢. nmmm. a¢ www.a ¢mo. mwmm. mbmm. : : oomv. 0050. boaw. nmwm. oaww. smbm. o¢ moo.a one. boun. 005m. = : m¢a¢. mumm. mmav. comm. gnaw. omnm. on Hmm.a mmo. «own. mmmm. = : mmmn. abom. omov. oanm. womn. ammo. mm mmm.a mam. mama. mmam. : : noun. comm. Hmmn. mmmm. mabn. munm. mm mmm.a mam. mumm. mmm . : : mobm. Qnmm. mmbn. @556. born. 005m. on oan.a boo. @mnm. numb. : : boom. ooam. mama. mmam. @mwm. whom. an mmw.a mmu. nmam. mbmu. = = Homn. mump. mmmn. numb. mama. ombu. wn mvw.a ¢mm. anon. coon. : : mnom. omOb. mman. mmmb. flown. oowb. an 00¢.H mpm. Hamm. ammo. m¢.A H.HA gnaw. abbo. nmmm. ammo. whom. mbmo. ma mmm.a mmm. mmom. mmam. mob¢. bmo.a moom. mmoo. babm. mbmw. vmom. comm. an mmm.a mam. meow. Oman. ombw. moo.a mamm. oooo. mmwm. mmaw. meow. onao. on «an.a ©¢m. mwmm. mumm. Hm¢¢. ono.a comm. mbbm. mowm. Dorm. mmwm. mmom. mm mom.a mam. Noam. mmmm. m¢a¢. abnm. momm. mmmm. wmmm. bmmm. mmmm. omam. mm mmm.a mam. mmom. nmm¢. oamm. comm. poem. nubw. mbom. oomw. mwom. mmuw. 5m mwa.a 09¢. mmma. mww. bmvn. mmom. wmpa. omaw. boma. mpaw. mama. oomw. om dmmo%‘aummhw h4.m.mxpomm~ mm.m.m‘pmomv bwa.m.m1pmomv\wm.m.m‘pmmmU Rm.m.mlpommw flmommm pnmmomp 1mun .Nmmm ¢-m[.Nmfimp . mm .wam mu¢ .Nomg Am-a .Nofimv .02 wah maonam nmamwoo flaws mmwmwmo mmmmImH.bm ZDm Aumosaoqoov m magma - 31 _ Table 3 Experimental data on couplers in position 1 (Head lessee in half inches as read on a 0014 differenr t1a1 manometer). Run: 7—Fieznmefere: Weir: , ( ea c e 1 3 0.6 2.4 0.7 2.6 .265 .471 2 14 1.0 3.0 0.9 3.1 .278 .504 3 7 1.1 3.4 1.0 3.3 .292 .540 4 22 1.1 3.8 1.1 3.7 .306. .577 5 8 1.1 3.9 1.2 3.8 .306 .577 6 23 1.2 4.2 1.3 4.1 .314 .599 7 21 1.3 4.4 1.3 4.5 .322 .621 8 15 1.4 4.6 1.4 4.7 .331 .645 9 28 1.5 5.3 1.4 5.2 .343 .679 10 1 1.6 6.0 1.5 5.9 .356 .716 11 24 1.7 6.4 1.6 6.5 .370 .756 12 16 1.8 711 1.8 7.0 .382 .791 13 4 1.9 8.8 2.0 8.9 .390 .815 14 9 2.0 9.4 2.0 9.3 .397 .835 15 6 2.3 11.2 2.2 11.5 .409 .872 16 32 2.3 11.9 2.4 12.1 .416 .893 17 13 2.5 12.5 2.4 12.9 .425 .921 18 29 2.6 13.8 2.6 13.7 .434 .948 19 2 2.7 14.7 2.7 14.3 .445 .983 20 10 2.9 14.8 2.7 14.2 .446 .986 21 25 2.9 15.5 3.0 15.4 .457 1.020 22 20 3.0 16.1 3.1 15.9 .470 1.062 23 5 3.3 16.4 3.3 16.3 .482 1.100 24 30 3.7 18.2 3.8 18.5 .496 1.146 25 33 4.3 21.3 4.2 20.9 .509 1.189 26 19 4.7 23.5 4.8 23.2 .521 1.233 27 11 5.1 23.9 5.0 23.7 .524 1.239 28 26 5.4 24.3 5.3 24.8 .535 1.276 29 12 5.8 25.1 5.8 25.5 .550 1.328 30 17 6.0 25.6 5.8 25.7 .555 1.345 31 34 6.8 28.5 6.7 28.7 .572 1.404 32 27 7.9 31.2 7.5 30.8 .587 1.456 33 35 8.5 34.9 8.3 35.0 .611 1.541 34 31 9.0 38.0 9.2 38.3 .625 1.592 35 18 9.9 41.1 10.1 41.9 .636 1.631 ‘ Order of experiment Table 4 Experimental data on couplers in position 1 (Head losses given in test of water and in lb./in3). Run 2'63, feet of Qipe wit. co fil'er _ ,0 E Piez. 1-2 Piez.5-6 b ' mt 2.s.i.l Ifeet 2.8.1.‘_ 1 .0150 .006495 .0175 .007577 2 .0250 .010825 .0225 .009742 3 .0275 .011907 .0250 .010825 4 .0275 .011907 .0275 .011907 5 .0275 .011907 .0300 .012990 6 .0300 .012990 .0325 .014072 7 .0325 .014072 .0325 .014072 8 .0350 .015155 .0350 .015155 9 .0375 .016223 .0350 .015155 10 .0400 .017320 .0375 .016223 11 .0425 .018402 .0400 .017320 12 .0450 .019485 .0450 .019485 13 .0475 .020567 .0500 .021650 14 .0500 .021650 .0500 .021650 15 .0575 .024897 .0550 .023815 16 .0575 .024897 .0600 .025980 17 .0625 .027062 .0600 .025980 18 .0650 .028145 .0650 .028145 19 .0675 .029227 .0675 .029227 20 .0725 .031392 .0675 .029227 21 .0725 .031392 - .0750 .032475 22 .0750 .032475 .0775 .033557 23 .0825 .035722 .0825 .035722 24 .0925 .040052 .0950 .041135 25 .1075 .046547 .1050 .045465 26 .1175 .050877 .1200 .051960 27 .1275 .055207 .1250 .054125 28 .1350 .058455 .1325 .057372 29 .1450 .062785 .1450 .062785 30 .1500 .064950 .1450 .062785 31 .1700 .073610 .1675 .072527 32 .1975 .085517 .1875 .081187 33 .2125 .092012 .2075 .089847 34 .2250 .097425 .2400 .099590 35 .2475 .107167 .2525 .109332 -33- Table 4 (Concluded) Run 20:19 with coupier) ' P18205‘7j ee .s.i. (W613) (Hei ht Dischar e feet o e .m. 1 .0600 .025980 .0650 .028145 .265 .47064 211.29’ 2 .0750 .032475 .0775 .033557 .278 .50384 226.138 3 .0850 .036805 .0825 .035722 .292 .54014 242.431 4 .0950 .041135 .0925 .040052 .306 .57675 258.862 5 .0975 .042217 .0950 .041135 .306 .57675 258.862 6 7 8 9 .1050 .045465 .1025 .044382 .314 .59878 268.750 .1100 .047630 .1125 .048712 .322 .62081 278.638 .1150 .049795 .1175 .050877 .331 .64532 289.638 .1325 .057372 .1300 .056290 .343 .67882 304.674 10 .1500 .064950 .1475 .063867 .356 .71574 321.245 11 .1600 .069280 ‘.1625 .070362 .370 .75607 339.346 12 .1775 .076857 .1750 .075775 .382. .79113 355.082 13 .2200 .095260 .2225 .096342 .390 .81471 365.666 14 .2350 .101755 .2325 .100672 .397 .83550 374.997 15 .2800 .121240 .2875 .124487 .409 .87180 391.289 16 .2975 .128817 .3025 .130982 .416 .8928? 400.755 17 .3125 .135312 .3225 .139642 .425 .92051 413.152 18 .3450 .149385 .3425 .148302 .434 .94843 425.683 19 .3675 .159127 .3575 .154797 .446 .98566 442.393 20 .3700 .160210 .3550 .153715 .446 .98566 442.393 21 .3875 .167787 .3850 .166705 .457 1.02041 457.990 22 .4025 .174282 .3975 .172117 .470 1.06167 476.509 23 .4100 .177530 .4075 .176447 .482 1.10076 494.054 24 .4550 .197015 .4625 .200262 .496 1.14637 514.525 25 .5325 .230572 .5225 .226242 .509 1.18918 533.739 26 .5875 .254387 .5800 .251140 .521 1.23262 553.236 27 .5975 .258717 .5925 .256552 .524 1.23913 556.158 28 .6075 .263047 .6200 .268460 .535 1.27636 572.8% 29 .6275 .271707 .6375 .276037 .550 1.32755 595.844 30 .6400 .277120 .6425 .278202 .555 1.34462 603.505 31 .7125 .308512 .7175 .310677 .572 1.40357 629.964 32 .7800 .337740 .7700 .333410 .587 1.45600 653.496 33 .8725 .377792 .8750 .378875 .611 1.54101 691.651 34 .9500 .411350 .9575 .414597 .625 1.59158 714.348 35 1.0275 .444907 1.0475 .453567 .636 1.63160 732.311 - 54 - Table 5 Experimental data on couplers in position 2 (Head . losses in half inches as read on a C014 differen- tial manometer). Run: Piezometers: Weir: ("1%. *7 11:2 173 5-5 *5-7) Height Disch) fleet) (cf‘s) 1 .5 0.8 2.7 0.7 2.7 0265 e471 2 15 1.0 3.9 0.9 3.6 .284 .519 3 11 1.2 5.1 1.2 4.9 .306 .577 4 19 1.3 6.3 1.4 6.4 .329 .640 5 8 1.5 7.2 1.5 7.1 .351 .701 6 1 1.8 7.5 1.7 7.3 .356 .716 7 22 2.0 8.3 1.9 8.4 .372 .762 8 4 2.3 9.1 2.2 9.2 .390 .815 9 12 2.4 11.9 2.4 12.0 .406 .863 10 6 2.5 12.2 2.4 11.9 .409 .872 16 2.6 13.5 2.7 13.2 .426 .924 7 2.7 14.1 2.8 13.9 .435 .951 20 2.8 14.0 2.8 14.3 .437 .959 2 3.1 14.5 3.0 1405 .445 .983 5 3.5 16.3 3.5 16.6 .482 1.101 23 3.7 17.5 3.9 ,17.3 .491 1.130 13 4.9 21.8 5.0 22.2 .512 1.200 9 5.6 24.5 5.5 24.2 .523 1.236 17 6.7 28.4 6.6 28.1 .545 1.341 21 7.6 31.2 7.8 31.4 .563 1.372 14 8.5 34.5 8.5 34.5 .586 1.453 18 9.8 39.0 9.9 38.7 .604 1.517 10 10.6 40.1 10.8 39.7 .620 1.574 fi Order of experiment 5 7o 050.a 000. 5mmw. 00mm. 0000. m00.a m0aa. 005m. 5vaa. 000m. 00 0a0.a $00. mmaw. 0500. amm¢. 005m. 050a. 0500. 000a. 0000. mm mme.a 0mm. 4050. mmom. 4050. nmom. ammo. mmam. ommo. mmam. am N50.a 000. mm00. 0005. 5500. 0005. 0800. 00ma. 0000. 00ma. om 000.a 000. a000. 0000. 0500. 00a5. ¢a50. 000a. 0050. 050a. ma 000. 000. ma0w. 0000. N000. 0ma0. 0m00. 050a. 0000. 000a. 0a 000.a ma0. 0000. 0000. m00m. 0000. a000. 000a. 0000. 0mma. 5a mma.a ama. m50a. 000w. «mma. 0508. 0080. 05m0. 0530. 0mm0. 0a 00a.a 00¢. 0m5a. omaw. 005a. 0503. 0500. 0500. 0500. 0500. 0a 00m. 080. 000a. 0000. m00a. 0m00. ¢m00. 0050. 0000. 0550. 0a 00m. 500. 5¢0a. 0500. 0a0a. 0000. 0000. 0050. 0000. 0050. 0a a0 . 00v. wo0a. 0500. 000a. 0m00. 0000. 0:00. mmmc. 0500. 0 00m. 000. 000a. 0000. 000a. 0500. 0mm . 0500. ammo. 0000. aa a50. m0¢. 000 05mm. 000 . 0000. m000. 0000. 0500. 0000. 0a N00. 000. mmma. 0000. 000a. 05mm. mnmo. 0000. m0mo. 0000. m 0am. 000. 0mm0. 000m. 00m0. 05mm. 0000. 0000. 0000. 0500. 0 a05. N50. m0m0. 00am. 0m00. 050m. 0000. 0500. 0am0. 0000. 5 0a5. 000. 0m50. 000a. aamo. 050a. 00a0. 0000. wmao. 0000. 0 a05. a00. 0050. 055a. m550. 000a. m0a0.. 0500. N0a0. 0500. 0 040. mm0. mm00. 000a. a000. 050a. a0a0. 0000. 03a0. 0000. w 050. 000. 0000. 000a. 0090. 050a. mmao. 0300. mmao. 0000. 0 man. 000. m000. 00m0. 0000. 05m0. 0000. 0000. 00a0. 0000. 0 05¢. 00m. 0mmo. 0500. 0mmo. 0500. 0500. 05a0. 0000. 0000. a m ca 050000 w .m.@ 5.000 afi.m.m, mom 1H.m.m pamMM 50.m.m, gammy .o 00000.0000m00 .510 .Nmam 0na .Nmam 70010 .Nmam mua .Noawv a Mama amwmmoo 0003 omwm ho .0a.0m amamdoo up“; mmwa Mo .00.m new .a.m.0 :a 0:0 Menu; Mo 5000 :a :m>a0 mmoa gammy m noapamog ca maoa0300 so 8580 aepqmsaammam 0 magma rs -.36 - Table 7 Experimental data on couplers in position 3 (Head losses in half inches as read on a 0014 differen- tial manometer). Zfifig: #fiiezgmeters: 5!. r: 19.. ’7 (1-2 1-§ 5—6 5-7} {Height Disch; feet are 1 3 1.0 2.9 0.9 2.8 .265 .471 2. 18 1.2 4.2 1.1 4.1 .296 .551 3 12. 1.4 5.6 1.5 5.7 .329 .640 4 1 1.6 7.3 1.7 7.4 .356 .716 5 7 1.8 7.4 1.8 7.4 .360 .727 6 16 1.8 7.5 1.9 7.6 .362 .733 7 4 2.4 9.4 2.4 9.5 .390 .815 8 9 2.6 10.3 2.7 10.1 .403 .853 9 6 2.7 12.4 2.8 12.7 .409 .872 10 19 2.9 13.4 3.0 13.3 .422 .911 11 13 3.2 14.5 3.2 14.5 .436 .955 12 2 3.4 15.2 3.3 15.0 .445 .983 13 21 3.4 15.5 3.4 15.4 .447 .989 14 5 4.1 17.5 4.0 17.1 .482 1.100 15 8 4.5 18.9 4.4 18.5 .488 1.120 16 14 5.1 20.8 5.0 20.5 .505 1.177 17 20 5.7 23.2 5.8 23.1 .522 1.233 18 10 6.2 25.6 6.3 25.5 .538 1.285 19 15 7.4 29.0 7.2 28.8 .557 1.351 20 17 8.4 32.4 8.0 32.5 .579 1.428 21 22 9.3 36.2 9.1 35.0 .596 1.488 22 11 11.2 39.5 11.0 38.9 .613 1.548 ’ Order of experilent - 37 m¢m.H mam. oamw. mmbm. mbmv. mvmo. omHH. Ombm. mama. oomm. mm >m¢.H mom. comm. whom. mama. omoo. mmmo. mumm. ammo. mmnm. Hm mm¢.a ohm. mama. mmam. boon. ooaw. memo. ooow. mooo. ooam. om omn.a ham. de0. 00mm. mean. ommb. ouro. oomH. Homo. omma. ma #mmwa mom. ombmq mbmo. Hubm. 00¢o. ammo. mbma. aboo. omma. ma mam.a «mm. oomm. mvbm. Hamm. oomm. bmoo. omwfl. baoo. mm¢a. pa oba.a mom. onN. mmam. Hmmmd oomm. H¢mo. ommH. mmmo. mpma. oH omH.H wow. moom. mmo¢. mwom. bmvw. obwo. ooaa. rm¢o. mmaa. ma ooa.a wm¢. HmmH. m>b¢. woma. mbnw. nnwo. oooa. wwwo. mmoa. «a mom. bvw. bmoaw ommn. bboaq mbmn., mono. ommo. memo. ommo. ma moo. mvw. nmoa. ombn. mwoaq oomn. bmno. ammo. mono. ommo. NH ¢mo. wow. mood. moon. woman mmon. owno. oomo. mwno. oowo. HH Ham. mmw. onwa. mmnm. omwa. omnm. «moo. ombo. Mano. mmbo. oa Hum. mow. ¢>naq man. mwwa. ooawq mono. ooro. womo. whoo. 0 now. now. mooa. mmmm. waaa. whom. ammo. mbmo. Homo. owoo. m ¢Hm. own. mNOH. obnw. bHoaq ommmq ammo. oooo. ammo. oooo. b nab. mon. mmmo. oomH. Hamoq whoa. momo. mbwo. ¢mHo. om¢o. o bob. own. Homo. omma. Homo. omma. ¢oHo. omvo. wmao. omwo. 0 mar. own. Homo. omma. ombo. mmwa. wmao. mm¢o. nrao. oowo. w 0¢o. own. rfioo. mmwa. wooo. omwfl. mwaow mpno. Hmao. omno. n omm. mom. nv¢o. mmoa. wmwo. omoa. oHHo. mbmo. mmao. oono. N 05¢. mom. mono. oovo. nano. mmbo. bmoo. mmmo. moao. ommo. H muaq, pmmww A.H.mqa [mummy nH.m.o amouo d¢w.m.gx pmowo \dfiam.a poomw. TnomngmE $5 in .33 nA 53nd, Ayn 533 - NA £331 .02 hams nmflmsoo npfia mafia mo .oH.om uoanzodwgnfia uofio Ho_.nm.m, cum .A.H.m.m cH cam 90pm: Mo pomm CH Cm>Hm mmOH ommmv m mofipwmom Ca mnmflmsov no wpmo kucmfiahmakm m mamas - 38 - For the second part of the study where the degree of alignment of two sections of tubing through a coupling was varied, a complete set of runs at different rates of dis- charge was made for one position; then the tubing was shifted to the next position and another series of measure- ment made at various rates of discharge. If there was a small difference in discharge readings, an average between the first and the second measurements was considered. If the difference was great, the run was dis- carded. For the three different positions the head losses were, at the beginning, determined for each rate of discharge, that is, the pipes had to move to give each one of the different positions for each discharge. Later it was noted that the best was to determine the head loss in each position, var- ying the discharge. This was done and Tables 3, 4, 5, 6, 7, and 8 give the results. -39.. PRESENTATION OF DATA Evaluation of exponents and coefficients in theggeneral pipe flow eguation. The general equation for friction loss in tubing is: do It may be modified and written in the forms: hf=sxqm for fiction loss in pipe; hL==KQm for the head loss in pipe and couplers; hO=KQm for the head loss in couplers; and he-stP for the head loss in elbows. By plotting experimental values of hf, hL' ho, andhe against corresponding values of Q on logarithimic paper, the value of the exponent m and the coefficient K is determined. The slope of the line is m, and K is the intercept at Q==l. hf and hL used in these plottings were the average of friction losses and head losses found in experiment. These values of hf and hL were determined from Figs. 13, 13, 14, and 15, and are given as follows on the base of losses per loo-foot length of tubing. Pipe '1thout coupleIOOOCOO0.0.0.000... hf: 1.471 Q1.881 Pipe with well set coupler (‘)....... hL==1.682 q}'831 Pipe with coupler in position 1 (*)... 111...... 1.683 Q1~978 Pipe with coupler in position 2 (*)... hL==1.a31 q}o917 Pipe with coupler in position 3 (*)... hL==1°911 Q10958 (’) See explanations on p. 19. -40.. Fig. 12 Friction loss vs. flow rate in 17.53' length of tubing, and head loss vs. flow rate in 20.16' length of tubing with one coupler correctly aligned with the second section of tubing. ,1 .2 .3 .4 .5 .6 .7 .8 .919 2 3 Flow rate (cfs) ‘ Friction loss (feet) - 41 - Fig, ;3 need loss vs. flow rate (20.16-fcot length of tubing and one connecting coupler in position "Uo‘UIOU el 02 e3 '04 e5 e6 e7 e80910 2 3 Flow rate (cfs) Friction loss (feet) wv'v YY Fig. 14 Head loss vs. flow rate (30.16-foot length of tubing and one connecting coupler in position 2 . hL= .369 'Q1°917- --(so.is")- 1.917 hL=l.831 Q (100') _ ~ 7" ‘ ”a I i i l ' ; __._,__-_ -__._,_-_ _gx_h___l_-_ --i_.____ _-.._.__._-._. ‘_ _ - _____-L___ .2.’ ‘o‘ ‘4 ,5 ,o ,7 .6 .8 1;; 2 5 Flow rate (cfs) e... — -7 Friction loss (feetl Fig. 15 Head loss vs. flow rate (20.16-foot length of tubing and one connecting coupler in position 3). i _4 - _n_. F'— - i i ___._ § ‘ -.. .1 - ., --L___._. - _... _ ._ -1— 9 . ' I I ‘ g ._ 'hL'g‘1385‘QELJQBBMfzoo-tfi‘)‘: . ———~. swim: oil-59.5,?“ (100') - _ ; I I § 7._. . W... ,-_- __ .-- ,.__-----_..-_- ..- _ can-.. - Y ' s , 3 1 , ' ‘ ~ ‘ 1 _ , ,i ‘ ‘ .-.- : . . I 0 _ _ I I I I , , s V | ‘ ‘ . ‘ i . ; . a _ i i __ _.__- _ .______L__ .. -_._i__1- ‘; _ 1,_-_ N O 0) .3: '01 O O O N e on (C )- C f\ (A. Flow rate (cfs) - 44 - The average value of the exponent m to the nearest hundreth is 1.92, and it is used to recalculate the value of I in the five equations above: Pipe without coupler hf: 1.500 Q1‘92 (1) Pipe with well set coupler ........ hLE=l.649 Q}’92 (8) 1.92 Pipe with coupler in position 1 ... hL==l.662 Q (3) Pipe with coupler in position 3 ... hL==l.836 QF°93 (4) Pipe with coupler in position 3 ... hL=él.885 Q}’92 (5) These equations (1 through 5) were used for calcu- lating the values of h: and hL for the various flow rates as shown in Table 9. Pipe without coupler Its equation for the friction factor in tubing as based on the form hszQm , was found to be h1=:1-471 Q}'881 . To solve for the expression hrs-K5 9,?" n d it is necessary to assume a value for n, as it is impossible to determine its value when only one diameter is tested. The value of n is assumed to be 1.14 to compare the result with those found by Olson (7, p. 17). In can be evaluated as follows: hf: m“. nmv‘“. In g vm an magmas“: 1.471;.489511'14 (.lBBZII‘BBI = .000281 L 100 ' Table 9 Loss of head per loo-foot length of six inches aluminum tubing with and without couplers. "finch. h and h values: (cfs gpnl, 1i) (2) (3) (47‘ (5) .1 45 .0180 .0198 .0199 .0220 .0227 .2 90 .0682 .0750 .0756 .0835 .0858 .3 135 .1486 .1634 .1647 .1819 .1868 .4 180 .2583 .2839 .2862 .3161 .3246 .5 225 .3964 .4358 .4393 .4852 .4982 .6 270 .5626 .6185 .6234 .6887 .7071 .7 315 .7563 .8314 .8380 .9257 .9504 .8 360 .9774 1.074 1.083 1.196 1.228 .9 404 1.225 1.347 1.358 1.500 1.540 -1.0 449 1.500 1.649 1.662 1.836 1.885 1.1 494 1.800 1.978 1.994 2.203 2.262 1.2 539 2.127 2.338 2.357 2.603 2.672 1.3 584 2.481 2.727 2.748 3.037 3.117 1.4 629 p 2.860 3.144 3.169 3.501 3.594 1.5 674 3.264 3.588 3.616 13.995 4.102 1.6 719 3.697 4.065 4.096 4.526 4.646 1.7 764 4.155 4.567 4.603 5.086 5.221 1.8 809 4.635 5.095 5.135 5.673 5.824 1.9 853 5.145 5.656 5.700 6.297 6.465 2.0 898 5.670 6.233 6.940 7.125 -45- 6.282 (1) hf: 1.500 Q}-93 (Pipe without coupler) (2) hL= 1.649 Q1°93 (Pipe with well set coupler) (3) hL==1.662 Q}'92 (Pipe with coupler in position 1) (4) hn==1.836 Q}°93 (Pipe with coupler in position 2) (5) - 11L: 1.885 Q1°93 (Pipe with coupler in position :5) - 45 - 80, hr = .000281 L v1°881 d1.14 ..........’(6) To compare the above equation with Olson's equation (7, p. 17) for hf = .000330 L V1378 and with values of d1.14 hf given by the Aluminum Company of America's general table, Table No. 10 was developed on the basis of loo-foot length of tubing for purposes of comparison. hf ' '000281 ____199___. Vl'sel = .0635 v1°881 ..... (7) (.4895)1'l4 hr = .000350 100 v1°78 = .0747 v1°78 ... (Olson) (.4895)1-14 Comparison of equations (Loss of head per lOO-foot length of six inches a1u- minum tubing without coupler) 221.12.22.19. _veI.'Disch. pl.aal v1.78 asangw Olson AfiEUK fitjsec) chsl 7 Lfeetl Tfeet) (gee? 1 .188 1.00 1.00 .063 .074 .070 2 .376 3.68 3.44 .234 ’.257 .250 3 .565 7.90 7.08 .503 .528 .510 4 .753 13.6 11.8 .865 .881 .850 5 .942 20.6 17.6 1.31 1.31 1.27 6 1.13 28.9 24.4 1.83 1.82 1.74 7 1.32 39.0 32.1 2.48 2.39 2.28 8 1.50 49.9 40.3 3.16 3.02 2.88 9 1.69 62.0 50.1 3.94 3.73 3.62 10 1.88 76.0 60.0 4.82 4.48 4.38 Coupler losses The head loss in couplers was determined by subtracting - 47 - the friction loss in 17.53-f00t length of tubing from the head loss in 20.16-foot length of tubing and coupler. To ac- complish this the equation hf - KQE for lOO-foot length of tubing was subtracted from the equation hL I KQm for 100- foot length of tubing and couplers: hf = 1,500 Q1°923 for 100 feet of tubing (5 couplers), hc ' hL - hf , so: W611 set coupler (*),,,,,.... 'h0 = .149 ql.92 Coupler in position 1 (s) ... ho : .152 Ql.92 Coupler in position 2 (a) ... he : .535 ql.92 Coupler in position 3 (3) ... hc : .385 ql.92 For each coupler the equation will be: .0298 Q1.92 (a) .0524 Q1°92 ’(9) .0572 Q1°92 (10) .0770 Ql°92 (11) Well set coupler (*) ........ .hc Coupler in position 1 (*) ... ho Coupler in position 2 (*) ... hc he Coupler in position 3 (*) ... Table 11 gives values of hc determined from the above equations for several flow rates. Loss coefficient for couplers The determination of the loss coefficient Kc for couplers in the equation for head loss in fittings, he = Kc V2, EE can be done as follows: (a) See explanations on page 19. 48 an coapamomv .d omba..uom Andy M No .Hd oamo. no: “Adv am soaoamoao mo. 6 mnoa._uom aoao m mm .m@ msoo. “on aoav 1a noanamomv mo. 8 omso._uoa Amao m ma ammo. "on any anon aaono .@ osoo. tom amao n .ma momo. "on “my mama. mesa. mmoo. memo. poaom aoenm. semma. nomaa 0.8 mooa. onea. Nose. memo. aaspm. macaw. maaaa. ammoa mom a.a mama. apea. coso. memo. macaw. eosom oaoso. mouse mom a.a mmoa. opaa. mono. aomo. mmmam. eapma. mammo. _ 8o. sob a.a aooa. mesa. aaso. amps. omoma. apnea. oposo. mambo. mas a.a mama. mmaa. aaso. ammo. nnaoa. pmoea. goose. emeoo. sap n.a moaa. amca. maso. aooo. mmpea. namma. msaoo. mmooo. amp. a.a masa. oona. muse. mpoo. anew . eaaaa. manna. mmmeo. amp a.a omsa. ooma. smso. oopo. oamoa. mmooo. 48840. @8840. map m.a assa. omna. mmao. esoo. osmoo. eoomo. memo o. osmoo. ems a.a omsa. mama. mmso. oboe. oosao. omspo. osmmo. enamo. owe a.a assa. mama. peso. nmpo. ommpo. ooeoo. seam amewo. 404 o. mmsa. oooa. moso. ampo. aaono. manoo. aaamo. aeoao. com 8. aoma. ssna. ooso. @980. mmmmo. mmmmo. o .ao. mooao. man s. mama. papa. peso. moso. pmmmo. ommmo. na.ao. saaao. can 8. pmma. omoa. ammo. mane. nnomo. oasao. ommoo. .mmsoo. mmm o. mom nsoa. mmso. anso. mmnao. osaao. smnoo. 8a oo. mma a. amma. mopa. name. meao. mpsoo. popes. amooo. pom oo. nna n. mama. masa. coma. maso. omnoo. nonoo. seaoo. nnaoo. co m. maam. mama. ammo. oamo. moooo. amooo. omooo. onooo. ma a. Rafi 1:8 a: a: L aaan a8 5 E 3% mum "mmdflmzr OK. "mdeEP 0C. uaMOnHQ. .mamaasoo no“ on pmmaoawgmoo mmoa was on comm we mmoa AH magma - 49 - 2 1 92 .92 2 h.=K‘V=KQ' ,. xzz xé' 2A KQ Kc: 64.4 (.1882)2 ref-08 z; 2.281KQ7'03 . So, for: Well set coupler K°==.0679 q-oOB (13) Coupler in position 1 .... Kc: .0739 qf'OB (13) Coupler in position 2 .... Kc =.153 QT'08 (14) ‘Ccupler in position 3 .... Kc =.l76 Qf’oa (15) Table 11 gives values of Kc obtained from the above equations. Elbow losses Experimental values of he and corresponding values of Q vere plotted on logarithmic paper (Fig. 16) to give the coef- ficient K and the exponent n of the equation beam,m . The equations become: .315 Q3-35 (16) .600 Q3-35 (17) For 90-degree elbow (piez. 7-8) ... he For 180-degree elbow (piez. 3-4) ... he Table 13 gives values of he for several flow rates ac- cording to equations (16) and (1?). ages coefficient for elbows As it was determined for couplers, Ke value is: O . 5 0 he: Xe :3 KQZ 35 Ke==2.281 Kg 3 so. 0Q 50- _ _ _ 1 _ . . _ _, _ . _ I _ _l + .0 I¢I0 I'll- a .u1OI J I? , _ w _ H _ a u . N a . a _ M a x .. a 1 . _. _ gree and 180- J1. .7 _. _ _ _ - - .. 1. . ;_ . X _ _.. m .5 x 1:. W -1 a!” n;- _ _ .54. w _i _ _ ".9” . _ . _ _ . 6 a "-7.” _ _ _bm AV ... , a. s O a. a o ..-- 19m-.1x. a. a _ h e. «u . ..I -o ..H 1.9 -- ( a e O a 1 ,ra : e . .-.l- g: .- t u 1 M 8.. .3 n m .,aflg?ma ' W m 0 m- .. _ n c w ) . cs _ um . _ 81. H ...... BO . o . 18 l 9 . d! n as _ O 1 Rd N a; w W H w .H O m . L m.-._-. _. _ . . _ n .. fl _ . _ n _ a g._ _ _ . ._ n _ a _. . _‘_ \M . . .a .|_ We ... . .. E- ..-!!! w. 3 1 a _. x... if- t- anomav mmoa :oapoaaa leoédegree elboi._ c . I I 35 , . ‘ . > o h. asdé'ie . ._. I I .0 9'11... -19 . a :L . Friction 1633 (feet) '. . ~vwv-V'w I: . . 1;) Fig. 16 | i .. I I (I) Head 108' VI. flow rate (90-degroe and 180- degroe elbows). 90—degree e1boI _ §*_ " 113...:515 Q3- .25 180-degree elbow _ he;:.600“Qz'35 C”. h . V _..-__i._1__j..i _L..__._..__.. 2 ,3 ,4 ,5 ,6 .7.u.919 ;- 3 Flat rate (019) - 51 - For 90 -degree elbow (piez. 7-8) xe = .718 0‘25 (18) For lBO-degree elbow (piez. 3-4) Ke=l.368 Q~35 (19) Table 12 gives values for Xe according to equations (18) and (19). Table 12 Loss of head he and loss coefficient K, for elbows. """Taisohi E56 1205 £65" ' ' 1‘36" lots Epm e g. #:g Kg *Tfeef) (feet) .1 45 .00177 .00337 .4041 .7696 .2 90 .00842 .01605 .4805 .9152 .3 135 .02098 .03996 .5318 1.013 .4 180 .04006 .07632 .5712 1.088 .5 225 .08621 .12612 .6041 1.151 .6 270 .0997 .1900 .6322 1.203 .7 315 .1411 .2689 .6572 1.251 .8 360 .1906 .3631 .6795 1.294 .9 404 .2485 .4733 .6998 1.333 1.0 449 .3150 .6000 .7185 1.368 1.1 494 .3902 .7434 .7355 1.401 1.2 539 .4750 .9048 .7524 1.433 1.3 584 .5685 ‘1.083 .7673 1.462 1.4 629 .6709 1.278 .7807 1.487 1.5 674 .7843 1.494 .7950 1.514 1.6 719 .9072 1.728 .8083 1.540 1.7 764 1.039 1.980 .8203 1.563 1.8 809 1.181 2.250 .8315 1.584 1.9 853 1.335 2.544 .8438 1.607 2.0 898 1.499 2.856 .8549 1.628 - 52 - CONCLUSIONS 1. The friction factor determined for new six-inch di- ameter aluminum tubing is in agreement with that presented in the literature for smooth tubing. Its equation for lOO-foot length of tubing hf: 1.471 Q1'881 1r written in the form of the general equation of pipe flow becomes: hr = .000281 L .v1°881 dIOII This equation is based on the result of experiments on only one size diameter and so its practical value is lim- ited. 2. The friction loss in loo-foot length of six-inch di- ameter aluminum tubing, plus the head loss in couplers set at 20-foot intervals (5 couplers in 100 feet) can be expressed by the following equations: Pipe without coupler .................... hf 1,500 Q1.92 Pipe with coupler well set and in alignment with the tubing .......... hL 1,549 Q1.92 Pipe with coupler in vertical offset, but in alignment with the tub- ing (POSition 1) eeoeeeoeoeoo....... 1.662 Q1092 :3" r." u Pipe with coupler in vertical offset and at 3-degree deflection in horizontal Position 2) ......,,,,., hL 1.836 Ql.92 Pipe with coupler in vertical offset and at 6-degree deflection in horizontal Position 3) ..........,. 1.885 ql.92 :3‘ t" I r 55 - 3. The head loss in each coupler can be written: Coupler well set and in alignment With the tUbing ....OOOOOOOOOOO Coupler in vertical offset, but in alignment with the tubing (POSition 1) OOOOOOOOOOOOOOOOOO Coupler in vertical offset and at 3-degree deflection in horizontal (Position 2)........ Coupler in vertical offset and at 6-degree deflection in horizontal (Position 3)........ hc hc hc ho 4. The loss coefficient Kc for couplers in h0 = Kc g; was determined as being: Coupler well set and in alignment with the tubing................ Coupler in vertical offset, but in alignment with the tubing (POSition1)....OOOOOOOOOOOOOOO Coupler in vertical offset and at 3-degree deflection in horizontal (Position 2)........ Coupler in vertical offset and at 6-degree deflection in horizontal (Position 3)........ .0298 01-92 .0672 01-92 .0770 01°92 the equation .067eq--08 .07380'o08 .153 Q'°08 .176 Q"08 5. The head loss in 90-degree and in ISO-degree elbows can be expressed: For 90-degree elbow (Piezometers 7-8).. he For lBO-degree elbow (Piezometers 3-4). he 6. The loss coefficient Ke for elbows was determined 454- and its value is: For 90~degree elbow (Piezometers 7-8). Xe: .718 Q.25 For lBO-degree elbow (Piezometers 3-4). xdgl.358 Q.25 - 55 - SUMMARY 1. Extruded aluminum tubing and couplers have been used extensively in portable sprinkler-irrigation systems in recent years. Recognizing the need for further research on the hydraulic characteristics of aluminum tubing, couplers, and elbows, the Perfection Sprinkler Company of Ann Arbor, Mich., made available to the Agricultural Engineering Depart- ment the 6—inch diameter of new aluminum pipe, couplers, and elbows used in this experiment. Investigations were made in the Spring of 1950 in the Hydraulic Laboratory of the Agricultural Engineering Department of Michigan State college. 2. The experiment was divided into two parts. The first part was the determination of the friction losses in the tubing and the head losses in couplers when the longitudinal pipe alignment was straight in all planes. The second part was the determination of the friction losses in couplers due to varying degrees of poor alignment of connecting sections of tubing through the coupling as follows: position 1 - coupler out of alignment in the vertical plane using the MAX? imum amount of vertical displacement within the coupler; position 2 - tubing vertically displaced as in the coupler of position 1 and in addition a three (3) degree deflection from true alignment through the coupler in the horizontal plane; position 3 - identical to position 2 except the angle of deflection was increased to six (6) degrees, the maximum allowed by the test coupling. The experiment includes also the determination of the head losses in 90-degree and in lBO-degree elbows. 3. A differential manometer filled with carbon tetra- chloride was used to determine the pressure differences be- tween two piezometers. The piezometers were set in such a way as to give the friction loss in pipe, the head loss in couplers, the head loss in couplers and pipe, and the head loss in elbows. The rate of flow was measured by a Cipolletti weir. 4. Results of investigations on friction loss in pipe and head loss in couplers when the longitudinal pipe align- ment was straight in all planes are in good agreement with those presented in literature for smooth tubing and sprinkler-pipe couplers. 5. Results of experiments with couplers out of align- ment in the vertical plane by using the maximum.amount of vertical displacement within the coupler (position 1) gave only a slightly higher value for the head loss coefficient as compared with the head loss coefficient for coupler when the longitudinal pipe alignment was straight in all planes. The same occurred when the head loss coefficient for 3- degree horizontal displacement (position 2) is compared with that for 6-degree deflection from true alignment (position 3). - 57 - However, the 3-degree deflection (position 2) gave a rela- tively much greater value for the head loss coefficient as compared with that in position 1. 6. The loss coefficient value for the ISO-degree elbow was found to be almost twice as great as the loss for the 90-degree elbow. 1. 5. 6. 10. 11. '58-. LITERATURE CITED I Christiansen, J. E. Irrigation by Sprinkling. California Agr. Exp. Sta. Bul 670. 1942. 7 Daugherty, R. L. Hydraulics. 4th ed. New York: McGraw Hill Book Co., 1937. Freeman, J. R. Experiments upon the Flow of Water in Pipes and Pipe Fittings. New York: American Society of Mechanical Engineers, 1941. Gibson, A. H. Hydraulics and its Applications. 4th ed. New York: Constable and Company Ltd., 1930 King, H. W., Wisler, C. 0., and Woodburn, J. G. Hydraulics. 5th ed. New Yerk; John Wiley and Sons, Inc., 1948. Le Conte, J. N. Hydraulics. lst ed. New York: McGraw Hill Book Co., Inc., 1926. Olson, H. M. The Determination of the Friction Factor for New and Used Aluminum Tubing and Head Loss in Sprinkler-Pipe Couplers. Thesis. Utah State A.C., 1950. Russel, G. E. Hydraulics. 5th ed. New York: Henry Host and Co., 1948. Unwin, W. C. A Treatise on Hydraulics. lst ed. London:‘ Adam and Charles Black, 1907. Vennard, J. K. Elementary Fluid Mechanics. 2nd ed. New York: John Wiley & Sons, 1947. Weston, E. B. Loss of Head Due to Friction of Water in Pipes. 3rd ed. New York: D. Van Nostrand Co., 1903. Rnn|| IFCQ\ ONLY ‘— "a . O 1 I O I 0 1| . " ’ I b I l . o “ ’ 9 I I ‘ I ‘ I. l . ‘v I - i ' o ROOM USE ONLY AP 23 fl ' U . I l I l I . I ‘ t .v y’_ ‘ . ;\' ‘ ‘ 3:. ._ . '.:' 1‘ I“, ._ g . 7 "W- ? "a ,1‘:; f K- 1 a)!“ ’ I ‘I ' ‘ “v i .. 'l‘ . -‘ '- ‘I t] ‘ l. 6" {1 . ' 3‘3’.‘ [ I“ ’7'. 9‘: .\.I . AI I. - ' 0 g. ‘ l- V H :- - ’a ' " [‘5' “ "‘2. 1"" {56" 4,2. . 5“" o‘r‘; 7&1» l f‘ e‘ '. fi fl"*(v" t‘ 'I 3‘ 5' Rd 1 \ . «6 . . ' ‘y n."’ \‘f 5 if (U. '12“ ., .4. .- «w- . « .7. w s. I W“ ‘1‘ 1 . " l‘n‘ I. 'l ) "1.71.334 g ~~.183‘u- u~ .‘7' ’ o" ‘ - 91-0.- . , . .A‘J' -5 ft “7 . 1 .s‘ . -~'I" '.. ‘ " ’ ['9 ‘-’ icy": F t‘ ' VK‘ .~ Inflam- 4544.741 «.... - m». w m» . .. : xv.- .._... Var-2.. ‘ .. .‘x' 1 ' r" 1 . 15' “ F, 'Js.’ I} 2”! '3, .1 . d *L r/nt’ 1*- J ', a.\‘:". Q-V' ‘I' '- I. '3" " '7“ P. "ft '74 ,§*:.4 I ‘5’ ‘ \1 'an .1. when: . ., r, .... “A . 'u'; ‘4’ .' " O. ’- ‘11,“?5 J~ ..." h'le“: .: 5' q ... ‘~‘ .' .r J. "r ‘l. .l 1" fi ‘ .kio‘ .' l _- I v "." K". ' fin? - I ' ’ n-‘o _ .‘ -\. v-\ .' .Y;. 1” '.I \v‘ ’ a7 '- 12 . V “'1 —vvv ‘- . v . 1 _- ..' .T on -. . l (I II II ll l l l