FACTORS THAT AFFECT DISTRIBUTION OF WATER FROM A MEDIUM PRESSURE ROTARY IRRIGATION SPRINKLER Thesis Ior the Degree O‘I Ph. D. MICHIGAN STATE UNIVERSITY WaIter K. Bilanski I956 fllfliflfl'l‘l’lflilfifll‘ll'uiliifi'il'lfiliifiiflflmfifll‘lfififil 3 1293 01686 1662 This is to certify that the thesis entitled Factors that Influence the Distribution of Water from a Iiedium Pressure Rotary Irrigation Sprinkler. presented by Walter K . Eilanski has been accepted towards fulfillment of the requirements for Pb Tl degree in Agricultural Engineering /. ,7 E. H. Kidder Major professor Date I—Zay 11) 1956 0-169 PLACE It RETURN BOXto romanthb Mutation your record. TO AVOID FINES mum on or baton date duo. DATE DUE DATE DUE DATE DUE MSU Is An Affirmative ActIOtVEanI Opportunity InotItmIon mum-mt FACTOR.e THAT AF?ECT DISTRIBUTION OF WATLR FROM A MEDIUM PRESSURE ROTARY IRRIGATION SPRINKLER BY Walter K. Bilanski AN ABSTRACT Submitted to the School for Advanced Graduate Studies of Michigan State University of Agriculture and Applied Science in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY Deaartment of Aaricultural Ensineerina E a a - r‘ "” 17:5 Abstract Walter K. Bilanski 1 In l9h6 less than 250,000 acres were irrigated by means of sprinkler irrigation; by the latter part of 19Sh an estimated 3,000,000 acres were being irrigated by this method and the acreage is increasing at an estimated 500,000 acres per year. Nearly all of the sprinklers in- stalled in the past ten years have utilized the revolving head sprinkler. Desirable distribution patterns from sprinklers range from a triangular-shaped pattern in which the fall-out is a maximum near the sprinkler and gradually tapers off to zero at the maximum trajectory distance, to a pattern in which the amount of fall-out is uniform.along the greater portion of the radius and then decreases gradually fOr the remainder of the trajectory distance. Because many sprinklers presently in use do not give either of the above distribution patterns of water, and since to date to the author's knowledge no de- tailed analysis has been made to determine what factors af- fect the distribution pattern, the objective of this study was to make such an analysis. This study was conducted indoors to eliminate weather variables. Only mediumppressure sprinklers were studied because this size was the most popular with irrigators and because it lent itself to study in a laboratory. Only one factor from one sprinkler with one nozzle was studied at a time; all other factors were in so far as possible, held constant. Walter K. Bilanski 2 The following factors were investigated and evaluated: oscillating arm, Operating pressure, orifice diameter, length of the cylindrical part of the nozzle, angle of taper in the sprinkler nozzle, angle of inclination of the nozzle, rate of rotation of the sprinkler, roughness in the cylin- Idrical part of the nozzle, length of the tube between the body of the sprinkler and the nozzle, non-circular orifices in the sprinkler nozzle, and use of cylindrical discharge tubes in place of nozzles. It was found that the factors discussed below had the greatest influence in approaching the desired distribution of water. The oscillating arm accentuated the fall-out of water near the sprinkler. A decrease in rate of rotation, an increase in the angle of inclination of the sprinkler nozzle from the horizontal and an.increase in the operating pressure all resulted in fall-out of the water approaching the desired distribution pattern. In general, the use of non- circular orifices or of short cylindrical tubes in place of conventional sprinkler nozzles resulted in a more desirable distribution pattern of water. The equilateral-triangular orifices in which the triangular shape extended for a con- siderable depth into the nozzle resulted in a distribution pattern approaching the ideal. The most desirable pattern was obtained from tube lengths ranging from 2 to h diameters. Walter K. Bilanski 3 Turbulence, distribution of velocities and amount of secondary motion affect the dispersion of the jet of water as it emerges from the sprinkler orifice. FACTORS THAT AFFECT DISTRIBUTION OF WATER FROM A MEDIUM PRESSURE ROTARY IRRIGATION SPRINKLER BY Walter K. Bilanski A THESIS Submitted to the School for Advanced Graduate Studies of Michigan State University of Agriculture and Applied Science in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY Department of Agricultural Engineering 1956 0t . : <)~‘ ACKNOWLEDGMENTS The author wishes to express his sincere thanks to Professor E. H. Kidder of the Department of Agricultural Engineering, under whose inspiration, constant supervision and unfailing interest this investigation was undertaken. Grateful acknowledgment is also extended to Mr. Crawford Reid, chief engineer of the Rainbird Sprinkler Company, for supplying the necessary sprinklers and sprink- ler nozzles for this study. He is greatly indebted to Professor H. Henry of the Civil Engineering Department and to Doctor 0. P. Wells of the Mathematics Department and Doctor D. J. Montgomery of the Physics Department, for their assistance. The author extends his sincere thanks to Messrs. Roland Wheaton, Edward Kazarian and Leon Sanderson of the Agricultural Engineering Department for their assistance and suggestions. He would also like to express his sin- cere gratitude to his wife, Shirley, for her assistance during the conducting of the tests and the writing of the thesis. Appreciation is also extended to Messrs. games Cawood and Glen Shiffer and all others who provided valuable aid during the conducting of the investigation. VITA Halter K. Bilanski candidate for the degree of Doctor of PhilosOphy Final examination: May 11. 1956, 2:00 P.M., Room 218, Agricultural Engineering Building Dissertation: Factors that Affect Distribution of Water from a Medium Pressure Rotary Irrigation Sprinkler Outline of Studies . Major Subject: Agricultural Engineering Biographical Items Born: December 16, 1927 Undergraduate Studies: Ontario Agricultural College, l9h8-52, B.S.A., 1952, major in Agricultural Engineering Graduate Studies: Michigan State College, 1952-Sh, MSAE, 195k; Michigan State University, lash-56 < Experience: Graduate Assistant, Michigan State College, 1952-5h; Graduate Research Assistant, Michigan State University, l9Sh-S6 Honorary Societies: Pi Mu Epsilon Society of the Sigma Xi Professional Societies: American Society of Agricultural Engineers TABLE OF CONTENTS Page Acknowledgments INTRODUCTION 0 O I O O O O O O O O O O O O O O O O O 1 Presentation 0f the PrOblem e o o o e e e o e o e 1 Approach to the Problem . . . . . . . . . 3 REVIEW OF LITERATURE O O O O O O O O O O O O O O O O O 5 APPARATUS AND MTHODOLOGY O O O O O O O O O O O O O O O 8 Apparatus e e e e e e e e e e o e e e e e e e e e 8 Location 8 Source of water 8 Pump 8 Delivery of water to sprinkler 8 Sprinkler shield 10 Anti-Splash device 10 water measurement 12 Sprinkler rotating mechanism 12 Pressure measurement 1h Sprinklers 1h HathOdOIOgy O O O O O O O O O I O O O O O O O 15 Oscillating arm 15 Operating pressure and size of orifice 15 Angle of inclination of the.sprinkler nozzle 17 Roughness in the cylinder of the sprinkler nozzle 19 Angle of taper in the sprinkler nozzle 20 Length of the cylindrical part of the nozzle 23 Length of the tube between the body of the sprinkler and the nozzle 25 Rate of rotation of the sprinkler 26 Non-circular orifices 26 Cylindrical discharge tubes 29 DISCUSSION OF RESULTS . . . . . . . . . . . . . . . . 31 Effect of the Oscillating Arm . . . . . . . . . . 31 Effect of Operating Pressure . . . . . . . . . . .35 Effect of Orifice Diameter . . . . . 39 Effect of the Angle of Inclination of a Nozzle . uh Effect of Roughness in the Cylinder of the Nozzle. 52 ii Effect of the Angle of Taper in the Sprinkler Nozzle Effect of the Length of the :Cylindrical Part of the Nozzle Effect of the Length of the Tube Between the Body of the Sprinkler and the Nozzle Effect of Rate of Rotation of Sprinkler Effect of Non-ciréular Orifices in the Sprinkler Nozzle TABLE OF CONTENTS (Cont.) O Triangular orifices Square orifices Rectangular orifices Quatrefoil orifices Other non-circular orifices Jet inversion Effect of Cylindrical Discharge Tubes CONCLUSIONS BIBLIOGRAPHY iii Page LIST OF FIGURES FIGURE PAGE 1. Point velocities and secondary flow in non-circular conduits O O O O O O O O O O O O O O O O O O O O 7 2. Storage tank, pump unit and pressure tank . . . . . 9 3. Laboratory where tests were conducted with sprinkler slotted barrel shield in the background . . . . . 11 h. Sprinkler-rotating mechanism. . . . . . . . . . . . 13 5. Angle of taper in a sprinkler nozzle . . . . . . . 21 6. Two types of entrances to the orifice in a nozzle . 27 7. Top view of nozzles with various shaped orifices . 28 8. Effect of oscillating arm.on fallout of water from a medium.pressure sprinkler . . . . . . . . . . . 33 9. General distribution curve from an irrigation sprinkler . . . . . . . . . . . . . . . . . . . . 35 10. Effect of pressure on distribution of water from irrigation Sprinkler e e e e e e o o e o e e e e e 36 11. Effect of orifice diameter on distribution of water no 12. Jet of water issuing at no psi from.a l/h inch diameter circular orifice (using sprinkler with 1/2 inch riser connection) . . . . . . . . . . . . h2 13. Effect of angle of inclination on distribution of water ' s O O O O O O O O O O O O O O O I O O O O 24.6 1h. Effect of angle of inclination on distribution of water ’ ' O C O O I 9 C O C I O O C O O C O O O . u? 15. Interrelationship of velocity head and jet elevation 50 16. Effect of roughness in the cylinder of nozzle on diatribUtion or water 0 e e e e e e e e e e o e o 5“ iv 17. 18. 19. 20. 21. 22. 23. 25. 26. 27. 28. 29. 30. 31. LIST or FIGURES (Cont.) Effect of angle of taper in the sprinkler nozzle on distribution of water . . . . . . . . . . . . Effect of length of cylinder in nozzle on water distribUtion eeeeoeeoeeeeeeoee Effect of length of cylinder in nozzle on water distribution 0 I O O O O O O O O O O O O O O 0 Jet of water issuing at no psi from.a l/h inch diameter circular orifice with cylindrical portion of nozzle removed at the end of the taper section Effect of length of tube between main body of sprinkler and nozzle on water distribution . . . Jet of water issuing at hO psi from a 1/h inch diameter circular orifice with a 6 diameter 6Xt6n810n tube 0 e e e e e e e e e o e e e e e 0 Jet of water issuing from.a l/h inch diameter circular orifice, pressure to psi (using sprinkler with 3/h inch riser connection) . . . Effect of rate of rotation of sprinkler on distribution of water . . . . . . . . . . . . . Effect of rate of rotation of sprinkler on d18tPibUt10n or water e e e e e e e e e e o e 0 Velocity components of water from a rotating Sprinkler e e e e e e o o e e o o e o e e e Forces acting on a particle trajected through air Jet of water issuing from an equilateral triangular orifice at no psi . . . . . . . . . . Jet of water issuing at hO psi from an isosceles triangular orifice with one vertex rounded . . . Jet oowater issuing at no psi from an isosceles triangular orifice with an abrupt entrance into’ the orifice O O O O I O O O O O O O O O O O O Nozzle with gradual entrance into equilateral triangUIRrorificeoeeeooeoeeeeoeo Page 57 59 6O 63 65 68 69 73 7h 76 33 85 88 32. 33. 3h. 35. 36- 37.‘ 38. 39. AO- hi. h2. h3. Uh. MS. LIST OF FIGURES (Cont.) Nozzle with abrupt entrance into equilateral triangular orifice . . . . . . . . . . . . . . . Distribution of water from.an isosceles and an equ1lateral orifice e e o e e e e e e e e e e 0 Distribution of water from square, rectangular and quatref01l Orifices e e e e e e e e e e e 0 Jet of water issuing from a square orifice at no p81 0 e o o e e o e o e e e o e o e e e e Jet of water issuing from a quatrefoil orifice at ’40 p81 0 O O O O O O O C O O O I O O O O O 0 Jet of water issuing at no psi from the nozzle With a Side SlOt e e o e o e e o e e e e o o o Sprinkler with 7/16 inch diameter tubel-l/Z inches long operating at no psi . . . . . . . . Sprinkler with 7/16 inch diameter tube cut off at body of sprinkler operating at no psi . . . . Jet of water issuing at no psi from a 5/16 inch diameter tube with a 3-1/h inch diagonal portion Effect of tube length on distribution of water . Effect of tube length on distribution of water . Effect of tube 5/32 inch and 1/2 inch long in Sprinkler With 1/2 inCh riser e o o e o e e o 0 Jet of water issuing at no psi from a 5/32 inch diameter tube soldered into the sprinkler body . Secondary flow and variation in head at a 90° Short-radius bend . e e o o e e e e e o o e e vi Page 90 93 95 96 99 102 105 106 107 109 lll~ 112 113 116 INTRODUCTION Presentation of the Problem Since l9h6, when less than 250,000 acres were irrigated by means of sprinkler irrigation, this method has spread from a few areas in the United States to the entire country. By the latter part of 195h an estimated 3,000,000 acres were being irrigated with sprinklers, and the acreage is increasing at an estimated rate of 500,000 acres per year. (1) Due to this increase in the use of irrigation sprinklers, and recognizing their ever-increasing importance, Secretary of Agriculture Ezra T. Benson in a letter to Mr. Joseph T. King, Secretary of the Sprinkler Irrigation Association, stated (1): The results achieved by the proper use and applica- tion of portable sprinkler irrigation equipment con- tribute to better management of our water supplies and are further testimony of industry's contribution in opening new agricultural frontiers. The tremen- dous growth in this method of irrigation has created a pressing demand for technical and general informa- tion on the engineering, design, layout, use and application of sprinkler irrigation equipment. Nearly all of the sprinkler systems installed in the past ten years have utilized the revolving head sprinkler. These sprinklers range from the small, low volume, low pressure, single nozzle type to the giant, high pressure, large volume, Inultiple nozzle sprinklers. The most widely used are the Inedium pressure (30 to 60 pounds per square inch) sprinklers (1). These may be either the single or the double nozzle type. Ideally water should be distributed uniformly over the entire area to be irrigated. However, as yet a sprinkler which will do this has not been developed. Since rotating sprinklers cover circular areas. some over-lapping will be necessary for complete coverage of the area to be irrigated, and even then one can only hope to approach ideal distribution. How closely the ideal is ap- 'proached will depend upon the geometric distribution pattern characteristic of the sprinkler employed and upon the spacing of the sprinklers. Under field conditions sprinklers placed on lateral lines are set out in some simple geometric design; lhence, it is necessary for the distribution pattern from the sprinkler to be adaptable to a simple layout. There are two distribution patterns which lend themselves to both over- lapping and to a simple arrangement of the sprinklers: l. A triangular-shaped pattern in which the fall-out is a maximum near the sprinkler and gradually tapers off to zero at the maximum trajectory distance. 2. A pattern in which the amount of fall-out is uniform along the greater portion of the radius and then decreases gradually for the remainder of the trajectory distance. The former pattern lends itself to either a rectangular or triangular spacing of sprinklers while the latter is more suited to triangular spacing. Because many sprinklers presently in use do not give either of the above two patterns, especially at lower pres- sures, and since to date to the author's knowledge no de- tailed analysis has been made to determine what factors af- fect the distribution pattern, it was the objective of this study to determine how the various factors influence the distribution pattern and how they could be improved. Approach to the Problem This study was conducted indoors to eliminate weather variables. Only the mediumppressure sprinklers were studied because this size was the most popular with irrigators and because it lent itself to study in a laboratory. Trends found in the study may be applicable to both high-pressure and low-pressure sprinklers. Only one factor from one sprinkler with one nozzle was studied at one time; in so far as was possible, all other .factors were held constant. Only factors which affect the the bearing nipple of the sprinkler to determine the effect on the distribution pattern when the vertical and the diagonal portions of the sprinkler were the same diamp eter (Figure hO). In these tests the length of the diagonal 3O portion of the tube was varied as in the previously discussed tests. All of the lengths of tube were tested without the os- cillating arm at the rate of one rotation per minute and at a pressure of no pounds per square inch. Wherever tube length permitted, tests were also conducted using the os- cillating arm to rotate the sprinkler. The 5/32 inch diameter tube at a length of one-half inch was also tested at pressures of 20, 30 and 50 pounds per square inch. 31 DISCUSSION OF RESULTS Effect of the Oscillating Arm The action of the oscillating arm caused the sprinkler to rotate and also increased the amount of water which fell out near the sprinkler. When a jet of water issuing from O a circular orifice was not interrupted by an oscillating arm, the minimum fall-out of water occurred near the sprink- ler. From this point the fall-out of water increased until it reached a maximum toward the outer portion of the trajec- tory distance. The rate of fall-out then decreased very rapidly to the outer limit of the trajectory radius of the Jet of water. The action of the oscillating arm was to frequently interrupt the jet of water issuing from the sprinkler. This regular interruption of the jet of water resulted in a considerable increase in the fall-out of water near the sPll’zinkler. The amount of fall-out decreased as the distance from the sprinkler increased until a minimum point was re ached somewhere around the first one-fourth point of the to‘tal trajectory distance of the jet of water. From this minimum point the rate of fall-out again began to increase, reached a maximum approximately three-fourths of the 32 distance along the trajectory radius and then sharply de- creased to the maximum trajectory distance as did the jet of water not interrupted by an oscillating arm. Figure 8 shows diagrammatically the distribution of water along the trajectory radius of a jet of water issuing from a sprinkler nozzle with a circular orifice and operated both with and without the oscillating arm. Since the in- fluence of an oscillating arm on the distribution of water from a sprinkler is dependent upon the operating pressure, size of nozzle, rate of rotation of the sprinkler, fre- quency of interruption of the jet by the oscillating arm, aI‘Igle at which the oscillating arm strikes the jet of water, and several other factors, it was felt that the use of any one particular distribution as an example might be misleading. Hence, Figure 8 depicts a general distribution pattern which might be expected (to a greater or lesser degree) from most medium-pressure sprinklers. ’ As indicated in Figure 8 the distribution curve for a 8Prinkler Operated with the oscillating arm did not rise as high as that for a sprinkler operated without the oscillating arm, This was mainly due to the fact that the oscillating arm deflected part of the jet of water so that it fell near the sprinkler; consequently less water was trajected to that part of the radius where the maximum fall-out of water °°¢urred. .aonCaadm cadmmcadoSdHer w Soho hope: no pzoaawo :0 She mcaueaaaomo no vacuum .w .msm iTIII seem as acamnsacn Sosa concomao (a . a3: ...*v.i ..,. ~33 ........... fi\ - (image i \ i.‘ -fi_- \ 3‘ (“x ..... -HL. . . c... —. H ML-.. ~— I Y ,, .....e‘ i . \ K \ l 4.1”" ._._._ sac wcaeeflacec new: .I .l -4...v_._..y.—H_. p—_. a. .-.... Pa— — F. -.__,,.._..‘. Lia; ‘ ,:ii: UH Sam waspeaaaouo oz -_., o «I‘vin‘i 9' eliiihiix b C . g “deficii- c.-- >—..._ ‘— Ho’s—1r” ._._ ‘ <9——-seqou; u; aeqan JO qqdeq 3’4 As mentioned previously the two desirable types of distribution curves are (l) a right triangular shaped one in which a maximum amount of fall-out of water occurs at the sprinkler and then gradually diminishes to zero at the maximum trajectory radius of the jet of water, and (2) a trapezoidal-shaped curve in which the amount of fall-out of water is constant from the sprinkler to a point some distance along the trajectory radius and then gradually diminishes to zero at the maximum trajectory radius. It may be seen from Figure 8 that neither of the two desired distribution curves was obtained regardless of whether the oscillating arm was used to rotate the sprinkler or it was rotated mechanically. In general the above distribution curves may be expressed mathematically. For this purpose the distribution curve will be broken up into two parts (Figure 9). The first part of the curve will extend in a straight line with a constant slope "m" from the "y" axis to a point where there is a change in slope. From this point the second part of the curve will extend in a straight line with a constant nega- tive slope until it reachesthe "x" axis at point "R", which is the maximum trajectory radius of the jet owaater from the sprinkler. Let I}; be the point along the trajectory radius where the slope of the distribution curve changes and "H" amount of fall-out of water occurs. If slope "m" is equal to or 35 less than zero, a desirable distribution will result; if "m" is greater than zero, a poor distribution will result. f(x) 8 mx +H-mg- 0952:9133 \\ RIP-1] 1751 P X‘R ‘\ Let PH 8 C ‘ e 1531 .\‘\ f(x) = .29. + c ‘ ----------- \ , R / / / x = any distance along // / ~ ,_~_ trajectory radius R 0L, I 4— t y = depth of water at any 3 X R point along R, trajec- p tory radius Fig. 9. General distribution curve from an irrigation . sprinkler. Effect of Operating Pressure For the pressures tested in this study, it was found that the higher the pressure, the more desirable the distri- bution. A higher pressure caused a greater break-up of the Btream of water as it left the nozzle. This breaking-up ef- fect of the jet was apparent for the range of nozzle sizes 8tudied. Also, as the pressure was increased, a greater trajectory‘distance was obtained. The drops of water appeared amfiller at the higher pressures. I Figure 10 shows that the difference between the maximmn and. minimum points of accumulation of water were very 36 .aoaxssadm coepwwazaa Bozo seen: no compassaumsc so cadences mo pomoom .OH .msm poem as acaxcsaam Soho consumao H ........ ........ .................................. ............... ...... ...................................... .............................................. ............ ................. o-‘o" OI’O seqou; u; Jeans JO wideq ...... ...... ......... ..ac ..... .1 o ......... .coapooacoo memes some m\H has: aeflscaaam Sam .omo on .Eca H .Hmc on .oauuos gha\mll ul. .Sam .oeo on .Eaz H Jud om .eansoc chH\ml.x.l. sue msmpmaaaomo .aen :N .Hmc oo .oanuo: :oa\mnl..lu Ens wcflpeaaaomo anon mm came on codewofi :oH\MIlllll ..... 37 pronounced when using a sprinkler with a one-half inch riser and a.three-sixteenths inch diameter nozzle, and operating at a.pressure of 30 pounds per square inch both with and ‘without the oscillating arm. When operating the sprinkler 'with.the oscillating arm, the decrease was as percent; with- out the oscillating arm, the decrease was 82 percent. When the sprinkler was operated with the same nozzle but at a pressure of 60 pounds per square inch, the percent of decrease 'with the oscillating arm was 15 percent, and without the os- cillating arm it was 60 percent.1 When operating the sprinkler at a pressure of 60 pounds per square inch with the oscillating arm, the maximum fall- out instead of occurring in a very short distance in the radius (in other words, coming to a peak as in the previous test) extended from 20 feet to 32 feet from the sprinkler. It then dropped to almost zero inches of water in the next 10 feet. The rate of decrease was about 0.01h inch of water per foot. The minimum.occurred at about In feet with the total low extending from 10 feet to 20 feet from.the sprinkler. In the distribution curve for the sprinkler with an os- cillating arm operating at a pressure of 30 pounds per square inch, no flat portion existed at the maximum. The minimum extended from a point 8 feet from the sprinkler to about 2k feet from the sprinkler. The fall-out of water then increased 1The rates of rotation for 60 and 30 psi with the oscil- lating arm were 2k and 25 seconds per rotation respectively; without the oscillating arm, the rate of rotation was 1 rpm. 38 quite rapidly, reaching a peak 30 feet from the sprinkler. After the peak was reached, there was a rapid decrease (about 0.0175 inch of water per foot) in the rate of fall-out. When operating the sprinkler without the oscillating arm, the peak for the higher pressure was 0.115 inch of water; for the lower pressure it was 0.180 inch of water. This was a very significant increase since there was over 14,0 percent more water discharged at a pressure of 60 pounds per square inch than at 30 pounds per square inch. As may be seen in Figure 10, the trajectory distance was increased only five feet by raising the pressure from 30 to 60 pounds per square inch when operating the sprinkler without the oscillating arm. The higher pressure caused a greater dispersion and break-up of the discharged stream of water re- sulting in smaller drops. Because the distance of travel of a drop of water is proportional to the size of the drOp,l Very small drops travel negligible distances. At high pres- surea which cause an excessive break-up of the jet of water, a further increase in the pressure may result in a decrease 0f total trajectory distance. However, the smaller drops re sulting from the higher pressures tend to have a less dele- tereous effect upon the soil due to their smaller impact. \ 1See equation (1) under Effect of Rate of Rotation. 39 Effect of Orifice Diameter There is a correspondingly greater quantity of fall-out of water along the trajectory distance from a larger diameter nozzle than from one with a smaller diameter operated at the same pressure. Hence, it would not be correct to make a direct comparison between the points of maximum and minimum accumulation of water from the different diameter nozzles. It seems much more reasonable to compare instead the maximum and minimum points for each particular diameter. When a sprinkler with a one—half inch riser connection was Operated with a one-eighth inch nozzle at a pressure of 1+0 pounds per square inch and was rotated by means of the oscillating arm at the rate of 103 seconds per rotation for one hour, the maximum fall-out was 0.075 inch,of water at 36 feet from the sprinkler and the minimum accumulation was was 0.011 inch of water at 16 feet from the sprinkler (Figure 11). This was a decrease of about forty-seven percent. Using the three-sixteenths inch nozzle and operating the a[Drinkler for one hour at a pressure of 14.0 pounds per square inch with the oscillating arm and at a rate of 92 seconds per rotation, the maximum accumulation of water was 0.115 inch at 30 feet from the sprinkler and the minimum accumula- tion was 0.11 inch at 20 feet; a decrease of about twenty-four Parcent. From this it may be seen that use of the nozzle hO .Aopwz we Soapsnaapmam no acpoSaHv ooaMHao M0 poouum pooh Ga acHxCHQQm 80am communan N .coapooqcoo Amman coca «\H on» new: soaaaaeam Sac .omo Spa: .Adn No .HH .«ma 0: .eaunoc =@H\MII_II., .omo new: when moa .«ma 0: .eanao: :m\JAI|¥II Sam .omo o: .Sda H .Hmd om .oauuo: :o\m Ital: . Sad .omo o: .Eda H . .amc om .oauaoc :©\H.llllu I . v m _ .mam seqou: u: Jeqen JO uqdea bl with the larger diameter orifice resulted in a more desirable distribution. When the same two nozzles (one-eighth and three-sixteenths inch diameter) were compared at a pressure of 30 pounds per square inch and without the oscillating arm, the nozzle with the three-sixteenths inch diameter again gave the better dis- tribution when the percentage of decrease of the minimum from the maximum accumulation is considered. The decrease here was eighty-five percent for the larger and ninety per- cent for the smaller size nozzle. It should be pointed out that the larger diameter nozzle was operated in what is con- sidered by sprinkler manufacturers to be an unfavorable pres- sure range. When a one-fourth inch diameter orifice was drilled into a nozzle for a one-half inch riser connection sprinkler, the distribution was improved still further (Figure 12). At a Pressure of 140 pounds per square inch and operating with an oscillating arm at the rate of 12h seconds per rotation, the decrease of the minimum from the maximum accumulation of Water was only fifteen percent. The trajectory 'distance in this instance was 142 feet. Tests run on the sprinkler with the three-fourths inch Piesr connection showed the same trend; however, it was not as pronounced (Figure 23). This size of sprinkler used a no2.2:.le with larger outside dimensions than those of the E Fig. 120 Jet of water issuing at no psi from a 1/h inch diameter circular orifice (using sprinkler with 1/2 inch riser connection . #2 #3 nozzle used by the smaller sprinkler. This resulted in a much greater length of taper in the nozzle of the larger sprinkler. The angle1 of taper for both nozzles, however, was the same; but, since there was much more taper length in the nozzle with the greater outside diameter, there was more guidance for the water through this nozzle when the same diameter orifice was used in both nozzles. Another point worth considering is that in the larger sprinkler the bend was more gradual and the distance between the bend and the nozzle greater than in the smaller sprinkler. These three factors, amount of taper, bend of sprinkler and distance between the bend and the nozzle,2 overshadowed the desirable characteristics of the higher angle of inclination of the nozzle of the larger sprinkler and resulted in a poorer dis- tribution of the water. The reason that a larger diameter opening in a given nozzle gave a more desirable distribution can best be des- cribed in this way: as the size of the orifice is increased, the length of the taper in the nozzle decreases until the nozzle approaches a tube. Since the sprinkler with the larger nozzle had a longer taper or cone leading toward the cylindrical opening, a much larger opening was required in it than would be in a smaller sprinkler nozzle in order to 12h-degree angle. These factors are discuSsed in more detail in another part of this study. approach a tube. It was found in another part of this study that a tube gives a more desirable distribution than a nozzle) especially when the discharge end of the tube is near the bend of the main body of the sprinkler. Effect of the Angle of Inclination of a Nozzle The angle of inclination of a sprinkler nozzle from the horizontal had a significant effect on the distribution or water. In Figure 13 a sprinkler with a one-half inch riser connection and a one-eighth inch nozzle was operated Without the oscillating arm at a pressure of thirty pounds Per square inch and at the rate of one rotation per minute for one hour. The angle of elevation was altered from 15 degrees to 30 degrees from the horizontal in increments of five degrees. At 15 degrees the maximum trajectory distance was about .30 feet with a maximum of 0.25 inch of water at 28 feet. With the sprinkler nozzle at a 20 degree angle of inclina- tion, the maximum trajectory distance was 31;. feet with a maximum of 0.175 inch of water at 32 feet. When the angle or inclination was 25 degrees from the horizontal, the maxi- mum trajectory distance became 38 feet with a maximum of O. 126 inch of water occurring at 35 feet. A 30 degree angle or inclination of the sprinkler nozzle resulted in a maximum 1+5 trajectory distance of 14.0 feet with a maximum accumulation of 0.12 inch of water occurring at about 36.5 feet. The rate of decrease from the point of maximum accumu- lation of water to the maximum trajectory distance was 0.12, 0.08, 0.014 and 0.03 inch of water per foot at an angle of inclination of 15, 20, 25 and 30 degrees respectively. It is significant to notice that the maximum accumula- tion of water decreased as the angle of inclination of the Sprinkler nozzle increased. The same trend is shown in Figure 11;. The tests depicted here were run at a pressure of 20 pounds per square inch. At this low pressure it was Possible to raise the angle of inclination of the sprinkler nozzle to 35 degrees from the horizontal without the jet or water hitting the ceiling. As indicated in Figure 1h a 35 degree angle of inclina- tion gave a more desirable distribution than a 30 degree angle. As stated previously it was not possible at the loca- tion in which the tests were conducted to test a larger angle or inclination because of the ceiling limitation. It should also be noted that as the angle of inclina- tion increased, the rate of decrease was diminished. That 18, the difference between the points of maximum accumula- ti on of water is not as pronounced between 25 degrees and 30 degrees as it is between 20 degrees and 25 degrees. From the tests that were conducted it could be deduced that a no degree angle of inclination would given an even h6 ........ . . .pepmz no Coausnwsumfio Go Goaumcaaocd mo oncm no vacuum .MH .wsm seem as poaxcaadm Scam occapmso om ........ ....... ...... ........ ..... ...... on .... ........ .......... ......... ..... ..... .... .......... ..................... mm as ea ...... ....... ‘w‘1_..wyx we om pa eopaaoeo one cannon nose m\H one soapooccoo meat noes N\H spa: amHaCaaam : = omH IIXII : : oON 1.01 z 2 elel 11 Hmpcoudaon Souk eon IIIII ....... 0H ...... foo t0 of seqout up Jeqem JO q; OZ’O deq 117 .souwz no aofipdnHApmHo so Compassaocfi mo mamas mo poommm .da .wam poem as aonCAadm Sosa oocwpmso .1 ..v c 4... .... ..y. .... ... ,... .... .... ..0. .. .5. . o... .v.. ....... I . . .... .... .. . . ........ .... . . .... ... .... .... .... o... . .. .... ...... v.- ‘ll i .... . I. . .. .... I‘ll. .. 1111......» an em on em mm ma ed as . e ‘1 ... .-1... SO'IOi, I. .. -n.-41-. Efix 1 ‘t.':' C‘ \ ‘\ ”V "‘1 L. ("it s..- » ~ ot'o —-1 - -—---41~v»--—o—u—.-. p." .. :1: \ . i I'..‘__.. w «an-9 \ x it o .. . . , . . .. .. .. . ... .....,. . .. ..i .. 1". . . ... .... ,. .1.-i....-.c ..,.... . v . . :. . . .. ......... . , . ..., , . . .. ,...y . . ......... . .. v. ... ....... . a. ., . . . . .,.... .. . v 4 . .... .............. .. . . ..v.,. . .. I, 1' ...- . . . . .. . ,. . ,.. wifl_.fl_h..m....‘..,fl-._._M..L. \. ....M.... m\e ea. costume... to... some «\H has: coaxcaaam .pH.;. 02 0" h a H H M x:. ,..., . . a o no _. U \x e,,;.:..; oepwaodo one cannon and my”: w ,:.:.... w M w in.....hxwwwh_z __ . : : oON llxll ; vmmmnm ’ \ w G, . , . . = : OmN 11011. ~. . ‘. . . .om .1: II dF" .»M.V.H . 1. a.pgouesoe gone .mm “'4 LM“*—‘— ’ ‘ ‘ *‘0-0—0-4 - ' 1 ‘ m‘. L ‘ ‘ ~‘ —— ——d¥ --y~—~‘- >-—-—— ymau—h— h.—.. p... .—-.—_ .LULW4 seqou; u: JGQBM JO qqdeq 148 more desirable distribution than the 35 degree angle. How- ever, it should be remembered that according to the pattern established above, this rise of five degrees in the angle of inclination will have a less pronounced effect on the distribution than the five degree difference between a 30 degree and a 35 degree angle of inclination. It was also found that pressure modified the effect of the angle of inclination. That is, at 35 pounds per square inch the difference between a 30 degree and a 25 degree angle of inclination from the horizontal was not as pronounced as it was at 30 pounds per square inch. When Figures 13 and 11.4. are compared, the same differences may be seen between the tests run at 20 and at 30 pounds per (square inch, but the angle of inclination was much more critical at the lower pres- sure than it was at the higher pressure. The tests.also in- C11 cated that the first 16 to 20 feet from the sprinkler were not: appreciably affected by the change in angle of inclina- tion of the sprinkler. Under field conditions the higher the trajectory angle, the more opportunity the wind would have to affect the distri- bution of the water. There are two reasons for this: 1. The higher the angle of inclination, the longer the droplet of water is in the air, thus affording the wind more time to influence it. 2. The higher the angle of inclination, the greater the trajectory height; and since the wind velocity increases 119 Ni th height, this higher velocity would have a greater effect on the distribution pattern. Hence,it would appear that if wind conditions are taken into account, the optimum angle of inclination of the sprinkler nozzle might be about 35 degrees from the horizon- tal. However, before any definite conclusions are reached, these tests should be conducted under field conditions. 'In order to explain the difference in distribution and trajectory distance at various angles of inclination, it VVCHlld be desirable to consider the kinematics of‘a projectile in flight. Consider the water leaving the sprinkler nozzle as a series of projectiles. These projectiles will have various masses and velocities. The angle of inclination of the sprinkler nozzle from the horizontal will be designated as 6. Hence, the water leaving the nozzle will have an angle 6 from the horizontal. Neglecting the effect of air resistance, the equation of trajectory, the range ”R” on a horizontal plane and the maximum altitudes "h" (in feet) reached in flight by any drop of water will be determined. Solution: With the air resistance being neglected, the only force acting upon the water droplet is its weight; hence, the acceleration at all times is due to gravity "g" directed vertically downward (Figure 15). Thus, ax = Ouand ay 2 -8- 50 Fig. 15. Interrelationship of velocity head and jet elevation. The resulting motion, then, is a superposition of two rectilinear motions with constant acceleration. 'With zero axzceleration in the "x"-direction, the horizontal distance tzraveled equals the constant horizontal component of velocity nnaltiplied by the time. Thus, x = ut cos 6 {File "y"-coordinate of the projectile may be stated as ‘ y=ut sinG-l/2gt2 {Pile equation of the trajectory is obtained by eliminating the "13" between the two expressions and is r y = x tan 6 - __E§E___ Zuzcosze Tile range "R" is obtained by equating the above expression rOI’ "y" to zero; hence, o=x(tane-—TK——xae) 2u cos 51 The above has two solutions: x = 0, which is of no concern; and x = R = 2uzsin9cos6 = u2s1n29 (l) 8 8 ' The maximum range occurs for sine26 = l, or 6 = 115 degrees, and is 2 Rmax .2. 8 The time of flight for the range "R" is obtained by letting y = o = t(u sine -11/2 gt) t = 2u sin 9 (2) 8 The maximum altitude is 2 2 2 2 2 h=y=u sine-gusin6-gsin26 (3) a 2 g? ‘ 23 From equation (1) it is apparent that for any water droplet leaving with velocity "u", the maximum distance "R" will be obtained when 6 is 14.5 degrees. Any angle smaller or greater than 15 degrees will decrease the distance. Equation (2) indicates that as the trajectory angle 9 18 increased, the time "t" that the drop will be in the air "1 ll be increasing until 0 is equal to 90 degrees, at which pOint the time will be a maximum. The altitude "h" for any angle 0 is indicated by equa- tion (3). The maximum altitude will be attained when 9 is e++ «ow-4ft- , .. .. , . ., J . . . a o 1 . . 7‘ . V ...... um seawaodo was caused some ....... oomH.o one Cospoennoo semen . coca :\m and: soaseauam .aam co .Eam .ono on camocmpellbxll .adm or .Saw .omo on .oosoanoAII .l. .adm moa .Sae -... -1-.. H, .ono and; oasecwumllall .aam moa .Sae .omo new: oocosmdoa is? ....... T'o _¢ -o -~<——- seuout u; JGQBM JO qqdeq z'o " . ._ T_._...._ fl _ . , ...,. *\ .. . 1* .. ~ , . . .. . 1... .... 11 .1 -1. .. . . ..—. .. .. ,, ._ _ . . . . . , 7...... 9-- .__‘, . ¢ I . ~ . . b—‘m ' ~ “NM rotated by means of the oscillating arm, where an excess of water due to the action of this arm usually occurs near the sprinkler. Roughening the inside of the nozzle changed the drop size distribution. The drops of a size that normally would fall out in the center portion of the trajectory radius were fewer and hence the fall-out in this portion of the trajec- tory radius was less than in the unroughened nozzle. How- ever, a greater amount of fall-out both near the sprinkler and toward the outer trajectory radius resulted. Houghening the nozzle changed the velocity distribution of the water through the nozzle. This change was reflected in the distri- bution pattern. Effect of the Angle of Taper in the Sprinkler Nozzle All of the tests in this part of the study were con- duoted using a sprinkler with a three-fourths inch riser Connection and nozzles one-eighth and three-sixteenths inch in diameter both with and without an extension tube and operating at a pressure of 14.0 pounds per square inch W1thout the oscillating arm at the rate of one rotation per minute. It was found that as the angle of taper was increased (that is, approached a sharp-edged orifice) the total 56 trajectory distance decreased. The amount of this decrease between 12 degrees and 80 degrees was about two feet. When the one—eighth inch diameter nozzle was used without the extension tube, there was little difference in the amount of fall-out of water in the first 16 feet from the sprinkler between the various angles of taper in the nozzles tested (Figure 17). Beyond this point, the fall-out of water in- creased as the angle of taper in the nozzle was decreased; that is, at the point of maximum accumulation of water, Which was between 31;. and 36 feet, the amount of fall-out from the nozzle with the 80 degree taper was about 0.07 inch, while from the nozzle with the 12 degree taper the 8«mount of fall-out was almost 0.09 inch. The same general Pattern of distribution of water resulted when the three- Sixteenths inch nozzle was used. When the extension tube was used, the same trend re- 8tilted; however, the total trajectory distance of each of 1She angles of taper tested was increased by about two feet. As the angle of taper in the nozzle was decreased, since the distribution curve rose to a higher position and the trajectory distance increased, more water was being dis- calarged. This agrees with the known fact that the coefficient or discharge must increase as the angle of taper is decreased. Henee, although the nozzles with the larger angle of taper 1mProved the distribution of water, this improvement was S7 .aoamz mo noHudnHaumHo so oHNwoa noncHAQm can GH sedan no chcm on» no poeuhm poem CH aechHacm Bonn oocwanm .Sda H pa Hmd o: as pepmaedo one oHNnoc nosH m\H one :oHpoessoo aana noun. a spa: aeHsaeaem .NH .3 coo .LH .maa seqou; u: JGQBM JO qqdeq 58 not justified in view of the resulting lower coefficient of discharge . Effect of the Length of the Cylindrical Part of the Nozzle It was found by varying the length of the cylindrical part of the nozzle that the shorter cylinder yields a more ' desirable distribution of water. Figures 18 and 19 give a representative illustration of the “effect of shortening the cylindrical part of the nozzle. These figures contain data from only four different cylinder lengths for a 9/614. inch nozzle. However, as discuSsed in the Method of Procedure, tests were also conducted using a one-quarter inch diameter nozzle and a one-eighth inch diameter nozzle. All of the 1Sests indicated the same trend shown in Figures 18 and 19 in which a 9/614 inch diameter‘nozzle was used. In these tests the sprinkler was operated for one hour without an oscillating arm at the rate of one rotation per minute and at a pressure of 30 and 50 pounds per square inch respec- tively. In all the tests conducted, the nozzle with the 1Ongest cylinder gave the poorest distribution. The greatest improvement in the distribution resulting from the decrease in the length of the cylinder occurred in about the first two-thirds of the total trajectory distance (Figures 18 and 19). When using the nozzle with the cylin- dep three diameters long, a fall-out of about 0.03 inch 59 .cOspanppeHo seam: Go eHNNoc CH aeocHHho ho npmceH no poemum peek GH aeHxCthe Bonn ecceueHo a . O t 5 v . » . . . . . . . . . e . . . o 1 v . . . . , . . . . u . § 5 . t a I . . n . A . v . . .000 c.........s$ o... .p.. vo.. ..... ...... . . ., .. .... .... ... o. ...,. . .e..... ... 1 . ....-.a ... ... . .coHpoescoo aechHade nemHa nocH :\m sz3 one. See mcheHHHomo esp psoanz .Sda H one eHNuo: nocH ..»‘.M.mmee\o as“: and om pa emuasmao o.:n.:| H loll 8 8 .. all enepeSeHo m .mH .eaa OH OI'O ..t.0fl. so-o' seqou: u; JGQBM JO qqdeq 60 .GOHaanhpeHo some: do eHNNoc CH aeocHHmo no numCeH mo poemmm .OH .mHm poem CH aeHstade Some eczepmHn 0: on . mm m :m om H . NH. . .m \‘1a. r o .. . . ., ...,. . .. , ..... .. .................v. , . .. .y. .. .. . ..... .. .. ... .. . .. ... :.. . ...: .1. .... ...f \ ... . .... ... .. .. . ..... . . . .... ....... .... ...\.... x. .. . . . I|I IR ‘ ... .... . ... ._ ... . ... .... . .. .. . .-. .. . ... .. . ... . .'Il\ \ g. x SO 0 1L; »‘ K: \‘ I. " deq I“ ;:\\ . :11: . ‘\.'.'.;::' 1V \. r’f 332/1”;2?3¥i 1,/ . ,/ . / . “: ; \ 11L; \ :g1 \\ \ I'O ---¢v/ \\ /: '1“ \ y H- j [zip ... - ...._,..._. - .... ....4 ...... -.H .... -4»...‘o—>—«‘._.-... _._._,..w._.—. .0 .1 e . st-o . --—-(>—- ..- seuout u; Jeqem JO qq .Eae mcheHHHomo esp H.“ psoanz .Edn H one eHuuoc ,y.. ...... ,;H;..,.t_.u . a.poeaae nose ee\o and: H; . ....... M...l.:. .p and om a. mess one: mesa HH< .. ,.._;mn..» 8’0 maepeEeHo o .le . n mhmpmgdfifi N 1.1011 n .. m; If” . l maeueEeHo 0 all III . i , n . s;:waL msoaoaaae NH pm-4>—~—.~ . p_..-N , W. .__._,_._. .— . _. 1 1 1 - 1 ...“ 1 61 of water occurred 18 feet from the sprinkler; while from the nozzle with the cylinder zero diameters long, the fall-out at the same distance was 0.0h5 inch of water-~an increase of about fifty percent. There was an increase of thirty percent in the amount of fall-out from the nozzle with the cylinder zero diameters long over that from the cylinder one diameter long (Figures 18 and 19). The curves for the cylinder lengths not shown in Figures 18 and 19 fit into the pattern estab- lished for the plotted cylinder lengths. The accumulation of the water toward the maximum tra- jectory distance was minimized by shortening the length of the cylinder. As indicated by Figures 18 and 19, the total trajectory distance for the nozzles with no cylinder as com- pared with those with a cylinder was shortened by one to two feet. Nozzles with cylinders 17 diameters long shortened the total trajectory distance by two feet from that produced by nozzles without a cylinder. This shortening of the trajec- tory distance was due principally to the high friction losses resulting from the high velocity1 of flow through the long cylinder. The increased amount of fall-out of water along the trajectory radius as the cylindrical part of the nozzle was shortened can be explained by considering the flow of water 1Approximately 65 and 85 feet per second through the 9/6h inch diameter nozzle at pressures of 30 and 50 pounds per square inch respectively, with a pressure drop of about 1 foot head of water at 30 psi and 17 diameters length. 62 through the nozzle. The stream lines converge through the tapered part of the nozzle toward the center. If the cylin- drical part of the nozzle is of considerable length, the ‘kinetic energy of the resulting excess turbulence will be dissipated through viscous shear and the effects of the ‘transition upon the velocity and pressure distribution no longer will be noted, and the stream lines will become parallel. Hence, the water coming out of the nozzle will be in a direct line with the cylinder walls. If, however, the nozzle consists of only the converging taper and no cylindrical portion to straighten out the converging stream lines, the jet of water emerges from the nozzle in a conical Arather than a cylindrical shape; that is, the water fans out fronlthe orifice. This cone is mdnimized by the surface tension of the water, yet much unsteadiness does exist with a breaking away of some of the drops. These drops fall nearer to the sprinkler than they would if the jet of water was not as turbulent. Figures 20 and 23 show the contrast in the breakup of a jet of water leaving a nozzle with and without a cylindri- cal tube. Both nozzles had an orifice opening one-fourth inch in diameter and both were operated at a pressure of no pounds per square inch. The hydraulic losses through a nozzle without a cylin- drical tube will be less than through a nozzle with a cylin- drical tube. Friction losses will be increased by the 63 . Jar-MM" ' i . Pig. 20. Jet of water issuing at no psi from a 1/h inch diameter circular orifice with cylindrical portion of nozzle removed at the end of the taper section. 61+ additional length of tube and by the dissipation of the kinetic energy of the excessive turbulence in a confined space. Effect of the Length of the Tube Between the Body of the Sprinkler and the Nozzle The effect of the length of the tube between the body of the sprinkler and the nozzle upon the distribution of water is shown in Figure 21. A sprinkler with a three-fourths inch diameter riser connection was operated without the os- cillating arm at one rotation per minute and at a pressure of 35 pounds per square inch using a nozzle one-eighth inch in diameter. The diameter of the inside of the tube was seven-sixteenths of an inch. This resulted in a mean velocity of the water through the tube of about seven feet per second and a Reynolds number of about 18,000,1 indicating that the flow was in the turbulent range. For a tube length of l? diameters, no measurable fall- out of water occurred in the first ten feet from.the sprink- ler. After operating for one hour, 0.010 inch of water was measured 20 feet from.the sprinkler and 0.02 inch of water 0 26 feet from the sprinkler. 1Sixty degrees F., temperature of water. .coapsnanumfip gene: co cannon emu 6cm aeaxcHadw mo hoop Gama neezuen and» Ho summed Mo poommm .HN .wam poem ca heaxcanam Sony commumun 65 .Eaa H as .oauuoc Sosa m\a one .coapooccoo aonaA.: mesa :\m e and mm we amaze“ cadmzopwo nae: eves mass HH< : a O ..l. c N II. o lxl. naeuwsddo ea A .I . ST'O OI'O SO'O OZ'O seqou: u; Jones 30 qqdea 66 1 In testing the sprinkler with no tube length the readings were 0.015 and 0.03 inch of water at 20 and 26 feet ruespectively after a one-hour run. This represented an in- crease of fifty percent in the amount of water measured at knoth of these distances over the amount measured at the same <1istance from.the 17 diameter tube. The major difference between the longer tube and the shorter one was the lengthening of the total trajectory .. .... e... . . .¢.. to .... .o-o . ...: .... ‘e o .- ...: .«.. . L. . .. ...- o u .. ... . o u to c- . .-e 1| 0. ... .... .. . v09. m u H .\\51. Hwy—-...“ te~ . . , ‘fiflg -\i6‘ bro IX. >~- Hw4_*.__ - ...... 7 -y—hh’ —. ........ cauuoc Sosa oa\m a and: ugamd on we eopeaodo Goauoonsoe onus soc“ m\a as“: sodaeasam he» new nan ..... ..... .. 51-0 . seqout ut Jeqen JO qqdeq OZ;O._ A l a . 75 For the medium-pressure sprinkler, it would seem that the rate of rotation should be less than one rotation per minute. It would appear that a rate between one rotation every 120 and every 214.0 seconds might be the desired range since between 2110 and 550 seconds any change in trajectory and maximum accumulation will be negligible. For high-pressure Sprinklers, which are capable of a greater trajectory dis- tance, the rate of rotation should be slower than for medium- pressure sprinklers. At this point some mention should be made of the reason that the trajectory distance decreased as the rate of rotation of the sprinkler increased. Analyzing the velocity relationship vectorially will show that the decrease in trajectory distance cannot be accounted for by the tan- gential component of velocity. The distance from the center of the sprinkler, or the center of the rotation, to the end of the nozzle for the sprinkler in Figure 26 was 1.25/12 feet; hence, at the rate of one rotation every three seconds the tangential velocity at the discharge end of the sprinkler nozzle was VT = 21rx if? x% = 0.22 feet per second The mean radial velocity "VI," of water was 60 feet per second. The rosultant velocity "v5" (Figure 26) will be only a negligible amount greater than the radial velocity ”Vr" since 2= 2+ 2 VB vT vr 76 1.25" fig—'7“ v, = evil/sagsflll. 9 “ ii i, ~ .. ”1'5: ” R eéo -~ , I ’t \2 ”/5“. 7)? 0 Fig. 26. Velocity components of water from a rotating sprinkler. and VT2 was 0.(1l8 feet per second. It is evident from the above tunat as the rate of rotation of the sprinkler is increased, tflae resultant velocity also increases, and that consequently, ‘theoretically, the trajectory distance should also be in- careased. Actually, however, the trajectory distance decreased .as the rate of rotation was increased. Since an increase in tangential velocity should theoreti- cally cause an increase in the trajectory distance, there Inust be another reason why the trajectory distance is short- ened by rotating the sprinkler. In a solid jet of water, iflne maximum air resistance or drag encountered by the water CH3curs at the surface of the jet. The magnitude of the drag Ccnltinues to decrease toward the center, at which point it 1&3 a minimum, since there it may be assumed, there is very liirble or no air to offer resistance. However, at the very Periphery of the jet, the air completely surrounds the jet andismotionless until the water moving through it causes 77 it to move.1 This contact of the moving water with the stationary air causes a maximum amount of drag on the moving water particles, but at the same time it accelerates the air in the same direction in which the particles of water are moving. It can be further concluded that as a stationary jet moves-through a medium,(in this instance, air) the velocity of the water and of the air at the outer surface of the jet come into equilibrium at the face of contact. Once this equilibrium is attained, a minimum amount of drag on the jet of water will ensue. If, however, the jet is not solid, but is instead a broken-up mass of water drops, a great deal of air is dis- persed between the drops, and the surface of each individual drOp is acted upon as in the above described solid jet. Hence, when equilibrium conditions are attained between the air and the water droplets, the whole mass of air between the dispersed droplets is caused to move at some velocity approaching that of the water in the jet. At this time the resistance of the air to the moving water droplets will be a minimum and consequently the trajectory distance will be a maximum. However, if the jet of water is continually made to change its position in space, it will not be in equilibrium, ¥ lWhen smoke was introduced into a steady stream of water, velocities of about 15 feet per second could be measured with a 3 tOp watch. 78 and the drag will no longer be a minimum but will be in- creasing with the rotational velocity until each drop acts as if it were moving through relatively stagnant air. Under this condition, maximum drag will be encountered and the trajectory dis tance shortened. It is possible to compute the theoretical distance that a drop of water of any given size will travel when trajected at any angle from the horizontal and taking air resistance into account. Although the velocity of the water issuing from a sprinkler nozzle often exceeds 100 feet per second, this is still within the range in which the air resistance can for a close approximation be con- sidered to be proportional to the first power of the veloc- ity (8). The distance that a drop of water will travel in any direction can be found from Newton's second law of mOtion as shown below. In these derivations the origin Was considered to be at the orifice (Figure 27). Fig. 27. Forces acting on a particle trajected through air. 79 horizontal distance vertical distance velocity mass time air resistance constant ll <; x = 0, y = 0, V c+ ll 0 <; II x Vo cos 00‘ y Vo sin 90 < II 0:13ch <‘4 H Tfime mathematical development of the equation for the dis- tance traveled by a particle in the “x” direction is 2 A 722.5 a -R cos 6 at?- :0 ll cV a. H II I <20 3 The above constants may be evaluated from the initial boundary conditions. Hence, x = m :2 E'vo cos 6 (1-e mt) (1? Tube distance traveled in the “y" direction is dt V R = cV E911+¢91=m8 dt dt + (313):! = mg 80 -.- '°t' - ffhe above constants may be evaluated from the initial boundary conditions. Hence, 2 - 2 t y §V° sin e (1-. at) + gag) (i-e'fi ) - 33“ (2) The time “t” can be found from equation (2) by letting y s 0 and solving for “t” as shown in equation (3). c ' t m 2 “ct - ‘m -+ o - % V0 sin 0(1 0 ) $05) (1 e m) 335815 z o (3) Using the above equations, the distance traveled by a drop of water can be calculated if the ratio ofvg'is known, since the other factors can be determined readily. When the sprinkler was operated at a pressure of 30 pounds per square inch with a three-sixteenths inch diameter nozzle and rotated at the rate of one rotation every three seconds, the diameter of the largest drop was found to be about three millimeters at the maximum.trajectory distance of 30 feet from the sprinkler. The mean velocity of the water as it left the sprinkler was 60 feet per second under the above operating conditions. In this instance the angle of trajection was 2h degrees from the horizontal. Green (9), using Laws' (10) data on the terminal velocities of water drops, calculated values for the ratio of«% for drops having various diameters. For a water drop three millimeters in diameter the ratio oflgrwas found by- 81 Green to be 0.82. Substituting these values in equation (3) the time 't' was found to be 1.2 seconds. Substituting all of these valued in equation (1), the maximum trajectory dis- tance “xl'was found to be 3h feet. This concurs fairly well with the actual distance which was 30 feet. Green found that as the diameter of a water drop ap- proached zero, the ratio of.% also approached zero. There- fore, from an examination of equation (1), it is apparent that a decrease in the drop size results in a shortening of the trajectory distance. Effect of Non-Circular Orifices in the Sprinkler Nozzles Since all of the non-circular orifices in the nozzles tested here were shaped manually, it was not possible to obtain perfect replicas of the desired shapes. This was especially true in nozz1es in which the non-circular shape extended a considerable depth into the nozzle. Such irregu- larities in the nozzle usually resulted in the emission of unsteady jets of water. Where the non-circular orifice was nothing more than a sharpéedged orifice (i.e., the irregular shape did not extend into the nozzle for any depth), precision of workmanship had a lesser effect. Imperfections which the author believes were due to workmanship will be pointed out. In this study of the non-circular orifices the nozzles were not changed so as to deposit the water at any particular 82 point along the distribution curve, but rather an attempt 'wgs made to make the orifices as symmetrical as possible and to report the data obtained without making any further changes in the nozzles. Triangular orifices. Of all the non-circular orifices tested, the triangular gave the most desirable distribution of water. This was especially true when the triangular shape extended some distance into the nozzle; that is, when it was not a sharp-edged orifice. In all of the tests con- ducted in this part of the study, the nozzle was inclined so that the jet of water would be issued at about 25 degrees from the horizontal. As may be seen from Figures 28, 29 and 30, the jet of water1 came out parallel to the walls of the orifice. This resulted in a trihedron-shaped jet of water, the apex of which appeared to be back in the orifice of the nozzle. The size of the base of this jet increased rapidly with the dis- tance from the orifice. As can be seen from the above figures, this jet of water spread out rather quickly as com- pared to jets of water issuing from circular orifices. The walls of the above triangular orifices were made as parallel as was manually possible. The top view of the nozzles used in Figures 28, 29 and 30 is shown in Figure 7.2 The nozzle used in Figure 28 had 1The operating pressure was 40 pounds per square inch. 2The first, second and third nozzles from the left side in the bottom row. 83 Fig. 28. Jet of water issuing from an equilateral triangular orifice- at no psi. 81+ Fig. 29. Jet of water issuing at )40 psi from an isosceles triangular orifice with one vertex rounded. F180 30. 85 I : 9’; , 0.. Jet of water issuing at no psi from an isosceles triangular orifice with an abrupt entrance into the orifice. 86 an equilateral triangular-shaped orifice in which each side was one-fourth inch long. The parallel sides extended about three-eighths inch back into the nozzle where they gradually began to diverge. , Figure 29 shows a jet of water issuing from a nozzle with an isosceles triangular-shaped orifice in which one of the apexes was rounded out. The two equal sides of the triangle were 7/32 inch long, and the base was 6/15 inch long. These sides extended three-eighths inch into the nozzle and as in the previously described nozzle gradually diverged. In both of these triangular shaped orifices the jet of water formed a solid stream. 8 The shape of the orifice used in Figure 30 was an unmodified isosceles triangle. The two equal sides of this triangle were five-sixteenths inch long and the base was 7/32 inch long. The sides extended one-eighth inch into the nozzle where they met the cylindrical tube of the nozzle, which was three-eighths inch in diameter. In this nozzle the line from the vertex tapered back into the nozzle instead of running parallel to the base. The resulting spread can be seen at the top of the jet of water. It should be noted that the jet of water from.this triangular orifice was not as solid as that from the other two triangular orifices (Figure 29). This was not due to any particular manner of orientation of the orifice or to the dimensions, but was mainly due to the entrance conditions into and through the triangular portion of the nozzle. 87 In each of the triangular-shaped orifices tested the break-up of the water jet appeared to be much greater than that from circular orifices.' This break-up of the water resulted in smaller drops and consequently the total trajec- tory distance was shortened. A greater percentage of the total amount of water being discharged was deposited near the sprinkler when using a triangular orifice than when using a circular orifice when operating the sprinkler without the oscillating arm. As may be seen in Figure 30, if the nozzle was turned through 180 degrees, so that the part of the jet directed up in the figure would be directed down, a considerably greater amount of water would be deposited nearer the sprinkler. This difference in the distribution pattern obtained by varying the position of the apex of the triangle was small when using the equilateral triangular- shaped orifice. The distribution curve of an equilateral triangular orifice with three-sixteenths inch sides which gradually diverged into the inner part of the nozzle which was oper— ated with the apex of the triangle up is shown in Figure 31. When the sprinkler was operated without the oscillating arm at the rate of one rotation per minute and at a pressure of no pounds per square inch, there was a fall-out of water of 0.095 inch six feet from the sprinkler. The amount of falleout increased with the distance from the sprinkler 88; .eoamaao poem Ga aoaxcaadm Scam oocmpnaa ....... .... ...-o .. o... ....w.~ n... a... .v ...-n NN ma :H OH o . u . ..... ...... So;o a l . . v ‘ l . . . . . . . r , . a . . e . l . > e e a n . e - l y... ,. . 40-O—J1r000. .0 adaswsmHAp Heacpeaasve once oo:e&a:e.aesoeam nae: cauuoz .Hm .mfim -..1 . ~9—o—o—47—o fl OI'O ........ 950: H r. .ndm co .adn 00H and o: n onenuoad wsflumAedo lumen nose Mo coapmAda .Eae weapmaaaomo oGIIXII ‘ SI’O OZ’O o-OAH eofiroo**l_. ... . . , . . . . -_..4,.._. ..- pm... , , . 1' I --ii Li... L. a r u .Eae weapmaanono and: _% prtm ;-._._..4».;_.- _ ...-.. Mil ._.u_l«, *H L..._. seuout u: Jeans 30 qqdeq 89 until a maximum of 0.125 inch occurred at 16 feet from the sprinkler. From this point to about 28 feet from the sprinkler there was a gradual decrease in the amount of fall-out of water; for the remainder of the trajectory distance, this decrease became more pronounced. When the sprinkler was rotated with the oscillating arm, at the same pressure and at the rate of one rotation every 160 seconds and using the same nozzle, a greater fall- out of water occurred near the sprinkler and decreased with the distance from the sprinkler until about 10 feet from the sprinkler where the amount of fall-out was about the same as that from the sprinkler being rotated mechanically without the oscillating arm (Figure 31). Beyond 10 feet from the sprinkler the two distribution curves follow each other quite closely, the one with the oscillating arm having a somewhat shorter trajectory distance due to the action of the oscillating arm. It is worthy of note that whether the sprinkler was operated with or without the oscillating arm, the maximum accumulation peak was not as pronounced when using the above orifice as when using a circular orifice and operating at the same pressure. Figure 32 represents the distribution of water from the same orifice as Figure 28; however, in this figure the ap- proach to the triangular orifice was altered. The sides were 9O .eoawaao aeHsmquau HdhOdeaddc one“ sequence unease new: eHusoz peem ca aechHadm Song coseunaa H .mm .wam .sm; ...-.... ,.. ‘.‘. a .... ... l... .... .... ... ... .., n ..... ..............- .......,..... .0.......... . .. .‘ H NH .m: . 33f. .. a . k W. ..... ...... ..... 50‘0” ot°d“‘ 4*. ‘ -—. My”.-- -4 ...... thw meaaeaaaouo has: .ama o: as coHueaooo anon N\H .uoeau noes ea\m spa: ooaeaso {an oom 98.50 Kod—~—- . . . , . . A . . . v . . . h . . '0—4 m (lifir ..m\\*lalrx.. wwl.fime/WH .... I u: aeqan jo qqdeq 'Sl‘o .Eam .oao nae: neon H sou . w;.; and o: .oasemoad wuauwaodo xrumwmmw shun OQH .L.$L*.u .ooaeano snoopuaasom.uxul. x.eV...e» "02°o ssqou thump; ‘ ‘ ‘ com .ooamano noHcomonH I! Y'-‘J . v . m i M .. , . . .O’LT. .‘lvlllelllllllllilrlo lava- a)... "but... .. Him . -..—...) _. --.. ..-ifir- ...... . O f 6 “fly-H- P“- 9h depth through the orifice. Over-all it would appear that the equilateral triangular—shaped orifice with considerable depth and then a gradual taper inward displayed favorable distribution characteristics. éggare orifices. The nozzles with the square orifices gave a more desirable distribution pattern of water than the nozzles with the circular orifices. Figure 3h shows the distribution of water from a nozzle with a square orifice. A sprinkler with a one-inch riser connection was operated at a pressure of forty pounds per square inch and rotated by means of the oscillating arm at the rate of about one ro- tation every 200 seconds. The square orifice had 5/32 inch sides which extended three-sixteenths inch back into the nozzle and then gradually diverged into the conical taper. A fall-out of 0.06 inch of water occurred between 10 and 12 feet from the sprinkler. This increased to a maximum of 0.105 inch at 26 feet. The rate of fall-out of water then decreased rather gradually to no feet which was the point of maximum trajectory. It should be noted here that there was no sharp accumulation peak. The discharge of a jet of water from a square orifice at a pressure of no pounds per square inch is shown in Figure 35. The jet of water issuing from the orifice ap- peared to be tetrahedral in shape, with the apex of the 95 .oloHao HHomospedo one acHsmcmueoa .oesddn Scam hope: no soapsnanpmHo poem ea noncHaam Scam oocepmaa .em .. .. m :m on ....y.......-. .... . ... ....... g .-- ....-. - ._1.- -_ -l -- l I ...—... 1 . " e - 7-7- .....17—o-._.._q_.-- {—77-er ~- 96 Fig. 35. Jet of water issuing from a square orifice at no psi. 97 tetrahedron appearing to be in the nozzle. The base in- creased very rapidly with the distance from the orifice until at about 12 inches from the orifice most of the re- semblance to a tetrahedron was lost. The jet of water issuing from this orifice appeared to be much more broken up and the drops smaller than that from a circular orifice operated at the same pressure. It may be seen upon close examination of the jet of water issuing from this orifice (Figure 35) that one side of the jet had an irregularity due to an bmperfection of workmanship in shaping the orifice. Rectangular orifices. The distribution of water from a rectangular orifice was similar to that from a square orifice. Likewise, the jet of water issuing from the rectangular ori- fice bore a close resemblance to that issuing from the square orifice except that a cross-section of this jet within the first few inches from the sprinkler would appear rectangular instead of square. The jet of water from the rectangular orifice also spread out very quickly as it left the orifice. The orientation of the rectangular orifice in respect to the vertical and horizontal was found to be pertinent. When the rectangular orifice was placed lengthwise (that is, with the width of the rectangle perpendicular to the horizon- tal), the jet of water would disperse more in the horizontal plane than in the vertical plane. The converse was true when 98 the nozzle was oriented so that the long axis of the rectangle was perpendicular to the horizontal. It is more desirable to have the jet of water dispersed in the vertical plane than in the horizontal since this type of dispersion results in a lesser concentration of fall-out of water in any particular segment along the trajectory radius. Figure 3h shows a distribution curve from a rectangular orifice. (A top view of this orifice is shown in Figure 7.) The sprinkler was operated at a pressure of hO pounds per ' square inch and rotated by means of the oscillating arm at a rate of approximately one rotation every 60 seconds. The rectangular orifice was 9/32 inch by 5/32 inch with the long axis perpendicular to the horizontal. The rectangular por- tion of the orifice extended three-eighths inch into the nozzle where it began to diverge gradually. The distribution curve from the rectangular orifice closely resembled that from the square orifice. However, the maximum trajectory distance and the total amount of fall- out of water were greater for the rectangular orifice than for the square orifice because of the larger cross-sectional area of the former. Quatrefoil orifices. Figure 36 shows water being dis- charged from a nozzle with a quatrefoil orifice at a pressure of MO pounds per square inch. The dimensions of this quatre- foil orifice ‘were such that it could be inscribed in a 1' ‘ urrrrumif ' . ‘ ’/ I _( . ,9 f. ‘ 99 Fig. 36. Jet of water issuing from a quatrefoil orifice at no psi. 1C0 one-fourth inch square. The walls of this orifice extended one-fourth inch into the nozzle and then gradually began to diverge. As may be seen from Figure 36, the jet of water as it issued from the nozzle closely resembled a quatrefoil, with a distinct jet of water issuing from each of the four foils. Within a few inches after leaving the orifice these separate jets blended into one another. A top view of the nozzle with the quatrefdil-shaped orifice is shown in Figure 7. Figure 3h shows the distribution obtained from the above nozzle operated at the same pressure and rotated by means of an oscillating arm at the rate of one rotation every 150 seconds. It may be seen by comparing the three curves that the quatrefoil shaped orifice showed no improve- ment in distribution over the square or the rectangular ori- fices. Since the quatrefoil shape is more complicated and would therefore be more difficult and expensive to manufacture than either the square or rectangular shapes, there seems to be no advantage in using this particular shape. Other non-circular orifices. In addition to the various shaped orifices discussed and shown in Figure 7, there were others that were tested. However, such shapes as a semi- circle or a pentagon shows no desirable distribution charac- teristics over those previously discussed. The distribution pattern from the circular nozzle with the "V"-shaped notch extending across it but not deep enough 101 to change the cross-sectional area or alter the shape of the cross-section of the circular orifice (Figure 7)1 was not materially altered from the distribution pattern of a nozzle with a circular orifice and without a "V"-shaped notch acress it. When the "V"-shaped notch did change the cross-sectional area of the orifice, the distribution characteristics were altered. The nozzle with the slit down one side in Figure 72 gave a very even distribution of water along the greater portion of the trajectory distance and then gradually de- creased. The discharge from this nozzle operating at a pres- sure of no pounds per square inch is shown in Figure 37. The break-up of the water from this nozzle appeared to be much greater than from a standard circular nozzle of the same size. 3 and a shortening of the total This resulted in smaller drops trajectory distance. The above nozzle was comprised of a small cylinder discharging into a larger cylinder. The walls of the larger cylinder were not parallel with those of the smaller one but rather were at an angle to them; hence, part of the jet of water emerging from the smaller cylinder struck the walls of the larger cylinder resulting in a break-up of the jet of water. Although the slit extended 1Top row, right-hand corner, Figure 7. 2Top row, left-hand corner, Figure 7; this was a commer- cially manufactured nozzle. 3Visua1 observation. 102 . 1’5 Fig. 37. Jet of water issuing at no psi from the nozzle with a side slot. 103 almost the entire depth of the larger cylinder, water did that emerge from the slit (Figure 37). Tests were also conducted on nozzles with a slot or an auxiliary orifice1 at an angle to the main orifice. The main jet of water issued from the larger orifice andan auxiliary jet issued from the slot. It was found that by the proper orientation of the slot, a concentration of ‘water'could be directed almost anywhere along the first three-fourths of the trajectory radius. Since any variation in angle, width, depth or orientation of such a slot would greatly change the distribution characteristics of the noz- zle, various distribution patterns were obtained; however, this still did not remedy the/sharp break-off that occurred toward the outer trajectory radius. Jet inversion. Although the jets of water issuing from the non-circular orifices showed more instability than those from the circular orifices, inversion of the jet of water could not be seen as such when Operating the sprinkler within the range of recommended operating pressures 0 However, when the pressure was decreased far below the recomp mended operating pressures, the inversion could be detected. In other words, the higher the velocity through the orifice the less pronounced this phenomenon became. :First row, third nozzle from the left in Figure 7. 10h Effect of Cylindrical Discharge Tubes A cylindrical tube when used in place of a nozzle showed a great deal of promise in giving a desirable dis- tribution of water from a sprinkler. In obtaining a desir- able distribution from such a tube, the length of the tube was very important. The mmst desirable pattern was obtained when the tube length was two to four diameters (of the inside diameter of the tube). This length.was measured from.the inside radius of the bend in the sprinkler body to the dis- charge end. When the tube was shortened beyond the above length, the distribution became undesirable since it resulted in a shortened trajectory distance and caused a great deal of water to fall out next to the sprinkler. The rate of fall-out of water quickly diminished along the trajectory radius. On the other hand as the tube was lengthened, the dis- tribution became more like that from.the conventional sprink- ler nozzles; that is, an increase of trajectory distance resulted from a lengthening of the discharge tube. Also less water was deposited near the sprinkler and a build-up of water at the outer trajectory radius resulted. Figures 38, 39 and no show the effect of the tube length on the break-up of the jet of water. The operating pressure was no pounds per square inch for all of these tests. Figure 38 shows a 7/16 inch inside diameter capper 105 Fig. 38. Sprinkler with 7/16 inch diameter tube 1 1/2 inches long operating at LLO p81. rig—Ali _ ii _. 106 Fig. 39. Sprinkler with 7/16 inch diameter tube cut off at body of sprinkler Operating at no psi. i Fig. LL00 Jet of water issuing at ho psi from a S/l6 inch diameter tube with a 3-l/h inch diagonal portion. 107 108 tube‘threaded into the body of a sprinkler so that l-l/2 inches of the tube extended beyond the body of the sprinkler. Figure 39 shows the same tube cut off next to the body of the sprinkler. In both care was taken not to leave any rough edges on the inside. It is evident in Figure 39 that the jet of water is diverging much more quickly than in Figure 38. Although the jet of water became less divergent and hence went a greater distance, eventually a length was reached at which the jet no longer converged. Beyond a given distance (depending on variables) from the bend, the increased turbulence, secondary motion and distribution of velocities caused by the bend did become dissipated. Figure hi shows the effects of the tube length on the distribution of water. A tube 7/16 inch in diameter was inserted into the body of the sprinkler as shown in Figure 38. The sprinkler was operated at a pressure of to pounds per square inch without an oscillating arm. When the length of the tube was three inches (measured from.the body of the sprinkler), the amount of fall-out increased with the dis- tance from the sprinkler. The maximum amount of fall-out ‘was 0.21 inch and occurred at no feet; the minimum amount iof fall-out occurred near the sprinkler and was about 0.03 inch. when the tube was cut off to zero right at the sprinkler (Figure 39), the distribution was almost linear 109 e c . . , . . . . e e 6 v e . . . . . e v . o e o o i .noumz no noapsnfinunap no newnea ens» mo pooumm poem CH noaxcauan Seam oonmpman :N e . . . . . a e . . a e c e . 4 . . . , . . . , . o e n e > i . . . o e v V cm 0H ‘4‘ .noapooccoo noman Soda \M .53 wcapmaauemo o: .ODSp song oa\~ .aoapenoao cayenne ma one «an o: and» send 0 IIKII end» soda H llall one» some m 111:: .He .wam VNH 50‘0 deq OI'O seqou: u: Jeien JO qq ST'O OZ'O 110 with a maximum fall-out of 0.1a inch of water at 28 feet and a minimum of 0.125 inch occurring near the sprinkler. Shortening the tube length from three inches to zero inches decreased the total trajectory distance by four feet. Figure h2 shows the distribution from.a 5/32 inch inside diameter tube of varied length and operated at a pressure of to pounds per square inch. The tube was bent as in Figure #2 so that the vertical height of the tube was one inch. It was found that the diameter of the vertical tube was not critical in the type of distribution obtained from the tube; the distribution still depended upon the tube length. It was found that as the vertical height of the tube was increased, the total discharge of water was decreased. From.Figure h2 it may be seen that a tube length of four inches resulted in a poor distribution while a length of one-half inch resulted in a desirable distribution. Had the oscillating arm been operating, it would have filled in the depression that occurred in the first 16 feet along the trajectory radius when using the one-half inch tube length. The effect of an oscillating arm on the distribution of water from.a sprinkler with a tube is shown in Figure A3. A tube 5/32 inch in diameter and one-half inch long was inserted into the sprinkler as shown in Figure uh. In this figure the sprinkler was Operated at a pressure of no pounds per square inch. 111 .eeuez do doahehheunan so hemmed ease no reeeem .m: .mam meow ca aoaxcthm Song ooCmpmaQ 1 to. .... v ... .... i . ........ ....t..-.... ........ . ... ... .... roe. . .e v...»- . . . .... ooevi .. to.-. . -.. $ ....... NH ..... ...... r e . v ....... ........ nnnnn , i , c . ..a—{r—o...‘- soto ...... *4 a rq'o—H} 1 ‘4 OI‘O )/ ML; X. ....... ... ....... .... \ . w?" §t°o w a? :5: z a . "3f \ :1. ._9... . i A 33 55 an .Enm mCauwHHHomo o: .Hna 0: 02'0 one» gene m H.|.x.|u ..v. ehsh seen m\H m.|u..|u one» non.“ : lllll. I .0 (.f- Ilellli‘l b--‘H>—..~ . r , . . . .>-~—o———o—._.....- ...—.l—M " “' 51L- -—— -—4>-Io-.—*"()‘ “"“ ’ Wow“ h... i . V i W . Terrier . . .. .,g_g H s. - seqou: u: sedan JO qqdeq 112 .Aomaa Sosa N\H Qua: noHMGHAQn 2H wcoa Sosa N\H was Quad Nm\m end» he vacuum pooh Ga nonCandn Beau eocmunan NH m .m: .waa ....... .... _ . . . . . . . . . . . . . . . r . . . . . . l . . . . . e . . . . . . e . e i . . . . e . . e . . . ON 0H ./-T:H' w . i H. ,. .m e w t H xr_u .;.a a p . - e1 m 1; .1" w. ._ l i i q ..... . .. m .. h H H . q r . \Avilu.“ I . w ,H M . n u ,.,t\:\\ 3? ,_ I , . a? H M . _ 1 . it .. /3 h. h Leif. i H _ / fl /..1 v a K .. .m . t/ .. I) t i in _ : I!“ 7 .e H W” It >—H—...—Jp..m.—. M» [ yk-v ..J 0.“ // H A . H, .i W. a. . / ;/./" i_;t_i -..-4 L... «on ON I.) and on In... ’ //L/'/v are o: l l and om -. p..-._l_._. n 1 WI)! Vfllo Vii i. - ...—7H“..- *1 w... _. -'>-—~—‘ {--.-.4”. ...—4by' -.- i m H i . i m l . n w w i w w A :19? iziha .L: a: w.: I: - h e .r;- :-L+. i I u a it 1:::+:iy . e _ * . . H _ . _ _ l n . . . _ ,. a i _ . . . b g _ i . . (JIFIYII.P(.L » .» H) .r Ll (r H . .-..--u. .I .L SO'O Jeqen JO qudeq OI‘O stto seqou; u; '0 113 i .- i r h u. A. I t ‘x M Night.- a . \ ‘. .. } 'I Fig. uh. Jet of water issuing at no psi from a 5/32 inch diameter tube soldered into the sprinkler bOdy e 11h When the sprinkler was operated at a pressure of no or 50 pounds per square inch, a fairly good distribution of water resulted. Neither one of the distribution curves at the above pressures had the characteristic low amount of fall-out of water near the sprinkler or the large fall- out toward the maximwm trajectory radius. These two curves show a gradual decrease in the amount of fall-out of water from the sprinkler to the maximum.trajectory radius, al- though in the last eight feet of the trajectory radius, the rate of drOp-off was slightly sharper than would be desired. This characteristic would have been improved by increasing the trajectory angle of the jet of water from.the horizontal.1 When the same sprinkler was operated at a pressure of 30 pounds per square inch, there was a slight rise (0.01 inch) in the amount of fall-out of water that occurred be- tween 20 and 32 feet from the sprinkler. At a pressure of 20 pounds per square inch the distribution curve shows a low of 0.075 inch at 20 feet from the sprinkler and a high of 0.15 inch at 30 feet, which is a considerable increase; however, this was a notable improvement over the distribution obtained when using a conventional nozzle. It appears from the results obtained that the distance of the outlet of the discharge tube from.the bend in the iIn these tests the trajectory angle of the jet of water was 2h° from the horizontal. 115 sprinkler is very important in the type of distribution obtained. Increasing the distance between the outlet and the bend in the body of the sprinkler diminished the secon- dary motion caused by the bend. A qualitative explanation of this secondary motion as given by Goldstein (11) is pre- sented below. When fluid is flowing along a curved pipe, there must be a pressure gradient across the pipe to balance the centrifu- gal force. The pressure must be greatest at the outer wall, or the wall farther from the center of curvature, and least at the inner wall, or wall nearer the center of curvature. The fluid near the top and bottom walls is moving more slowly, however, than the fluid in the central portions, and requires a smaller pressure gradient to balance its cen- trifugal force. Consequently, a secondary flow is set up in which the fluid near the top and bottom moves inward and the fluid in the middle moves outward (Figure hS). The pres- sure at the outer wall is greater at the middle of the pipe than at the t0p or the bottom, while at the inner wall it is less. The secondary flow is superimposed on the main stream so that the resultant flow is helical in the top and the bottom.of the pipe. As a result, the region of maximum velocity is displaced from the center of the pipe toward the outer wall. 116 Scciion AB Fig. hS. Secondary flow and variation in head at a 90° short—radius bend (12). The secondary flow also explains why there is a much thicker layer of slowly moving fluid at the inside wall of a curved pipe than at the outside. The faster-moving fluid at the middle is moving outward, pushing the fluid in the boundary layer at the outer wall to the top and bottom, and along the top and bottom walls toward the inner wall. Thus fresh fluid is continually being brought into the neighborhood of the outer wall and then forced around toward the inner wall, being continually retarded. There is thus an accumu- lation of retarded fluid at the inner wall. Goldstein goes on to show that the dynamical similarity found under such flow conditions depends only on the fol- lowing parameter K' = (.2)8 (352E) L v 117 where“a” is the radius of the pipe, “ L" the radius of the curvature of the axis of the pipe, °v"the viscosity of the liquid and “Won the mean velocity in flow through a straight pipe under the same pressure gradient as that along the pipe axis in the curved pipe. This is true when the ratio of 8%,. H u is small and the terms of order ‘\ IO pared with the terms of order .% . 1 Thus, it is apparent rma are neglected when comp that the dynamic similarity depends on the diameter of the curved pipe, the radius of curvature of the pipe and the viscosity and velocity of the fluid flowing through the pipe. 1These limits were stated by Goldstein since the above formula is a simplification of one presented in a paper by Dean. 138 CONCLUSIONS When a sprinkler was operated without the oscillating arm there was very little fall-out of water near the sprink- ler. The amount of fall-out gradually increased until a maximum.was reached near the outer limit of the trajectory distance. When the oscillating arm was used to rotate the sprinkler, the amount of fall-out of water near the sprink- ler was considerably greater. This fall-out decreased to a point about one—fourth of the distance along the trajectory radius and then began to rise, reaching a maximum toward the outer limit of the trajectory radius. The depth of maximum accumulation of water obtained when using the oscillating arm was lower than that obtained when the oscillating arm was not used. Operating the sprinkler at higher pressures resulted in a more desirable distribution of water. There was also a decrease in the mean drop size and an increase in the maxi- mum trajectory distance. Increasing the size of the orifice of a sprinkler nozzle, keeping all other factors constant, resulted in a better distribution of water. Increasing the angle of inclination of a sprinkler nozzle from the horizontal re- sulted in a marked improvement in the distribution of the water. 119 When the cylindrical portion of a sprinkler nozzle was artificially roughened, the distribution of water was poorer than that from an unroughened nozzle. Changing the angle of taper in a sprinkler nozzle from a very gradual taper to one approaching a sharp-edged orifice resulted in little or no change in the amount of fall-out of water near the sprinkler; however, the one approaching a sharp edged orifice caused a lesser amount of fall-out along the remainder of the trajectory distance than did the other angles of taper. Lengthening the cylindrical portion of the nozzle re- sulted in a poorer distribution of water. The best distri- bution was obtained using a convergent tube. When the distance between the nozzle and the main body of the sprinkler was varied by using extension tubes of dif- ferent lengths, it was found that the longer extension tube resulted in an increase in the trajectory distance and les- sened the amount of fall-out of water near the sprinkler. However, beyond a certain length, a further increase in the length of the extension tube did not further affect the tra- jectory distance or the amount of fall-out of water near the sprinkler. A slow rate of rotation resulted in a more desirable distribution of water than did a rapid rate of rotation. As the rate of rotation was increased, the trajectory distance decreased and there was a greater amount of fall-out of water both near the sprinkler and at the point of maximum accumulation near the outer trajectory radius. rhe use of a short cylindrical tube in place of a sprink- ler nozzle resulted in a more desirable distribution of water. The most desirable distribution pattern was obtained when the tube length was two to four diameters (of the inside of the tube) as measured from the beginning of the bend in the sprinkler body to the discharge end. In general, the distribution patterns from nozzles with nonecircular orifices were mcre desirable than from those with a circular orifice. The equilateral-triangular shaped orifices in which the triangular shape extended for a considerable depth into the nozzle gave the most desirable distribution. In the majority of the above discussed factors, the improvement in the distribution pattern was due to some characteristic imparted to the jet by physical changes made in the sprinkler. In this study three factors which could have affected the flow characteristics of the jet of water *1. as it emerged from the sprinkler so as to mprove the dis- tribution pattern for irrigation purposes stand out. These are turbulence, distribution of velocities and the amount of secondary motion in the jet. 1‘- 2. 9. 10. 11. 12. 121 BIBLIOGRAPHY Sprinkler Irrigation Association, S rinkler Irri ation, Sheiry Press, Washington, D. C., 185;. Christiansen, J. E., Irri ation b S rinklin , University rof California, Berkeley, OaIIfor%1a, 5511. £70, October 19u2. A Sprinkler Irrigation Association. {92. cit., p. 23h. Levine, G.,“Effects of irrigation droplet size on in— filtration and aggregate breakdown.” A r. En r. J , September 1952. ‘ Hall, U. A. and P. A. Boving.;\Non-circular orifices fo§6sprink1er irrigation.” Agr, Egg. Journal, January 19 . . Knudsen, J. G., and D. L. Katz, Fluid Dynamics and Heat Transfer, University of Michigan, Ann Arbor, Michigan, Bull. 37, September 1953. ~ Adam, N. K., ghe Physics and Chemistry of Surfaces, Ed. 2., Oxford at the Claredon Press, Oxford University Press, London, p. 386. Synge, J. L., and B. A. Griffith, Princi 163 of Mechanics, Ed. 2., McGraw-Hill Book Company, Inc., New YofE, p. 139. Green, R. L. ‘A photographic technique for measuring the sizes and velocities of water drops from irrigation sprinklers.” Agr. Eng. Journal, September 1952. Laws, J. 0-,“Moasurement of the fall velocity of water drops and rain dropso” WWW Quinn. 19,41- Goldstein, 8., Modern ngelopmontvin Fluid Dynamics, Ed. 1., Oxford at the Claredon Press, Oxford University Press, London. Vol. 1, pp. Bu-BS, 312, 1952. Rouse, 3., Elementary Mechanics of Fluids, John Wiley and Sons Inc., New York, p. 325} 1950, ‘ ROOM USE ONLY . y". :5 _'3 ‘4 4‘. '1.