DROP SIZE DISTRIBUTION AND ENERGY OF FALLING DROPS FROM A.MEDIUM PRESSURE IRRIGATION SPRINKLER AN ABSTRACT Water drops from an irrigation Sprinkler had the same deleterious effects on soil as did raindrOps. The impact of falling water drOps altered the Open structure of the top fraction of an inch of the soil, reduced the effective pore size and formed a more dense layer of soil which hindered the infiltration of water. Large drops from an irrigation sprinkler reduced the infiltration capacity of the soil by as much as 90 per cent. A.reduced infiltration capacity was accompanied by an increased erosion loss. Insufficient data are available to permit accurate design of Sprinkler irrigation systems which.minimize detri- mental structural changes in the soil. Research is necessary to determine the effect of nozzle shape, nozzle size, and pressure at the nozzle upon the size of drops striking the soil surface and upon the energy imparted by the drops to the soil. The purpose of this study was (1) to measure the size of drops from an irrigation sprinkler, (2) to develOp a tech- nique for measuring, and (3) to determine the energy imparted by drops from a sprinkler striking a target near the soil surface. A Rainbird Model 20 irrigation sprinkler was used for all tests in this study. Two nozzle sizes at two pressures were tested. A.5/52-inch diameter nozzle was tested at thirty and thirty-five pounds per square inch and a 3/16-inch diameter nozzle was tested at thirty-five and forty pounds per square inch pressure. For both nozzle sizes the pressures selected were below and above the dividing line recommended by the manufacturer as the minimum pressure for operation on bare soils. All tests were conducted in a laboratory to remove the variable factors of weather. The Sprinkler was placed into a 55-gallon barrel open at the bottom. A vertical slit was cut into the barrel per- mitting the jet of water from the nozzle to emerge unmolested. A.general purpose flour or dental plaster (plaster of Paris) was used as the medium for collecting the water drops. Samples of drOps were taken at five-foot intervals along a radius emanating from the sprinkler. DrOps falling into the medium formed pellets. The mixture of medium and pellets was separated into size classes of pellets by means of a set of standard sieves. The Spectrum of pellet sizes received at each loca- tion was converted to the equivalent Spectrum of water dr0ps. A single number, called "median drop mass," representing the particular spectrum of drops at each location was calculated. A.transducer was constructed whereby the physical displacement of an elastic member was changed into an electri- cal signal by the use of strain gages. The elastic member 'with an attached target was placed near the ground level along a radius emanating from the Sprinkler. The water drops from the Sprinkler struck the target causing a deflection and oscillation of the elastic member. The resulting deflections were recorded by an oscillograph. The energy added to the elastic member and target by the dr0ps striking the target was calculated. The total energy received by the system during the time drops were striking the target was also calculated. The following results were obtained: (1) The logarithm of the median drop mass varied linearly with distance from the nozzle, increasing rapidly with greater distance from the nozzle. An increase in pressure of five pounds per square inch.had little effect on the size of drops falling within approximately twenty feet of the nozzle. Changes hi drOp size caused by a change in nozzle pressure in- creased with distance from the nozzle. (2) The logarithm of the energy imparted by drops from a Sprinkler striking a target near the ground level varied linearly with distance from the nozzle, in- creasing rapidly with greater distance from the noz- zle. Greatest amounts of energy were received from the drop Spectrum from.a 5/52-inch diameter nozzle operating at thirty pounds per square inch. Less energy was imparted by the drop Spectrums from the remaining three combinations of nozzle size and pres- sure tested. (3) True water application rates based upon the actual time of water application were as high as 7.5 inches per hour ranging from thirty to ninety times as great as the application rates based upon total elapsed time. The increment of pressure increase recommended by the sprinkler manufacturer as the difference be- tween undesirable and desirable operation on bare soils was effective in reducing the highest applica- tion rates occurring in the area farther than thirty feet from the Sprinkler. DROP SIZE DISTRIBUTION AND ENERGY OF FALLING DROPS FROM A.MEDIUM PRESSURE IRRIGATION SPRINKLER BY Paul Edward Schleusener 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 1957 ACKNOWLEDGMENTS The author wishes to express his appreciation to Professor E. H. Kidder and other members of the Agricultural Engineering Department for their guidance and assistance in the performance of this study. The author also wishes to express his gratitude to Dr. C. 0. Harris of the Applied Mechanics Department for his advice in the completion of the study. The author is eSpecially indebted to his wife for her understanding and continued inSpiration throughout the study. SOLI DEO GLORIA ii TABLE OF CONTENTS INTRODUCTIONOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOCOOOOO Effect of water drops on soil.................... Protective measures.............................. Need for research on water distribution pattern from Sprinkler80000000000o00.00.000.000 Purpose Of the studYOOOOOOOOOOOOOOOOOOO00.0.0.0.0 (mcn .eva I--l APPARATUS AND METHODOLOGY............................. 7 Irrigation equipment used........................ 7 Apparatus for determining drop size.............. 7 Apparatus for determining energy imparted by falling drop3...OOOOOOOOOOOOOOCOOOOOOOOCO... 10 Energy of falling water drops.................... 10 Applicability of stress analysis techniques...... 10 Methodology for determining drop size distributionOOCOOO0.000000000000000000000000.0. 11 Complex nature of drop formation from a Sprinkler.................................... 11 Simplifying assumptions.......................... 1? Pellet and drop size distribution................ 18 Pellet calibration............................... 18 Method employed for obtaining drop size.......... 22 Procedure for calculation of median drOp msss.... 24 Methodology for determining energy of drOps Strikirlg the targetOOOIOOO‘OOOOOOOOO...O.0...... 33 PREsmTATION AND AIQJSLYSIS OF DATAOCOOCOOOOOO00.0.00... 56 Pellet calibration,.eoeo.o.eo000.000.0000e00000.0 36 Median drOp mass ............................... 38 Energy of drops striking target.................. 46 Energy imparted by drops compared with.the energy required to move sand from a target..... 52 Water application rates.......................... 53 CONCLUSIONSQOOOOOOOOOOOOOOOOOOOOOOOOOOO0.0.0.0.0000... 56 111 TABLE OF CONTENTS (CONT.) PAGE mcohfl'lENDAr-PIOIQ’SOOOOOOOOOOOOOOCOQOOOIQOOOOOOOOOOOOOOOOOO 58 BIBLIOGRAPHY: Literature cited...0.0.0.0....OOOOOOOOOOIOOOOOOOOO 61 Additional references............................. 68 APPENDIX A, Weight per pellet for dental plaster....... 71 APPENDIX B, Weight per pellet for flour................ 72 APPENDIX C . APPENDIX D, Energy loss per cycle during damping....... 74 APPENDIX E, Equations for calculating median drOp maSSQOOOOOOOOOOCOOOOOOOOOOOOOOOOO0.00.... 75 APPENDIX F, Erlergy Of falling drops..00.0.0.0...0000... 76 iv TABLE I. II. III. IV. V. VI. VII. VIII. LIST OF TABLES Calculation of Linear Regression............... Distribution of Pellet Sizes Fifteen Feet from a 5/32-inch Nozzle Operating at Thirty Pounds per Square Indh................ Calculation of Cumulative Percentages of Mass of Water Striking Ground................ Fitting a Straight Line to Data by the Method of Least Squares...................... Plaster Pellet Calibration..................... Flour Pellet Calibration....................... Calculation of Mass of Drop.................... Median Drop Mass............................... Water Application Rates........................ PAGE 20 27 29 32 37 59 40 41 54 FIGURE 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 13. 14. 15. 16. LIST OF FIGURES Transducer and instrumentation for pickup, magnification, and recording of the signal from the transducer................... The cantilever beam............................ The Styrofoam target........................... Calibration of flour pellets................... Pan of flour prepared for receiving water drops........................................ Pan of flour after receiving water drops at a point near the sprinkler................... Pan of water after receiving water drops at the farthest point from the Sprinkler nozzle. Determination of equivalent drop mass.......... Assignment of rectangular coordinates for fitting straight line to data................ Rate of change of energy....................... Effect of pressure on median drop mass......... Effect of pressure on median drop mass......... Effect of nozzle Size on median drop mass...... \Effect of nozzle pressure on energy of drops... Effect of nozzle size on energy of drape....... Effect of nozzle pressure on energy of drops... vi PAGE 13 14 21 23 25 26 30 31 35 43 44 45 47 48 49 DROP SIZE DISTRIBUTION AND ENERGY OF FALLING DROPS FROM A.MEDIUM PRESSURE IRRIGATION SPRINKLER INTRODUCTION Effect of Water Drops on Soil The deleterious effect of raindrop'impact on bare soil was noted as early as 1874. Baver (:5) stated that Wollny (73) found "The loose granular structure of the un- protected soils was not only broken down to cause a compac- tion of the soil but the nonrcapillary porosity was also de- creased as a result of the percolation of turbid water into the large pores and the subsequent clogging up of these pores with fine particles." Wollny's results have been confirmed by Lowdermilk (48) who reported that suspended particles in runoff water were filtered out at the surface of bare soils and sealed the seepage openings. Laboratory experiments (57) in in to of which silt and clay were incorporated in rainfall resulted the fine material being deposited in the top one sixteenth one fourth of an inch. Effective downward translocation the clogging surface layers did not occur although as much twenty-seven inches of rainfall were applied. Clay applied suSpension blanketed the surface of a field plot, checked normal infiltration, and induced runoff very quickly. The reduction of infiltration rates on cultivated land appeared to be caused by the development of a compact layer (22) only a few millimeters thick on the surface of the soil ihich.did not permit rapid penetration of water. The compact layer was formed through alteration of the struc- ture at the surface by the impact of rain drops and by further assortment of particles and wedging and fitting of these into close formation by running water, all of which slowed down.the entrance of water through the immediate surface. The results indicated that the development of the compacted layer on the surface of a cultivated‘bare soil had a greater effect on in- take of water than the combined effect of differences in soil type, degree of slope, previous moisture content of the soil, or rate of rainfall. . The amount of crust formed by applying rain artifici- ally (12) varied with.the amount of rainfall. Microscopic studies of the changes occurring in soil structure during com» pression (19) (at the lower plastic limit) showed a progres- sive closing of the interaggregate Spaces as the pressure was increased. Crusts and thin surface seals were formed in arti- ficially prepared soils (52) which had volume weights of about 1.4 compared to 1.1 or less for the "soil" below the crusts. The impact of raindrops altered the open structure of the top fraction of an inch of the soil, reduced the effective pore size (57), and formed a more dense layer which hindered the infiltration of water (55). Laws (45) determined.that the infiltration rate decreased by as much as 70 per cent as drOp size increased. The erosion losses resulting from the reduced infiltration rates increased by as much as 1200 per cent. Ellison's data (28) showed conclusively that a varia- tion in either drop size or drOp velocity will cause a change in infiltration capacity of the soil. Changes in drop velo- city had greatest effect, changes in drop size were second, and changes in rainfall intensity were least effective. A small amount of surface sealing occurred on the soils tested without raindrOp impact (50). Sealing was associated with the effects of wetting, slacking, and with adjustments of soil surface particles under the influence of surface water. The rates of such sealing were shown to be very slow and fairly uniform.throughout a long time interval. Decreases in in- filtration were also reported from.the use of large drops from an irrigation Sprinkler (47). Increased surface runoff of water accompanied a reduc- tian in infiltration (55) thereby requiring more protection against erosion. Erosion at La Crosse, Wisconsin (54) was proportional to the maximum amount of rainfall occurring in any given thirtydminute period. The same relationship was found to be approximately true at stations in Texas, Oklahoma, South Carolina, and New Jersey. The amount of a standard sand transported by water drop impact (27) was found to be directly proportional to the intensity of precipitation. The erosive 4 capacity of a falling mass of water depends on the energy per unit area of the individual drop. The kinetic energy of the falling drOp determined the force of the blow that must be absorbed at each impact, while the horizontal area of the drop determined the amount of soil that must sustain that blow.(26) Protective Measures Vegetative protection of the soil from the impact of raindrops was observed by Wollny (74). Vegetation protected the soil from the impact of raindrOps to such an extent that the non-capillary porosity was 54 to 55 per cent higher than in unprotected soils. The decrease in volume of a cultivated soil was related to the density of the vegetation and the rapidity with which a vegetative canopy was established. Wbllny concluded that the major effect of vegetation upon the properties of the soil was due to the protective influences of the canopy against the impact of raindrOps. The striking force of rain in the open bore a positive relation to rainfall intensity, whereas the striking force under a pine canOpy apparently remained unchanged as the rate of precipitation increased (13). Under such a canopy(twenty- eight feet above the soil surface) the kinetic energy of rain- fall for each inch of rain per square foot of soil surface was greater than in the open. Intake rates were reduced much more gradually on plots artificially covered with a straw mulch than on bare plots (21,23). The basic intake rate was higher on the covered plots. The mulch appeared to have a retarding effect on the formation of the compact layer on the surface. Need for Research on Water Distribution Pattern from.Sprinklers Water drops from.irrigation sprinklers had the same 'puddling" effect on soil as did raindrops (11). Christian- 'sen (14) pointed out that the largest drape from a Sprinkler were carried to the outside of the area covered, while the smallest drops fell near the Sprinkler. As the pressure was increased, more of the water fell near the sprinkler, and the average size of the drops became smaller. More detailed re- search (47) verified Christiansen's observations and also showed as much as a 90 per cent decrease in infiltration ca- pacity when large water drops from an irrigation sprinkler were applied to a soil. Sprinkler manufacturers (55, 67) recognized the deleterious effect of large water dr0ps on soil by recommending minimum pressures for various nozzle sizes. Unfortunately, insufficient data are available to per- mit accurate design of sprinkler irrigation systems to mini- mize structural changes in the soil. Research is necessary to develop a technique for measuring the energy imparted by water. drape from a sprinkler. Trials should then be made to deter- mine the physical changes occurring in a soil when a known precipitation and resulting energy are applied to the soil. Such information would permit sprinkler manufacturers to make necessary changes in nozzle design to meet the requirements of the soil; irrigation system designers would be more readily able to select proper nozzle size and operating pressure to minimize deleterious structural changes in the soil caused by excessive application rates; and the irrigator would be able to use the equipment without severe damage to soil structure. Purpose of the Study The purpose of this study was (1) to measure the size of drOps from an irrigation sprinkler, (2) to develop a technique for measuring, and (3) to determine the energy imparted by drops'from a sprinkler striking a target near the ground. APPARATUS AND METHODOLOGY Irrigation Equipment Used A Rainbird Model 20 irrigation sprinkler was used for all tests in this study. This sprinkler was a medium pressure Sprinkler adapted for use in agriculture and had a sufficiently low trajectory to be used inside a laboratory. All tests were conducted indoors to remove the variable factors of weather. Two nozzle sizes at two pressures were tested. The nozzle sizes were 5/52-inch and 5/16-inch diameter. The 5/52- inch diameter nozzle was tested at thirty and thirty-five pounds per square inch pressure and the 3/16-inch.diameter nozzle was tested at thirty-five and forty pounds per square inch.pressure; In both cases the pressures selected were be- low and above the dividing line recommended by the manufac- turer as the minimum pressure for operation on'bare soils (33). Apparatus for Determining Drop Size The physical characteristics of water drops have been reported as early as 1894. worthington (75) made sketches of drop action when drops strike another surface. Photographs taken just prior to the presentation of his paper verified the sketches. Studies on the measurement of the frequency distri- 8 bution of various sizes of drops, fall velocity, electrostatic charge, number and form of falling drops, chemical composition, pH, temperature of rain and the intensity of rain are reported in German literature (58). Drop size determinations were made by Bentley (5), Defant (20)., and Landsberg (42) (who measured the size of sleet drops). In 1919 Harkins made a detailed study of the surface tension of water drOps (36). Edgerton used a high Speed motion camera to analyze the stresses in a pendant drop (24). Modern electronic equipment was used by Gunn and Kinzer to obtain terminal velocities of drops (35). Sizes of water drops have been determined by various methods. Bentley (5) allowed raindrops to fall into a layer of fine, uncompacted flour. The drops were allowed to remain in the flour until the dough pellet that each drop always pro- duced at the bottom of the cavity was dry and.hard. An.inves- tigator in Germany (72) used absorbent paper for determining drop Sizes. Niederdorfer (59) estimated the average error in using the absorbent paper method to range from.fourteen per cent of the drop weight at 0.037 milligram to six per cent for a dr0p weight of 37 milligrams. Measurement of the size of drops by freezing them artifically was attempted (58, 68). Controlled draplet sizes were obtained from.a rotating disk (76) and from a vibratory apparatus (18). Screens of various materials coated with soot (8) or nylon hosiery mesh.treated chemically and dusted with sugar (10) were successfully used to measure drop Sizes. An optical instrument (16) in which a 9 beam of light was interrupted by a drop measured the resulthng shadow area by the output level of a photomultiplier tube. An impact type of unit permitted drops to strike a membrane (16). The resulting oscillations were picked up by an oscillograph and photographed. The force of impact was used as a measure of drOp size in Australia (15). Each drop produced a transi- ent modulation in an air-borne transmitter carrier to an ex- tent which depended on drop size. A receiver on the ground demodulated the transmission and reproduced impulses which were a measure of drop size. Auxiliary circuits sorted the pulses into a number of amplitude groups and the total count was reg- istered on electric counters. The change in capacity of a parallel plate condenser caused by a drOp falling between the plates was used as'a measure of drop size at Cambridge, England .(62, 63). Spray deposits were obtained on slides coated with magnesium oxide (39). Photographic techniques have been used to determine drop sizes as well as drop velocities (17, 34, 44, 55). Schmidt (61) measured the velocity of raindrOps by using two disks mounted on an axle and rotated at a known rate. A.drop, which by chance fell through a small sector cut in the upper disk, fell upon a piece of absorbent paper fas- tened to and rotating with the lower disk. The location of the Spot relative to the projection of the sector on the paper gave a measure of the velocity, while the diameter of the spot gave a measure of the drop size. The use of flour or dental plaster appeared to offer 10 the most reliable method of determining drop sizes without requiring detailed and lengthy photographic analyses. Bent- ley (5) stated that the dough pellets corresponded very closely in size with the raindrOps that made them. Apparatus for Determining Energy Imparted by Falling Drops Energy of falling_water drops. The energy of falling drape from.either rainfall or irrigation Sprinklers must be converted to other forms of energy such as heat or must do work. Falling drops may do work in overcoming the surface tension of the drops when the parent drop is shattered and smaller ones formed; soil aggregates may be torn apart (49, 50); soil particles may be moved horizontally and vertically (26, 27, 29, 32, 34, 51, 52); Shattered drops may be imparted with.a.horizonta1 and vertical velocity (4); turbulence may be introduced into surface runoff waters (29). The task of research is similar to that expressed for natural rainfall (28). First, the total energy of the falling drops must be ‘determined--the energy which is available for damaging the surface soils, moving soil particles and reducing infiltra- tion rates. Second, the amount of total energy used in dele- terious effects on the soil must be determined. .Applicability‘p£_stress analysis techniques. The energy of moving water drops can be measured directly (41, 56). A device, called a transducer (60), can'be constructed whereby 11 the physical diSplacement of an elastic member is changed in- to an electrical signal by the use of strain gages. Proper instrumentation is needed to pick up and magnify such a signal for recording and study (Figure l). A steel cantilever beam was selected for the elastic , member. A target of Styrofoam* was attached to the free end of the cantilever beam. The energy imparted by the water drops striking the target area caused the beam to deflect resulting in a strain in the elastic member. Since maximum strain occurs at the fixed point of a cantilever beam, strain gages were attached near that point. The transducer construc- ted for measuring the energy imparted by the falling drops is shown in Figures 2 and :5. Methodology for Determining Map Size Distribution Complex nature of drop formation from a sprinkler. The formtion of water drops from a sprinkler nozzle is quite com- plicated and extremely difficult to analyze. Actual velocities of a water jet emerging from an orifice vary from near zero at the perimeter to a maximum at the center of the stream. The relationship between the average) velocity, which can be readily _measured, and the maximum velocity is a function of Reynold's number (66). *Styrofoam has low density, thereby keeping the iner- tia of the system to a minimum. t is also resistant to water penetration. 12 Figure l. Transducer and instrumentation for pickup, magnification, and recording of the signal from the transducer. The ampli- fier (center) is a Universal Amplifier Model BL-520 manufactured by Brush Electronics Company. The recorder (right) is a Model BIL-202 Double-Channel Oscillograph manufac- tured by Brush Electronics Company. 15 Figure 2. The cantilever beam was a steel strap 1 7/8" x 3/64". The beam had an over- hang of 4 inches. The Styrofoam target was mounted on a stove bolt secured to the end of the cantilever beam. Two strain gages (SBA Type A912) were fastened to the top of the beam and two on the underside of the beam. Gages and electrical connections were carefully waterproofed. 19678 a -':e\m r; sew :3; has 55 seas. If! OOJ 0:21 ewes; arm can: .ae- 'i‘tevellfnai 4 Law ismui SAT ."§‘\E qsi 'infloqgjt. SJ; . 3 r; fetuses died khan! uw‘I .rhs '. vii oi benesanf sue. 'fc eble'rsérn E .. n :fisennro Isrftsesf. Q 05'2" 06‘ _ 14 Figure 3. The Styrofoam target was 16.5 centimeters by 30.3 centimeters with the greater dimension placed along a radius emanating from the Sprinkler nozzle. 15 Initial breakup of the stream into variously sized drops occurred after the stream passed the vena contracts. The variation in stream velocity and the mechanical diaper- sion caused by the Sprinkler rotation initiated drop forma- tion. Further breakup was a function of the surface tension of the water and the resistance of the air to the passage of water drops. The surface tension tended to hold the drops intact in a Sphere, while air resistance tended to cause ob- lation by flattening the leading side of the drops. When ablation occurred to such a degree that the surface tension was overcome, drops broke up into two or more drops (34). Drops may collide and coalesce with other drops (69). Drops suspended in a vertical air stream which came into a region within six centimeters above another drop usually began to fall in an ever tightening spiral until collision took place (9). Bombardment of large drops with a spray of small droplets showed that not all the small droplets coales- ced with the large dr0ps. Some of the smaller drops rolled across the under surface of the large drop exhibiting a ”bounce-off" effect. Even after the drops formed, their characteristics were not constant, but dynamic. Two types of deformation occurred (7). When the drop was deformed to an ellipsoidal shape a rotational deformation occurred. Drops artificially develOped and placed into an air stream for observation ro- tated on their minor axis with the minor axis vertical. The 16 second mode of deformation was free of rotational effects, but consisted of an oscillation. Such oscillation caused the drOp to oscillate between ellipsoidal shapes ninety de- grees apart in the horizontal plane. Surface tension began to draw the drop together. But since the vertical dimension was unchanged, the horizontal axis perpendicular to the plane of the paper increased. Thus, like a pendulum, too much con- traction of the major axis occurred and the minor axis was transformed into the major axis and the process repeated. Theoretical determinations of the ratio of vertical and hori- zontal axes of ellipsoidal drape and the ratio of the hori- zontal cross sections of Spherical and ellipsoidal drops were made by Spilhaus (65). Aymathematical analysis (34) of the distance of travel and the velocity of drops from an orifice resulted in the following relationship: 1‘ - Vo(m/k)(l - 9437““ -s(m/k)2(e'(k/m)t - 1) - g(m/k)t. where ' r 3 distance from the orifice; 70 I initial velocity; in I mass of the drop: k = a constant: e - 2.718 . . .;(38) t I time; g = gravitational acceleration. As the value of m/k approached zero as its limit the value of 17 "r" also approached zero, Consequently, small drops traveled only negligible distances (34). Actual measurements of drOps from an irrigation Sprinkler showed a rapid increase in the diameter of the drop as the distance from the sprinkler in- creased (47). .§igplifying assumptions. To avoid the difficulties encountered in attempting to analyze a dynamic, shifting stream of colliding and oscillating drops, this study was based upon samples taken at the ground level. The following assumptions were made to permit analysis of the data: 1. The break up of the stream into dr0p sizes was con- sidered equivalent to the action in which some homo- geneous substance was broken into fine particles by some random process. DrOp formation, then, was sub- ject to the laws of probability and the number of drOps in the size classes followed a normal distri- bution. 2. The drops were spherical in shape. Ekern (26) reported Spilhaus' calculated ratios of the horizontal cross sections of Spherical and ellipsoidal drops (65). For a 2.74 millimeter dr0p the ratio was ninety-three one hundredths and for a 6.52 millimeter drop the ratio was seventy-nine one hundredths. If all the drOps were ellipsoidal in shape when they entered the pellet for- ming medium, the error would be less than 20 per cent. It is not probable that such a situation would occur. 18 3. Evaporation from the time the drops struck the pan until the pellets were formed was negligible (44). 4. Four samples, taken from successive rotations of the Sprinkler, adequately represented the drop population. Pellet and drgp size distribution. The frequency dis- tribution of raindrop sizes was initially reported by Lenard (46). In 1904 he published tables Showing the frequency of occurrence of drops of differentsizes in several rains. Size distribution analyses were made more frequently in later years indicating that the procedure formed a powerful tool for the quantitative determination of thunderstorm dimensions and characteristics in rain-intensity distribution (40, 45) and should be equally valuable in the study of water distribution from.an irrigation Sprinkler. A consideration of the theory of probability seemed to lead to a rational equation represen- ting the distribution curves of dispersed materials (1). Sam- ples of solid materials (quartz, hornblende and orthoclase feldSpar) were ground up and analyses made. The data followed the calculated curve closely (31). It was concluded that the physical processes that break down soil minerals of various kinds involve primarily the theory of probability. Similarly, the processes that break up a stream of water from.an irriga- tion sprinkler and diSpersal into various drop sizes may also be considered to involve the theory of probability. Pellet calibration. Actual drop dimensions could not be found from the dimensions of the sieve openings. The drop 19 undergoes a certain amount of flattening in becoming a pellet '(40). The mass of the average pellet retained on a given sieve was used to define that size class. The average pellet mass was obtained by dividing the mass of the total drops re- tained on a sieve by the number of pellets retained. TO con- vert the mass of the averagetpellet into the mass Of the average drOp required the use of a "mass-ratio"--that is, the ratio of the mass of the drop to the mass of the pellet. The mass-ratio for flour was reported by Laws in 1941 (44) and in 1943 (45). Use of Laws' data in a linear regression analysis (Table I) resulted in the following equation plotted in Figure 4: R I l.008,3 MQ'051'582, where R I the mass-ratio = m333_9f dEQP 3 mass of pellet M I the mass of the pellet in milligrams. Drop sizes larger than those occuring in natural rain (two milligrams) were not anticipated from the Sprinkler. Early analyses of drOps from a sprinkler indicated that pellet :masses as low as one tenth of a milligram would'be Obtained. DrOpS smaller than 0.877 milligram were not Obtained by Laws 'by using tubes of different diameters. Hair-like capillaries coated with paraffin were used and pressure was introduced to hasten dripping. Nevertheless, the small drops were not Ob- tained. Extension of the mass-ratio calibration to the drOpS between one tenth.and one milligram (five hundred to twelve hundred microns in diameter) was desirable to avoid the neces- TABLE I CALCULATION OF LINEAR REGRESSION Log of Pellet Mass Log Of Mass- Ratio Deviations from Mean Squares of Deviations 20 Products of Deviations 7X 0.175,09 0.380,21 0.698,97 0.977,72 l.079,18 1.462,40 1.740,55 2.000,00 ‘Y 0.010,72 0.013.84 0.017,os 0.035,42 0.049,22 0.053,08 0.064,46 0.056,90 Sum. 8.514,93 Mean 1.064,37 /\ 'Y 3 A 2' = 0.297,67 0.057.21 y+ é? 0.037,21 X —0.888,28 "0.684 ’16 “0.365 ’40 -0.086,65 0.014,81 0.398,03 O.675,99 0.935,63 -0. 000 ’03 m-E) p 0 091 y x? ~0.026,49 0.789,041 -0.024,37 0.468,075 -0.020,18 0.133,517 -OQOOS,79 00°07’508 0.012.01 0.000,2l9 0.0l5,87 O.158,428 0.037,25 O.456,962 0.019,69 0.875,405, xy 0.023,551 0.01o,e75 0.007,374 0.000,328 0.0oo,l78 0.006.517 0.018,421 0.018,423 -0.000,01 2.889,153 245 ' _;___:___ X - 1.064 7 2.889, ‘ ’3 ) 153 0.037,21 + 0.031,582.I - 0.033,615 0.003,595 e 0.031,582 X Antilog 0.003.595 = 1.00893 1.m8'3 “0.031,5& R I R mass-ratio I mass of droE mass of pellet mass Of pellet in milligrams 0.091.245 n ,9 21 God :.hefimcoch O» 3 . Om. .nvma .mmw .d .vw.ao> .COHSD .nmsmoec .aoE< .ncspe eufimnuoapafiom mo soapaaom: .nSOwasm .< eassoa 8 «duo .m .okqg: .me .scHHom sneak MO was: C.OH C.m C.H m.o H.O moaaom do nusz. 1.41)-? -QOAD ho was: *mEHRQmm wrouk k0 ZOHB77 1 1 «A 1 1 1 1 1 16 77 i w 7 11L .I, , 1 1 1 1 , 1 o 1 1 , 1 1 1 1 1 1 1 , 1 7 11 77, 7 1 ,f a 71 1 , 1 , 1 , 1 o 1 1 ,1 , O 1 11 1 , 1 1 1 1 1 1 O , 1 1 ,2 T7 . 7 1 77 77 7 7 71 77 777i77777 1 , , o 1 1 1 17 1 1 1 1 1 1 1 1 1 1 1 1 1 1 ,1 ,1 1 ,1, , 1 1 1 O 1 1 1 7777777777t77777 7777 r 7 -77777nv,v77 7 777717 77 777 7 77777777777 T7 1 1 a 1 1 1 1 , 1 7f: 1 ,. T777 7 , 7 1, 1 , 1 1 . 1 1. 1 ,, 1 1 1 1 1 , , , 1 1 1 1 , 1 1.7 . I II 771 7 7“7 7 , 1 1 _ , 1 o O 1,1,_11211,,,11, 07 7 7 i _7,,,1_,- A 7 7 d (5111111111111,11, O 4 .21111111 0 Seconds THne, 52 energy. The maximum rate of change of energy observed in this investigation was forty-seven ergs per second. This extreme value was measured forty feet from the 5/32-inch nozzle op- erating at thirty pounds per square inch. Energy Imparted by Drape Compared with the Energy Required to Move Sand from a Target The energy imparted to the target under the conditions reported herein was much less than the energy required to move sand from a target area. An initial energy unit of five thousand ergs per square centimeter was required to move fine sand. (26) However, only about 2 per cent of the total energy possessed by the drOps was imparted to splashed sand (27). An initial energy unit of one hundred ergs per square centimeter must be imparted to the sand for it to be moved from the tar- get. Drops from the 5/32-inch nozzle Operating at thirty Pounds per square inch imparted about one fortieth of an erg or energy per square centimeter. to the target placed forty f'eet from the nozzle. Assuming that all the energy imparted to the target would be exerted to splash sand from the tar- 891; area, four thousand revolutions of the sprinkler would be ‘18 cessary to provide the initial energy unit of one hundred aI‘gs. With the sprinkler requiring about seven minutes to c=<>mp1ete one revolution, it is not likely that sufficient eIlergy would be received at the target area to move fine sand during an irrigation. 53 Water Application Rates Water application rates have been determined for sprinklers by using catchment cans and by averaging the to- tal fall out of water over the total period of time the sprinkler was operated (6, 14, 71). Similar calculations were used to obtain the data in columns three and five in Table IX. The true water application rate is shown in the even- numbered columns of Table IX. True application rates were obtained by averaging the total fall out of water over the time interval during Which it fell on a particular target area. The true application rates were thirty to ninety times greater than the conventionally calculated application rates. An increase of operating pressure from thirty to thirty-five pounds per square inch on the 5/{52-inch nozzle caused lower application rates at points beyond thirty feet from the nozzle. At thirty-five pounds per square inch an increase in nozzle size from.5/32- to 5/16-inch diameter caused an increase in the application rates at the points tested. An increase of Operating pressure from thirty-five to forty pounds per square inch on the 3/16-inch nozzle caused a reduction in application rates at points greater than twenty-five feet from the sprinkler. The increment of pressure increase recommended by the manufacturer (33) as the difference between undesirable and desirable operation on bare soils was effective in reducing 54 TABLE IX WATER APPLICATION RATES (Inches per hour) 5/32-inch diameter noZzle Distance Averaged Averaged Aweraged Averaged from over over over over Nozzle, Application Total Application Total ft. Time Time Time Time 50 psi 55 psi 25 0.5 0.01 109 0.04 30 1.9 0.05 2.4 0.05 35 4.0 0.06 2.2 0.05 40 5.4 0.11 4.6 0.07 3/16-inch diameter nozzle 35 psi. _ 40 psi 25 2.1 0.04 5.4 0.10 30 5.6 0.05 ' 5.5 0.12 35 4.8 0.06 3.7 0.11 ‘ 40 7.5 0.08 6.8 0.13 45 0.86 0.08 55 the highest application rates occurring in the area farther than thirty feet from the nozzle. Such reductions tended to make the application rates more uniform along a radius ema- nating from the Sprinkler. The calculation of true application rates included a possible error of as much as 30 per cent. Nevertheless, a clearer understanding of the phenomena of water application by rotating sprinklers and their effect upon the soil may be obtained by calculating water application rates on the basis of actual time of application. 56 CONCLUSIONS The following conclusions may be drawn from the data reported herein: 1. The spectrum of drop sizes received at points Spaced along a radius emanating from a small irrigation sprinkler may'be expressed as a single number that represents that par- ticular spectrum. Such a number was called "median drop mass." 2. The logarithm of the median dr0p mass varied linearly with distance from the nozzle. Median drop mass increased rapidly with greater distance from the nozzle. An increase in pressure of five pounds per square inch had little effect on the size of drops falling within approximately twenty feet of the nozzle. Changes in drop size caused by a change in nozzle pressure increased with distance from the nozzle. 5. The logarithm of the energy imparted by drops from a sprinkler striking a target near the ground varied linearly with.distance from the nozzle. The energy increased rapidly with greater distance from the nozzle. Greatest amounts of ' energy were received from the drop Spectrum from.a 5/32-inch diameter nozzle Operating at thirty pounds per square inch. Some reduction in energy was obtained by increasing the pres- sure to thirty-five pounds per square inch. A.reduction in energy occurred at thirty-five pounds per square inch.hy in- creasing the nozzle size from 5/32-inch to 5/16-inch diameter. 57 Additional reduction in energy was obtained by increasing the pressure at the 3/16-inch.nozzle to forty pounds per square inch. 4. Energy was delivered to the target during one to three and one half per cent of the total time. 5. Assuming that all of the energy imparted to the target was exerted to splash sand from the target area, fine sand (26) would not be splashed from the target area during an irrigation. 6. True application rates based upon the actual time of water application were as high as 7.5 inches per hour and ranged from thirty to ninety times as great as the applica- tion rates based upon total elapsed time. The increment of pressure increase recommended by the manufacturer as the difference between undesirable and desirable operation on bare soils was effective in reducing the highest applicaé tion rates occurring in the area farther than thirty feet from the nozzle. 58 RECOMMENDATIONS 1. Detailed studies of the energy imparted by drops from.irrigation sprinklers should be continued. The trans- ducer used to obtain the data reported herein was capable of sensing eighty milligrams per line on the oscillograph (2.51 x 10"5 centimeters of deflection of the beam per line on the oscillograph and 550 milligrams required for one micron of beam deflection). Further studies of medium pressure sprinklers will require an element capable of sensing two milligrams per line on the oscillograph. The system.should include automatic adjustments for changes in inertia load on the target. 2.‘ Similar equipment should be used to determine true water application rates of irrigation sprinklers. 3. Energy patterns similar to those reported herein should be applied to typical irrigated soils to measure changes in soil condition caused by that application of energy. Evaluation of the changes caused by the energy application will: a. Assist the sprinkler manufacturer to make necessary changes in nozzle design to meet prevailing soil con- ditions; b. Permit irrigation system designers to be more readily able to select the proper combination of nozzle size Co 59 and operating pressure to minimize harmful structu- ral changes in the soil caused by excessive quantities of energy applied to the soil; and Permit irrigators to use properly designed and selected equipment withOut severe damage to soil physical characteristics. BIBLIOGRAPHY 51 LITERATURE CITED (1) Affleck, C., "Application of the Theory of Prob- ability to the Size Distribution of Soil Aggregates," Soil Science, 588115-119, 1954. (2) Anderson, Lloyd J., "Drop-Size Distribution Measurements in Orograghic Rain," Bulletin American Meteoro- logical Society, 29:56 -566, 1948. (5) Baver, L. D., "Ewald Wollny, a Pioneer in Soil and Water Conservation Research," Soil Science Society.gf America Proceedings, 38550-533, 1939. (4) Bennett, H. H., Forrest G. Bell, and Bert D. Robinson, Raindrops and Erosigg. United States Department of Agriculture Circular No. 895, 1951. 25 pp. (5) Bentley, W. A., "Studies in Raindrops and Raindrop Phenomena," Egnthly Weather Review, 523450-456, October, 1904. (6) Bilanski, walter K., "Factors that Affect Distri- bution of Water from.a Medium.Pressure Rotary Irrigation Sprink- ler." Unpublished Doctor's dissertation, michigan State Uni- versity, East Lansing, 1956. (7) Blanchard, D. 0., "Observations on the Behavior of Water Drops," General Electric Research Lab Report.§2..z Project Cirrus, 1948. (8) Blanchard, D. C., "The Use of Sooted Screens for Determining RaindrOp Size and Distribution," General Electric Company Occasional Report 33. 16 Project_girrus, 1949. 11 pp. Cited byBoucher, Roland J., "Results of Measurements of Rain- drop Size," Illinois State Water Survey Bulletin 41, Conference 23 Water Resources, pp. 295-297, 1951. (9) Blanchard, Duncan 0., "The Behavior of Water Drops at Terminal Velocity in Air," Transactions American Geophysi- cal Union, 518856—842, December 1950. (10) Boucher, Roland J., "Results of Measurements of Raindrop Size," Illinois State Water Survey Bulletin 41, Conference gg_Water.§gsources, pp. 295-297, 1951. (11) Bureau of Reclamation, Sprinkler Irrigation. Uni- ted States Department of the Interior, Washington, Revised December 1949, 61 pp. (i (Q 62 (12) Carnes, A., "Soil Crusts," Agricultural Engineer- ing, 15:167, 1934. (l5) Chapman, Gordon, "Size of Raindrops and Their Striking Force at the Soil Surface in a Red Pine Plantation," Transactiogg American Geophysical_§nion, 292664, October 1948. (14) Christiansen, J. E., Irrigation by_§prinkling. University of California Agricultural Experiment Station, Berkeley, Bulletin 670, October 1942. 124 pp. (15) 000per, B. F., "A.Balloon-Borne Instrument for Telemetering RaindrOp-Size Distribution and Rainwater Con- tent of Cloud," Australian Journal-g; Applied Science, 2845- 55, 1951. (16) Cunningham, Robert M., "Airborne Raindrop Size Measurement and Instrumental Techniques," Illinois State Water Survey Bulletin 41, Conference'gn‘Water Resources, pp. 285‘291, 1951. (17) Davis, J. M., A Photographic Method for Recording Size 9: Spray Drops. United States Department ofmAgriculture, Agricultural Research Administration, Bureau of Entomology and Plant Quarantine, Washington, ET-272, July, 1949. 7 pp. (18) Davis, J. M.,.A.Vibratory Apparatus Egg Producing Drops 22 Uniform Size. United States Department of Agriculture, Agricultural Research Administration, Bureau of Entomology and Plant Quarantine, Washington, ET-295, April, 1951. 5 pp. (19) Day, P. R., and G. G. Holmgren, "Microscopic Changes in Soil Structure During Compression," Soil Science Society‘gf America Proceedingg, 16:75-77, 1952. 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Slater, "Factors that Affect Surface Sealing and Infiltration of Exposed Soil Sur- faces," Agricultural Engineering, 26:156-162, 1945. (51) Evans, P. W., "Theory of Probability and Size Distribution of Soil Aggregates," Soil Scienqg, 728245, 1951. (52) Free, George R., "Soil Movement by Raindrops," Agricultural Engineeripg, 553491, 1952. (55) Gray, Alfred S., Sprinkler Irrigation Handbook. Edited by Crawford Reid. Fifth Edition; Glendora California: Rain Bird Sprinkler Manufacturing Corporation, 1952. 40 pp. (54) Green, Robert L., "A Photographic Technique for Measuring the Sizes and Velocities of Water Dr0ps from Irri- gation Sprinklers,” Agricultural Engineering, 553565, 1952. (55) Gunn, Ross, and Gilbert D. Kinzer "The Terminal Velocity of Fall for Water Droplets in Stagnant Air," Journal. of Meteorology, 68243-248, 1949. 64 (56) Harkins, W. D., and F. E. Brown, "Determination of Surface Tension (Free Surface Energy) and the Weight of Falling Drops,“ Journalflgf the_§merican Chemical Society, 41:499-524, 1919. (57) Hendrickson, B. E., "The Choking of Pore Space in the Soil and Its Relation to Runoff and Erosion," Trans- actiopg American Geophysiogl Union, 153500-505, 1954. (58) Hodgman, Charles D., editor in chief, Handbook 23 Chemistry and Physics. Thirty-fourth edition; Cleveland, Ohio: Chemical Rubber Publishing Company, 1952. 2950 pp. (59) Hogan T. W., "The Ground Recovery and Drop Spectra of Sprays DiSpersed from Two Types of Aircraft, Australian Journal o£_Agricultura1 Research, 23502-521, 1951. (40) Horton, R. E., "Statistical Distribution of Drop Sizes and the Occurrence of Dominant Drop Sizes in Rain," Transactions American Geophysical Union, 293624-650, 1948. (41) Katz, Isadore, "A.Momentum Disdrometer for Measuring Raindrop Size from Aircraft," Bulletin Americgg Meteorologic§1_§ociety, 553565-568, 1952. (42) Landsberg, H., and H. Neuberger, "0n the Fre- quency Distribution of Drop Sizes in a Sleet Storm," Bulletin Americgp Meteorological_§ociety, 193554-556, 1958. (45) Laws, J. 0., "Recent Studies in Raindrops and Erosion,"_Agricultural Engineering, 213451, 1940. (44) Laws, J. Otis, Measurements g§_the Fall-Velocities 'QQIWater-Drops and Raindrops. United States Départment of Agriculture,fiSoil Conservation Service, Washington, SCS-TP-45, November, 1941. 55 pp. Also appears in Transactions Ameriogn Geophysical Uniop, 223709-721, 1941. (45) Laws, J. Otis, and Donald A. Parsons, “The Re- lation of Raindrop-Size to Intensity," Transactions American Geophygical Union, 243452-460, 1945. (46) Lenard, P., "Ueber Regen,” Meteorologische Zeit- achrift, 213248-262, June 1904. (47) Levine, Gilbert, "Effects of Irrigation Droplet Size in Infiltration and Aggregate Breakdown,” Agricultural Engineering, 553559, 1952. (48) Loudermilk, W. C., "Influences of Forest Litter on Runoff, Percolation and Erosion," Journal'g£,Forestgy, 283 474, 1950. """"' 65 (49) McCalla, T. M., "Influence of Biological Pro- ducts on Soil Structure and Infiltration," Soil Science Society 2;,Amerigg Proceedings, 73209-214, 1942. (50) McCalla, T. M., "Water-Drop Method of Determining Stability of Soil Structure," Soil Science, 583117-121, 1944. (51) Mech, S. J., and G. R. Free, "Movement of Soil During Tillage Operations," Agricultural Engineering, 253579, 1942. (52) "Mighty Raindrop," Farm Quarterly, 4 N0. 4372, 1950. (55) Musgrave, G. W., "The Infiltration Capacity of Soils in Relation to the Control of Surface Run-off and Erosion," JournalIQQ American Society o£_Agronomy, 273556, 1955. (54) Musgrave, G. W., "The Quantitative Evaluation of actors in Water Erosion -- a First Approximation," Journal f Soil and Water Conservation, 2:155, 1947. F O (55) Neal, J} R., Th3 Effect'gg the Degree 2; Slope and Rainfall Characteristics.gg Bun-off and Soil Erosion. University of Missouri Agricultural Experiment Station, Columbia, Missouri, Research Bulletin 280, 1958. (56) Neal, J. H., and L. D. Baver, "Measuring the Impact of.Raindrops," Journa1.g£ American Society 9; Agronomy, 293708, 1957. (57) Nelson, W. R., and L. D. Baver, "Movement of Water through Soils in Relation to the Nature of the Pores," Soil Science Societngg America Proceedingg, 5369, 1940. (58) Neuberger, Hans, "Notes on Measurement of Rain- dr0p Sizes," Bulletin American Meteorological Society, 253274, 1942. (59) Niederdorfer, E., "Messungen der Groesse der RegentrOpfen," Metggrologische Zeitschrift, 4931-14, 1952, cited by Laws and Parsons, llThe Relation of RaindrOp-Size to Intensity," Transactions American Geophysigg; Union, 24:452- 460, 1945. (60) Perry, 0. C., and H. R. Lissner, The Strain Gagg Primer. New York: McGraw-Hill Book Company, Inc., 1955. 281 pp. (61) Schmidt, W., "Eine unmittelbare Bestimmung der Fallgeschwindigkeit von Regentr0pfen," Sitzungsberichte.gg§ MathematischsNaturwissenschaftlichen Klasse der_§aiserlichen Akademie'Qgg.Wissenschaften, CXVIII Band Abteilung IIa, Wien, 66 1909, cited by Laws, J. Otis, Measurements of the Fall-Veloci- ties of Water-Drops and Raindrops.“ United.states Department '3T_AgFIcu1ture,‘Soil Conservation hervice, Washington, SCS-TP- 45, November, 1941. (62) Smith, L. 0., "New Method to 1measure RaindrOp Size," Illinois State Water Survey Bulletin 41, Conference pp Water Resources, p. 299, 1951. (65) Smith, L. G. "The Electric Charge of Raindro s," $uarterly Journal 2: the Royal Meteorological Sociofiy, 813 5- ’ o (64) Snedecor, George W., Statistical Methods A lied to Experiments Ag Agriculture and Biolor . IFiTEH EHItIon; 'Afies, lowa: Iowa a e 0 age Pfess, 6. 554pp. (65) Epilhaus A. F., "Raindrop Size, Shape and Falling Speed," Journ of Meteorology, 5:109, 1948. ———.— (66) Stanton, T. E , and J. R. Pannell "Similarity of Motion in Relation to the Surface Friction of Fluids, Trans- actions Royal bociety (London), A214, 1914. (67) Strong, Winston C.,_Agricu1tura1 Sprinkle; Irp;- gation Manual. John B. Gill, editor; First edition; Fresno, California: Buckner Manufacturing Company, Inc., 1955. 51 pp. (68) Taylor, E. H. and D. B. Harmon, Jr., "Measuring Drop Sizes in bprays," Industrial_gnd_Eng;neering Chemistry, 463145541457, July, 1954. (69) Telford, J. W.,N. S. Thorndike, and E. G. Bowen, "The Coalescence Between Small Water Drops,' Quarterly Journal g£_the Royal meteorologicgl Society, 513241-25 , 1955. (70) Van Bavel, C. H. M. "Mean Weight-Diameter of a Soil Aggregate as a Statistical Index of Aggregation," Soil Science Society g; America Proceedings, 14:20, 1949. (71) Wiersma, John L., Effect of Wind Variation on gator Distribution from Rotatin S rI ers. S uth Danta g cUIturaI‘EXp€% u on, rookings, Technical Bulletin No. 16, May 1955. 18 pp. (72)_Wiesner, J., "Bietraege zur Kenntniss des tropischen Regens," Sitzungsberichte der Mathematisch-Naturwissenschaft- lichen Klasse der Kaiserlichen Akademie der Wiesenschaften, 104: 1597-1454, 1895. (75) Wollny, E., "Untersuchungen uber den Einfluss der Pflanzendecke und der Beschattung auf die physikalischen Eigen- schaften des Bodens," Forsch. Geb.‘Agri-Phys., 103261-544, 1887, O I p ,. o O O u f 4 67 cited by Baver, "Ewald Wollny, A Pioneer in Soil and Water Conservation Research," Soil Scienpg Societong America Pro- ceedingg, 53550-555, 1959. (74) wellny, E., "Untersuchungen uber den Einfluss der Pflanzendecke und der Beschattung auf die physikalischen Eigen- schaften des Bodens," Forsch. Geb. Agri-Phys., 12:1-75, 1889, cited by Baver, "Ewaldfiwollny, A Pioneer in Soil and Water Con- servation Research," Soil Science Society'gg America Proceed- in S, 53550-553, 1959. (75) Worthington A, N. "The Splash of a Drop and Allied Phenomena," Annua Report-2; Board‘gg Regents.g£ Smithsonian Institute, 19 , 18 . ‘ (76) Yates, Wesley E., "An Analysis of Atomization by the Rotating Disk for Controlled Droplet Size." Unpublished Master's thesis, The University of California, Davis, 1951. 68 ADDITIONAL REFERENCES Atlas, David, and Shepard Bartnoff, "Cloud Visibility, Radar Reflectivity, and Drop-Size Distribution," Journal‘pi Meteorology, 103145-148, 1955. Atlas, David, and Vernon G. Plank, "DrOp-Size History During a Shower," Journal 2£_Meteorology, 103291-295, 1955. Best, A. C., "The Size Distribution of Raindrops," ¥uarter1y Journal 2; the Royal meteorological Society, 76:16, 50. Best, A. C., "Emperical Formulae for the Terminal Velocity of Waterdrops Falling Through the Atmosphere," _Quarterly Journal 2; the Royal Meterological Society, 763502, 1950. . Blanchard, D. C., "A Simple Recording Technique for Determining Raindrop Size and Time of Occurrence of Rain Shows," Transactions American Geophysical Union, 543554, 558, 1955. Bowman, G. B., and J. Rubin, "Soil Puddling," Soil Sciengg Society 22 America Proceedingg, 15327, 1949. Bowen, E. C., and K. A. Davidson, "A Raindrop Specto- graph," Quarter1y_gpurnal'p§ the Royal Meteorological Society, 773445, 1951. Gumbel, E. J., "On the Frequency Distribution of Ex- treme Values in Meteorological Data,".Bulletin American Meteoro- logica1 Society, 25395-105, 1942. ' ‘ Gunn, Ross,and Charles Devin, Jr., "Raindrop Charge and Electric Field in Active Thunderstorms," Journal 2; Meteorology, 103279-284, 1955. McDonald“ James E., "The Shape and Aerodynamics of Large Raindrops, .Journa1.g£ Meteoro ogy, 113478-494, 1954. Magono, Choji, "0n the Shape of Water Drops Falling in Stagnant Air," J0urna1lg§_Meteorology, 11:77-79, 1954. Marshall, J. S., and W. McK. Palmer, "The Distribution of Raindrops with Size," Journal 23 Meteorology, 53165-166, 1948. Osborn, Ben, "Soil Splash.by Raindr0p Impact on Bare Soils," Journal p§_Soil and Water Conservation, 9:55-58, 45, 49, January 195 . ,e ,1 69 Osborn, Ben, "Effectiveness of Cover in Reducing Soil Splash by Raindrop Impact," Journal pf Soil and Water Conser- vation, 9370-76, March 1954. Russell, E. W., and R. V. Tamhane, "The Determination of the Size Distribution of Soil Clods and Crumbs," Journal .2: Agricultural Science, 503210-254, 1940. Shanks, G. L.“ and J. J. Paterson, "Technique for Spray Nozzle Testing, Agricultural Engineering, 293559, 1948. Sp ilhaus Athelstan P., "Drop Size, Intensity, and Radar Echo of Rain," Journal of Meteorology, 5:161- -164, 1948. Wilcox, J. C., and J. N1. McDougald, "Water Distribu- tion Patterns from Rotary Sprinklers," Canadian Journal of Science, 55: 217-228, 1955. APPENDIXES APPENDIX A WEIGHT PER PELLET FOR DENTAL PLASTER (For 5/16-inch nozzle at 55 and 40 psi) Screen Total Wt. Total No. Weight per Opening, of Pellets Pellets Pellet microns Retained, Retained Retained, gm. mg. 420 15.480 152,655 0.088,504 589 15.500 47,571 O.527,204 855 29.600 59.782 0.744,055 1,168 29.020 15,979 2.075,971 1,651 22.720 5,475 4.151,288 1,981 15.775 1,756 7.844,555 2,562 17.755 1,444 12.295,706 2,850 14.760 684 21.578,947 5,560 10.170 575 27.265,416 4,000 9.555 196 48.750,000 - 4,699 6.045 64 94.455,125 APPENDIX B WEIGHT PER PELLET FOR FLOUR (For 5/52-indh nozzle at 50 and 55 psi) Screen Total Wt. Total No. Weight per Opening, of Pellets Pellets Pellet microns Retained, Retained Retained, gm. mg. 420 16.856 160,544 0.104,999 589 26.565 158,764 0.189,999 840 44.245 85,155 0.519,582 1,168 9.954 7,945 1.250,546 1,597 26.757 12,861 2.080,476 1,900 19.081 2,867 6.655,589 2,562 12.899 941 12.707,758 2,850 14.858 750 19.784,000 5,560 11.408 529 54.674,772 4,000 6.115 105 58.258,095 4,699 4.552 46 ' 94.175,915 72 APPENDIX C WMWIIIwm mmmwwmmm4 IMImmmm [MWWWWH "m WW “mun“ "mmlmw. "mm wIII "iwwmwmw AAMMMMAAEAAEWMAA' ,Mm. W%WW%WEW%WMw%WW‘ A.ET 'AwwnWMI ofimmmmwm IRMA mmmwmm IMMI I AmmmmmmA7Ammemmw IIIIIIIIIIIIIIIII ’,I I I‘III‘ AhuwmmmmA“ I In - ' MWAA'HMNH wmmmmmwmim' Inn 1,..- Imwmmmmmm II Imwn; HI"P "$19!”, I'll". “W “in _ IIWWAMHAM hdwnfifiF "WWWWWWWWE 1W» HIUHWWMHL “I “‘3 ‘III‘IIIAIII'I’S‘I'IIIT”"I‘ III III - I i341 IMIIIIII II AhmmeIAtfiAmidfimII ,HIIIAIIII"inb’IIIIflmI ;; “W: Li: {“4 II MIA”; I. M 'I-nzAflwm} ‘ H! III "1“ ”W”: -,.x _‘ h ‘ .; :jn': :, :31, [i ‘ _. "1' IIIII'"; IIIIIII I ‘ 'III 'I:; “III 7" £1; I,?!i:h'r( '1'." "in“; £le II «In; I I IGI‘H'M I ' W” "WWI I. . III wwwwmwwm Wmmmmem- .mmmwwmmg “fidNHWNMWWWWflIISNMMmmm AIMNHAE WWWWWWWTM Eéwm I I I: MIMI} NANA : wwmflfiwwWw TIIIII II! III! I I -‘ III ‘I‘IIIIIIII; "II II I III III i: IAIIIIII' III» II" '"IIIIIIIIAI A 75 APPENDIX D ENERGY LOSS PER CYCLE DURING DAMPING AE/E = 0.722 - 0.009,7 320.030 B .AE/E - B IsE/E % 0.717 10% 0.620 1 0.712 11 0.615 1% 0.707 11% 0.610 2 0.703 12 0.606 2% 0.696 12% 0.601 3 ,0.693 13 0.596 3% 0.666 13% 0.591 4 0.663 14 0.566 4% 0.676 14% 0.561 5 0.674 15 0.576 5% 0.669 15% 0.572 6 0.664 16 0.567 6% 0.659 16% 0.562 7 0.654 17 0.657 7% 0.649 17% 0.552 6 0.644 16 0.547 6% 0.640 16% 0.543 9 0.635 19 0.536 9% 0.630 19% 0.533 10 0.625 20 0.526 APPENDIX E EQUATIONS FOR CALCULATING MEDIAN '75 DROP MASS Distance from 5/32-1nch nozzle Nozzle, ft. 30 psi 35 psi 5 y - 0.50951: - 40.2315.65 y - 0.44041: - 25.10 $4.61 10 y I 0.52651: - 32.59t4.82 y I 0.53411: - 32.08t3.44 15 y = 0.56371: - 28.7134.80 y I 0.47911: - 22.53 35.12 20 . y I 0.63781: - 30.911: 4.71 y I 0.57281: - 24.63 335.31 25 y I 0.71271: - 23.7135.72 y I 0.56861: - 17.70 135.02 30 y = 0.7546x " 17002 $6097 y = 0.6752}: " 17064 24077 35 y -'-' 1.24331: - 52.951: 8.97 y I 0.91581: - 25.76 £8.23 40 y I 1.50061: - 69.43 $14.81 y I 1.01921: - 25.92 212.23 3/16-inch nozzle 35 psi 40 psi 5 y I 1.23431: - 82.44 £3.10 y I 1.23671: - 84.03 32.11 10 y = 0.71541: - 40.871: 3.32 y I 0.81161: - 55.101.14.75 15 y I 0.69121: - 32.41t5.01 y = 0.68831: - 32.78 £4.31 20 y I 0.89671: - 48.85t4.30 y I 0.75521: - 52.66t5.58 25 y = 0.90611: - 40.08:5.76 y I 0.94601: - 31.6536.70 30 y = 1.00431: - 38.09 £8.19 y = 1.08491: - 32.17t9.97 35 y = 1.19621: - 54.42 $10.30 y I 1.04561: - 31.55 9:11.54 45 y = 2.10781: - 118.00 '3: 8.47 (Ergs on target area of 500 sq. cm.) APPENDIX.F ENERGY 0F FALLING DROPS Distance from 5/32-1nch.nozzle 3/16-inoh nozzle Nozzle, ft. 30 psi 35 psi 35 psi 40 psi 25 0.140.8 0.189 8:8§§:§ 8:8§%:8 0.175.2 0.124 0.08210 0.120.5 Ave. 00158,0 0.156’5 00060,5 0.11.5.5 so 0.554,8 0.325,6 o.14o,o 1.004,8 0.502 0.128.4 0.356,4 0.68618 .415 0.060.4 0.073l6 Ave. 0.748,8 o.457,5 0.171,5 o.190,o 35 1.844 ' 1.124 0.751,2 2.244 1.445 1.058 0.313,6 2.092 1.697 0.908 0'409I6 Ave. 2.060 1.571 1.030 o.491,5 40 8.72 6.512 3.612 2.004 18.58 6.788 6.716 0.552 10.640 8.200 7.864 1.500 Ave. 12.58 7.100 6.064 1.285 45 ' 1.996 0.236,4 0.22228 Ave. 0.818,4 76 77 APPENDIX.F (CONTINUED) ENERGY 0F FALLING DROPS (Ergs per sq. cm. on target area of 500 sq. cm.) Distance 5/32-inch nozzle 3/16-inch nozzle Nfiggge, 30 p81 35 p81 55 psi 40 p81 ft. 25 0.000,316 0.000,513 0.000,121 0.000,251 50 0.001,5o o.ooo,915 o.ooo,545 0.000,380 55 o.oo4,12 0.005,14 o.ooz,oe o.ooo,9es 40 0.025,2 0.014,2 0.012,1 0.002,57 45 0.001,54 (Mai. single observation 0.003,99) r9”-F‘7s? w: ‘a {'4 ”’4?th 9;. b1, .9 '1; I“ U 0’. A‘ - s-k