Center for Irrigation Technology
 

- Standards Notes -
Laser Optical Measurement of Sprinkler Drop Sizes 1
by Kenneth H. Solomon 2 , David F. Zoldoske 3 and  Joe C. Oliphant 4
CATI Publication #961101 © Copyright November 1996, all rights reserved

  Irrigation sprinklers apply water by spraying it through the air. Various mechanical and hydraulic factors cause the spray to disperse into a collection of individual drops, covering a range of sizes (Heermann and Kohl, 1980). The sizes of sprinkler drops are known to influence a number of factors important to irrigators.
  IMPORTANCE OF SPRINKLER DROP SIZES
  Sprinkler drop sizes and their effects can influence equipment selection, system design, and irrigation uniformity and efficiency. There are at least five major reasons why drop sizes are of significance in sprinkler irrigation.
  Sprinkler Pattern Distortion Due to Wind
  Christiansen (1942) showed that wind distorts the application pattern of a sprinkler. This distortion may affect the uniformity of water application and irrigation efficiency. The extent of the wind effect depends on wind speed and direction, and on the sizes of drop in the spray. Since wind exerts a force proportional to the cross-sectional area of the drop (a function of drop diameter squared), while the inertia of the drop resisting the wind's force is proportional to its mass (a function of drop diameter cubed), wind tends to affect small drops more than large ones.
  Evaporation and Wind Drift Losses
  The amount of water that evaporates from a drop depends on the surface area of the drop, and on how long the drop is in the air. Both of these factors are related to drop size. For small enough drops, it can be shown that even a slight wind can keep the drop suspended long enough that it will evaporate before it hits the ground (Inoue, 1963). Thus droplet size distribution can affect the percentage of applied water that will be lost to evaporation and wind drift for a given set of climatic conditions.
  Wind Drift - Effluent Water
  Sprinklers may apply effluent water for waste disposal and/or to stretch water supplies. Depending on its source and treatment level, effluent water may contain a variety of obnoxious constituents, which must be confined to the application site. A drop's size determines its wind drift, and for effluent systems wind drift means both water loss and the undesirable off-site application of constituents (Addink, et al., 1980).
  Soil Compaction and Infiltration Rate Reduction
  Certain soils are subject to compaction under sprinkler application. This tends to seal the surface soil layer, reducing the infiltration rate. For a given soil and application rate, the extent of the infiltration rate reduction depends on the impact energy of the spray (Stillmunkes, 1980; King and James, 1984). A drop's impact energy is determined by its mass and impact velocity. Large drops strike the soil with greater kinetic energy than small drops. This is probably not a factor when irrigating sod or established grass, but can be significant when sprinkling bare soil.
  Penetration of Plant Canopies
  Some greenhouse managers feel (Zoldoske, 1991) that fine drops give them better penetration within and throughout plant canopies, improving the distribution of water, nutrients and other waterborne chemicals throughout the plant.
   
  SPRINKLER DROP SIZE DISTRIBUTIONS
  Sprinklers deliver drops of many sizes, and the size distribution varies with distance from the sprinkler. Manufacturers want to know what drop sizes and volumes are deposited where in order to compare products, evaluate new designs, and study the effects of operating conditions (such as pressure). With a knowledge of the size distribution and the amount of water applied at each distance, one can compute the portion of the sprinkler's applied water volume that falls in drops within various size ranges.
   
  Measurement of Sprinkler Drop Sizes
  Solomon, et al. (1985) reviewed techniques for measuring irrigation drop sizes. Pellet and stain methods are inexpensive, but time and labor intensive. Photographic measurement systems minimize time and labor requirements, but are quite expensive. CIT has developed an intermediate alternative: a laser-optical system for the measurement of sprinkler drop sizes based on the GBPP-100S "Ground Based Optical Array Precipitation Smart Probe" (Figure 1) from Particle Measuring Systems 5 in Boulder, Colorado (about $18,500 in 1985). CIT has made a number of hardware and software additions to the system to increase its capability.
 
   
  Droplet Size and Velocity Measurement
  The drop size measuring process uses a flat beam of laser light, directed by mirrors to a horizontal array of photo-sensitive diodes. As each drop passes through a screening area (Figure 1), it crosses the beam, casting a shadow and causing some of the diodes to register "no light." With one exception, the number of diodes in shadow determines the width of the drop. The exception is that any drop which shades the last diode on the end of the array is not counted, since there is no way to tell where the edge of the drop really was.

The PMS Model No. GBPP-100S does not measure velocities. However, CIT added a timing circuit and software that checks diode status thousands of times per second to determine when shadows start or end. The "clock" is also checked to measure the duration of shadow time (Figure 2). It is assumed that the drop is spherical. The drop velocity is determined by dividing the diameter by the shadow time (T1 in Figure 2). Calibration runs made with metal pellets and water drops indicate that the drop diameter and velocity measurements are both consistent and accurate. In this way, the laser-optical system records a diameter and velocity for each drop falling through the screening area. This raw data must be screened and adjusted, however, to deal with some of the geometric peculiarities of the situation.
 
   
  Identification of Double Images
  Kohl, et al. (1985) have identified coincidence error as a significant potential problem with the laser optical approach to drop size measurement. The CIT system uses drop velocities to identify and screen out "doubles," or coincident drops. "Doubles" are really individual drops positioned so they cast overlapping shadows (Figure 3). If the shadows overlap side to side (Figure 3a), the system sees one wide drop, moving very fast. If the shadows overlap top and bottom (Figure 3b), the system sees a single drop moving very slow. These occurrences are identified (and rejected) by disregarding any drops whose velocities fall outside the typical range for drops of that size at a given distance from the sprinkler.

Each time a drop of a given size is detected, its measured velocity is stored in an array with columns for each drop size, and 500 rows (limited solely by computer space). When a given column is full, drop measurement is temporarily suspended for a velocity check on "doubles."

The mean and standard deviation of the 500 velocities are computed. Any drops with velocities more than two standard deviations away from the mean are discarded (Figure 4). In our experience, drop velocities vary with drop diameter and distance from the sprinkler, and don't relate to theoretical terminal velocities at all. So we determine "typical" velocities empirically, and use this criterion for identifying "unusual" velocities. After the screening has been done on the sample of 500, then data for the "good" drops are stored, the collection process is restarted and continues until another size column is filled with 500 velocities. Normally a sample of 10,000 drops is collected at each distance from the sprinkler.
 
 
Drop size tests are done along with a traditional test of the sprinkler application rate as a function of distance from the sprinkler. While this procedure cannot be guaranteed to eliminate all "doubles" (nor can any other, we suspect), we believe that most (enough) of the bad data has been eliminated, and that the resulting laser data is a good value in terms of information gained per test dollar spent.
   
  Adjustment Due to Sampling Window Size
  As noted above, drops cannot be counted if their image shadows the end diode of the array. This means that the width of the sampling window varies with drop size (Kohl et al.,1985). Larger drops have decreasing window sizes. The number of drops (or water volume falling in drops of a certain size) must be adjusted to the number (volume) that would have been caught with a window of a constant size. Thus the correction factor for a given size is the ratio of maximum window width to effective window width for that size.

The drop size distribution for an entire sprinkler may be arranged as in Table 1. The values in the "Overall" row are not merely the sum of the percentages for each distance, but are weighted in accordance with the amount of water applied by the sprinkler at each distance.
 
  DROP SIZE PARAMETERS FOR SPRINKLER PERFORMANCE EVALUATION
  The result of a CIT drop size test is a large table that lists, for each distance, the percentage of the water volume that occurs in drops of the various sizes (Table 1). This table provides the full detail needed for research purposes, but is far too massive to be easily interpreted or used by the general irrigation community. So CIT, in consultation with industry members, has developed special drop size parameters to aid in the evaluation of sprinkler performance. These parameters can give an indication of which sprinklers, nozzles and pressures may be susceptible to pattern distortion by the wind, and which may be susceptible to infiltration rate reduction when irrigating bare soil.
  Indicator Sizes
  Median Drop Diameter: This diameter, in the middle of the range of drop sizes from the sprinkler, has the following special property: half the sprinkler's water volume falls in drops smaller, and half falls in drops larger than the median size.

Other Indicator Sizes: These are diameters that mark the lower 10%, the lower 25%, the upper 25% and the upper 10% of the sprinkler water volume. For example, 10% of the sprinkler water volume falls in drops smaller than the Lower 10% Diameter, and 25% of the volume falls in drops larger than the Upper 25% Diameter.

The Median Diameter typifies those drops in the middle of the drop size range. The Lower 10% Diameter typifies the smallest drops from the sprinkler, while the Upper 10% Diameter typifies the largest. The Lower and Upper 25% Diameters further refine our understanding of the sizes of drops falling from the sprinkler.
   
  Per Cent Fines
  As discussed before, small drops are affected by the wind more than large drops. Even a relatively low wind condition can cause small drops to drift as they fall. If too much of the water from a sprinkler occurs in small drops, or "fines," it will be very susceptible to wind drift and pattern distortion by the wind.

For irrigation purposes, a "fine" water drop is considered to be any drop with a diameter of 1.0 millimeters or smaller. According to Delavan Corporation (1982), a one millimeter drop will drift more than one and one-half meters (five feet) during a fall from a height of three meters (10 feet) in the presence of a five km/hr (three mile/hr) wind. Smaller drops have greater drift distances (Table 2).
 
  The CIT laser drop measuring system determines the volume of water falling in drops of sizes 0.2, 0.4, 0.6, 0.8, 1.0 mm, and larger sizes, and it is an easy calculation to compute the percentage of the water volume falling in drops of diameter 1 mm or smaller, the % Fines. Sprinklers with larger % Fines are more likely to have their patterns distorted by the wind. Other things being equal, a sprinkler with a smaller % Fines is to be preferred over one having a larger value. Design of the nozzle, sprinkler and turning mechanism, and operating pressure can all effect the % Fines value.

  Sail Index
  The Sail Index is the cross-sectional area per unit volume of water of the drops comprising the sprinkler spray. The force exerted by the wind on a drop is proportional to the cross-sectional area of the drop. In other words, the bigger the "sail area," the more push the wind will give the drop. A given volume of water presents the greatest sail area to the wind when the volume is broken up into small drops. Sail Index is measured in square meters per liter of water (square feet per gallon of water). The greater the Sail Index the greater the potential for wind distortion of the pattern.
   
  Impact Power and Impact Rate
  Both of these parameters are related to the kinetic energy delivered to the soil by the drops in the sprinkler spray. Impact Power 6 is the rate at which drops deliver kinetic energy to the soil, in watts or horsepower. Other things being equal, sprinklers with finer drops have less Impact Power than those with larger drops.

The term "power" is used because in physics, energy per unit time is defined as power. Impact Power is analogous to sprinkler discharge (liters per second or gallons per minute). Larger sprinklers, those with greater flow rates, have more Impact Power than smaller sprinklers. Impact Power is a property of the sprinkler (and nozzle and pressure). But the soil responds only indirectly to Impact Power. Infiltration rate reduction depends on how the Impact Power is spread over the soil - whether it is focused on a small space or disbursed over a wide area (Stillmunkes, 1980; King and James, 1984).

Impact Rate 7 is the Impact Power per unit area. Impact Rate is a function of sprinkler and spacing. Larger sprinklers will have larger Impact Powers, but they will be spaced farther apart too, so Impact Rate is not necessarily governed by sprinkler size alone. Impact Rate indicates how much Impact Power is focused on each part of the soil surface. Impact Rate is analogous to application rate (mm/hr or in/hr). Impact Rate is measured in units of HP per square foot, or watts per square meter. Potential damage to the soil is greatest with sprinkler/spacing combinations that have high Impact Rates.

The total damage done to the soil will depend on the impact total energy delivered: the product of the Impact Rate and the irrigation time. This is analogous to the product of application rate and irrigation time, which gives the total depth of water delivered to the soil. These relationships are summarized below.
   
  SUMMARY
  The measurement of sprinkler drop sizes can help in the evaluation of sprinkler performance and sprinkler selection. Sprinkler drop size influences important aspects of irrigation such as sprinkler pattern distortion by the wind; evaporation and wind drift losses; wind drift when irrigating with effluent water; soil infiltration rate due to soil compaction or surface sealing; and penetration of plant canopies in greenhouses.

Special adaptations to an off-the-shelf laser measuring system made by CIT enable the measurement of drop velocity as well as size. Velocity measurements are crucial to the identification and elimination of "doubles," where separate drops cast what appears to be a single image of distorted size. Velocity measurements are also needed in the calculation of impact power and impact rate, which relate to a sprinkler's potential for reducing the infiltration rate of the soil irrigated.

CIT, in consultation with industry, has developed special drop size parameters to aid in the evaluation of sprinkler performance. These parameters can give an indication of which sprinklers, nozzles and pressures may be susceptible to pattern distortion by the wind, and which may be susceptible to infiltration rate reduction when irrigating bare soil. The parameters include Median Diameter (also other Indicator Diameters); % Fines; Sail Index; Impact Power and Impact Rate.
   
  NOTES
 
1 This paper was first presented at the American Society of Agricultural Engineers Symposium and Exhibition "Automated Agriculture for the 21st Century," December 16-17, 1991, Chicago, Illinois, in conjunction with the 1991 ASAE Winter Meeting. Proceedings, Pgs 87-96.
2 Kenneth H. Solomon, past director; Center for Irrigation Technology
3 David F. Zoldoske, interim director; Center for Irrigation Technology
4 Joe C. Oliphant, Hydraulics Laboratory Technician, Center for Irrigation Technology
5 Mention of company names is for convenience in reference only, and does not imply recommendation or endorsement over other companies not mentioned.
6 Alternate terms used in the literature for Impact Power are "impact energy flux" and "impact energy per unit time."
7 Alternate terms used in the literature for Impact Rate are "impact power density," "specific power" and "energy flux density."
   
  REFERENCES
 
1 Addink, J.W., J. Keller, C.H. Pair, R.E. Sneed and J.W. Wolfe. 1980. Design and Operation of Sprinkler Systems, Chapter 15 in Jensen M.E., editor, Design and Operation of Farm Irrigation Systems, ASAE, St. Joseph, MI, pp. 658-660.
2 Christiansen, J.E. 1942. Irrigation by Sprinkling. University of California Agricultural Experiment Station Bulletin 670, 124 p.
3 Delavan Corporation. 1982. Ag Spray Products (Catalog). Delavan Corporation, West Des Moines, Iowa, p. 27.
4 Heermann, D.F. and R.A. Kohl. 1980. Fluid Dynamics of Sprinkler Systems, Chapter 14 in Jensen. M.E., editor, Design and Operation of Farm Irrigation Systems, ASAE, St. Joseph, MI, pp. 592-594.
5 Inoue, H. 1963. Experimental Studies on Losses Due to Wind Drift in Sprinkler Irrigation. Technical Bulletin of the Faculty of Agriculture, Kagawa University, December 1963, 15(1):50-71.
6 King, B.A. and L.G. James. 1984. Determining Specific Power and Impact Energy of Sprinkler Droplets. ASAE Paper No. 84-2081, ASAE, St. Joseph, Michigan
7 Kohl, R.A., R.D. von Bernuth and G. Huebner. 1985. Drop Size Distribution Measurement Problems Using a Laser Unit. Trans. ASAE 28(1):190-192.
8 Solomon, K.H,. D.C. Kincaid and J.C. Bezdek. 1985. Drop Size Distributions for Irrigation Spray Nozzles. Trans. ASAE 28(6):1966-1974.
9 Solomon, K.H., D.F. Zoldoske and G.S. Jorgensen. 1990. The Center for Irrigation Technology: Beyond the First Decade. Proceedings, 3rd National Irrigation Symposium, American Society of Agricultural Engineers, Phoenix, Arizona, October 28-November 1, 1990, pp 416-421.
10 Stillmunkes, R.T. 1980. Impact Energy of Water Droplets Beneath Sprinkler Irrigation Systems. Masters Thesis, Department of Agricultural Engineering, Washington State University, Pullman, Washington, 77 pgs.
11

Zoldoske, D.F. 1991. Personal Communication.

 
 
 
 
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