Irrig Sci (2015) 33:367–374 DOI 10.1007/s00271-015-0472-6

ORIGINAL PAPER

Comparison of fluidic and impact sprinklers based on hydraulic performance Xingye Zhu1 · Shouqi Yuan1 · Jianyuan Jiang1 · Junping Liu1 · Xingfa Liu1 

Received: 24 September 2014 / Accepted: 17 June 2015 / Published online: 10 July 2015 © Springer-Verlag Berlin Heidelberg 2015

Abstract  A comparative study of an outside signal sprinkler (OS), a fluidic sprinkler (FS), and an impact sprinkler (IS) was carried out. The OS, FS, and IS were evaluated individually under indoor experimental conditions. Water distribution evaluations were measured under four operating pressures at a 1.5-m nozzle height (above the ground). Approximately 36 individual trials were performed. The results show that the discharge coefficient of the OS and FS was slightly larger than that of the IS. The water distribution profiles of the OS, FS, and IS were parabola-shaped, ellipse-shaped, and doughnut-shaped, respectively. The wetted radius for the OS was similar to the wetted radius of the FS and was 8.7–12 % less than the IS. An accurate and simple empirical equation for the wetted radius of OS and FS is reported. Additionally, equations of water application rate, with regard to distance from the sprinklers, are given. The average coefficients of determination for the OS, FS, and IS were 91.8, 89.2, and 79.1 %, respectively. Individual spray sprinkler water distributions were mathematically overlapped to calculate the combined uniformity coefficient (CU). Maximal combined CUs of 80.88, 80.92, and 78.12 % were found for the OS, FS, and IS, respectively. Both the OS and FS were found to have greater CU values than the IS, which indicates that the OS and FS provided a better water distribution pattern than the IS at low pressure.

Communicated by G. Merkley. * Xingye Zhu [email protected] 1



Research Center of Fluid Machinery Engineering and Technology, Jiangsu University, Zhenjiang 212013, Jiangsu, China

Introduction Water is the main yield-determining factor in the majority of agricultural systems. To sustain agricultural production in the future, it is important to optimize irrigation systems. Sprinkler irrigation is characterized by a high-potential irrigation efficiency (Clemmens and Dedrick 1994), and it has been widely used in agriculture for water conservation. The sprinkler head is regarded as a key component of any sprinkler irrigation system, and its hydraulic performance can affect the irrigation efficiency of sprinkler systems. Bilanski and Kidder (1958) studied the effects of various sprinkler components, including pressure and nozzle size, on the pattern shape and radius but made no general conclusions. Seginer (1963) developed standardized patterns and related the pattern radius to the pressure head for certain nozzle sizes. Solomon and James (1980) used a clustering algorithm to group pattern test data into typical standard shapes and used the pattern radius to define a relative distance from the sprinkler. Kincaid (1982) proposed an analytical approach suitable for describing the combined effects of nozzle size, pressure, and nozzle discharge on sprinkler pattern radius. Much research has been conducted on sprinklers and has focused on factors such as sprinkler nozzle characteristics, operating pressure, flow rate, riser characteristics, water distribution patterns, sprinkler irrigation uniformity, and environmental factors (Culver and Sinker 1966; Chen and Wallender 1985; Edling 1985; Fischer and Wallender 1988; Louie and Selker 2000; Faci et al. 2001; Mateos 2006; Zhu et al. 2012; Liu et al. 2013a; Burillo et al. 2013; Dwomoh et al. 2013). There is a general trend in sprinkler machines to decrease energy costs. The measurement of sprinkler water distribution patterns is required for the research and development of new sprinkler prototypes.

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Fig. 1  Photographs of the studied sprinklers. a OS, b FS, c IS

The water distribution from a sprinkler system depends on (1) the type of the sprinkler, (2) the size, number, and internal design of the nozzles, and (3) the working pressure. Water distribution tests of individual sprinkler heads have been reported in numerous publications (Seginer 1963; Bean 1965; Pair 1968; Hermsmeier 1972; Seginer et al. 1992; Tarjuelo et al. 1999); however, information is lacking on water distribution comparisons under many types of operating sprinkler systems. The wetted radius of agricultural sprinklers is important as it determines the wetted area, the average application rate, and the runoff potential. The lateral area wetted by a sprinkler is approximately proportional to the wetted radius. From an economic standpoint, the wetted radius determines the maximum sprinkler spacing necessary to obtain acceptable uniformity and, thus, determines equipment costs and/or labor requirements. Sprinkler irrigation uniformity is also an important measure of performance. Water losses, which can decrease the irrigation efficiency of sprinkler systems, partly depend on the type of sprinkler and water application. These are all important factors that can cause energy losses (Keller and Bliesner 1990). Today, impact sprinklers (IS) are widely used throughout the world (Frederick 2009). The rocker arm is known to collide with the sprinkler body to achieve the rotation for IS. The service life of the sprinkler would be easily affected by the instability of the spring. Therefore, it is necessary to develop a new type of sprinkler that can overcome the problem of the spring impacting the sprinkler. Two new sprinkler prototypes, developed in China, may become a substitute for the IS in the near future (Li et al. 2006; Zhu et al. 2009, 2012; Li et al. 2011). Three types of sprinklers with different nozzle size combinations were used in this study [outside signal sprinkler (OS), Fig. 1a, fluidic sprinkler (FS), Fig. 1b, and IS, Fig. 1c]. The reason for using these three sprinkler types was to compare the hydraulic performance quality of the relatively new FS with the popular and highly utilized IS. For the new types of sprinklers (OS and FS) in this study, there is little reported research, and comparisons

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Table 1  Basic parameters of the three sprinkler types Sprinkler type

Sprinkler nozzle Equivalent diamshape eter (mm)

Sprinkler jet angles (°)

OS FS

Ellipse type Waist type

4.57 4.58

27 22

IS

Circular type

4

23

of hydraulic parameters are quite limited. This study was designed to investigate the hydraulic performance of the newly designed FS in comparison with the well-known and widely used IS, as well as to offer recommendations for the improvement of the FSs operational performance. In this study, a comparison of OS, FS, and IS was performed. The aims of this study were (1) to compare the hydraulic performance of individual OS, FS, and IS in indoor conditions, (2) to compare the uniformity coefficient resulting from the overlapping of individual sprinklers with different spacings, and (3) to introduce several empirical equations for the newly developed sprinklers for further use in model refinements. Results were used to determine the effect of these factors on the performance of three types of sprinklers.

Materials and methods Spray sprinklers The three types of sprinkler heads were specially fabricated for this study. The OS and FS were developed by the Research Center of Fluid Machinery Engineering and Technology (Jiangsu University, P. R. China). The OS was specifically manufactured as an experimental sample; the FS was manufactured by Shanghai Watex Water-economizer Technology Co, Ltd., China, and the IS was from the Nelson Irrigation Co., Walla Walla, Washington, USA. Table  1 shows the basic parameters of three sprinkler

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types. The main differences between the OS, FS, and IS are that the OS was equipped with a 4.57-mm ellipse type nozzle (equivalent diameter); the FS had a 4.58-mm waist type nozzle; and the IS had a 4-mm circular nozzle. Additionally, the sprinkler jet forms a 27° angle for the OS, 22° for the FS, and 23° for the IS (with respect to the horizontal). The working principles for the OS, the FS, and the IS were different. The working theory of the OS and FS primarily depends on the pressure difference between the left and right sides. The driving moment is achieved by the flow reaction, and the fluidic direction is changed. The main differences between the working theories of the OS and the FS are as follows: The OS receives a signal flow from outside the cover plate, but the FS receives its flow from inside the fluidic component (Li et al. 2006, 2011; Zhu et al. 2009, 2012). In summary, the working theory of the IS is that the rocker arm collides with the sprinkler body to achieve the rotation, which primarily depends on the stability of spring. In short, the OS and FS designs are new to overcome the spring problem that could be occurring in the IS. Experimental setup and procedure Experimental conditions and scheme The experiments were conducted in the indoor facilities of the Research Center of Fluid Machinery Engineering and Technology, (Jiangsu University, P. R. China). The laboratory is a test building that is circular in shape with a diameter of 44 m and a height of 18 m. Performing the experiment in an indoor facility ensured uninterrupted radial water distribution and avoided wind resistance to rotation (Sourell et al. 2003; Liu et al. 2013a, b). A schematic diagram of the experimental conditions in the laboratory is shown in Fig. 2. A centrifugal pump supplied water to the irrigation system from a constant level reservoir. Discharge was measured by an electromagnetic flowmeter with an accuracy tolerance of 0.5 %. Pressure was measured at the base of the sprinkler head using a pressure gauge with an accuracy tolerance of 0.4 %. The catch cans used in the

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study for testing radial water application were cylindrical in shape with a height of 0.6 m and an inside diameter of 0.2 m. Catch cans, which were used to collect water, were spaced at 1-m intervals from the sprinkler in two singlecollector lines in opposite directions. The water collected in each can was measured using a graduated cylinder. The application rate was calculated based on the diameter of the catch cans and the duration of each test. The radial application rate distributions for the sprinklers were then determined in the laboratory. The sprinkler heads were mounted on a 1.5-m riser at a 90° angle to the horizontal and were approximately 0.9 m above the top of the catch cans. The sprinklers used in this study were OS, FS, and IS. The corresponding operating pressures were 200, 250, 300, and 350 kPa, respectively. All nozzle sizes and operating pressures were within the manufacturer’s recommendations. Air and water temperature was approximately 25 °C, and the sprinkler was run for a few minutes in order to standardize environmental conditions before performing the experiments. The following standards were adopted in the design of the experimental setup and in the experiment itself: ASAE S.330.1 (1985a), ASAE S.398.1 (1985b), and ISO 7749-2 (1990), MOD GB/T 19795.2 (2005). A minimum of three replications were conducted for each pressure and nozzle combination, and data were averaged and used as the final experimental data. Four experimental pressures were considered in the discharge–pressure relationship experiments: 200, 250, 300, and 350 kPa. The operating pressure at the base of the sprinkler head was regulated and maintained by a valve. For each sprinkler-nozzle-pressure setting, the duration of the test was 30 min. In the experiments, the pressure gauge as well as the electromagnetic flowmeter was used to read the pressure and flow rate, respectively. The sprinkler discharge profiles were observed under windless conditions. The effect of the different types of sprinklers on the discharge can be expressed in terms of the discharge coefficient, c. The relationship between the discharge and the operating pressure for a sprinkler is generally expressed as follows:

Fig. 2  Schematic diagram of the experimental conditions in the laboratory

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q = cA(2gH)1/2

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(1)

where q is the volumetric discharge of the sprinkler (m3 s−1), A is the nominal cross-sectional area of the nozzle (m2), g is the gravitational acceleration (m s−2), H is the pressure head (m), c is the discharge coefficient, and the discharge exponent for the sprinklers was 0.5. Calculation of combined uniformity coefficient The combined coefficient of uniformity CU (%), developed by Christiansen (1942), was calculated using the following equation:    n    hi − h¯  CU = 100 1.0 − (2) nh¯ i=1

where hi  = water depth of calculated point i, mm h−1; h¯   = mean water depth of all calculated points within the area, mm h−1; and n  = total number of calculated points used in the evaluation. Many factors affect combined CU, including sprinkler type, lateral configuration, pressure, and environmental conditions. A great deal of research has been conducted on the effects of these factors (Branscheid and Hart 1968; Fukui et al. 1980; Nderitu and Hills 1993; Li and Kawano. 1996; Playan et al. 2006; Zhang et al. 2013). After the tests of radial application rate, matrix laboratory (MATLAB) was used as the computational program. Radial data of water distribution were modified into net data for the sprinklers. The final calculated average radial application rate distribution data were the same in all directions from the OS, FS, and IS. This result indicates that the available data points are distributed in a manner similar to a spider web. A grid of data points is converted to calculate the coefficient of uniformity. The depth of the net point depends on the distance away from the sprinkler. The water depth of every interpolating point, assumed to be a continuous variable value, was calculated using mathematical model of interpolating cubic splines (Han et al. 2007; Zhu et al. 2009). The model for converting radial data into the net data’s insert function was established as follows: Point A is the net point between two adjacent radial rays, and (xA, yA) is its coordinate. P1, P2, P3, and P4 are the four nearest points to point A on the two adjacent radial rays, and (ρ1, θ1), (ρ2, θ2), (ρ3, θ3), and (ρ4, θ4) are their coordinates. Their positions are therefore xi = ρicosθi (i = 1, 2, 3, 4) and yi  =  ρisinθi (i  = 1, 2, 3, 4). Their water depths are h1, h2, h3, and h4, and the distances away from point A are r1, r2, r3, and r4, respectively. Thus,  (3) ri = (xi − xA )2 + (yi − yA )2 (i = 1, 2, 3, 4) The water depth of point A can be expressed as

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(4)

hA = C1 h1 + C2 h2 + C3 h3 + C4 h4 , 2

2

2

where C1 = (r2r3r4) /R, C2 = (r1r3r4) /R, C3 = (r1r2r4) /R, C4  = (r1r2r3)2/R, and R  = (r1r2r3)2  + (r1r3r4)2  + (r1r2r4)2  + (r2r3r4)2. According to the actual measurements, the water depth of every net point can be calculated using Eq. (3). The combined CU can then be calculated for the overlapping of spray sprinklers with different lateral spacings.

Results and discussion Comparison of operating pressure and discharge All of the sprinklers used in the experiments are summarized in Table 2. The discharge increased as the operating pressure increased, and they were almost linearly related. The discharge coefficient, c, for the OS, FS, and IS was determined based on the observed pressure–discharge data. After calculation using Eq. (4), the value of c for OS ranged from 0.75 to 0.77 with an average value of 0.76; the value of c for FS ranged from 0.74 to 0.79 with an average value of 0.77; the value of c for IS ranged from 0.67 to 0.71 with an average value of 0.68. The average discharge coefficients and the standard deviation for the OS, FS, and IS are listed in the columns of Table 2. According to our calculations, the discharge coefficients for the sprinklers varied little with different operating pressures, and it can be concluded that the discharge coefficient is independent of operating pressure. Similar findings have been previously reported by a number of authors (Seginer et al. 1992; Li et al. 1995; Zhu et al. 2012). The discharge coefficient of OS is similar to that of FS; the IS discharge coefficient is slightly lower (by approximately 0.1). The new types of sprinklers, OS and FS, had the advantages of a larger discharge coefficient. Comparison of wetted radius The wetted radius and the sprinkler application rate were measured together under different operating pressures, and the wetted radius of the OS, FS, and IS is summarized.

Table 2  List of sprinklers and discharge coefficient used in the experiments Sprinkler

Nozzle diameter (mm)

Discharge coefficient

Standard deviation

OS FS

4.57 4.58

0.76 0.77

0.008 0.019

IS

4.00

0.68

0.012

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Figure 3 compares the wetted radius for the OS, FS, and IS at 200, 250, 300, and 350 kPa. As shown in Fig. 3, the wetted radius increased with the operating pressure. The IS had the largest measured wetted radius of the three sprinklers. For the OS, the wetted radius was 10.4, 10.6, 10.8, and 11.1 m at 200, 250, 300, and 350 kPa, respectively. These radii were, on average, less than the IS by 8.7, 10.4, 12.0, and 9.9 %, respectively. For the FS, the wetted radius was 10.3, 10.7, 10.9, and 11.1 m at 200, 250, 300, and 350 kPa, respectively. These radii were, on average, less than the IS by 9.7, 9.3, 11.0, and 9.9 %, respectively. The wetted radius for the OS was similar to that of the FS and was 8.7–12 % less than the wetted radius of the IS. Compared to the IS, the wetted radius reduction in the OS and FS may be due to the two-phase fluidic working theory. Gas and liquid were mixed inside the sprinkler, and the outlet water for the OS and FS was more dispersed than the outlet water for the IS. Therefore, a reduction occurred for these sprinklers. Special attention was given to the development of the first empirical equation for the OS and FS and is as follows:

R = 1.45d 0.43 H 0.41

(5)

Compared to the other reported equations, there was little deviation from the expected values overall, though the

Fig. 3  Comparison of wetted radius subject to different operating pressures

average deviation was 5.50 % for OS and 5.28 % for FS. The proposed equations for the OS and FS proved to be sufficiently accurate and simple to use. Comparison of water distribution patterns Figure  4 presents the radial application rate distribution profiles for the OS, FS, and IS at 200, 250, 300, and 350 kPa. The OS produced parabola-shaped profiles. The water application rate was high near the sprinkler and decreased approximately linearly as the distance from the sprinkler increased. For the various operating pressures, the average values of the OS application depth varied from 0.6 to 5.91 mm h−1. The maximum value of application rate was obtained for the four analyzed pressures (4.00 mm h−1 at distances of 3 m from the sprinkle for 200 kPa, 4.82 mm h−1 at 4 m for 250 kPa, 5.17 mm h−1 at 3 m for 300 kPa, and 5.91 mm h−1 at 5 m for 350 kPa). Starting from this distance, the application rate decreased until it reached the minima. For 200 kPa at 10 m, 250 kPa at 10 m, 300 kPa at 10 m, and 350 kPa at 11 m, the minimum values were 1.11, 1.09, 1.07, and 0.6 mm h−1, respectively. The FS produced ellipse-shaped profiles. As the distance from the sprinkler increased, the water application rate first increased to a maximum value and then decreased sharply. The application rates of FS varied from 0.42 to 4.91 mm h−1. The maximum value of application rate was obtained for the four analyzed pressures (4.00 mm h−1 at 8 m for 200 kPa, 4.08 mm h−1 at 8 m for 250 kPa, 4.69 mm h−1 at 8 m for 300 kPa, and 4.91 mm h−1 at 8 m for 350 kPa). Starting from this distance, the application rate decreased sharply to reach the minima. For 200 kPa at 10 m, 250 kPa at 10 m, 300 kPa at 11 m, and 350 kPa at 11 m, the minimum values were 1.04, 1.40, 0.42, and 0.49 mm h−1, respectively. The IS produced doughnut-shaped profiles, which has been previously described by several authors (Chen and Wallender

Fig. 4  Water application profiles for different operating pressures. a OS, b FS, c IS

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1985; Li et al. 1994). The application rate of IS varied from 0.62 to 2.87 mm h−1. The high value of application rate was obtained at a distance of 1 m from the sprinkler for the four analyzed pressures (2.87 mm h−1 for 200 kPa, 2.6 mm h−1 for 250 kPa, 2.13 mm h−1 for 300 kPa, and 2.16 mm h−1 for 350 kPa). Starting from this distance, the application rate decreased to reach local minima. For 200 kPa at 6 m, 250 kPa at 3 m, 300 kPa at 3 m, and 350 kPa at 3 m, the values were 1.29, 1.51, 1.38, and 1.36 mm h−1, respectively. At farther distances, the application rate increased to reach higher values of 2.27 mm h−1 at 10 m for 200 kPa, 2.27 mm h−1 at 10 m for 250 kPa, 2.04 mm h−1 at 9 m for 300 kPa, and 2.09 mm h−1 at 9 m for 350 kPa. The comparison of water distribution from three types of sprinkler heads operating under the same conditions showed that the IS produced a lower average maximum application rate than the OS or FS. These differences can be attributed to two factors. First, the flow rate in the same operating pressures was much higher for the OS and FS than the IS, and second, the instantaneous water application rate for IS varied from minimum to maximum several times and then returned to zero. Under the OS and FS, the instantaneous water application rate does not have the wide variation caused by the IS, and this results in a higher average maximum water application rate for these sprinkler heads.

Special attention was given to the development of empirical equations of water application rate with regard to distance from sprinkler for the OS, FS, and IS. Table 3 presents the equations of those profiles. The coefficient of determination for OS ranged from 85.3 to 94.7 %, with an average of 91.8 %; for FS, it ranged from 84.4 to 89.2 % with an average of 87.0 %; and for IS, it ranged from 70.4 to 89.1 % with an average of 79.1 %. Comparison of combined uniformity coefficient The combined CUs were calculated using the method described above. The square spacing for lateral radius times of 1.0, 1.1, 1.2, 1.3, 1.4, 1.5, 1.6, 1.7, and 1.8 was chosen for each of the three sprinklers used in the study. The calculated combined CUs for OS, FS, and IS at 200, 250, 300, and 350 kPa are shown in Fig. 5. Figure 5 presents the relationship between the combined CU and spacing along the main axis, and the horizontal axis is radius time rather than distance from the sprinkler. All three sprinklers produced ellipse-shaped CU profiles. The CU value first increased to the maxima and then subsequently decreased with increasing spacing. The range of combined CU values for OS was (at different pressures) as follows: 46.69 % at a spacing of 1 (time of wetted radius) to 80.88 % at 1.6 times (200 kPa), 52.09 % at 1 time to 79.19 % at 1.5 times (250 kPa), 51.63 % at 1.8

Table 3  Equations of water application rate with regard to distance from sprinkler Sprinkler

Mathematical model

Calculated value 200 kPa

OS

h = Al2 + B

FS

h = Al3 + Bl + C

IS

h = Al3 + Bl2 + Cl + D

250 kPa

350 kPa

A

B

C

A

B

C

A

B

C

A

B

C

−0.028

4.16

–

–

–

–

1.14

0.54

2.59

−0.042

6.32

0.68

−0.041

5.63

1.02

−0.038

5.11

0.70

0.71

2.24

−0.015

0.29

−1.59

−0.015

0.27

−1.40

−0.008

0.14

−069

−0.007

0.12

−0.50

−0.0065 D = 4.05

−0.0063 D = 3.69

Fig. 5  Combined CU for different operating pressures. a OS, b FS, c IS

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300 kPa

−0.0055

D = 2.51

−0.0064

D = 2.27

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times to 75.5 % at 1.4 times (300 kPa), and 47.7 % at 1 time to 76.42 % at 1.5 times (350 kPa). Using 200 kPa as an example, the highest CU occurred at 1.6 times spacing. Uniformity increased with spacing from 1 to 1.6 times and ranged from 46.69 to 80.88 % (average 65.34 %). Thereafter, the uniformity decreased with spacing. From 1.6 to 1.8 times spacing, the CU ranged from 75.68 to 80.88 % with an average of 78.94 %. The range of combined CU values for FS was (at different pressures) as follows: 58.92 % at 1 time to 80.92 % at 1.6 times (200 kPa), 54.59 % at 1 time to 76.62 % at 1.6 times (250 kPa), 56.48 % at 1 time to 79.31 % at 1.4 times (300 kPa), and 48.51 % at 1 time to 78.63 % at 1.5 times (350 kPa). Using 200 kPa as an example, the highest CU occurred at 1.6 times spacing. Uniformity increased with spacing from 1 to 1.6 times and ranged from 58.92 to 80.92 % (average 72.12 %). Thereafter, uniformity decreased with spacing. From 1.6 to 1.8 times spacing, the CU ranged from 69.75 to 80.92 % with an average of 75.93 %. The range of combined CU values for IS was (at different pressures): 45.88 % at 1 time to 67.85 % at 1.7 times (200 kPa), 42.00 % at 1 time to 73.85 % at 1.7 times (250 kPa), 48.17 % at 1 time to 77.94 % at 1.6 times (300 kPa), and 48.28 % at 1 time to 78.12 % at 1.6 times (350 kPa). Using 350 kPa as an example, the highest CU occurred at 1.6 times spacing. Uniformity increased with spacing from 1 to 1.6 times and ranged from 48.28 to 78.12 % (average 65.63 %). Thereafter, uniformity decreased with spacing. From 1.6 to 1.8 times spacing, the CU ranged from 61.52 to 78.12 % with an average of 70.60 %. The comparison of the CU from the three types of sprinkler heads reveals that there was little difference between the calculated CU values for the OS and FS. Both OS and FS gave higher CU values than the IS for a given pressure and sprinkler spacing, especially when operated at low pressure. This indicates that the OS and FS provided a better water distribution pattern than the IS at low pressure. One possible explanation for this could be that for the two-phase FSs, the internal turbulent flow was less uniform from the nozzle outlet, and more water was applied near the sprinkler, resulting in a higher combined CU.

Conclusions This study presents a comparison of the hydraulic performance for three types of sprinklers: an OS, a FS, and an IS. The following conclusions are supported by this study: 1. The discharge coefficients of the OS and FS were slightly larger than that of the IS (by approximately 0.1).

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2. An empirical equation for the wetted radius of the OS and FS R  = 1.45d0.43H0.41 was reported in this study for the first time. The proposed equation was sufficiently accurate and simple to use for both the OS and FS. 3. For the water distribution profiles, the OS, FS, and IS were parabola-shaped, ellipse-shaped, and doughnutshaped, respectively. The IS had a lower average maximum application rate than the OS or FS. The equations of water application rate, with regard to distance from sprinkler, were reported, and the coefficients of determination for the OS, FS, and IS were 91.8, 89.2, and 79.1 %, respectively. 4. The maximal combined CUs of OS, FS, and IS were 80.88, 80.92, and 78.12 %, respectively. Both the OS and FS produced higher CU values than the IS for a given pressure and sprinkler spacing, especially when operated at low pressure, indicating that OS and FS provided a more acceptable water distribution pattern at low pressure. Acknowledgments  The authors are greatly indebted to the Program for National Hi-Tech Research and Development of China (863 Program, number 2011AA100506), the National Natural Science Foundation of China (number 51309117), the Postdoctoral Science Foundation Special Support of China (number 2014T70484), the Postdoctoral Science Foundation of China (number 2015M570415) and the Six Talent Peaks Project in Jiangsu Province (number ZBZZ018), which provided sponsorship for the study.

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