#### 3.2. Radial Water Application Rate

The radial water application rate of the sprinkler with the three nozzle sizes under different working pressures is represented in

Figure 6. The radial application rate of the sprinkler presented a unimodal distribution under the lowest working pressure of 100 kPa. The peak values of application rate at the lowest working pressure of 100 kPa were 8.51, 7.28, and 11.35 mm h

^{−1} for nozzle sizes of 4.4, 4.8, and 5.2 mm, respectively. That was because when the working pressure was low, the breakup degree of the jet flow released from the sprinkler was low, leading to an insufficient diffusion of water along the radial direction, which easily formed a high peak value of the application rate. As the working pressure increased, the peak value of the application rate decreased, and the radial water distribution of the sprinkler became more uniform. At a given working pressure, the application rate of the sprinkler increased with an increase in the nozzle size (

Figure 6). Taking the working pressure of 250 kPa as an example, the average application rates of the sprinkler were 1.97, 2.17, and 2.64 mm h

^{−1} at the nozzle diameters of 4.4, 4.8, and 5.2 mm, respectively. In addition, it can be seen from

Figure 6 that the wetted radius of the sprinkler increased with the increases in working pressure and nozzle size.

As shown in

Figure 6, the error bars for the application rate for all nozzle sizes were largest under the lowest working pressure of 100 kPa, which illustrates a non-uniform water distribution in a circular direction. This can be explained because under the lowest pressure of 100 kPa, the impact force from the nozzle to the plate was not sufficiently large to overcome its resistance, and an unstable rotation was observed, which made the rotation speed randomly decrease; hence, the error bars became large. Therefore, the difference in peak error values for the three nozzles can be attributed to the different rotation speeds of the nozzles. At the lowest working pressure of 100 kPa, the peak error values for the application rate were 3.49, 1.08, and 2.17, and the sprinkler times per rotation were 184.86, 113.25, and 162.86 s (

Table 1) for the nozzle sizes of 4.4, 4.8, and 5.2 mm, respectively. With an increase in working pressure, the impact force increased, the rotation speed of the sprinkler increased, and the error bars became small. Consequently, the rotation speed of the sprinkler influenced spray uniformity. If the rotation speed is unstable, the water distribution of the sprinkler is non-uniform in the circular direction.

#### 3.3. Droplet Size

The VMDs of the sprinkler under different operating pressures are shown in

Figure 7. The droplet diameter increased exponentially with distance from the sprinkler, in accordance with the previous studies [

14,

19,

34]. However, the sprinklers of interest in these studies were impact sprinklers and FSPSs. As seen in

Figure 7, the droplet VMD values at the same distance from the sprinkler decreased with increasing working pressures, which verified the conclusion of Montero et al. [

35] that the working pressure is the main factor affecting the droplet-size distribution of the sprinkler.

As seen in

Figure 7, with an increase in the distance from the sprinkler, the droplet VMD values reached the maximum at the perimeter of the radius of throw. Under working pressures of 100, 150, 200, 250, and 300 kPa, the maximum VMD values for the nozzle size of 4.4 mm were 3.29, 4.12, 3.94, 2.94, and 2.79 mm, those for the nozzle size of 4.8 mm were 4.18, 4.41, 5.31, 3.42, and 4.22 mm, and those for the nozzle size of 5.2 mm were 5.96, 4.54, 2.99, 3.39, and 3.29 mm, respectively. It can be seen that the maximum VMD values increased initially and then decreased or decreased with the increase in working pressure. For most sprays, the formation process of water droplets was that (1) the water ejected from the nozzle and formed a jet, and then (2) through oscillation and air drag, the jet was finally broken into small water droplets. The droplet diameters were related to the thickness of the jet. Generally, the thicker the jet was, the larger the droplets were [

36]. When the working pressure increased, the flow rate of the sprinkler increased, and the thickness of the jet also increased, resulting in an increase in the droplets’ size. However, above a critical point, due to the effects of air drag and liquid surface tension, the coarse droplets broke up into fine droplets [

14]. Therefore, when the working pressure increased to a critical point, the maximum VMD values of the sprinkler decreased. An independent sample

t-test was used to test the significance in droplet VMD under different working pressures, nozzle sizes, and distances from the sprinkler.

The results indicate that the effects of the working pressure and distance from the sprinkler on droplet VMD were significant (

p < 0.01), but the effect of the nozzle size on droplet VMD was not significant (

p = 0.147). Considering the factors of the working pressure, distance to the sprinkler, and nozzle size on the influence of droplet VMD distribution, an empirical equation of VMD can be derived Equation (10).

where

d_{V} is the estimated VMD value in mm;

D is the nozzle diameter in mm;

P is the working pressure in kPa;

x is the distance from the sprinkler in m. The accuracy between the measured and calculated VMD values was evaluated by Equation (10). The value of RMSE is 0.351 and that of R

^{2} is 0.897 indicating a good agreement between observed and estimated VMD values.

The cumulative volume percentages of different droplet sizes at given distances from the sprinkler are presented in

Figure 8 for different working conditions. The gradients of the cumulative volume were greater when the droplets were near the sprinkler, and the droplet size was small. However, the cumulative droplet volume distribution of the low-pressure sprinkler is different from conventional sprinklers, such as spray plate sprinklers and complete fluidic sprinklers. With an increase in the distance from the sprinkler, the cumulative droplet volume of fine droplets (

d < 1 mm) decreased initially and then increased. For example, under the operating pressure of 200 kPa and distances from the nozzle of 2, 4, 6, 8, 10, and 12 m, the cumulative volume percentages of fine droplets (

d ≤ 1 mm) with the nozzle size of 4.4 mm were 100%, 96.16%, 83.86%, 72.27%, 81.69%, and 94.57%, respectively, those of fine droplets with the nozzle size of 4.8 mm were 100%, 97.14%, 85.60%, 82.47%, 85.95%, and 94.66%, respectively, and those with the nozzle size of 5.2 mm were 99.99%, 97.12%, 83.75%, 84.83%, 84.60%, and 98.06%, respectively. These results differ from those of other studies, which found that the cumulative volume percentages of fine droplets decreased with an increase in distance from the sprinkler [

14,

19]. This may be attributed to the differences in the structure and functioning principle of the sprinkler. The low-pressure sprinkler has a diffuser in front of the plate, which can promote the breakup of the jet and change the droplet size distribution pattern. However, for spray plate sprinklers and complete fluidic sprinklers, jets break up into fine spray due to dominant forces, such as drag and surface tension, that influence droplet size [

14]. Additionally, the droplets deposited at each observed distance were not of the same diameter but varied (

Figure 8), implying that the process of droplet formation and breakup is continuous along the jet.

#### 3.4. Droplet Velocity

Droplet velocity is one of the important characteristic indexes that influence the droplet kinetic energy.

Figure 9 represents the relationship between droplet mean velocity and the droplet diameter of the sprinkler with the nozzle size of 4.8 mm under three different working pressures. It can be seen that the droplet mean velocities increased as droplet diameters increased under different working conditions. An independent sample

t-test was used to test the significance in droplet mean velocity under different droplet diameters and distances from the sprinkler. The results indicate that the effect of the droplet size on droplet mean velocity was significant (

p < 0.01), but the effect of the distance from the sprinkler on droplet mean velocity was not significant (

p = 0.143). In previous studies [

14,

30], a logarithmic relation was derived between droplet diameter and mean droplet velocity Equation (12).

where

ῡ_{d} is the mean velocity of a droplet of

d mm in diameter in m s

^{−1};

a and

b are coefficients. The coefficients were obtained using regression analysis for each nozzle size and working pressure combination.

The logarithmic relationships between droplet mean velocity and diameter are shown in

Table 2. The

R^{2} values are greater than 0.837 in all cases, indicating a good overall fit between droplet velocity and diameter.

As seen in

Figure 9 and

Table 2, at a given droplet diameter, the mean droplet velocity increased with an increase in the working pressure. Taking the nozzle size of 5.2 mm as an example, the mean velocities of a droplet of 1 mm in diameter under operating pressures of 100, 200, and 300 kPa were 3.62, 3.77, and 3.85 m s

^{−1}, those of a droplet with a diameter of 2 mm were 5.66, 6.08, and 6.58 m s

^{−1}, and those of a droplet with a diameter of 3 mm were 6.89, 7.53, and 7.74 m s

^{−1}, respectively. The effect of the working pressure on droplet velocity can be attributed to the flow rate of the sprinkler increasing with the increasing working pressure. The flow rate (

Q, m

^{3} s

^{−1}) is equal to the velocity of the jet (

v, m s

^{−1}) multiplied by the cross-sectional area of the nozzle (

A, m

^{2};

Q =

Av). As a given nozzle size, the velocity of the jet increases with the increasing flow rate. Therefore, the velocity of the droplet increased with an increase in the working pressure. The result of the significance test showed that the effect of nozzle size on droplet velocity was not significant (

p = 0.319).

Considering the influence of the factors of working pressure and nozzle size on mean droplet velocity, an empirical equation of droplet mean velocity can be derived Equation (13).

where

ῡ_{d} is the mean velocity of a droplet of

d mm in diameter in m s

^{−1};

D is the nozzle diameter in mm;

P is the working pressure in kPa.

#### 3.6. Kinetic Energy

The kinetic energy per unit droplet volume (

KE_{di}) values at different distances from the sprinkler are presented in

Figure 11. The

KE_{di} value near the sprinkler was low in all cases and increased with an increase in the distance from the sprinkler. The analysis of variance showed that working pressure had a significant effect on the

KE_{di} (

p < 0.01). At the same radial location, the

KE_{di} decreased with increasing working pressure, which was similar to the effect of the working pressure on the droplet size. In addition, under the low working pressures of 100 and 150 kPa, the maximum

KE_{di} value increased with an increase in nozzle size. Under the lowest working pressure of 100 kPa, the maximum

KE_{di} values with nozzle sizes of 4.4, 4.8, and 5.2 mm were 22.24, 27.92, and 33.97 J L

^{−1}, and they were 29.69, 30.54, and 32.23 J L

^{−1} under the working pressure of 150 kPa. Considering the influence of the factors of working pressure, nozzle size, and distance from the sprinkler on

KE_{di}, Equation (14) gives an empirical equation for

KE_{di}.

where

D is the nozzle diameter in mm;

P is the working pressure in kPa;

i is the distance from the sprinkler in m.

Specific power represents the rate at which kinetic energy is transferred to the soil surface; it is also referred to as droplet energy flux [

37]. The radial SP of the low-pressure sprinkler was calculated based on the droplet diameter, droplet velocity, and water application rate at each sampling point (

Figure 12). Under the low pressures of 100 and 150 kPa, along the wetted radius, the computed SP value increased and then decreased, with a peak value at a certain distance. When the working pressure increased from 100 to 300 kPa, the peak value of SP decreased, and the radial SP distribution of the sprinkler became more uniform. Under the working pressures of 100, 150, 200, 250, and 300 kPa, the peak SP values with the nozzle size of 4.4 mm reached 0.023, 0.033, 0.018, 0.012, and 0.013 W m

^{−2}, those with the nozzle size of 4.8 mm were 0.038, 0.036, 0.018, 0.015, and 0.017 W m

^{−2}, and those with the nozzle size of 5.2 mm were 0.091, 0.029, 0.022, 0.019, and 0.017 W m

^{−2}, respectively. The peak value of SP increased with an increase in the nozzle size under the same working pressure. Since the SP value depended on the water application rate, the effects of working pressure and nozzle size on SP were similar to those of pressure and nozzle size on the application rate. The maximum SP value was observed for the sprinkler with the largest nozzle size under the lowest working pressure in all cases, as illustrated in

Figure 12.

As seen in

Figure 12, when the distance from the sprinkler was less than 6 m, the SP was less than 0.012 W m

^{−2}; this is due to the low droplet velocity and small droplet size near the sprinkler. The peak values and distances of peak points of SP and application rate from the sprinkler are shown in

Table 3. It can be seen that the peak points of application rate and SP for the low-pressure sprinkler were almost overlapping. Although the size and velocity of water droplets reached their maximum values at the outer end, the peak value of SP was not at the outermost end of the wetted radius, and the rapid decrease in sprinkler application rate led to the decrease in SP. Furthermore, although the droplet velocity was lower under the lowest operating pressure of 100 kPa, the high application rate of the sprinkler led to a high SP value. Therefore, the SP peak occurs only when the droplet size, velocity, and application rate are maintained at a high level. The high kinetic energy of spray water results in a soil surface seal, which often reduces the infiltration rate and promotes runoff, resulting in soil erosion and a waste of water resources.