# Teaching Sprinkler Irrigation Engineering by a Spreadsheet Tool

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## Abstract

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^{®}spreadsheet licensed by 2018 Microsoft©. The objective of this tool is to offer an alternative to students in irrigation engineering, particularly for those training in the design of sprinkler irrigation systems so they can develop their theoretical knowledge and practical skills acquired in laboratory and field experiments. The main findings reported in this paper address well-agreed methodologies for evaluating radial patterns of precipitation rates, diameter distribution frequency, ballistic simulation of water drops’ movement through air, kinetic energy, and performance indicators as part of the core parameters of efficient irrigation system management. This computing tool provides outcomes in tabular and graphical formats that are consistent with those found in studies previously published in specialized literature on related topics. Likewise, spreadsheets have been proven to be adequate pedagogical instruments on the path to achieving meaningful learning; however, this assertion still needs to be confirmed through a rigorous study of students who have used the developed tool.

## 1. Introduction

^{®}spreadsheet tool licensed by 2018 Microsoft© [34] for solid-set sprinkler irrigation assessment to encourage irrigation engineering learning. The main goal is to reinforce mathematical thinking as well establish as its relational value for sprinkler irrigation using a practical spreadsheet tool. A special emphasis on a ballistic model applied to water drop diameter distribution, optimal numerical simulation by means of Runge–Kutta pairs, the application rate for isolated sprinklers, kinetic energy and specific power for water drop impact on surface soil or crop canopy, and sprinkler irrigation performance through uniformity and efficiency indicators were considered for a number of configurations.

## 2. Background

#### 2.1. Mathematical Model for Sprinkler Irrigation

_{a}is the air density [M L

^{−3}]; ρ

_{w}is the water density [M L

^{−3}]; A is the water drop acceleration in the air [L T

^{−2}]; $\varphi $ is the drop diameter [L]; g is the gravity acceleration [L T

^{−2}]; C

_{d}is the aerodynamic drag coefficient, which can be expressed as a function of the Reynolds number [adim] [45,46], or as a function of the operating pressure, drop diameter, equivalent diameter, and nozzle discharge coefficient [adim] [47]; V is the drop’s velocity in the air [L T

^{−1}]; ${\mathrm{U}}_{\mathrm{x}}=\frac{\mathrm{dx}}{\mathrm{dt}},\text{}{\mathrm{U}}_{\mathrm{y}}=\frac{\mathrm{dy}}{\mathrm{dt}}$, and ${\mathrm{U}}_{\mathrm{z}}=\frac{\mathrm{dz}}{\mathrm{dt}}$ are components of drop velocity [L T

^{−1}]; and W

_{x}, and W

_{y}are components of the wind velocity [L T

^{−1}], both with respects to a coordinate system. Terms between square brackets correspond to dimensions of each variable.

_{x}, v

_{y}, and v

_{z}denote the initial drop velocity at x, y, and z coordinates [L T

^{−1}], respectively, and $\mathrm{b}=\frac{3}{4}\frac{{\rho}_{\mathrm{a}}}{{\rho}_{\mathrm{w}}}\frac{{\mathrm{C}}_{\mathrm{d}}}{\varphi}\mathrm{V}$ [T

^{−1}]. By knowing the vertical distance between a datum and the sprinkler nozzle, it is possible to establish coordinates at which the water drops land, as well as their corresponding velocities. Regarding the aerodynamic drag coefficient (C

_{d}), computed as a function of the Reynolds number (R

_{e}) for a spherical shaped droplet, this has been formulated in several ways by different authors. Equations (10)–(12) are expressions proposed by Okamura [45] to determine this value.

_{d}from R

_{e}magnitude was proposed by Park et al. [46], such as that which is argued in Equations (13) and (14).

_{d}can be obtained by accounting for the operating pressure, drop diameter, equivalent diameter, and nozzle discharge coefficient (Equations (15) and (16)).

^{2}T

^{−1}]; P is the operating pressure [M L

^{−1}T

^{−2}]; ${\mathrm{D}}_{\mathrm{e}}=\frac{4{\mathrm{A}}_{\mathrm{h}}}{{\mathrm{P}}_{\mathrm{w}}}$ is the equivalent diameter [L]; A

_{h}is the hydraulic area of nozzle [L

^{2}]; P

_{w}is the wetted perimeter [L]; C is the nozzle discharge coefficient [adim]; D is the volume mean drop diameter [L]; A

_{1}, A

_{2}, and A

_{3}are the regression coefficients [adim]; and D

_{n}is the nozzle diameter [L].

#### 2.2. Numerical Approach to Simulating Water Drops’ Trajectory and Velocity

_{n+1}) are estimated on the basis of the preceding value (Ψ

_{n}) added to the product of the time step (Δt) and a weighted slope resulting from estimating the K

_{1}, K

_{2}, K

_{3}, and K

_{4}constants. It should also be clarified that due to the inherent characteristics of the spreadsheet used, it is difficult to define a time interval for executing an iterative process; instead, the computational tool has, by default, a configuration for performing 750 iterations automatically.

#### 2.3. Kinetic Energy and Power

_{kϕ}) [M L

^{2}T

^{−2}] was determined according to the method introduced by Kohl et al. [56] (Equation (20)).

_{kΩ}) [M L

^{−1}T

^{−2}] within a domain (

_{Ω}) per unit volume of water applied can be determined from the drops’ kinetic energy and total volume of a given set of drops of size n (Equation (21)).

_{kd}is useful for characterizing individual drops, E

_{kΩ}conveys information regarding the agronomic effects of sprinkler irrigation in a certain sprinkler-irrigated area (R) [L T

^{−1}]. If E

_{kΩ}is combined with precipitation falling in domain (R

_{Ω}) [L

^{3}T

^{−1}], kinetic power (P

_{kΩ}) [M L

^{2}T

^{−3}] can be determined according to Equation (22). Furthermore, it is also common to obtain specific power (δ

_{p}) [M T

^{−3}] as the ratio of sprinkler kinetic energy and sprinkler irrigated area (Equation (23)). Switching from energy to power is important in the context of sprinkler irrigation, since irrigation time (per irrigation event, per season, …, among others) is an important management variable. Once the power is obtained, multiplying it times a certain irrigation duration will result in the kinetic energy of a given irrigation event or a set of irrigation events.

#### 2.4. Irrigation Performance Indices

^{−1}]. In addition, the distribution uniformity (DU) [L L

^{−1}] index, proposed by Merriam and Keller [8], is also widely used. Naturally, both indicators complement each other; while the first one allows one to identify how the applied water is used, the second one provides information on how uniformly this water volume is distributed in the plot. CU and DU are written as Equations (24) and (25), respectively.

_{i}[L] is the irrigation water depth received in an individual pluviometer, $\overline{\mathrm{x}}$ [L] is the average irrigation water depth received in pluviometers, and n is the number of pluviometers evenly distributed in an irrigated plot. The Christiansen [58] coefficient was also applied to kinetic energy in sprinkler spacing (CU

_{Kϕ}) [F L T

^{−1}F

^{−1}L

^{−1}T]. In standard irrigation evaluation procedures, sprinkler spacing is divided into a matrix of rectangular domains with a catch can network located inside the sprinkler configuration. These collectors are used to estimate the precipitation rate at each domain. In this work, the sprinkler spacing was divided into several cells (Nc) wherein the area is known (A

_{i}) [L

^{2}], then such an indicator is estimated for a particular solid-set sprinkler arrangement conforming to a total area of evaluation (A) [L

^{2}]. As a consequence, CU

_{Kϕ}can be expressed as Equation (26). Analyzing the kinetic power within the sprinkler spacing allows for the production of power maps. Locating the areas within the sprinkler spacing with high or low kinetic power has relevant agronomic and irrigation management implications from a design point of view.

## 3. Results

^{®}spreadsheet [34] named «Sprinkler irrigation tool» has been developed for use as a didactic tool in order to complement students’ theoretical knowledge and that acquired during field practice. Figure 2 shows an overall view of the sheets previously described (Radial pattern, Frequency, Runge–Kutta pairs, Kinetic energy and power, Performance indicators, Toolbox, and Graphs). These categories comprise columns of different colors: blue, green, orange, and white; the data should be input in this order so as to obtain correct information output.

^{®}platform.

#### 3.1. Sprinkler Irrigation Tool: Radial Patterns and Drop Diameter Frequency

^{−1}) derived from the precipitation rate accounting for each test duration and operating pressure combination as described in Table 1. This information is useful for students looking to compare radial application patterns for a specific experimental sprinkler setup operating at different pressures. The shape of the radial curves, maximum irrigation distance against pressure, precipitation rate variability along irrigation distance, and maximum and minimum local values of the precipitation rate are some of the magnitudes that can be analyzed, giving an idea of the water drop distribution for each particular impact sprinkler in different experimental conditions.

#### 3.2. Sprinkler Irrigation Tool: Drop Motion Simulation

^{−1}; meanwhile, for 1.0 mm it is 4.50 m s

^{−1}, for 2.0 mm it is 6.37 m s

^{−1}, and for 3.0 mm it is 7.80 m s

^{−1}. Regarding this matter, the resulting values for all four reference alternatives are significantly lower in drops of water with a diameter of 0.5 mm, but as diameter increases, the differences between Nave [63] and those calculated by Okamura [45], Park et al. [46], Li and Kawano [47] and Hills and Gu [48] decrease, with an increase in the terminal velocity for a 3.0 mm drop diameter. If the average and range for the different options are taken into account, the percentage differences are ≳ 2% (0.8% to +8%), 45% (24% to 72%), 10% (0.2% to 27%) and 0.2% (5% to +3%), respectively. An analogous procedure can be followed in relation to drops’ flight time, such that values obtained with the sprinkler irrigation tool can be compared with those reported in the literature for similar experimental conditions, e.g., those reported by Thompson et al. [64] and Lorenzini [65], and show the contrasts between them.

^{−1}(Okamura [45]), (−2.96, 0.02) mm s

^{−1}(Park et al. [46]), (−1.32, 0.10) mm s

^{−1}(Li and Kawano [47]), (−0.62, 0.12) mm s

^{−1}(Hills and Gu [48]), and (−1.82, 0.07) mm s

^{−1}(Thompson et al. [64]). All refer to the negative slope in the first case, and to the positive slope in the second drop velocity, which is computed from the respective tabular data.

^{−1}of wind velocity for wind directions of 60°, 180°, 225°, 270°, and under no-wind conditions. It is evident that there is an effect of wind on water drop trajectory: as wind maintains a greater opposition to the direction in which the water drop travels, a shorter distance is reached, and vice versa. In other words, when wind direction is totally opposite to drop direction (180°), its distance to a datum is 7.2 m, while for those cases in which wind direction is 60°, 225°, and 270°, drop distance reaches 13.3 m, 8.4 m, and 11.2 m, respectively.

^{−1}and 270°).

#### 3.3. Sprinkler Irrigation Tool: Add-On Resources

^{−7}J, 33.73 × 10

^{−7}J, 96.98 × 10

^{−7}J, and 242.28 × 10

^{−7}J for 3 m, 6 m, 9 m, and 12 m, respectively. A similar trend follows for the E

_{kΩ,}P

_{kΩ,}and δ

_{p}variables. It is worth noting that the values reported here are comparable to the previous findings of Kincaid [39] and DeBoer [66] for different impact sprinklers and operating conditions and those of DeBoer and Monnens [67] for a rotating spray plate sprinkler. However, it should also be pointed out that generally these data are not reliable, but the potential effects are linked to the energy with which the water drops impact the soil surface to cause soil erosion, alterations in infiltration rates, and soil surface sealing, among others.

^{®}Premium version, licensed by Addinsoft 2022.5.1 1394. Kinetic energy under no-wind conditions for rectangular and triangular sprinkler spacings are discussed for spacings R18 × 18, R15 × 15, T18 × 18, and T15 × 15. Maps were produced for combinations of each spacing and 400 kPa of hydraulic working pressure for an irrigation time of 1 h. The contrast of kinetic energy per unit of time on each surface is visible in each subfigure. Its distribution depends, to a large extent, on the spacing between sprinklers and arrangement choice. In an R18 × 18 configuration, the kinetic energy attained maximum values at the central part of the framework (around 6000 J h

^{−1}); such value gradually decreases, reaching 1000 J h

^{−1}, as it is moves closer to the framing edges. In relation to the R15 × 15 arrangement, the kinetic energy varies from the sprinklers towards the central portion of surface; its value is close to 5000 J h

^{−1}around the sprinklers and then decreases to 1000 J h

^{−1}before increasing to 4700 J h

^{−1}and again decreasing to 3000 J h

^{−1}. As for the triangular arrangements, in T18 × 18 most of the surface receives, in the course of one hour, a kinetic energy approaching 3800 J, although in some areas values oscillate between 1200 and 1600 J, and in certain small circular portions, the value reaches 4680 J. For T15X15, kinetic energy increases from the base to the upper vertex and height becomes an axis of symmetry; these values are between 3000 J h

^{−1}and 6400 J h

^{−1}.

## 4. Discussion

^{®}spreadsheet which includes methods and techniques that support an efficient engineering design of sprinkler irrigation systems equipped with stationary devices. The sprinkler irrigation tool provides outcomes in tabular (Table 3, Table 4 and Table 5) and graphical formats (Figure 3, Figure 4, Figure 5, Figure 6 and Figure 7) with the aim of offering students with alternatives that will allow them to acquire knowledge of sprinkler irrigation design. However, the spreadsheet only generates numerical values as far as the evaluation of the kinetic energy is concerned; hence, XLSTAT

^{®}software has been selected to perform an interpolation process using the ordinary Kriging method and then plot contour maps, as illustrated in Figure 8.

^{−2}equal to 1 mm, first to calculate kinetic power in watts and then using that same equivalence to determine the specific power in watts m

^{−2}, brings serious difficulties in understanding; clearly this is an aspect of formative deficiency that must be solved in the the first years of undergraduate studies when taking basics subjects in science and engineering. In spite of this, such academic weakness arises as a possibility for improving the computer sprinkler irrigation tool and is therefore an option for further research for enhancing the Excel

^{®}spreadsheet.

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Drop movement schematization from the sprinkler device to reach a datum. Forces acting on water drops traveling throughout the air are drag force (${\overrightarrow{\mathrm{F}}}_{\mathrm{d}}$) and gravitational force (m$\overrightarrow{\mathrm{g}}$). $\overrightarrow{\mathrm{V}}$ is the water drop’s velocity relative to air and $\overrightarrow{\mathrm{U}}$ and $\overrightarrow{\mathrm{W}}$ are water drop velocity and wind velocity relative to the Cartesian coordinate system, respectively; $\overrightarrow{\mathrm{r}}$ is water drop vector position and m is its mass (following the methodology of Robinson and Robinson [38] for drop forces and velocities).

**Figure 4.**Histogram of drop diameter and curves of cumulative volume at 3 m (red continuous line), 6 m (green dash line), 9 m (blue continuous line), and 12 m (purple dash line) from the sprinkler at 200 kPa.

**Figure 5.**Ballistic movement simulation with the Okamura [45] drag coefficient method for a 4 mm water drop within 0.200 s (brown circle), 0.100 s (red circle), 0.050 s (blue circle), and 0.025 s (green circle and line) as time step values. (

**a**) represents the X–Z drops trajectory, (

**b**) flight time versus X and Z travel distances, and (

**c**) flight time versus X, Z, and water drop velocities.

**Figure 6.**Two-dimensional water drop movement simulation for 0.5 mm (green), 1.0 mm (blue), 2.0 mm (red), and 3.0 mm (brown) diameters with 1.20 m sprinkler elevation, 300 kPa operating pressure, and no-wind conditions. Using the methodology of drag model of (

**a**) Park et al. [46], (

**b**) Li and Kawano [47], (

**c**) Hills and Gu [48], and (

**d**) Okamura [45].

**Figure 7.**Three-dimensional water drop movement simulation under different velocities and directions of wind. This shows results using a 1.50 m sprinkler elevation, 200 kPa operating pressure, and Okamura [45] as the drag coefficient model. (

**a**,

**b**) are the drop elevation and the drop movement in Y axis for different wind conditions in function of the distance from the sprinkler, respectively, meanwhile (

**c**) shows the drops landing from the sprinkler in both X and Y axis, finally, (

**d**) shows the wetted radii in X and Y axis in function of the drop diameter.

**Figure 8.**Kinetic energy contour maps for rectangular and triangular arrangements for a 1 h irrigation time.

**Table 1.**Average precipitation rate (l s

^{−1}) at different distances from the irrigation sprinkler (obtained from Bautista-Capetillo et al. [59]).

Precipitation rate (l s^{−1}) | |||||||||||

Pluviometer | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | |

Distance (m) | 0.6 | 1.2 | 1.8 | 2.4 | 3.0 | 3.6 | 4.2 | 4.8 | 5.4 | 6.0 | |

Operating pressure (kPa) | 200 | 90.0 | 70.0 | 46.0 | 35.0 | 29.0 | 28.0 | 27.0 | 27.0 | 26.0 | 24.0 |

300 | 100.0 | 80.0 | 50.0 | 39.0 | 32.0 | 30.0 | 31.0 | 31.0 | 32.0 | 32.0 | |

400 | 120.0 | 100.0 | 61.0 | 45.0 | 38.0 | 36.0 | 34.0 | 35.0 | 36.0 | 37.0 | |

Precipitation rate (l s^{−1}) | |||||||||||

Pluviometer | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | |

Distance (m) | 6.6 | 7.2 | 7.8 | 8.4 | 9.0 | 9.6 | 10.2 | 10.8 | 11.4 | 12.0 | |

Operating pressure (kPa) | 200 | 22.0 | 21.0 | 21.0 | 25.0 | 33.0 | 40.0 | 50.0 | 54.0 | 62.0 | 63.0 |

300 | 31.0 | 32.0 | 34.0 | 38.0 | 41.0 | 44.0 | 48.0 | 49.0 | 51.0 | 50.0 | |

400 | 38.0 | 40.0 | 44.0 | 47.0 | 49.0 | 51.0 | 55.0 | 55.0 | 55.0 | 53.0 | |

Precipitation rate (l s^{−1}) | |||||||||||

Pluviometer | 21 | 22 | 23 | 24 | 25 | 26 | 27 | 28 | 29 | 30 | |

Distance (m) | 12.6 | 13.2 | 13.8 | 14.4 | 15.0 | 15.6 | 16.2 | 16.8 | 17.4 | 18.0 | |

Operating pressure (kPa) | 200 | 59.0 | 46.0 | 19.0 | 2.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 |

300 | 47.0 | 43.0 | 36.0 | 27.0 | 17.0 | 6.0 | 0.0 | 0.0 | 0.0 | 0.0 | |

400 | 50.0 | 48.0 | 44.0 | 39.0 | 32.0 | 25.0 | 11.0 | 2.0 | 0.0 | 0.0 |

**Table 2.**Water drop diameter and velocity characterization for combinations of operating pressure and distance from the sprinkler.

Operating Pressures (kPa) | Variable | Distance from Irrigation Sprinkler (m) | |||
---|---|---|---|---|---|

3 | 6 | 9 | 12 | ||

200 | Diameter (mm) | 0.86 | 1.04 | 1.50 | 3.08 |

Velocity (m s^{−1}) | 2.72 | 3.06 | 4.19 | 6.06 | |

300 | Diameter (mm) | 0.81 | 1.03 | 1.22 | 2.06 |

Velocity (m s^{−1}) | 2.45 | 2.92 | 3.82 | 5.13 | |

400 | Diameter (mm) | 0.86 | 0.96 | 1.19 | 1.45 |

Velocity (m s^{−1}) | 2.43 | 2.96 | 3.72 | 4.42 |

**Table 3.**Time of flight, travel distance, error, and terminal velocity for each simulation drag coefficient model used for the sprinkler features and operating pressure under no-wind conditions. This was adapted from the originals for presentation purposes within this paper.

Drag Coefficient Model | Drop Diameter (mm) | |||||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

Time of Flight (s) | Travel Distance (m) | Error (m) | Terminal Velocity (ms^{−1}) | |||||||||||||

0.5 | 1.0 | 2.0 | 3.0 | 0.5 | 1.0 | 2.0 | 3.0 | 0.5 | 1.0 | 2.0 | 3.0 | 0.5 | 1.0 | 2.0 | 3.0 | |

Okamura, [45] | 2.74 | 1.93 | 1.92 | 2.02 | 2.87 | 6.03 | 10.90 | 14.29 | 0.24 | 0.10 | 0.09 | 0.11 | 2.21 | 4.01 | 6.45 | 7.82 |

Park et al., [46] | 3.37 | 1.89 | 1.92 | 1.92 | 2.05 | 4.59 | 10.49 | 13.02 | 0.38 | 0.34 | 0.13 | 0.10 | 1.97 | 3.54 | 6.34 | 7.74 |

Li and Kawano, [47] | 2.48 | 1.82 | 1.93 | 2.02 | 2.23 | 6.07 | 11.19 | 14.39 | 0.12 | 0.12 | 0.08 | 0.07 | 2.18 | 4.31 | 6.57 | 7.87 |

Hills and Gu, [48] | 2.13 | 1.82 | 1.90 | 2.05 | 2.77 | 6.46 | 10.01 | 15.91 | 0.22 | 0.14 | 0.11 | 0.12 | 2.56 | 4.49 | 6.08 | 8.45 |

**Table 4.**Geometrical and kinematical drop characterization at 3 m, 6 m, 9 m, and 12 m of distance from a sprinkler operating at 400 kPa of pressure.

Drops | Distance from the Sprinkler (m) | |||
---|---|---|---|---|

3 | 6 | 9 | 12 | |

Number | 114 | 106 | 102 | 98 |

ϕ_{range} (mm) | 0.50–1.70 | 0.50–1.90 | 0.50–2.20 | 0.80–2.50 |

∀_{m} | 1.19 | 1.25 | 1.46 | 1.78 |

V_{range} (m s^{−1}) | 1.55–3.55 | 1.96–4.39 | 2.20–5.35 | 3.28–5.79 |

V_{m} (m s^{−1}) | 2.43 | 2.96 | 3.72 | 4.42 |

E_{kϕrange} (J × 10^{−7}) | 0.62–134.53 | 1.03–359.08 | 1.77–711.99 | 19.37–1422.98 |

E_{kΩ} (JL^{−1}) | 3.640 | 5.530 | 8.880 | 12.150 |

P_{rate} (mm h^{−1}) | 1.880 | 1.830 | 2.420 | 2.620 |

P_{kΩ} (W × 10^{−6}) | 0.002 | 0.003 | 0.006 | 0.009 |

δ_{p} (W m^{−2} × 10^{−3}) | 1.900 | 2.800 | 6.000 | 8.800 |

_{m}is volumetric mean diameter, V and V

_{m}are velocity and average velocity, respectively, J is Joules, L is liters, and W is watts. Values correspond to 400 kPa of operating pressure (www.eead.csic.es/drops, accessed on 5 September 2023).

**Table 5.**Irrigation and kinetic energy performance indicators for rectangular and triangular arrangements.

Framework (m × m) | Operating Pressure (kPa) | |||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|

200 | 300 | 400 | 200 | 300 | 400 | 200 | 300 | 400 | 200 | 300 | 400 | |

CU (%) | DU (%) | CU_{Kϕ} (%) | DU_{Kϕ} (%) | |||||||||

R15 × 15 | 83.4 | 79.7 | 66.1 | 88.6 | 77.4 | 67.5 | 57.2 | 53.4 | 27.8 | 44.1 | 38.1 | 10.8 |

R18 × 18 | 68.2 | 75.9 | 76.3 | 67.4 | 77.9 | 81.2 | 22.9 | 22.1 | 45.6 | 20.3 | 40.3 | 31.9 |

T15 × 15 | 63.8 | 78.3 | 84.5 | 64.5 | 73.9 | 85.1 | 60.2 | 62.1 | 52.8 | 19.1 | 64.4 | 47.2 |

T18 × 18 | 66.0 | 80.3 | 87.3 | 67.5 | 82.0 | 87.9 | 47.7 | 73.3 | 41.4 | 37.0 | 21.2 | 22.9 |

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**MDPI and ACS Style**

Bautista-Capetillo, C.; Robles Rovelo, C.O.; González-Trinidad, J.; Pineda-Martínez, H.; Júnez-Ferreira, H.E.; García-Bandala, M.
Teaching Sprinkler Irrigation Engineering by a Spreadsheet Tool. *Water* **2023**, *15*, 1685.
https://doi.org/10.3390/w15091685

**AMA Style**

Bautista-Capetillo C, Robles Rovelo CO, González-Trinidad J, Pineda-Martínez H, Júnez-Ferreira HE, García-Bandala M.
Teaching Sprinkler Irrigation Engineering by a Spreadsheet Tool. *Water*. 2023; 15(9):1685.
https://doi.org/10.3390/w15091685

**Chicago/Turabian Style**

Bautista-Capetillo, Carlos, Cruz Octavio Robles Rovelo, Julián González-Trinidad, Hugo Pineda-Martínez, Hugo Enrique Júnez-Ferreira, and Martín García-Bandala.
2023. "Teaching Sprinkler Irrigation Engineering by a Spreadsheet Tool" *Water* 15, no. 9: 1685.
https://doi.org/10.3390/w15091685