# Verification of IRRILAB Software Application for the Hydraulic Design of a Micro-Irrigation System by Using IRRIPRO for an Apple Farm in Sicily

^{1}

^{2}

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## Abstract

**:**

## 1. Introduction and Theoretical Background

_{u}, the number of emitters in the downhill lateral, n

_{d}, the minimum emitter pressure head in the downhill lateral, i

_{min}, and the slope of the lateral, S

_{0,L}, providing the simple explicit relationships as a function of 16 calibration constants, with relative errors that were less than 2% compared with the Step-By-Step (SBS) procedure that is unanimously recognized and assumed to have the greatest level of accuracy. Moreover, an easy method to determine the best position of the manifold (BMP) associated to the optimal lateral length on uniform slopes, which could be 0 or 0.5 in flat field and 0 and 0.24 in sloping fields, was proposed.

## 2. IRRILAB and IRRIPRO Software

#### 2.1. IRRILAB Software

#### 2.2. IRRIPRO Software

#### 2.3. Motivation of Joint Use of IRRILAB and IRRIPRO

## 3. IRRILAB and IRRIPRO Applications

^{3}, as shown in Figure 3b. The reservoir is located at 103 m below the apple farm (Figure 3b), so a lot of energy is required by the micro-irrigation system, and the farmer is interested in reducing the required energy and increasing the emission uniformity as much as possible.

#### 3.1. IRRILAB Applications

_{0,L}) and manifold (S

_{0,M}) directions, which are sensitive parameters in IRRILAB, were calculated by minimizing the mean square error between the actual elevation distribution of each sector, and that of the equivalent rectangular plane, described by the corresponding plane Equation (1):

_{0,L}

^{2}− S

_{0,M}

^{2}). As an example, Figure 4 shows two different 3D views of sector #4 illustrated in Figure 3a. In Figure 4, the red color indicates the actual morphology of sector #4, while the blue color indicates the corresponding equivalent sector with uniform slopes. Figure 4 also shows the vector u (S

_{0,L}, S

_{0,M}, c) normal to the equivalent plane (blue line).

_{0,L}and BMP, and those of the manifold (M1, M2), which depend on S

_{0,M}and BIP, are involved in all the considered layouts (#6, #7, and #22), and are illustrated in Table 1a,b, respectively (rearranged by Baiamonte [28]). Therefore, as can be seen in these tables, designing each sector by IRRILAB and detecting the corresponding layout requires BMP, BIP, and the sign (negative downward and positive upwards) of the laterals and manifold slopes to be established (S

_{0,L}, S

_{0,M}).

_{opt}

_{,L}, the lateral inside diameter, D

_{L}, the emitters spacing, (S = 1 m), the laterals spacing, (S

_{rows}= 3.8 m), as well as the pressure head tolerance for both the laterals, δ

_{L}, and the manifold, δ

_{M}. The output data are the design variables, namely the nominal (average) emitter pressure head, h

_{n}, the design emitter flow rate, q

_{n}, the manifold inside diameter, D

_{M}, the number of rows, n

_{rows}, the required inlet flow rate, q

_{in}, and the inlet pressure head, h

_{in}[28].

_{L}, and to the manifold pressure head tolerance, δ

_{M}, which can be arbitrarily fixed. If one wanted to fix the pressure head tolerance of the irrigation unit (δ = 10%) and that of the lateral δ

_{L}(<0.1), the manifold pressure head tolerance, δ

_{M}, can be calculated by the relationship, δ = (1 + δ

_{L}) (1 + δ

_{M}) − 1, suggested by Baiamonte [28], which yields (Equation(2)):

_{min}= h

_{n}(1 − δ), and the theoretical maximum admitted pressure head, h

_{max}= h

_{n}(1 + δ), only if the planform geometry of the sector is rectangular and the sector is uniform in slope.

_{0,L}, and S

_{0,M}, providing the already mentioned 25 layouts (Figure 1). In the following, for the Layouts #6, #7, and #22, which were considered in the present study and that can be solved by using the same design relationships (see layouts #6, #7, and #22 in Table 5 reported in Baiamonte [29]), the IRRILAB procedure is shortly summarized. First, the nominal emitter pressure head, h

_{n}, and the nominal emitter flow rate, q

_{n}, need to be calculated according to [29] Equations (3) and (4):

_{opt}

_{,L}, could be determined by the known emitter spacing, S, and by the optimal number of emitter, n

_{opt}, r

_{L}and s

_{L}are the flow rate and the inside diameter exponent of the flow resistance equation (Blasius or Hazen-Williams) adopted for the laterals (Table 2), α is the coefficient of nominal pressure head, and α

^{′}is the coefficient of nominal flow rate (Table 1a) as a function of the calibration constants, B

_{1}, B

_{2}, and BMP, which are also reported in Table 2.

_{e}, to be chosen:

_{rows}, which can be installed in the manifold, Baiamonte [28] applied the relationship derived for the laterals to the manifold, considering that a manifold can be seen as a lateral with laterals in place of emitters. Thus, by replacing the lateral pressure head tolerance, δ

_{L}, with the manifold pressure head tolerance, δ

_{M}, the emitter’s spacing, S, with the drip laterals spacing, S

_{rows}, and lateral’s slope, S

_{0,L}, with the manifold slope, S

_{0,M}, the relationship of the number of rows, n

_{rows}, was derived starting from that expressing the number of emitters for the laterals (Equation (3)), yielding:

_{1}and BIP. The symbol $\mathsf{\Delta}=1+{\delta}_{L}$ indicates an amplification factor for the manifold pressure tolerance, that for the manifold, contrarily to the laterals where the pressure head tolerance has to be referred to the design pressure, h

_{n}, it has to be referred to the maximum pressure achieved in the laterals, h

_{M}= h

_{n}(1 + δ

_{L}).

_{M}, is calculated by considering that the flow rate of each lateral can be obtained by multiplying the emitter flow rate, q

_{n}, with the optimal number of emitters, n

_{opt}[28]:

^{′}

_{M}corresponds to the α

^{′}coefficient of Table 1a, referred to the manifold calibrations constants (B

_{1,M}, B

_{2,M}) and to the manifold resistance equation coefficients (k

_{M}, r

_{M}, Table 2). By substituting Equation (4) into Equation (7), Baiamonte [29] derived an explicit and compact relationship of the inside manifold diameter, D

_{M}:

^{′}is the manifold inside diameter coefficient (Table 3), as a function of BMP, r

_{M}, s

_{M}, and the numerical constant reported in Table 2.

_{rows}and D

_{M}can only be applied for a new irrigation unit, where any possible number of laterals can be installed in a manifold (Equation (6)). For the applications performed here, where IRRILAB is applied to an already designed irrigation system, so that the number of rows is imposed, the IRRILAB explicit relationships need to be reformulated, since the emitters’ characteristics (x, k

_{e}) that match n

_{rows}are required, because in this case, n

_{rows}is an imposed parameter.

_{e}coefficient of the emitter can be derived by combining Equations (3)–(5), which provides the following k

_{e}relationship:

_{rows}, the corresponding manifold pressure head tolerance, δ

_{M}, can be derived by Equation (6):

_{M}also has to satisfy Equation (2). Thus, by imposing Equations (2) and (11) as equal, an explicit relationship of the lateral pressure head tolerance, δ

_{L}, can be derived:

_{M}. Equation (12) can be usefully substituted into Equation (9) to derive the emitter’s characteristic k

_{e}that needs to be set, for a fixed x, when the number of rows, n

_{rows}, is assigned:

_{M}, as Equation (12), helps with detecting the optimal emitter’s characteristics (k

_{e}, x) for a fixed n

_{rows}and can be used for both CE and PCE emitters. Indeed, for PCE, that is when x = 0, Equation (13) reduces to:

_{opt}, n

_{rows}, S

_{0,L}, S

_{0,M}) and drip laterals diameter (D

_{L}), to determine the emitter’s characteristic k

_{e}, for CE and PCE, respectively. Of course, the manifold diameter, D

_{M}, then needs calculating by Equation (8).

#### 3.2. IRRIPRO Applications

_{s}(see the reservoir in Figure 3b), that makes it possible to impose the inlet pressure head provided by IRRILAB (h

_{in}= Δh

_{n}(1 + δ

_{M})) at the inlet of each sector.

_{min}and h

_{max}, in addition to other useful output parameters that will be discussed later.

## 4. Results and Discussion

#### 4.1. Results for the Actual “Non-Uniform” Five Sectors

_{L}= 12.98 mm, was chosen for the laterals, which are characterized by the exponent x = 0.5 for CEs (Equation (5)) and by x = 0 for PCEs.

_{n}) and in under-pressure (h < 0.9 h

_{n}). This is probably because the actual five sectors did not fully fit the sectors regularity that IRRILAB requires.

_{s}, than those that IRRILAB provided without attempts, which may affect the required energy [37].

_{L}= 17.8 mm rather than D

_{L}= 12.98 mm) to find the design solutions, because for the attempts the user made for D

_{L}= 12.98 mm, and by fixing different tentative D

_{M}, the IRRIPRO algorithm did not converge. This is because the IRRIPRO procedure does not include a D

_{M}calculus as IRRILAB does (Equation (8)).

_{n}= k

_{e}= constant), the EU value cannot be controlled by IRRIPRO, since EU = 100% (and CV = 0) are imposed (Table 5). In addition, the exponent emitter discharge, x, was assumed as equal to zero, indicating a constant flow rate for the wider range of pressure head. For PCEs, results were satisfying for both IRRILAB and IRRIPRO, in terms of both inlet pressure and pressure head distributions.

#### 4.2. Subdividing the Apple Farm in Seven and in Nine Sectors

_{in}, and pressure head distribution, as can be observed by comparing sector #1 and sector #7 in Figure 7, with the new sectors #1A, #1B, #7A, and #7b, in Figure 8a.

_{L}= 12.98 to 17.8 mm. Moreover, for sectors #1, #1b, #3, and #4, high values of the inlet pressure heads were achieved, indicating that the results obtained by IRRILAB, without attempts, could be considered more suitable than those obtained by IRRIPRO with attempts, which also required an increase of the laterals’ inside diameter, increasing the material cost. For CEs and for the nine sectors, the corresponding pressure head distributions map derived by the IRRIPRO stand-alone application is reported in Figure 8b.

#### 4.3. Evaluating Energy Consumption by Using IRRILAB and IRRIPRO with Common Emitters and Pressure Compensating Emitters

_{s}), the discharge in the source (Q

_{s}), and the nominal emitter flow rate (q

_{n}). Some additional parameters that are necessary for the energy calculus were set as equal in both IRRILAB and IRRIPRO, to make the comparison homogeneous. In particular, the pump and motor drive efficiency (η), the yearly total water application (V), and the years of the irrigation seasons (Y).

^{−3}), and Q

_{s}(m

^{3}s

^{−1}) and h

_{s}(m) are the discharge and the pressure head at the source. When applying IRRIPRO, h

_{s}was imposed in order to obtain the same inlet pressure head, h

_{in}, provided by IRRILAB, at the inlet of each sector. The pump and motor drive efficiency, η, was fixed at 0.75.

_{rows}= 3.8 m):

_{n}(L/h) is the emitter flow rate. According to Equations (15) and (16), the total energy consumption, E (kWh), for both IRRILAB and IRRIPRO, when using CEs and PCEs, was calculated as:

_{min}= h

_{n}(1 − δ) and h

_{max}= h

_{n}(1 + δ)).

## 5. Conclusions

- The IRRILAB application showed its sensitivity to the planform geometry and to the slope uniformity of the laterals and of the manifold, indicating that the more uniform in slope and the more rectangular the sector is, the better and better the design results (in terms of emission uniformity and energy-saving) will be.
- IRRILAB, which is based on analytical solutions and does not require attempts and the trial-and-error technique, offers a valuable solution in designing a micro-irrigation system using CEs or PCEs, and makes it possible to save energy for both emitter types, especially when sectors are almost rectangular and uniform in slope.
- The energy-saving provided by IRRILAB with respect to IRRIPRO, applied by attempts, resulted higher for CEs (−15% for five sectors and −9% for nine sectors) than for PCEs (−7% for five sectors and −6% for nine sectors). However, in absolute terms, the energy required was greater for five-sector subdivision than for nine-sector subdivision.
- PCEs could be considered a good solution for saving energy in the sloping field, but their contraindications need to be mentioned: they are more expansive, more complicated structurally, and the working mechanism is not clear, which causes difficulty in their research and development. The latter causes their damage in the short term and the increase of the manufacturing variation coefficient can frustrate the benefit found in terms of energy-saving.
- For sloping fields, CEs, usually chosen only for flat fields, should be recommended, if a design procedure such as that suggested by IRRILAB is applied, especially for sectors uniform in slopes and rectangular planform geometry.

## Author Contributions

## Funding

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 1.**25 irrigation sector layouts considered by IRRILAB, by varying the lateral slope (S

_{0,L}< 0, S

_{0,L}> 0, S

_{0,L}= 0), the best manifold position (BMP = 0, 0.24, 0.5), the manifold slope (S

_{0,M}< 0, S

_{0,M}> 0, S

_{0,M}= 0), and the best inlet position (BIP = 0, 0.24, 0.5). Qualitative pressure head distribution lines are represented for a lateral and for the manifold. Reprinted with permission from ref. [29], Copyright 2020, Elsevier (Amsterdam, The Netherlands).

**Figure 2.**The two main interfaces of IRRIPRO software, (

**a**) the main output data panel, and (

**b**) the main input data panel.

**Figure 3.**The MELIDIONALE apple farm (Sicily), (

**a**) three-dimensional (3D) Google Earth view, actually subdivided into five cultivated sectors, and (

**b**) two-dimensional (2D) Google Earth view of the apple farm, illustrating the reservoir location (859 m a.s.l.).

**Figure 4.**Two different 3D views of sector #4 belonging to the apple farm subdivided in five sectors (numbered in Figure 3a), and the corresponding equivalent sector (blue color) with uniform slopes (S

_{0,L}= −0.054 and S

_{0,M}= −0.180).

**Figure 5.**Emitters’ pressure head distribution maps, pertaining to the design parameters of IRRILAB (

**a**,

**c**) and IRRIPRO (

**b**,

**d**) software applications, for the actual “non-uniform” five sectors of the apple farm, in case of using common emitters (CE) (

**a**,

**b**) and pressure compensating emitters (PCE) (

**c**,

**d**).

**Figure 6.**The apple farm subdivided into nine sectors, illustrating (

**a**) the 1 m contour lines, and (

**b**) the DEM with flow directions for laterals (brown lines) and manifold (blue lines). For each sector, the inlet position (•) is also reported.

**Figure 7.**Emitters’ pressure head distribution map, pertaining to the design parameters of IRRILAB, by using common emitters (CEs) for the farm subdivided into seven sectors.

**Figure 8.**Emitters’ pressure head distribution maps, pertaining to the design parameters of IRRILAB (

**a**,

**c**) and IRRIPRO (

**b**,

**d**) software applications, for the farm subdivided into nine sectors, in case of using common emitters (CE) (

**a**,

**b**) and pressure compensating emitters (PCE) (

**c**,

**d**).

**Figure 9.**Comparison between the energy required by the micro-irrigation sectors with the parameters designed by IRRILAB and with those designed by IRRIPRO, by using common emitters (CE) and pressure compensating emitters (PCE), (

**a**) for the actual five sectors, and (

**b**) for the seven and nine sectors.

**Table 1.**(

**a**) Lateral’s sketch of the considered lateral layouts L2 and L5, and corresponding coefficients of the nominal emitters’ pressure head and flow rate design relationships, α and α

^{′}, as a function of the calibration constants mentioned in Table 2. Rearranged with permission from ref. [29], Copyright 2020, Elsevier (Amsterdam, The Netherlands); (

**b**) Manifold’s sketch, of the considered manifold layouts M1 and M2. Rearranged with permission from ref. [29], Copyright 2020, Elsevier (Amsterdam, The Netherlands).

(a) | |||||

LateralLayout(Figure 1) | Slope, S_{0,L} | BMP | Lateral’sSketch | Nominal PressureHead Coefficientα Equation (1) | Nominal FlowRate Coefficientα^{′} Equation (2) |

L2 | < 0 | 0 | $\frac{1}{\left(1-BMP\right){B}_{1,L}}$ | $\frac{{B}_{2,L}}{{B}_{1,L}{k}_{L}^{1/{r}_{L}}}$ | |

L5 | > 0 | 0 | $\frac{1}{BMP{B}_{1,L}}$ | $\frac{{B}_{2,L}}{{B}_{1,L}{k}_{L}^{1/{r}_{L}}}$ | |

(b) | |||||

ManifoldLayout(Figure 1) | Slope, S_{0,M} | BIP | Manifold’sSketch | ||

M1 | < 0 | 0.24 | |||

M2 | < 0 | 0 |

**Table 2.**Resistance equation parameters of the laterals (r

_{L}, s

_{L}, k

_{L}), best manifold position (BMP), and calibration constants (B

_{1}, B

_{2}), for Blasius and Hazen-Williams formula. Rearranged with permission from ref. [29], Copyright 2020, Elsevier (Amsterdam, The Nether-lands).

Resistance Equation | r_{L} | s_{L} | k_{L} | BMP | B_{1} | B_{2} |
---|---|---|---|---|---|---|

Blasius | 1.750 | 4.750 | 7.788 10^{−4} | 0.24 | 7.35 | 2.34 |

Hazen-Williams | 1.852 | 4.871 | 10.675 C^{−r} | 0.25 | 7.07 | 2.34 |

**Table 3.**For layouts #6, #7, and #22, considered in the IRRILAB applications, coefficients of number of rows and manifold inside diameter design relationships, β and β

^{′}, as a function of the calibration constants, which were reported in Table 1. Rearranged with permission from ref. [29], Copyright 2020, Elsevier (Amsterdam, The Netherlands).

Layout | Lateral Layout | Manifold Layout | β | Different Resistance Equation for L and M β ^{′} | Same Resistance Equationfor L and M β ^{′} | ||||
---|---|---|---|---|---|---|---|---|---|

# | S_{0,L} | BMP | # | S_{0,M} | BIP | ||||

6 | L2 | <0 | 0 | M1 | <0 | 0.24 | ${B}_{1,M}$ | ${k}_{1}{\left({B}^{*}\left(1-BMP\right){B}_{1,L}\right)}^{\raisebox{1ex}{${r}_{M}$}\!\left/ \!\raisebox{-1ex}{${s}_{M}$}\right.}$ | ${\left(\left(1-BMP\right){B}_{1}\right)}^{\raisebox{1ex}{$r$}\!\left/ \!\raisebox{-1ex}{$s$}\right.}$ |

7 | L2 | <0 | M2 | <0 | 0 | $\left(1-BIP\right){B}_{1,M}$ | ${k}_{1}{\left({B}^{*}\left(1-BMP\right){B}_{1,L}\right)}^{\raisebox{1ex}{${r}_{M}$}\!\left/ \!\raisebox{-1ex}{${s}_{M}$}\right.}$ | ${\left(\left(1-BMP\right){B}_{1}\right)}^{\raisebox{1ex}{$r$}\!\left/ \!\raisebox{-1ex}{$s$}\right.}$ | |

22 | L5 | >0 | M2 | <0 | $\left(1-BIP\right){B}_{1,M}$ | ${k}_{1}{\left({B}^{*}BMP{B}_{1,L}\right)}^{\raisebox{1ex}{${r}_{M}$}\!\left/ \!\raisebox{-1ex}{${s}_{M}$}\right.}$ | ${\left(BMP{B}_{1}\right)}^{\raisebox{1ex}{$r$}\!\left/ \!\raisebox{-1ex}{$s$}\right.}$ |

**Table 4.**Geometric and hydraulic design parameters for the actual “non-uniform” five sectors of the apple farm designed by IRRILAB, for common emitters (CE) and pressure compensating emitters (PCE).

Geometric Parameters | ||||||||||||||

Sector | #Layout | BMP | BIP | n_{rows} | L_{opt}_{,L}(m) | L_{opt}_{,M}(m) | S_{0,L} | S_{0,M} | CE | PCE | ||||

D_{L}(mm) | D_{M}(mm) | D_{L}( mm) | D_{M}( mm) | |||||||||||

1 | 6 | 0 | 0.24 | 72 | 88.96 | 273.6 | −0.0210 | −0.1202 | 12.98 | 39.3 | 12.98 | 39.3 | ||

2 | 49 | 78.49 | 186.2 | −0.0898 | −0.1259 | 45.8 | 45.8 | |||||||

3 | 37 | 99.17 | 140.6 | −0.0747 | −0.0586 | 46.7 | 46.7 | |||||||

4 | 7 | 0 | 42 | 90.33 | 159.6 | −0.0540 | −0.1799 | 39.9 | 39.9 | |||||

5 | 37 | 84.04 | 140.6 | −0.0414 | −0.1566 | 37.1 | 37.1 | |||||||

Hydraulic parameters for common emitters (CE) with x = 0.5 | ||||||||||||||

Sector | δ | δ_{L} | δ_{M} | k_{e} | h_{n}(m) | q_{n}(L/h) | h_{in}(m) | h_{min}(m) | h_{mean}(m) | h_{max}(m) | Q_{s}(m^{3}/h) | h_{s}(m) | CV | EU(%) |

1 | 0.06 | 0.004 | 0.056 | 0.400 | 80.2 | 3.58 | 85.0 | 73.2 | 84.7 | 102.3 | 22.98 | 196.7 | 3.23 | 89.2 |

2 | 0.08 | 0.023 | 0.056 | 1.247 | 55.7 | 9.30 | 60.1 | 49.7 | 55.8 | 71.1 | 34.45 | 157.3 | 4.21 | 89.4 |

3 | 0.05 | 0.027 | 0.022 | 0.947 | 49.0 | 6.63 | 51.4 | 41.9 | 47.2 | 58.8 | 23.12 | 145.3 | 3.60 | 89.9 |

4 | 0.10 | 0.015 | 0.084 | 0.779 | 60.2 | 6.04 | 66.2 | 49.1 | 54.5 | 70.0 | 21.15 | 189.9 | 4.71 | 89.3 |

5 | 0.09 | 0.012 | 0.077 | 0.784 | 50.7 | 5.58 | 55.3 | 43.2 | 49.0 | 58.8 | 16.11 | 176.0 | 3.59 | 89.7 |

Hydraulic parameters for pressure compensating emitters (PCE) with x = 0 | ||||||||||||||

Sector | δ | δ_{L} | δ_{M} | k_{e} | h_{n}(m) | h_{in}(m) | h_{min}(m) | h_{mean}(m) | h_{max}(m) | Q_{s}(m^{3}/h) | h_{s}(m) | CV | EU(%) | |

1 | 0.425 | 0.030 | 0.384 | 3.578 | 11.3 | 16.1 | 5.1 | 16.6 | 34.9 | 22.35 | 128.2 | 0 | 100 | |

2 | 0.342 | 0.097 | 0.223 | 9.301 | 13.0 | 17.5 | 6.3 | 13.3 | 29.4 | 34.42 | 115.4 | |||

3 | 0.168 | 0.091 | 0.071 | 6.627 | 14.6 | 17.0 | 6.9 | 12.6 | 24.4 | 23.56 | 111.2 | |||

4 | 0.26 | 0.038 | 0.214 | 6.044 | 23.1 | 29.2 | 7.4 | 13.7 | 33.3 | 22.26 | 155.9 | |||

5 | 0.29 | 0.040 | 0.241 | 5.582 | 15.7 | 20.3 | 6.2 | 12.9 | 23.9 | 16.39 | 142.5 |

**Table 5.**Geometric and hydraulic design parameters for the actual “non-uniform” five sectors of the apple farm, designed by IRRIPRO, for common emitters (CE) and pressure compensating emitters (PCE).

Geometric Parameters | |||||||||||

Sector | Area(m^{2}) | n_{rows} | L_{L}(m) | L_{M}(m) | S_{0,L} | S_{0,M} | CE | PCE | |||

D_{L}(mm) | D_{M}(mm) | D_{L}(mm) | D_{M}(mm) | ||||||||

1 | 24,339 | 72 | 87.3 | 328.3 | −0.0210 | −0.1202 | 17.8 | 78.0 | 12.98 | 41.6 | |

2 | 14,616 | 49 | 75.8 | 213.5 | −0.0898 | −0.1259 | 38.0 | ||||

3 | 13,944 | 37 | 96.3 | 139.4 | −0.0747 | −0.0586 | 38.0 | ||||

4 | 14,416 | 42 | 87.9 | 263.2 | −0.0540 | −0.1799 | 41.6 | ||||

5 | 11,815 | 37 | 79.6 | 152.5 | −0.0414 | −0.1566 | 38.0 | ||||

Hydraulic parameters (CE) | |||||||||||

Sector | k_{e} | x | q_{n}(L/h) | Q_{s}(m^{3}/h) | h_{s}(m) | h_{in}(m) | h_{min}(m) | h_{mean}(m) | h_{max}(m) | CV | EU(%) |

1 | 1.253 | 0.5 | 12.87 | 80.36 | 239.6 | 100.2 | 94.2 | 105.6 | 131.6 | 4.33 | 89.3 |

2 | 1.253 | 0.5 | 11.71 | 43.33 | 183.6 | 82.4 | 77.4 | 87.4 | 105 | 3.79 | 89.6 |

3 | 1.253 | 0.5 | 9.04 | 32.12 | 146.8 | 49.8 | 46.2 | 52.1 | 62.1 | 3.57 | 89.9 |

4 | 1.253 | 0.5 | 12.32 | 45.39 | 219.2 | 84.5 | 84.3 | 96.8 | 115.3 | 2.97 | 89.8 |

5 | 1.253 | 0.5 | 12.46 | 36.59 | 213.1 | 84.8 | 85.1 | 98.9 | 108.9 | 2.45 | 89.9 |

Hydraulic parameters (PCE) | |||||||||||

Sector | k_{e} | x | Q_{s}(m^{3}/h) | h_{s}(m) | h_{in}(m) | h_{min}(m) | h_{mean}(m) | h_{max}(m) | CV | EU(%) | |

1 | 5 | 0 | 31.23 | 140.7 | 25.7 | 9.1 | 20.6 | 37.2 | 0 | 100 | |

2 | 7 | 25.91 | 113.7 | 19.2 | 9.1 | 14.6 | 25.8 | ||||

3 | 7 | 24.89 | 126.2 | 31.4 | 9.1 | 19.7 | 33.8 | ||||

4 | 7 | 25.78 | 163.6 | 34.8 | 9.1 | 16.2 | 38.3 | ||||

5 | 7 | 20.56 | 159.6 | 35.6 | 9.1 | 18.6 | 38.5 |

**Table 6.**Geometric and hydraulic design parameters for the apple farm subdivided into seven or nine sectors, by splitting sectors #1 and #7 in two sectors (background gray colored), characterized by an “almost uniform” slope and planform geometry, designed by IRRILAB, for common emitters (CE) and pressure compensating emitters (PCE).

Geometric Parameters | ||||||||||||||

Sector | #Layout | BMP | BIP | n_{rows} | L_{opt}_{,L}(m) | L_{opt}_{,M}(m) | S_{0,L} | S_{0,M} | CE | PCE | ||||

D_{L}(mm) | D_{M}(mm) | D_{L}(mm) | D_{M}(mm) | |||||||||||

1 | 7 | 0 | 0 | 63 | 55.5 | 239.4 | −0.0911 | −0.0993 | 12.98 | 58.7 | 12.98 | 58.7 | ||

1A | 22 | 43 | 23.5 | 165 | 0.0429 | −0.0610 | 31.5 | 31.5 | ||||||

1B | 7 | 63 | 39.3 | 239.4 | −0.1148 | −0.1260 | 58.6 | 58.6 | ||||||

2 | 7 | 44 | 45.1 | 167.2 | −0.0203 | −0.1476 | 34.5 | 34.5 | ||||||

3 | 22 | 43 | 82.3 | 163.4 | 0.0351 | −0.1463 | 25.1 | 25.1 | ||||||

4 | 7 | 50 | 66.8 | 190 | −0.0143 | −0.1486 | 33.5 | 33.5 | ||||||

5 | 7 | 33 | 65.5 | 125.4 | −0.1639 | −0.0918 | 53.2 | 53.2 | ||||||

6 | 7 | 44 | 73.6 | 167.2 | −0.0631 | −0.1740 | 42.3 | 42.3 | ||||||

7 | 7 | 40 | 81.5 | 152 | −0.0335 | −0.1503 | 36.8 | 36.8 | ||||||

7A | 7 | 39 | 55.7 | 148.2 | −0.0322 | −0.1502 | 36.2 | 36.2 | ||||||

7B | 7 | 21 | 51.7 | 79.8 | −0.0403 | −0.1528 | 30.1 | 30.1 | ||||||

Hydraulic parameters for common emitters (CE) with x = 0.5 | ||||||||||||||

Sector | δ | δ_{L} | δ_{M} | k_{e} | h_{n}(m) | q_{n}(L/h) | h_{in}(m) | h_{min}(m) | h_{mean}(m) | h_{max}(m) | Q_{s}(m^{3}/h) | h_{s}(m) | CV | EU(%) |

1 | 0.04 | 0.007 | 0.033 | 1.167 | 129.1 | 13.26 | 134.2 | 103.7 | 116.9 | 145.9 | 44.07 | 243.2 | 4.01 | 89.43 |

1A | 0.07 | 0.017 | 0.052 | 1.109 | 33.7 | 6.43 | 36.0 | 24.6 | 27.3 | 39.3 | 5.46 | 136.3 | 4.52 | 89.51 |

1B | 0.1 | 0.013 | 0.086 | 2.713 | 62.1 | 21.38 | 68.3 | 51.3 | 56.8 | 79.4 | 47.68 | 179.3 | 4.99 | 89.18 |

2 | 0.1 | 0.004 | 0.096 | 1.022 | 45.8 | 6.92 | 50.4 | 43.1 | 46.2 | 54.6 | 13.01 | 154.1 | 2.98 | 92.88 |

3 | 0.1 | 0.028 | 0.070 | 0.213 | 59.2 | 1.64 | 65.1 | 49.8 | 54.8 | 65.6 | 5.56 | 153.7 | 2.57 | 92.25 |

4 | 0.1 | 0.003 | 0.096 | 0.529 | 52.3 | 3.83 | 57.5 | 43.4 | 49.0 | 60.6 | 12.32 | 147.0 | 4.04 | 89.36 |

5 | 0.08 | 0.039 | 0.040 | 2.227 | 49.8 | 15.72 | 53.8 | 41.8 | 47.5 | 56.0 | 32.88 | 148.9 | 3.27 | 89.95 |

6 | 0.1 | 0.014 | 0.085 | 1.043 | 60.4 | 8.11 | 66.5 | 52.8 | 57.7 | 68.5 | 25.55 | 187.6 | 2.71 | 92.45 |

7 | 0.06 | 0.006 | 0.053 | 0.584 | 76.3 | 5.10 | 80.9 | 63.8 | 71.0 | 86.2 | 15.7 | 199.1 | 3.96 | 90.13 |

7A | 0.1 | 0.007 | 0.092 | 1.111 | 43.1 | 7.29 | 47.4 | 38.2 | 42.1 | 51.6 | 14.96 | 164.0 | 4.08 | 90.44 |

7B | 0.08 | 0.012 | 0.068 | 1.577 | 32.0 | 8.92 | 34.5 | 28.1 | 31.6 | 37.2 | 8.92 | 134.1 | 3.80 | 89.86 |

Hydraulic parameters for pressure compensating emitters (PCE) with x = 0 | ||||||||||||||

Sector | δ | δ_{L} | δ_{M} | k_{e} | h_{n}(m) | h_{in}(m) | h_{min}(m) | h_{mean}(m) | h_{max}(m) | Q_{s}(m^{3}/h) | h_{s}(m) | CV | EU(%) | |

1 | 0.150 | 0.026 | 0.121 | 13.263 | 34.4 | 39.6 | 5.3 | 20.3 | 49.8 | 46.35 | 149.9 | 0 | 100 | |

1A | 0.132 | 0.032 | 0.097 | 6.433 | 17.9 | 20.2 | 7.2 | 10.2 | 21.9 | 6.06 | 120.5 | |||

1B | 0.316 | 0.041 | 0.264 | 21.377 | 19.7 | 25.9 | 7.1 | 13.1 | 35.8 | 49.94 | 138.5 | |||

2 | 0.467 | 0.017 | 0.443 | 6.921 | 9.8 | 14.4 | 7.1 | 10.3 | 18.8 | 12.96 | 118.2 | |||

3 | 0.337 | 0.093 | 0.223 | 1.638 | 17.6 | 23.5 | 6.8 | 11.8 | 23.5 | 5.78 | 112.2 | |||

4 | 0.286 | 0.009 | 0.274 | 3.825 | 18.3 | 23.5 | 7.9 | 13.8 | 25.4 | 12.73 | 113.2 | |||

5 | 0.241 | 0.116 | 0.112 | 15.720 | 16.5 | 20.5 | 6.6 | 13.6 | 22.8 | 33.7 | 116.3 | |||

6 | 0.368 | 0.051 | 0.302 | 8.108 | 16.4 | 22.5 | 7.0 | 12.3 | 24.9 | 26.16 | 144.0 | |||

7 | 0.211 | 0.023 | 0.184 | 5.099 | 21.7 | 26.3 | 5.5 | 13.8 | 31.7 | 16.28 | 144.8 | |||

7A | 0.323 | 0.024 | 0.292 | 7.295 | 13.3 | 17.6 | 7.1 | 11.3 | 22.0 | 15.16 | 134.4 | |||

7B | 0.222 | 0.032 | 0.184 | 8.917 | 11.5 | 14.1 | 7.2 | 11.0 | 16.8 | 8.99 | 113.7 |

**Table 7.**Geometric and hydraulic design parameters for the farm subdivided into nine sectors, by splitting sectors #1 and #7 into two sectors (background colored), characterized by an “almost uniform” slope and planform geometry, designed by IRRIPRO, for common emitters (CE) and pressure compensating emitters (PCE).

Geometric Parameters | |||||||||||

Sector | Area(m^{2}) | n_{rows} | L_{L}(m) | L_{M}(m) | S_{0,L} | S_{0,M} | CE | PCE | |||

D_{L}(mm) | D_{M}(mm) | D_{L}(mm) | D_{M}(mm) | ||||||||

1 | 13,275 | 63 | 55.7 | 274.8 | −0.0911 | −0.0993 | 17.80 | 78.0 | 12.98 | 41.6 | |

1A | 3876 | 43 | 22.2 | 159.6 | 0.0429 | −0.0610 | 12.98 | 50.0 | 38.0 | ||

1B | 9399 | 63 | 37.3 | 248.7 | −0.1148 | −0.1260 | 12.98 | 50.0 | 38.0 | ||

2 | 7540 | 44 | 42.8 | 170.9 | −0.0203 | −0.1476 | 12.98 | 50.0 | 38.0 | ||

3 | 13,437 | 43 | 82.3 | 195.3 | 0.0351 | −0.1463 | 17.80 | 78.0 | 41.6 | ||

4 | 12,681 | 50 | 66.8 | 218.9 | −0.0143 | −0.1486 | 17.80 | 78.0 | 41.6 | ||

5 | 8215 | 33 | 65.2 | 121.2 | −0.1639 | −0.0918 | 12.98 | 78.0 | 38.0 | ||

6 | 12,282 | 44 | 73.6 | 192.4 | −0.0631 | −0.1740 | 12.98 | 50.0 | 41.6 | ||

7 | 12,386 | 40 | 80.1 | 187.7 | −0.0335 | −0.1503 | 17.80 | 78.0 | 41.6 | ||

7A | 8256 | 39 | 53.6 | 184.1 | −0.0322 | −0.1502 | 12.98 | 50.0 | 38.0 | ||

7B | 4129 | 21 | 48.3 | 76.0 | −0.0403 | −0.1528 | 12.98 | 50.0 | 38.0 | ||

Hydraulic parameters (CE) | |||||||||||

Sector | k_{e} | x | q_{n}(L/h) | Q_{s}(m^{3}/h) | h_{s}(m) | h_{in}(m) | h_{min}(m) | h_{mean}(m) | h_{max}(m) | CV | EU(%) |

1 | 1.253 | 0.5 | 11.86 | 42.49 | 203.9 | 95.6 | 85.0 | 94.3 | 122.0 | 4.12 | 90.05 |

1A | 7.05 | 6.64 | 135.6 | 35.3 | 29.0 | 31.7 | 44.8 | 3.99 | 91.00 | ||

1B | 10.35 | 24.18 | 175.4 | 72.4 | 61.5 | 68.4 | 90.5 | 4.26 | 89.80 | ||

2 | 10.41 | 19.49 | 168.3 | 63.5 | 63.2 | 69.0 | 81.5 | 3.42 | 91.60 | ||

3 | 11.14 | 39.28 | 173.4 | 75.7 | 70.2 | 79.1 | 96.3 | 3.07 | 90.60 | ||

4 | 11.46 | 38.15 | 173.4 | 76.2 | 76.0 | 83.8 | 100.6 | 4.00 | 90.50 | ||

5 | 10.13 | 21.71 | 153.0 | 61.4 | 57.8 | 65.4 | 75.2 | 3.10 | 90.40 | ||

6 | 9.89 | 31.91 | 188.7 | 64.9 | 57.0 | 62.3 | 72.3 | 2.28 | 92.90 | ||

7 | 11.62 | 37.09 | 198.85 | 74.6 | 75.1 | 86.0 | 96.2 | 2.81 | 90.11 | ||

7A | 9.74 | 20.24 | 171.3 | 53.3 | 53.3 | 60.5 | 68.4 | 2.59 | 90.90 | ||

7B | 9.04 | 9.11 | 148.9 | 49.3 | 46.2 | 52.1 | 59.6 | 3.55 | 90.00 | ||

Hydraulic parameters (PCE) | |||||||||||

Sector | k_{e} | x | Q_{s}(m^{3}/h) | h_{s}(m) | h_{in}(m) | h_{min}(m) | h_{mean}(m) | h_{max}(m) | CV | EU(%) | |

1 | 5 | 0 | 17.48 | 133.1 | 32.0 | 9.1 | 19.3 | 43.4 | 0 | 100 | |

1A | 9 | 8.48 | 121.0 | 20.4 | 9.1 | 12.1 | 24.5 | ||||

1B | 9 | 21.02 | 143.5 | 41.1 | 9.1 | 19.4 | 41.2 | ||||

2 | 9 | 16.86 | 121.4 | 17.0 | 9.1 | 12.6 | 21.3 | ||||

3 | 7 | 24.69 | 131.8 | 39.2 | 9.1 | 19.0 | 39.2 | ||||

4 | 7 | 23.30 | 123.5 | 31.3 | 9.1 | 18.4 | 32.4 | ||||

5 | 9 | 19.30 | 112.7 | 21.7 | 9.1 | 14.1 | 23.2 | ||||

6 | 9 | 29.04 | 157.0 | 34.3 | 9.1 | 15.8 | 36.0 | ||||

7 | 6 | 19.16 | 146.6 | 27.7 | 9.1 | 20.4 | 32.8 | ||||

7A | 9 | 18.70 | 142.3 | 24.6 | 9.1 | 14.3 | 28.6 | ||||

7B | 9 | 9.07 | 113.0 | 13.3 | 9.1 | 14.5 | 21.6 |

**Table 8.**Energy, E, required for the micro-irrigation system of the apple farm subdivided in the actual “non-uniform” five sectors, designed by both IRRILAB and IRRIPRO software, for common emitters (CE) and pressure compensating emitters (PCE).

Sector | IRRILAB | IRRIPRO | ||
---|---|---|---|---|

E (kWh) | E (kWh) | |||

CE | PCE | CE | PCE | |

1 | 34,866 | 22,100 | 41,292 | 24,249 |

2 | 16,074 | 11,789 | 18,743 | 11,611 |

3 | 13,991 | 10,905 | 14,398 | 12,386 |

4 | 18,342 | 15,846 | 22,291 | 16,624 |

5 | 14,021 | 11,546 | 17,272 | 12,938 |

SUM | 97,295 | 72,187 | 113,996 | 77,807 |

**Table 9.**Energy, E, required for the micro-irrigation system of the apple farm subdivided in the “almost uniform” seven sectors and nine sectors, by splitting sectors #1 and #7 into two sectors (background gray colored), designed by both IRRILAB and IRRIPRO, for common emitters (CE) and pressure compensating emitters (PCE).

Sector | IRRILAB | IRRIPRO | ||
---|---|---|---|---|

E (kWh) | E (kWh) | |||

CE | PCE | CE | PCE | |

1 | 22,306 | 14,456 | 20,164 | 12,845 |

1A | 3192 | 3134 | 3525 | 3145 |

1B | 11,037 | 8928 | 11,308 | 9252 |

2 | 7994 | 6107 | 8693 | 6276 |

3 | 14,401 | 10,925 | 16,868 | 12,829 |

4 | 13,070 | 10,396 | 15,926 | 11,344 |

5 | 8592 | 6877 | 9047 | 6670 |

6 | 16,317 | 12,824 | 16,797 | 13,978 |

7 | 16,914 | 12,758 | 17,516 | 12,917 |

7A | 9280 | 7705 | 9824 | 8159 |

7B | 3702 | 3164 | 4140 | 3142 |

TOTAL 7 sectors | 99,594 | 74,343 | 105,011 | 76,859 |

TOTAL 9 sectors | 87,585 | 70,060 | 96,128 | 74,795 |

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## Share and Cite

**MDPI and ACS Style**

Baiamonte, G.; Di Dio, P.; Elfahl, M.
Verification of IRRILAB Software Application for the Hydraulic Design of a Micro-Irrigation System by Using IRRIPRO for an Apple Farm in Sicily. *Water* **2021**, *13*, 694.
https://doi.org/10.3390/w13050694

**AMA Style**

Baiamonte G, Di Dio P, Elfahl M.
Verification of IRRILAB Software Application for the Hydraulic Design of a Micro-Irrigation System by Using IRRIPRO for an Apple Farm in Sicily. *Water*. 2021; 13(5):694.
https://doi.org/10.3390/w13050694

**Chicago/Turabian Style**

Baiamonte, Giorgio, Pietro Di Dio, and Mustafa Elfahl.
2021. "Verification of IRRILAB Software Application for the Hydraulic Design of a Micro-Irrigation System by Using IRRIPRO for an Apple Farm in Sicily" *Water* 13, no. 5: 694.
https://doi.org/10.3390/w13050694