# Hydraulic Performance and Modelling of Pressurized Drip Irrigation System

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Study Area

#### 2.2. Data Collection

#### 2.3. Drip Irrigation System Layout

#### 2.4. Measurement of Hydraulic Parameters of the Irrigation System

#### 2.5. Hydraulic Performance Evaluation

#### 2.6. Numerical Modelling and Model Performance

_{f}is friction loss of the pipe (m), L is pipe length (m), D is the pipe’s internal diameter (m), V is the velocity in pipe (m/s), g is the acceleration due to gravity (9.81 (m/s

^{2})) and f is the friction coefficient (-). The friction coefficient, f is determined by f = 0.302/(R

_{e})

^{0.25}for 2000 < Re < 36,000 [5]. The minor loss can be determined in a general form as given in Equation (2) [7].

_{Lminor}is the head loss due to fitting and insertion of emitter, k is the head loss coefficient, v is the velocity in pipe (m/s), and g is acceleration due to gravity (9.81 (m/s

^{2})). The k coefficient due to insertion of emitter can be expressed as [7]

_{g}/D

_{i})

^{17.83}− 1]

## 3. Results and Discussion

#### 3.1. Hydraulic Performance of an Existing Drip Irrigation System

#### 3.2. Comparing Model Results and Measurement: Pressure and Discharge in Lateral Pipes 1 and 2

_{f}, considering both friction and minor losses for lateral pipe 1 shows an increasing loss, starting lower, h

_{f}= 0.49 m at the lateral front and higher, h

_{f}= 4.63 m at the lateral end. The measured pressure of the last emitter, i.e., point 100 is 21.77 m, slightly higher than the model’s pressure which is 21.40 m.

_{f}, considering both friction and minor losses for lateral pipe 2 shows an increasing loss, starting lower, h

_{f}= 0.13 m at the emitter front and higher, h

_{f}= 4.62 m at the emitter end.

#### 3.3. Model Performance

^{2}pressures for both lateral pipes are 0.99, indicating a perfect fit between measurement and model. This shows that the model yields good performance in term of discharge.

^{2}discharge for lateral pipe 1 is 0.97 while for lateral pipe 2, it is 0.91. This could be due to the condition of the emitters and the lateral pipes. A minor clogging is expected to occur, which leads to inconsistent results between lateral pipes 1 and 2. Although R

^{2}for lateral pipe 2 is slightly lower than that for lateral pipe 1, a good fit between measurement and model is achieved. This shows that the model gives good performance in terms of pressure. According to [42,43], the maximum error between the model and observation results should be less than 10%. In this study, the errors calculated are below 10%, i.e., 2.2% and 3.0% for pressure and 1.7% for discharge in lateral 1 and lateral 2, thus indicating that the model’s performance is good. This indicates that this model replicates the existing drip irrigation system and therefore can be used to improve the performance of any new drip irrigation systems in the future, provided that a similar design layout is applied.

## 4. System Curve and Pump Curve

## 5. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Study area. Inset represents the location of study area. The map was captured using Google Maps [22].

**Figure 3.**Emitter locations for the measurement of pressure and flow rate. The numbers in the planter pot indicate the plant pot numbers where the measurements were done. Photos in the diagram show the spaghetti emitter used in the existing system. Each lateral pipe has 100 emitters.

**Figure 4.**Parameters involved in calculating minor loss for online type emitters [7].

**Figure 5.**Comparison between measured and modelled discharges and pressures at emitters in lateral pipe 1 and lateral pipe 2. (

**a**) Discharge at emitters on lateral pipe 1; (

**b**) Pressure at emitters on lateral pipe 1; (

**c**) Discharge at emitters on lateral pipe 2; (

**d**) Pressure at emitters on lateral pipe 2.

**Figure 6.**Modelled and observed pressure (upper) and discharge (lower) on lateral pipe 1 and lateral pipe 2. (

**a**) Pressure on lateral pipe 1; (

**b**) Pressure on lateral pipe 2; (

**c**) Discharge on lateral pipe 1; (

**d**) Discharge on lateral pipe 2.

**Table 1.**The coefficients involved in the calculation of hydraulic performance include coefficient of uniformity (CU), emission uniformity (EU), coefficient of variation (CV), and emitter flow variation (EFV) [20].

Emission Uniformity (EU) | Coefficient of Variation (CV) | Emitter Flow Variation (EFV) | Coefficient of Uniformity (CU) | |||||
---|---|---|---|---|---|---|---|---|

Performance Indicator | ≥90% | Excellent | <0.05 | Excellent | ≤10% | Desirable | ≥90% | Excellent |

80–90% | Good | 0.05–0.07 | Average | 10–20% | Acceptable | 80–90% | Good | |

70–80% | Fair | 0.07–0.11 | Marginal | >25% | Unacceptable | 70–80% | Fair | |

≤70% | Poor | 0.11–0.15 | Poor | 60–70% | Poor | |||

>0.15 | Unacceptable | >60% | Unacceptable | |||||

Equation | $\mathrm{EU}=100\text{}\left(\frac{\mathrm{qn}}{\mathrm{qa}}\right)$ | $\mathrm{CV}=100\text{}\frac{\mathrm{SD}}{\mathrm{qavg}}$ | EFV = 100 [1 − $\frac{\mathrm{Qmin}}{\mathrm{Qmax}}$] | $\mathrm{CU}=100\text{}\left(1-{\displaystyle \sum}\frac{\Delta \mathrm{q}}{\mathrm{qn}}\right)$ | ||||

Definition | EU = Emission uniformity qn = average rate of discharge of the lowest one fourth of the field data of emitter discharge readings (L/h) qa = average discharge rate of all the emitters checked in the field (L/h). [20] | CV = the coefficient of variation of emitter discharge. SD = standard deviation of emitter discharge. qavg = average discharge in the same lateral lines (L/h) [20] | EFV = emitter flow variation (%) Qmin = minimum emitter discharge rate in the system (L/h) Qmax = average or design emitter discharge rate (L/h) [20] | Cu = Christiansen’s uniformity coefficient in percentage ∆q = average deviation of individual emitters discharge (L/h). q = average discharge (L/h). n = number of observations [20] |

Statistical Error Index | Description |
---|---|

$\mathrm{RMSE}=\sqrt{\frac{{{\displaystyle \sum}}_{\mathrm{i}=1}^{\mathrm{n}}{({\mathrm{X}}_{\mathrm{obs},\mathrm{i}}-{\mathrm{X}}_{\mathrm{model},\mathrm{i}})}^{2}}{\mathrm{n}}}$ | The Root Mean Square Error (RMSE) is a frequently used measure of the difference between values predicted by a model and the values observed from the field. These individual differences are also called residuals, and the RMSE serves to aggregate them into a single measure of predictive power [36] |

$\mathrm{MBE}=\frac{1}{\mathrm{n}}{\displaystyle {\displaystyle \sum}_{\mathrm{i}=1}^{\mathrm{n}}}\left({\mathrm{X}}_{\mathrm{model},\mathrm{i}}-{\mathrm{X}}_{\mathrm{obs},\mathrm{i}}\right)$ | Mean bias error (MBE) is primarily used to estimate the average bias in the model and to decide if any steps need to be taken to correct the model bias. MBE captures the average bias in the prediction. The lower values of errors and considerably higher value of correlation coefficient for the variable and direction are of greater importance [37] |

$\mathrm{MAPE}=100\times \frac{1}{\mathrm{n}}\times {\displaystyle {\displaystyle \sum}_{\mathrm{i}=1}^{\mathrm{n}}}\left(\frac{{\mathrm{X}}_{\mathrm{obs},\mathrm{i}}-{\mathrm{X}}_{\mathrm{model},\mathrm{i}}}{{\mathrm{X}}_{\mathrm{obs},\mathrm{i}}}\right)$ | The mean absolute percentage error (MAPE) is a measure of prediction accuracy of a forecasting method in statistics. The MAPE measures the size of the error in terms of percentage. It is calculated as the average of the unsigned percentage error [38] |

_{obs}is the observed value and X

_{model}is the modelled value at time or place, i.

**Table 3.**Coefficient values and classification of hydraulic parameters of the existing drip irrigation system.

No | Hydraulic Parameter | Pressure (m) | |||
---|---|---|---|---|---|

15.3 | 20.4 | 25.5 | 28.6 | ||

1 | Coefficient of uniformity, CU (%) | 98.20 | 98.28 | 98.23 | 97.87 |

Classification | excellent | excellent | excellent | excellent | |

2 | Coefficient of variation, CV (-) | 0.02 | 0.02 | 0.02 | 0.023 |

Classification | excellent | excellent | excellent | excellent | |

3 | Emission uniformity, EU (%) | 97.54 | 97.53 | 97.12 | 96.75 |

Classification | excellent | excellent | excellent | excellent | |

4 | Emitter flow variation, EFV (%) | 10.29 | 10.00 | 10.00 | 13.60 |

Classification | acceptable | desirable | desirable | acceptable |

Discharge (L/h) | |||
---|---|---|---|

Error Index | RMSE (L/h) | MAPE (%) | MBE (L/h) |

Lateral pipe 1 | 0.04 | 1.7 | 0.03 |

Lateral pipe 2 | 0.04 | 1.7 | 0.02 |

Pressure (m) | |||

Lateral pipe 1 | 0.61 | 2.2 | 0.51 |

Lateral pipe 2 | 0.79 | 3.0 | 0.68 |

© 2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Sharu, E.H.; Ab Razak, M.S.
Hydraulic Performance and Modelling of Pressurized Drip Irrigation System. *Water* **2020**, *12*, 2295.
https://doi.org/10.3390/w12082295

**AMA Style**

Sharu EH, Ab Razak MS.
Hydraulic Performance and Modelling of Pressurized Drip Irrigation System. *Water*. 2020; 12(8):2295.
https://doi.org/10.3390/w12082295

**Chicago/Turabian Style**

Sharu, Eddy Herman, and Mohd Shahrizal Ab Razak.
2020. "Hydraulic Performance and Modelling of Pressurized Drip Irrigation System" *Water* 12, no. 8: 2295.
https://doi.org/10.3390/w12082295