The Lugeon Test: Methodology, Interpretation, and Applications in Geotechnical Engineering

 

Introduction

Designing a Pressurized Irrigation Network System (PINS) involves a systematic process that translates field requirements, topography, crop characteristics, and water source parameters into a fully functional network of pipes, emitters, and control devices. This article presents a detailed example of such a design using assumed data for a hypothetical agricultural setup. The example is structured to demonstrate real-world applications of design formulas and considerations, providing practical insights for engineers, students, and practitioners.

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1. Assumed Project Information

• Total area: 10 hectares (split into 5 fields of 2 hectares each)

• Crop type: Citrus orchard

• Soil type: Sandy loam (medium infiltration)

• Topography: Gently sloping (average elevation change of 3 m)

• Water source: Borewell with available static head at source = 0 m

• Crop water requirement: 5.5 mm/day (peak season)

• Irrigation method: Subsurface drip irrigation

• Irrigation interval: Once every 2 days

• Irrigation efficiency: 90%

• Emitter discharge: 2 L/h

• Emitter spacing: 1 m

• Lateral spacing: 4 m

• Working hours/day: 8 hours

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2. Crop Water Requirement and System Flow Rate

2.1 Volume of Water Needed

$$\text{Net irrigation requirement} = 5.5\ \text{mm/day} = 5.5\ \text{L/m}^2/\text{day}$$
$$\text{Total area} = 10\ \text{ha} = 100,000\ \text{m}^2$$
$$\text{Daily water volume} = 100,000 \times 5.5 = 550,000\ \text{L/day}$$
$$\text{Gross water requirement} = \frac{550,000}{0.90} \approx 611,111\ \text{L/day}$$
$$\text{Flow rate (Q)} = \frac{611,111}{8 \times 3600} \approx 21.2\ \text{L/s}$$

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3. Layout and Emitter Requirement

Each field (2 ha) will have:

• 2 ha = 20,000 m²

• Lateral lines spaced 4 m apart → 20,000 / 4 = 5,000 m of laterals per field

• Emitters spaced every 1 m → 5,000 emitters per field

• Each emitter = 2 L/h

$$\text{Total emitters} = 5,000 \times 5 = 25,000$$
$$\text{Total emitter discharge} = 25,000 \times 2 = 50,000\ \text{L/h} = 13.89\ \text{L/s}$$

(We design for 21.2 L/s to cover peak requirements + distribution losses + safety margin)

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4. Pipe Sizing and Friction Loss Calculation

Assume:

• Mainline length = 400 m

• Pipe material = HDPE

• Flow through mainline = 21.2 L/s

• Using Hazen-Williams formula:

$$h_f = 10.67 \cdot \frac{L \cdot Q^{1.852}}{C^{1.852} \cdot D^{4.87}}$$

Assume:

• C = 140 (HDPE)

• D = 90 mm (0.09 m)

• L = 400 m

• Q = 0.0212 m³/s

$$h_f \approx 10.67 \cdot \frac{400 \cdot (0.0212)^{1.852}}{140^{1.852} \cdot (0.09)^{4.87}} \approx 6.5\ \text{m}$$

Minor losses (valves, bends, fittings):
Assume K = 2.5, velocity v ≈ 3.33 m/s

$$h_m = K \cdot \frac{v^2}{2g} = 2.5 \cdot \frac{(3.33)^2}{2 \cdot 9.81} \approx 1.41\ \text{m}$$

Elevation head (H_g) = 3 m
Required pressure at field inlet (H_e) = 10 m (for emitters)

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5. Total Pumping Head and Pump Selection

$$H = H_g + H_f + H_m + H_e = 3 + 6.5 + 1.41 + 10 = 20.91\ \text{m}$$

Pump requirement:

• Flow rate = 21.2 L/s

• Total dynamic head = ~21 m

• Power estimation:

$$P = \frac{Q \cdot H \cdot \gamma}{\eta \cdot 1000} = \frac{0.0212 \cdot 21 \cdot 9.81}{0.7} \approx 6.2\ \text{kW}$$

→ Select a 7.5 kW (10 HP) centrifugal pump

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6. Uniformity and Pressure Check

• Use pressure-compensating emitters

• Ensure pressure variation <10% across laterals

• Use pressure regulators where needed

Christiansen’s Uniformity Coefficient (CU) can be expected > 90% if layout and pressure are balanced.

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7. Cost Estimation (Rough)

Component	Estimate (INR)
Pipes and fittings	₹3,00,000
Pump and motor	₹1,00,000
Emitters and laterals	₹1,50,000
Installation and labor	₹80,000
Electrical and wiring	₹40,000
Total	₹6,70,000

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Conclusion

This example demonstrates a practical design of a PINS system for a 10-hectare citrus farm using subsurface drip irrigation. The process involves calculating crop water requirements, sizing pipes and pumps, accounting for friction and elevation losses, and ensuring efficient system performance. While simplified for illustrative purposes, this example offers a solid foundation for real-world system design and customization.