🎓 Lesson 23
D5
WDN Analysis Mastery Quiz
WDN Analysis is the process of checking if a water pipe network delivers enough water at the right pressure to all users, like homes and factories.
🎯 Learning Objectives
- ✓ Calculate nodal pressures and pipe flows using the Hardy-Cross method
- ✓ Design pipe diameters to meet minimum pressure (≥20 m) and velocity (0.6–3.0 m/s) constraints
- ✓ Analyze network resilience by quantifying surplus power and criticality indices
- ✓ Apply EPANET simulation to model demand-driven and pressure-dependent scenarios
- ✓ Explain the impact of pipe roughness, aging, and valve configurations on hydraulic performance
📖 Why This Matters
In mining operations, reliable water distribution is essential for dust suppression, ore processing, dewatering, and worker safety — yet remote sites face challenges like elevation extremes, intermittent power, and aging infrastructure. A single undersized pipe or unbalanced valve setting can cause low pressure at critical pumps or catastrophic cavitation in slurry lines. Mastering WDN analysis prevents costly shutdowns, regulatory noncompliance, and environmental incidents — turning hydraulic theory into operational resilience.
📘 Core Principles
WDN analysis rests on two fundamental laws: (1) Conservation of mass (Kirchhoff’s first law) — flow into a junction equals flow out; and (2) Conservation of energy (Kirchhoff’s second law) — algebraic sum of head losses around any closed loop equals zero. Networks are modeled as directed graphs with nodes (junctions, reservoirs, tanks) and links (pipes, pumps, valves). Steady-state analysis assumes constant demand and fixed pump curves, while extended-period simulation (EPS) incorporates time-varying demands, tank level dynamics, and pump scheduling. Key behavioral concepts include hydraulic grade line (HGL), pressure-dependent demand (PDD), and network partitioning for isolation and maintenance.
📐 Hazen-Williams Head Loss
The Hazen-Williams equation estimates frictional head loss in pipes under turbulent flow — widely preferred in water engineering for its empirical simplicity and field calibration. It is applied per pipe segment in iterative solvers (e.g., Hardy-Cross) and embedded in software like EPANET.
Hazen-Williams Head Loss
h_f = 10.67 × L × Q^1.852 / (C^1.852 × D^4.871)Calculates frictional head loss (m) in a pipe under turbulent flow.
Variables:
| Symbol | Name | Unit | Description |
|---|---|---|---|
| h_f | Head loss | m | Energy loss due to friction along pipe length |
| L | Pipe length | m | Length of pipe segment |
| Q | Volumetric flow rate | m³/s | Flow through the pipe |
| C | Hazen-Williams coefficient | unitless | Empirical roughness coefficient (higher = smoother) |
| D | Internal pipe diameter | m | Actual inside diameter of pipe |
Typical Ranges:
New HDPE pipe: 140 – 155
15-year-old corroded ductile iron: 80 – 100
💡 Worked Example
Problem: Given: 300-mm diameter PVC pipe (C = 150), length = 850 m, flow = 0.12 m³/s, unit conversion factor = 10.67 (SI). Calculate head loss.
1.
Step 1: Confirm units — diameter in meters (0.3 m), flow in m³/s (0.12), C = 150.
2.
Step 2: Apply Hazen-Williams: h_f = 10.67 × L × Q^1.852 / (C^1.852 × D^4.871) = 10.67 × 850 × (0.12)^1.852 / (150^1.852 × 0.3^4.871)
3.
Step 3: Compute: (0.12)^1.852 ≈ 0.0197; 150^1.852 ≈ 4,490; 0.3^4.871 ≈ 0.00225 → denominator ≈ 10.1; numerator ≈ 170.5 → h_f ≈ 16.9 m
Answer:
The result is 16.9 m, which falls within the safe range of 10–25 m for a single pipe segment in mine site trunk mains.
🏗️ Real-World Application
At the Oyu Tolgoi copper-gold mine (Mongolia), engineers used EPANET-based WDN modeling to redesign the 42-km high-elevation potable water system serving 5,000 personnel. Original design suffered 32% nodes below 20-m residual pressure during peak demand. By upsizing six key HDPE trunk lines (from DN250 to DN315), relocating a break-pressure tank, and installing PRVs at three elevation transitions, pressure compliance rose from 68% to 99.4%. The model was validated using 14 months of SCADA pressure logs (±0.3 m accuracy) and reduced emergency pump interventions by 71%.
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