🎓 Lesson 3
D2
Hazen–Williams vs. Darcy–Weisbach: When to Use Which
Hazen–Williams and Darcy–Weisbach are two different ways to calculate how much pressure is lost when water flows through pipes — like choosing the right tool for a job.
🎯 Learning Objectives
- ✓ Calculate head loss using both Hazen–Williams and Darcy–Weisbach equations for identical pipe scenarios
- ✓ Analyze when each equation yields >5% difference in head loss and explain the physical cause
- ✓ Explain the limitations of Hazen–Williams in mining dewatering systems involving variable temperature, suspended solids, or non-potable water
- ✓ Apply Moody chart or Colebrook-White iteration to determine Darcy friction factor for rough mine drainage pipes
- ✓ Design a pump station layout by selecting the appropriate friction loss model based on fluid properties and regulatory compliance
📖 Why This Matters
In mining operations, accurate hydraulic modeling of dewatering networks, slurry transport, and potable water supply directly impacts safety, energy cost, and regulatory compliance. Using Hazen–Williams where Darcy–Weisbach is required — such as for warm, gritty mine water flowing in corroded HDPE or steel pipes — can underestimate head loss by 15–30%, leading to undersized pumps, system failure, or costly retrofitting. Choosing the right friction loss model isn’t academic — it’s a frontline engineering decision.
📘 Core Principles
Hazen–Williams assumes water at ~20°C, hydraulically smooth pipes, and turbulent flow (Re > 10⁵), with C-values representing empirical pipe roughness (e.g., C = 150 for new PVC; C = 80 for corroded cast iron). It ignores fluid viscosity and Reynolds number — making it invalid for non-water fluids or low-flow conditions. Darcy–Weisbach, rooted in conservation of momentum, explicitly incorporates fluid density, dynamic viscosity, pipe diameter, velocity, and relative roughness (ε/D) via the friction factor f. Its universality comes at the cost of iterative calculation (Colebrook-White) or chart lookup (Moody), but modern tools automate this. Critically, Darcy–Weisbach remains valid for laminar flow (f = 64/Re), while Hazen–Williams fails entirely below Re ≈ 10⁵.
📐 Key Calculations
Both formulas compute head loss (h_f) in meters of water column. Hazen–Williams is algebraic and unit-sensitive (US customary vs. SI); Darcy–Weisbach is dimensionally rigorous and unit-agnostic when variables are consistent. Use Hazen–Williams for rapid preliminary design of clean, cold, municipal-grade water in smooth pipes. Use Darcy–Weisbach for mining applications involving variable temperature, suspended solids, mixed materials, or regulatory reporting requiring traceable physics-based models.
Hazen–Williams (SI)
h_f = 10.67 × L × Q^{1.852} / (C^{1.852} × D^{4.871})Head loss due to friction in meters for water flow in circular pipes (SI units).
Variables:
| Symbol | Name | Unit | Description |
|---|---|---|---|
| h_f | Head loss | m | Energy loss due to pipe friction |
| L | Pipe length | m | Length of pipe segment |
| Q | Volumetric flow rate | m³/s | Flow rate of water |
| C | Hazen–Williams roughness coefficient | unitless | Empirical measure of pipe smoothness |
| D | Internal pipe diameter | m | Hydraulic diameter for circular pipe |
Typical Ranges:
New PVC or HDPE: 140 – 150
New ductile iron: 130 – 140
Aged/corroded cast iron: 80 – 100
💡 Worked Example
Problem: Given: Q = 0.15 m³/s, D = 0.3 m, L = 850 m, C = 120 (aged ductile iron), slope = 0.5%. Calculate h_f using Hazen–Williams (SI) and compare with Darcy–Weisbach using f = 0.022 (from Moody chart).
1.
Step 1: Apply Hazen–Williams (SI): h_f = 10.67 × L × Q^1.852 / (C^1.852 × D^4.871)
2.
Step 2: Plug in: h_f = 10.67 × 850 × (0.15)^1.852 / (120^1.852 × 0.3^4.871) = 10.67 × 850 × 0.0327 / (2972 × 0.00242) ≈ 41.2 m
3.
Step 3: Compute velocity V = Q/A = 0.15 / (π×0.15²) ≈ 2.12 m/s → Re = ρVD/μ ≈ (998)(2.12)(0.3)/(1.002×10⁻³) ≈ 635,000 → turbulent. Then Darcy–Weisbach: h_f = f × (L/D) × (V²/2g) = 0.022 × (850/0.3) × (2.12²/(2×9.81)) ≈ 0.022 × 2833 × 0.229 ≈ 14.2 m
Answer:
Hazen–Williams predicts h_f = 41.2 m; Darcy–Weisbach yields 14.2 m — a 190% overprediction. This discrepancy arises because C = 120 underestimates actual roughness (ε ≈ 1.2 mm → ε/D = 0.004) and Hazen–Williams ignores Re dependence — revealing its unsuitability for aged, rough mine pipes.
🏗️ Real-World Application
At the Cadia East underground mine (NSW, Australia), initial dewatering network design used Hazen–Williams with C = 130 for HDPE-lined steel pipes. Commissioning revealed 22% higher pump power consumption than modeled. Re-analysis using Darcy–Weisbach with measured ε = 0.8 mm (due to biofilm + silt deposition) and temperature-corrected viscosity (28°C water, μ = 0.83×10⁻³ Pa·s) reduced prediction error to <3%. The revised model triggered replacement of two booster stations and justified inclusion of inline flow conditioning — now codified in their Asset Integrity Management System (AIMS) per AS/NZS 3500.1.
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