🎓 Lesson 1
D1
Getting Started with Fluid Flow and Transport Phenomena
Fluid flow and transport phenomena describe how liquids, gases, and particles move and mix in mining systems—like water draining from a pit or explosive gases pushing rock apart.
🎯 Learning Objectives
- ✓ Calculate volumetric flow rate and Reynolds number for mine dewatering pipes
- ✓ Analyze pressure drop across a ventilation duct using the Darcy–Weisbach equation
- ✓ Explain the physical significance of dimensionless numbers (Re, Fr, Eu) in scaling blasting-related fluid dynamics
- ✓ Apply Fick’s first law to estimate diffusion time of toxic gases in confined blast areas
- ✓ Design a minimum air velocity for dust suppression in haulage tunnels based on particle settling theory
📖 Why This Matters
In mining, fluid behavior directly impacts safety, efficiency, and environmental compliance: poor ventilation spreads NO₂ after blasting; inadequate dewatering floods excavations; mistimed slurry flow causes pipeline blockages. Understanding how fluids move—and how heat, mass, and momentum transfer within them—is not theoretical—it’s the foundation for designing reliable, compliant, and cost-effective mining systems.
📘 Core Principles
Transport phenomena unify three interrelated domains: fluid mechanics (momentum transfer), heat transfer (energy transfer), and mass transfer (diffusion, convection, dispersion). All obey conservation principles expressed as partial differential equations—the Navier–Stokes, energy, and continuity equations. At the engineering scale, we simplify these using dimensional analysis, boundary conditions, and empirical correlations. Key insights include laminar vs. turbulent flow regimes, boundary layer development, and the role of fluid properties (viscosity, density, diffusivity) in controlling transport rates—especially critical when modeling explosive gas expansion, dust cloud dispersion, or groundwater inflow into stopes.
📐 Reynolds Number for Flow Regime Identification
The Reynolds number (Re) predicts whether flow is laminar, transitional, or turbulent—a prerequisite for selecting correct friction factor correlations and estimating mixing/dispersion behavior in blast fumes or ventilation ducts.
Reynolds Number
Re = \rho V D / \muDimensionless number predicting flow regime (laminar, transitional, turbulent) based on inertial and viscous forces.
Variables:
| Symbol | Name | Unit | Description |
|---|---|---|---|
| ρ | Fluid density | kg/m³ | Mass per unit volume of the flowing medium |
| V | Characteristic velocity | m/s | Average or bulk velocity in the flow domain |
| D | Characteristic length | m | Hydraulic diameter for ducts or particle diameter for suspensions |
| μ | Dynamic viscosity | Pa·s | Measure of fluid resistance to shear deformation |
Typical Ranges:
Mine ventilation ducts: 1 × 10⁵ – 2 × 10⁶
Slurry pipelines (high-solids): 1 × 10⁴ – 5 × 10⁵
Blast gas expansion near borehole: 1 × 10² – 1 × 10⁴ (transient, compressible)
💡 Worked Example
Problem: Given: Air at 25°C flowing in a 1.2 m diameter ventilation duct at 8 m/s. Air density = 1.184 kg/m³; dynamic viscosity = 1.86 × 10⁻⁵ Pa·s.
1.
Step 1: Identify known parameters — ρ = 1.184 kg/m³, V = 8 m/s, D = 1.2 m, μ = 1.86 × 10⁻⁵ Pa·s
2.
Step 2: Apply Re = ρVD/μ = (1.184)(8)(1.2) / (1.86 × 10⁻⁵) ≈ 613,000
3.
Step 3: Compare to typical ranges — Re > 4000 indicates fully turbulent flow; 613,000 confirms turbulent regime requiring Colebrook equation or Moody chart for friction factor.
Answer:
The result is Re ≈ 6.13 × 10⁵, which falls within the turbulent range (>4000), confirming that turbulent flow models must be used for accurate pressure loss prediction.
🏗️ Real-World Application
At the Boddington Gold Mine (Western Australia), post-blast NO₂ concentrations exceeded 25 ppm in secondary development headings due to insufficient ventilation velocity. Engineers applied mass transport modeling—including advection (duct flow), turbulent diffusion (k–ε CFD), and chemical decay kinetics—to redesign airflow paths and increase minimum face velocity from 0.5 to 1.2 m/s. This reduced hazardous gas residence time by 73% and brought compliance with WA Mines Safety Standard 12.3 (max 5 ppm NO₂ exposure over 15 min).
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