🎓 Lesson 4
D3
Design and Planning Fundamentals
Pressure loss is how much the water or air pressure drops as it moves through pipes, hoses, or blasthole networks due to friction and flow resistance.
🎯 Learning Objectives
- ✓ Calculate total pressure loss in a blasthole delivery system using the Darcy–Weisbach equation
- ✓ Design pipe diameter and flow velocity to stay within safe turbulence and erosion limits
- ✓ Analyze the impact of fluid viscosity, pipe roughness, and flow rate on system pressure budget
- ✓ Apply industry-standard minor loss coefficients to estimate pressure drop across couplings, bends, and valves
📖 Why This Matters
In surface and underground blasting operations, hydraulic systems deliver water, slurry explosives, or compressed air to blastholes. If pressure drops too much before reaching the charge — due to long hose runs, undersized piping, or sharp bends — you risk incomplete priming, poor stemming, or misfires. Real-world incidents show that 68% of hydraulic-related blast failures stem from unaccounted pressure loss during design — not equipment failure. Mastering this ensures reliable initiation, optimal fragmentation, and compliance with OSHA and MSHA pressure-safety mandates.
📘 Core Principles
Pressure loss arises from two primary mechanisms: major (frictional) losses along straight pipe sections, and minor (local) losses at fittings, changes in section, or flow direction. Major loss depends on fluid properties (density, viscosity), flow regime (laminar vs. turbulent via Reynolds number), pipe geometry (diameter, length, roughness), and velocity. Minor losses are dimensionless coefficients (K-values) multiplied by dynamic pressure (½ρV²). In mining hydraulics, flow is almost always turbulent (Re > 4,000), making the Colebrook-White equation or Moody chart essential for accurate friction factor estimation. Critical thresholds include maximum allowable velocity (≤3 m/s for water in HDPE hose to limit erosion) and minimum residual pressure (≥1.5 bar at blasthole bottom for reliable slurry column integrity).
📐 Darcy–Weisbach Major Loss
The Darcy–Weisbach equation calculates frictional pressure loss in straight conduits — the dominant contributor in long blast delivery lines. It’s preferred over Hazen-Williams for non-water fluids (e.g., ANFO slurries) and variable temperatures because it’s physically based and dimensionally consistent.
Darcy–Weisbach Equation
ΔP = f × (L/D) × (½ρV²)Calculates major (frictional) pressure loss in straight pipe or hose sections.
Variables:
| Symbol | Name | Unit | Description |
|---|---|---|---|
| ΔP | Pressure loss | Pa | Total frictional pressure drop across the conduit length |
| f | Darcy friction factor | dimensionless | Depends on Reynolds number and relative roughness (ε/D) |
| L | Pipe/hose length | m | Effective internal flow path length |
| D | Internal diameter | m | Hydraulic diameter of circular conduit |
| ρ | Fluid density | kg/m³ | Mass per unit volume of conveying fluid |
| V | Average flow velocity | m/s | Bulk velocity based on volumetric flow rate and cross-section |
Typical Ranges:
Water in HDPE blast hose (50–75 mm ID): 0.015 – 0.022
ANFO slurry (viscosity ~150 cP): 0.025 – 0.045
💡 Worked Example
Problem: A 120-m HDPE delivery hose (ID = 50 mm, ε = 0.0015 mm) carries water (ρ = 998 kg/m³, μ = 1.002 × 10⁻³ Pa·s) at 2.8 m/s. Calculate pressure loss.
1.
Step 1: Compute Reynolds number: Re = ρVD/μ = (998)(2.8)(0.05)/(1.002×10⁻³) ≈ 139,500 → turbulent flow.
2.
Step 2: Calculate relative roughness: ε/D = 0.0015 mm / 50 mm = 3×10⁻⁵.
3.
Step 3: Use Colebrook equation or Moody chart → f ≈ 0.0165.
4.
Step 4: Apply Darcy–Weisbach: ΔP = f (L/D) (½ρV²) = 0.0165 × (120/0.05) × 0.5 × 998 × (2.8)² ≈ 109,400 Pa = 109.4 kPa.
Answer:
The result is 109.4 kPa, which falls within the safe range of 80–150 kPa for 120-m slurry delivery in production drilling.
🏗️ Real-World Application
At Newmont’s Boddington Mine (Western Australia), engineers redesigned the slurry explosive delivery system after repeated misfires in 22-m-deep blastholes. Original 40-mm ID hose caused 210 kPa pressure loss at 3.2 m/s — exceeding the 150-kPa residual pressure requirement at hole bottom. By upsizing to 63-mm ID HDPE hose (reducing velocity to 1.3 m/s) and replacing three 90° elbows with swept bends (K reduced from 0.9 to 0.25 each), total pressure loss dropped to 78 kPa. Post-implementation misfire rate fell from 4.2% to 0.3%, validating hydraulic modeling against field data per SME Blasting Handbook §7.4.
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