🎓 Lesson 3 D2

Equipment and Materials Overview

Pipe flow hydraulics is how water or slurry moves through pipes—like understanding how pressure, pipe size, and fluid speed work together to keep mining slurries flowing safely and efficiently.

🎯 Learning Objectives

✓ Calculate frictional head loss in a pipeline using the Darcy–Weisbach equation
✓ Analyze flow regime (laminar, transitional, turbulent) using Reynolds number
✓ Design pipe diameter for a given slurry flow rate and allowable pressure drop
✓ Explain the impact of solids concentration and particle size on hydraulic gradient in non-Newtonian slurries
✓ Apply Moody chart or Colebrook-White correlation to determine friction factor for turbulent flow

📖 Why This Matters

In mining, over 70% of tailings, ore pulp, and process water move through pressurized pipelines. A single miscalculation in pipe hydraulics can cause catastrophic pipeline blockage, pump failure, or excessive energy consumption—adding millions in OPEX and risking environmental releases. Understanding pipe flow hydraulics ensures reliable, safe, and energy-efficient material transport from crusher to concentrator to tailings storage.

📘 Core Principles

Flow in pipes is classified by Reynolds number (Re): Re < 2,300 = laminar; 2,300–4,000 = transitional; > 4,000 = turbulent. In mining, most slurry flows are turbulent due to high velocities and solids loading. Friction loss dominates total head loss and depends on pipe roughness (ε), diameter (D), velocity (V), and fluid properties (ρ, μ). For non-Newtonian slurries (e.g., high-solids coal or iron ore), the Bingham plastic or Herschel–Bulkley models replace simple Newtonian assumptions. Local losses (valves, bends, tees) add 5–30% to system head and must be included in pump selection.

📐 Darcy–Weisbach Friction Loss

The Darcy–Weisbach equation calculates major (frictional) head loss in circular pipes. It is universally applicable across flow regimes when the correct friction factor (f) is used—determined via Moody chart, Colebrook-White iteration, or Swamee–Jain approximation for turbulent flow.

Darcy–Weisbach Equation

h_f = f \cdot \frac{L}{D} \cdot \frac{V^2}{2g}

Calculates frictional head loss (m) in a straight pipe section.

Variables:

Symbol	Name	Unit	Description
h_f	Frictional head loss	m	Energy loss due to wall shear stress
f	Darcy friction factor	dimensionless	Function of Re and relative roughness ε/D
L	Pipe length	m	Length of straight pipe segment
D	Internal pipe diameter	m	Hydraulic diameter for circular pipe
V	Average flow velocity	m/s	Based on volumetric flow rate Q and cross-section area
g	Gravitational acceleration	m/s²	Standard value = 9.81 m/s²

Typical Ranges:

Mine process water main: 0.008 – 0.025

High-solids iron ore slurry (65% w/w): 0.035 – 0.072

💡 Worked Example

Problem: A 300-mm-diameter HDPE pipeline (ε = 0.0015 mm) carries water (ν = 1.004 × 10⁻⁶ m²/s) at 2.1 m/s over 850 m. Calculate total frictional head loss.

1. Step 1: Compute Reynolds number: Re = V·D/ν = (2.1)(0.3)/(1.004×10⁻⁶) ≈ 627,500 → turbulent

2. Step 2: Compute relative roughness: ε/D = 0.0015/300 = 5×10⁻⁶

3. Step 3: Use Swamee–Jain to estimate f: f = 0.25 / [log₁₀((ε/D)/3.7 + 5.74/Re⁰·⁹)]² ≈ 0.0132

4. Step 4: Apply Darcy–Weisbach: h_f = f·(L/D)·(V²/2g) = 0.0132 × (850/0.3) × (2.1²/(2×9.81)) ≈ 17.8 m

Answer: The frictional head loss is 17.8 m, which falls within the typical range of 15–25 m for comparable mine water mains.

🏗️ Real-World Application

At the Antamina Mine (Peru), engineers redesigned the 12-km tailings pipeline from 400 mm to 450 mm HDPE after repeated plugging at bends. Hydraulic modeling revealed that at 4.2 m/s and 58% w/w solids, the original line operated near the deposition velocity threshold. Increasing diameter reduced velocity to 3.3 m/s and cut frictional head loss by 22%, extending pump life and reducing power use by 1.8 MW annually—validated by full-scale commissioning tests per SME Guideline G-2021-01.