🎓 Lesson 6
D3
Node and Link Typology: Junctions, Reservoirs, Tanks, Pumps, Valves
A node is a point in a water network where pipes meet or connect to equipment like tanks or pumps, and a link is the pipe or device that carries water between nodes.
🎯 Learning Objectives
- ✓ Identify and classify node types (junction, reservoir, tank, pump, valve) based on their hydraulic function and boundary condition requirements
- ✓ Analyze how each node and link type influences hydraulic grade line (HGL) continuity, energy conservation, and system stability in EPANET or similar solvers
- ✓ Design a minimal network segment incorporating at least one reservoir, two junctions, one tank, and one PRV—specifying correct input parameters for steady-state simulation
- ✓ Apply head-loss and pump characteristic equations to calculate flow and pressure across a pump–valve–tank configuration
📖 Why This Matters
Every water distribution model—whether for mine dewatering systems, camp water supply, or tailings pond recirculation—starts with correctly defining nodes and links. Misclassifying a tank as a junction or omitting pump controls can cause convergence failure, unrealistic pressures, or unsafe over-pressurization. In mining contexts, errors here directly impact pump selection, pipe wall thickness, and emergency shutoff reliability—making typology mastery foundational for safe, compliant design.
📘 Core Principles
Nodes serve as hydraulic anchors: reservoirs fix total head (elevation + pressure), tanks store volume and modulate pressure via level-dependent head, junctions conserve mass (ΣQ = 0) but require iterative head solution, and pumps/valves impose directional energy gain or loss. Links define flow pathways: pipes obey Darcy–Weisbach or Hazen–Williams; pumps follow head–flow curves (H = a − bQ²); valves enforce constraints (e.g., pressure reduction, flow throttling). The network must satisfy both mass conservation (at nodes) and energy conservation (along links)—the dual pillars of Newton–Raphson solution algorithms used in industry-standard software like EPANET and Bentley WaterGEMS.
📐 Pump Head–Flow Relationship
Centrifugal pumps are modeled using a second-order polynomial head curve. This equation enables prediction of discharge head under varying flow conditions—critical for sizing booster pumps in high-elevation mine water transfer lines.
Pump Characteristic Curve
H = a − bQ²Empirical quadratic model for centrifugal pump head versus flow, derived from factory test data.
Variables:
| Symbol | Name | Unit | Description |
|---|---|---|---|
| H | Pump head | m | Total dynamic head delivered by pump |
| Q | Volumetric flow rate | L/s | Flow through the pump |
| a | Shut-off head coefficient | m | Head at zero flow (y-intercept) |
| b | Resistance coefficient | m·s²/L² | Slope governing head decay with flow |
Typical Ranges:
Medium-duty mine dewatering pump: a = 60–120 m; b = 0.005–0.025 m·s²/L²
💡 Worked Example
Problem: A mine dewatering pump has coefficients a = 85 m, b = 0.012 m/(L/s)². Calculate head at Q = 42 L/s.
1.
Step 1: Identify knowns — a = 85 m, b = 0.012 m·s²/L², Q = 42 L/s
2.
Step 2: Apply H = a − bQ² → H = 85 − (0.012)(42)²
3.
Step 3: Compute: 42² = 1764; 0.012 × 1764 = 21.168; H = 85 − 21.168 = 63.832 m
Answer:
The pump delivers 63.8 m of head at 42 L/s, within the typical operating range of 55–70 m for medium-duty mine service pumps.
🏗️ Real-World Application
At the Cadia East underground mine (NSW, Australia), a 3.2 km, 300 mm HDPE rising main transports dewatering water from 850 m depth to surface storage. The model includes: (1) a reservoir node at the sump (fixed head = 850 m elevation + 10 m static pressure), (2) 12 junction nodes along the pipeline (with friction losses calibrated to field flow tests), (3) a variable-speed pump node governed by a 3-point head–flow curve, (4) a surge tank node at mid-elevation (modeled as a cylindrical tank with 20 m³ volume and 3.5 m diameter), and (5) a pressure-reducing valve (PRV) link downstream of the tank set to maintain 450 kPa at the surface reservoir. This typology enabled accurate transient analysis during pump trip events—preventing column separation and pipe collapse.
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