1 · Flow rate and head pressure
Two numbers define the state of any point in a water network: flow rate (how much water is moving) and head (the energy available to push it). Head is expressed in metres of water column — it bundles pressure, velocity, and elevation into one comparable number.
Flow rate Q
L/s or m³/h
Volume passing a point per second
Pressure head H
metres (m)
Energy per unit weight of water
Hydraulic grade line
HGL
Head at every network point
Min. service pressure
7–10 m
Regulatory floor at consumer tap
2 · The Hazen-Williams equation — pipe friction model
Every pipe segment loses head due to friction. The Hazen-Williams equation calculates exactly how much:
hf = 10.67 · L · Q1.852 / (C1.852 · D4.87)
| Symbol | Meaning | Typical value |
|---|
| hf | Head loss due to friction (metres) | Calculated output |
| L | Pipe length (metres) | 10 – 5 000 m per segment |
| Q | Flow rate (m³/s) | 0.001 – 1 m³/s |
| C | Roughness coefficient | 150 new PVC → 70 old cast iron |
| D | Internal pipe diameter (metres) | 0.05 – 1.2 m |
Why C matters for AI: As pipes age, mineral deposits lower C from ~150 (new PVC) to ~70 (old cast iron). The ML calibration layer continuously updates C for every pipe segment by comparing predicted vs. measured pressures — keeping the model accurate without expensive physical surveys.
Live friction loss calculator
Fixed: 50 L/s flow through a 300 mm pipe. Adjust pipe length and roughness.
Head loss
3.4 m
~0.22 kW extra pump power
Pressure drop
33 kPa
1 m head ≈ 9.81 kPa
3 · Pump physics — affinity laws
Pump behaviour at different speeds is precisely described by the affinity laws. The cubic relationship between speed and power is why AI variable-speed scheduling saves so much energy.
Q ∝ N | Head ∝ N² | Power ∝ N³
The cube law in practice
The MPC opportunity: If demand drops 20% and the AI slows the pump to 80% speed, power drops to 51% — saving nearly half the electricity for a modest reduction in output. A traditional fixed-speed pump throttled by a valve wastes that energy as heat instead.
Specific energy (optimised)
0.35 kWh/m³
AI scheduling + VFDs
Specific energy (baseline)
0.92 kWh/m³
Fixed-speed, reactive
Typical saving
25–40%
On pump energy alone
4 · What you control vs. what you don't
| Control lever (AI sets these) | Environmental / demand (given) |
|---|
| Pump speed setpoint (% via VFD) | Consumer demand per zone per hour |
| Number of pumps running (staging) | Elevation profile (gravity head) |
| PRV setpoint (metres of head) | Pipe roughness C — ML tracks drift |
| Tank fill / draw schedule | Fire-flow reserve requirements |
| Zone isolation valve position | Water quality / chlorine constraints |
5 · Where the biggest savings come from
- Shift pumping to off-peak tariff windows — the elevated tank stores water pumped cheaply at night; gravity delivers it during expensive peak hours.
- Reduce pump speed during low-demand periods — the cube law means even modest speed reductions save disproportionate energy.
- Optimal pump staging — run fewer, larger pumps at their best efficiency point rather than many small pumps at low load.
- Reduce excess pressure — every 10 m of excess head costs pump energy and accelerates pipe joint wear. PRV optimisation trims this.
- Early leak detection — a 5% leak on a 100 MLD supply wastes 5 MLD of pumped water every day. ML detects and localises in hours, not weeks.
6 · Overall components & flow
How water travels from the source all the way to the consumer tap:
Reservoirraw source
→
Pump stationadds head
→
Elevated tankstores energy
→
Trunk mainsdistribution
→
PRV / zonespressure step-down
→
Consumer tapmin 7 m head
The reservoir supplies water at near-zero head. The pump station adds ~50 m head by expending electricity. The elevated tank is the system battery — gravity gives it potential energy that maintains network pressure even when pumps are off. PRVs step down head at zone boundaries, protecting downstream pipes. The consumer tap must receive at least 7–10 m head for adequate flow.