Water & wastewater
Centrifugal pump
A double-suction split-case pump, drawn down to the equations.
A pump like this runs thousands of hours a year, so a small loss in efficiency is a big power bill. Its curve, its suction margin and its bearings all follow equations we can write down. That is what lets us tell wear from a change in demand.
2.0 m³/s at 55 m, 1,500 kW, 600 rpm
- Duty point
- 1.89 m³/s at 56.4 m
- Efficiency at BEP
- 87.7%
- Shaft power at BEP
- 1,228 kW
- Wire-to-water at BEP
- 85.0%
Anatomy and nameplate
- 1Suction pressure. Feeds NPSH available and the cavitation margin.
- 2Discharge pressure. With suction pressure, gives the head the pump is making.
- 3Flow meter. Puts the operating point on the pump curve.
- 4Wear rings. Clearance grows with wear. Leakage rises, efficiency falls.
- 5Impeller and volute. Vane pass at 6× shaft speed. Erosion shows as lost head.
- 6Mechanical seal. Seal chamber temperature and leakage track face wear.
- 7Bearing vibration. Accelerometers on both bearings. Each bearing part has its own frequency.
- 8Bearing temperature. Heat from friction. Rises late, after damage has started.
- 9Coupling. Misalignment shows up at 2× shaft speed.
- 10Motor current. A power meter that is already installed.
| Hydraulic | |
|---|---|
| Type | Horizontal axially split-case, double suction, single stage, closed impeller |
| Rated flow (BEP) | 2.0 m³/s (7,200 m³/h, 31,701 gpm, 45.6 MGD) |
| Rated head (BEP) | 55 m (180 ft) |
| Shutoff head | 68.8 m |
| Speed | 600 rpm (12-pole at 60 Hz, 10-pole at 50 Hz) |
| Specific speed | 30 metric per eye (1,534 US units) |
| Impeller | 1,150 mm diameter, 6 vanes |
| Suction / discharge | 1,000 mm / 800 mm, PN 16 |
| Efficiency at BEP | 87.7% |
| Shaft power at BEP | 1,228 kW |
| NPSH required at BEP | 6.1 m |
| Preferred operating range | 70–120% of BEP (1.4–2.4 m³/s) |
| Motor and drive | |
| Motor | 1,500 kW (2,012 hp), 12-pole, air-to-air cooled |
| Supply | 6.6 kV, 3-phase, 60 Hz |
| Full-load current | 148 A |
| Motor efficiency at full load | 96.6% |
| Drive | Medium-voltage variable frequency drive, 97.8% at full speed |
| Mechanical | |
| Drive-end bearing | 22330 spherical roller, 19 rollers per row, oil lubricated |
| Non-drive-end bearing | 22328 spherical roller, oil lubricated |
| Seal | Split cartridge mechanical seal, silicon carbide on silicon carbide |
| Materials | Cast iron casing, bronze impeller, stainless steel shaft sleeves |
| Wear ring clearance | 0.45 mm radial new, replace at 1.20 mm |
| Bearing frequencies | BPFO 78.8 Hz, vane pass 60.0 Hz, shaft 10.0 Hz |
The physics
The equations behind every curve on this page.
Pump curve
H = H0 − k·Q²
Head falls as flow rises. The curve is set by the impeller and the speed.
System curve
H = Hs + K·Q²
The pipe asks for lift plus friction. Where the two curves cross is where the pump runs.
Affinity laws
Q ∝ N H ∝ N² P ∝ N³
Slow the pump a little and power drops a lot.
Power
P = ρ·g·Q·H / η
Power is water moved, lifted, divided by efficiency.
Suction margin
NPSHa − NPSHr > 1 m
Keep the suction head the system gives above what the pump asks for.
Wear-ring leakage
Q_leak = Cd·π·D·c·√(2·g·ΔH)
Leakage grows with the clearance. It is the cleanest wear signal the twin has.
Where the pump runs
Every pump has one curve and every pipe has one curve. Their crossing is the duty. The best efficiency point (BEP) is the flow where the water meets the impeller cleanly.
Pump curve, system curve and operating point
Double-suction split-case pump, 600 rpm, 1.5 MW motor
- Pump curve, new rings
- Pump curve, rings worn to 1.20 mm
- System curve (35 m static)
- BEP
- 2.0 m³/s at 55 m
- Duty, new rings
- 1.89 m³/s at 56.4 m
- Duty, worn rings
- 1.87 m³/s at 56.1 m
Where the pump curve crosses the system curve is where the pump runs. Wear drops the pump curve, so the crossing slides left and flow falls.
H = H0 − k·Q² | H_sys = Hs + K·Q² | H0 = 68.8 m, Hs = 35 m, K = 6.0 m per (m³/s)²
Efficiency and the best efficiency point
- New rings
- Rings worn to 1.20 mm
Efficiency peaks at the BEP and falls on both sides. Run far from it and the pump wastes power and shakes itself apart.
η = P_hyd / P_shaft = ρ·g·Q·H / P_shaft
Slow it down, pay less
The affinity laws tie speed to flow, head and power. They are why a variable speed drive saves energy and a throttle valve does not.
Affinity laws: slowing the pump moves the whole curve
- 100% speed (600 rpm)
- 90% speed (540 rpm)
- 80% speed (480 rpm)
- 70% speed (420 rpm)
- System curve
A pump at 80% speed makes 80% of the flow, 64% of the head and 51% of the power at matching points. With static lift in the system, flow falls faster than that.
Q2 = Q1·(N2/N1) H2 = H1·(N2/N1)² P2 = P1·(N2/N1)³
Power at reduced flow: valve versus speed control
- Fixed speed, valve throttled
- Variable speed drive
- At 1.35 m³/s
- 312 kW saved (29%)
Throttling burns the extra head across a valve. Slowing the pump lets the same flow run on far less power.
P_elec = ρ·g·Q·H / (η_pump · η_motor · η_drive)
The suction side
A pump can only pull so hard. When the pipe cannot supply what the impeller asks for, water boils at the eye and the bubbles collapse on the metal.
NPSH available versus NPSH required
Clear well at the pump centerline at low level, 15 °C water
- NPSHa (the system gives)
- NPSHr (the pump needs)
When the pump needs more suction head than the system gives, vapor bubbles form and collapse on the impeller. The margin is the safety distance.
NPSHa = (P_atm − P_vap)/(ρg) + z_suction − h_loss(Q) Cavitation when NPSHa < NPSHr
Wire-to-water power
The utility bill sees the whole chain: drive, motor, pump. The twin tracks each link, so a loss can be put on the right machine.
Wire-to-water efficiency and energy per 1,000 m³
- Pump
- Motor
- Wire-to-water
- kWh per 1,000 m³ (right axis)
What the meter sees is wire-to-water efficiency: pump times motor times drive. Energy per cubic meter is lowest at the BEP.
η_w2w = ρ·g·Q·H / P_electrical = η_pump · η_motor · η_drive
Motor current across the flow range
6.6 kV, 3-phase, 1.5 MW motor, constant speed
- New rings
- Rings worn to 1.20 mm
Motor current is a free power meter. At a given flow, current that sits above the twin means the pump is working harder for the same water.
I = P_in / (√3 · V · pf)
Where the electricity goes
1,267 kW at the meter, 2.0 m³/s at 55 m
- Water power
- 1,077 kW (85%)
- Pump losses
- 150 kW (12%)
- Motor losses
- 39 kW (3%)
Wire-to-water efficiency is 85.0%. Pump losses are mostly leakage, friction and recirculation. Motor losses are heat in the windings and core.
What failure looks like
Each failure mode leaves its own mark. These are the vibration spectra the twin predicts for a bearing, a misaligned coupling and a cavitating impeller.
Bearing outer-race wear
- Healthy bearing
- Outer-race defect
Each bearing part rings at a frequency set by its geometry. A growing line at 7.88× shaft speed and its harmonics points at the outer race.
BPFO = (Z/2)·f_r·(1 − d/D·cos θ) with Z = 19 rollers, f_r = 10.0 Hz
Shaft misalignment
- Aligned
- Misaligned coupling
Misalignment forces the shaft to flex twice per turn. The 2× line climbs above the 1× line and 3× appears.
f_n = n · RPM / 60 (n = 1, 2, 3 …)
Cavitation
- NPSH margin healthy
- Cavitating
Collapsing vapor bubbles hit the metal like gravel. That shows as a broad hump of high-frequency noise, with no clean line to point at.
Detect when high-frequency energy rises while NPSHa − NPSHr falls below 1 m
Catching it early
Wear is slow. Demand changes every day. Once the twin takes out what the duty explains, the slow drift is what is left.
Impeller and wear-ring wear: raw power versus twin residual
Variable-speed high-service pump, flow and clear-well level change every day
- Measured kW (swings with duty)
- Twin residual, 7-day mean (%) (right axis)
- Raw kW range
- 1,005–1,446 kW
- Lead time
- 97 days before the limit
Raw kW moves with demand, so a plain alarm sees nothing. The twin removes what the duty explains, and the leftover is wear.
residual = (P_measured − P_twin(Q, H, clearance0)) / P_twin
Wear-ring clearance and what it costs
- Leakage
- Extra power (right axis)
- Detection day
- 59
Water that leaks back through the rings is water the impeller already paid to pump. The loss grows with every tenth of a millimeter.
Q_leak = Cd · π·D·c · √(2·g·ΔH) per ring, two rings
Bearing defect: twin band energy versus the overall alarm
- Overall vibration (what a fixed alarm sees)
- BPFO band energy (what the twin tracks)
- Lead time
- 92 days before the fixed alarm
The overall number barely moves while the defect is small. Watching only the band the geometry predicts finds it months earlier.
Band energy = RMS of the spectrum within ±3% of BPFO and its harmonics
Failure modes
What breaks, what it looks like, what the twin does about it.
| Failure mode | The physics | Signals that show it | How the twin catches it |
|---|---|---|---|
| Bearing wear | A pit on the outer race is struck by each ball. The strike rate is fixed by bearing geometry. | Vibration line at BPFO (78.8 Hz) and harmonics. High-frequency envelope. Temperature last. | Tracks band energy at the predicted frequencies, so a small defect stands out long before overall vibration moves. |
| Impeller and wear-ring wear | Larger clearance lets pressurized water flow back to the eye. The impeller pumps water twice. | Less head at the same flow. More power per cubic meter. Higher drive speed to hold flow. | Solves for the clearance that explains the power residual and reports it in millimeters. |
| Cavitation | NPSHa falls below NPSHr. Vapor bubbles form at the eye and collapse on the vanes. | Broadband high-frequency noise. Falling suction pressure. Unsteady current. | Computes the NPSH margin every minute from suction-well level, flow and temperature. It warns before the noise starts. |
| Misalignment | The shaft flexes twice per turn between coupling halves. | 2× shaft speed rises above 1×. Axial vibration. Coupling and bearing heat. | Compares the harmonic ratios with the twin’s expected values at the current speed. |
| Seal leak | Worn faces open and heat builds between them. The fluid film flashes. | Seal chamber temperature rise. Drips at the gland. Flush pressure change. | Runs a heat balance on the seal chamber. A rise that friction and process temperature cannot explain is a leak. |
How we catch it early
A physics twin and a PINN, working on one centrifugal pump.
The twin is a set of equations for this machine, tuned to its nameplate. Give it the flow, speed and conditions and it returns what every reading should be. It always gives the same answer for the same inputs.
A physics-informed neural network, or PINN, sits on top. It is trained on the plant’s own data and it is penalized whenever it breaks a physics rule. So it can only learn what the equations leave out: wear, fouling, friction. It cannot invent an answer that the machine could never produce.
Step 1
Measure
Flow, pressure, current, temperature, vibration. Whatever the asset already has.
Step 2
Physics twin
The equations of this machine, set to its nameplate. It says what the readings should be right now.
Step 3
Residual
Measured minus expected. Demand, weather and speed are already taken out.
Step 4
PINN
A small neural network that learns the cause of the gap, under the physics rules.
Step 5
Finding
A named cause, a date, and the kWh or hours at stake. An engineer reviews it.
loss = (measured − predicted)² + λ · (physics residual)²
The second term is the rulebook. It is zero when the network obeys the equations.
Why this beats black-box AI
A black-box model learns patterns from history. It needs examples of each failure, and it goes quiet when the pump runs at a point it has not seen. The twin starts from physics, so it works on day one. The PINN adds what physics cannot know about this particular machine.
That is also what makes the savings countable. The baseline is a calculation, not a guess, so the gap between baseline and meter is a number a customer can check.
What the twin checks on this asset
- Operating point against the curve: 1.89 m³/s
- NPSH margin: 3.6 m at 1.86 m³/s
- Cavitation starts near 2.79 m³/s
- Wear flagged on day 59, ring limit on day 156
- Bearing defect flagged on day 73, fixed alarm on day 165
| Fixed alarm | Black-box AI | Twin + PINN | |
|---|---|---|---|
| Needs failure history to learn | No | Yes, lots | No |
| Says what is wrong | No | Rarely | Yes, by name |
| Works at a flow it has never seen | No | Often fails | Yes, the equations still hold |
| Puts a number on the saving | No | No | Yes, in kWh and dollars |
| Lead time on slow wear | Late | Varies | Weeks to months |
| Every number can be traced | Yes | No | Yes, to an equation |
What the twin puts a number on
Energy and cost, from the equations.
Worn rings at 1.20 mm
29 kW
1,225 kW new, 1,254 kW worn at 1.86 m³/s
Energy per year
203,000 kWh
7,000 hours a year at $0.09 per kWh
Cost per year
$18,270
One pump, one wear mode
Valve to drive at 1.35 m³/s
312 kW
779,759 kWh and $70,178 over 2,500 hours
What we do for you
We watch it. We catch it. We prove it.
Our reliability engineers run the twin on your centrifugal pump, review every finding, and help your crew fix it. After the repair we compare the meter to the baseline and write the result in the ledger.