§ 7.5 Module 7 — Matching and Optimising
Capital cost is paid once and therefore remembered. Pumping energy is paid quietly, for as long as the station exists.Module 7
By the end of this lesson
Power answers what the station draws now; energy answers what it costs over time. For a pumping duty, Pwire = ρgQH/(ηpumpηmotorηdrive). Divide by flow and convert joules to kilowatt-hours to obtain specific energy: e = ρgH/(3.6×10⁶ηwire-to-water), in kWh/m³. Flow cancels explicitly, but head and efficiency still depend on flow through the operating point.
At 25 m total dynamic head and 72% wire-to-water efficiency, water at 15 °C requires about 0.0945 kWh/m³. A 1.20 million m³ annual volume therefore uses about 113,000 kWh if that duty represents every cubic metre. Real stations do not have one duty, so calculate each load bin separately and sum its energy.
Build an annual duty profile from measured or justified flows and levels. For each bin, find the pump/system intersection, obtain efficiency from the submitted curve, calculate wire power and multiply by hours. Check that hours total 8 760 in a non-leap year and that pumped volumes reconcile with the demand or inflow forecast. This catches the common error of applying peak-duty power to every hour, or average-duty efficiency to a station that stages pumps.
| Bin | Hours/y | Flow | TDH | Wire η | Energy |
|---|---|---|---|---|---|
| low | 4 800 | 35 L/s | 19 m | 66% | 47 MWh |
| normal | 3 200 | 65 L/s | 24 m | 74% | 66 MWh |
| peak | 760 | 95 L/s | 31 m | 70% | 31 MWh |
| illustrative total | 145 MWh/y | ||||
Do not use the illustrative table as a design value
The rows show method and reconciliation, not a standard load profile. A sewage station follows inflow, wet-well cycling and staging; a potable station follows demand, storage and pressure control. Site data or a stated planning forecast must supply the hours.Reducing speed moves the pump curve, but static lift, minimum transport velocity, motor cooling and control deadbands do not scale with it.
Use affinity laws to generate candidate duty, then re-intersect the real system and recheck every service constraint.
Life-cycle cost places alternatives on one economic date. For a constant real annual cost A, life n years and real discount rate r, the present value is PV = A[1 − (1+r)−n]/r. Add installed capital, planned maintenance and replacements, and subtract residual value on the same real or nominal basis. If energy escalation is modelled separately, do not also hide general inflation in a nominal discount rate.
annual energy cost $44,160/y
real discount rate 3.0%
analysis period 25 y
uniform-series factor 17.413
present value of energy $768,965
installed capital +$310,000
present value of planned renewals +$55,000
life-cycle cost $1,133,965A transparent constant-real-cost comparison.
The least-capital alternative is rarely guaranteed to be least-cost because the energy term repeats. The least-energy alternative is not guaranteed either: extra pipe, excavation, electrical gear or standby capacity can cost more than the energy recovered. “Optimal” means the lowest stated objective over the stated boundary, subject to capacity, resilience, safety and regulatory constraints.
Check your understanding
Keep the economics consistent
1 auto-graded question with an explanation for every wrong answer. Requires JavaScript. (m7-l5-q1)
Interactive lab bench
Pay once for pipe, then every year for head
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At minimum, vary annual pumped volume, static levels, design-age roughness, efficiency degradation, electricity price, discount rate and asset life. For sewage, add inflow growth and the duty-cycle consequence of solids transport; for potable water, add pressure-zone and storage operations. Report the switching value where the preferred option changes. A conclusion that survives the credible range is useful; one that reverses under a small input change is a request for better evidence.
Why life-cycle costing entered pump guidance
Energy crises and rising operating budgets made the purchase-price habit visibly incomplete. Europump and the Hydraulic Institute published pump life-cycle-cost guidance that organized acquisition, installation, energy, operation, maintenance, downtime and disposal into one comparison. The categories are a framework, not default percentages: each project must supply its own boundary and evidence.
Lab 7.5
Present-value an energy bill
Write presentValue(annualCost, realRate, years) for a constant real end-of-year cost. If the rate is zero, return annualCost × years . Graded in the browser against 2 assertions; the editor and harness require JavaScript.
Examination score
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An optimum without a boundary, time horizon and sensitivity range is only a preference.