How this calculation works
Scale hydraulic flow with speed and head with speed squared. Scale hydraulic power with speed cubed, convert back through each row’s entered combined efficiency and compare the same daily operating hours.
Electric power at speed fraction s = reference electric power × reference efficiency × s³ / new efficiencyA worked example
A 10 kW reference at 80% combined efficiency uses about 5.461 kW at 80% speed and 75% efficiency in this model. Two full-speed hours plus four reduced-speed hours use about 41.845 kWh per day.
Good to know
Ideal centrifugal-pump scenario, not guaranteed savings or a VFD design. Same-hours reference usually moves a different water volume. Static head, system mismatch, cavitation and minimum operating limits are excluded.
Reference: US Department of Energy: improving pumping system performance (opens in a new tab) ↗
The cube law applies to hydraulic power
Reference electric power includes conversion losses. Multiply it by reference combined efficiency to recover the modeled hydraulic basis before applying the speed-cubed relationship.
Divide the changed hydraulic requirement by the new combined efficiency to estimate electric input. Simply cubing the electric reference assumes efficiency stays unchanged, which this tool does not force.
The appliance stepped tariff bill calculator adds build an appliance energy ledger and compare the incremental bill through entered cumulative tariff bands, fixed charges and one explicit tax convention. The ideal motor power factor correction calculator adds compare lagging-load power triangles and ideal reactive compensation, with branch capacitance explicitly distinguished for single-phase, star and delta models.
Same hours are not the same delivered service
At reduced speed, modeled flow is lower and head is lower. Comparing the same number of hours therefore does not hold the pumped volume or useful hydraulic service constant.
The output states daily pumped volume beside the energy comparison. A positive cost difference is a difference between entered scenarios, not proof that the reduced-speed schedule meets the original system’s needs.
Check whether the assumed operating point exists
Affinity laws describe an idealized family of pump conditions. A real system curve, static lift, control requirement or operating limit can prevent the entered speed from delivering the modeled flow.
The page does not choose a safe minimum speed, certify motor cooling or size a drive. Keep those equipment checks separate from this transparent energy arithmetic.
Use the result with the next measurement
The battery recharge stage time calculator also separates useful power from conversion losses, but it models energy stored over SOC segments rather than a pump’s speed-dependent operating point.
Ideal centrifugal-pump scenario, not guaranteed savings or a VFD design. Same-hours reference usually moves a different water volume. Static head, system mismatch, cavitation and minimum operating limits are excluded.
A few questions, answered
Is efficiency assumed constant?
No, each schedule row has its own entered combined efficiency.
Is equal annual energy the same water service?
No, compare modeled flow and volume too.
Does this design a VFD installation?
No, operating-point and electrical design checks are outside the model.