Pump Fan Affinity Law Scaling Calculator

Calculator overview

Inputs and outputs

This summary comes from the calculator's published input and output contract.

Inputs

AFL Target Speed Conditional: About this input

Nonnegative target speed used only for the Target speed basis. Zero produces an explicit stopped-state ideal extrapolation.

Unit rpm Default 1087 Range At least 0
AFL Scaling Basis: About this input

Enter either the target rotational speed or the target-to-known speed ratio. Only the visible basis input participates in validation or calculation.

Default Target speed Allowed Target speed, Target speed ratio
AFL Unit System: About this input

Select coherent SI or U.S. customary units. Changing the selector relabels values; it does not reinterpret or automatically convert previously entered numbers.

Default SI metric Allowed SI metric, US customary
AFL Target Speed Ratio Conditional: About this input

Nonnegative dimensionless target-to-known speed ratio used only for the Target speed ratio basis. Zero produces an explicit stopped-state ideal extrapolation.

Unit ratio Default 0.738 Range At least 0
AFL Machine Type: About this input

Identify the fixed-geometry rotodynamic machine as a pump or fan. The ideal exponents are the same, while pressure labels and reviewer context follow the selected machine.

Default Pump Allowed Pump, Fan
Known pump differential pressure: About this input

Positive differential or static pressure rise at the known point. The same coherent pressure measure must be used for the scaled result.

Unit kPa Default 248.6 Range At least 0
AFL Known Flow Rate: About this input

Positive volume flow at the known operating point. The calculator does not infer this value from pressure, head, density, or a curve.

Unit m^3/h Default 83.7 Range At least 0
AFL Known Speed: About this input

Positive rotational speed associated with the known operating point. The synthetic shipped value is not a rated or synchronous machine speed.

Unit rpm Default 1473 Range At least 0
AFL Known Shaft Power: About this input

Positive mechanical shaft power at the known point. Motor input power and drive losses are outside the ideal scaling equation.

Unit kW Default 31.47 Range At least 0

Outputs

AFL Scaling Assessment: About this output

Identifies stopped-state extrapolation, unchanged speed, speed reduction, or speed increase without asserting suitability of the resulting operating point.

No unit declared
AFL Scaled Shaft Power: About this output

Known mechanical shaft power multiplied by the cube of the target-to-known speed ratio, assuming unchanged efficiency.

Unit kW
AFL Target Rotational Speed: About this output

Target speed entered directly or reconstructed from the entered speed ratio and known speed.

Unit rpm
Model Status: About this output

Returns actionable NOT VALID text for malformed or unsupported arithmetic, CHECK text for zero or unchanged speed, and OK otherwise. It does not approve equipment operation.

No unit declared
AFL Target To Known Speed Ratio: About this output

Dimensionless speed ratio r used by all three affinity equations.

Unit ratio
AFL Power Ratio: About this output

Shaft-power ratio, equal to r cubed, shown explicitly for affinity-law review.

Unit ratio
AFL Flow Ratio: About this output

Flow ratio, equal to r, shown explicitly for affinity-law review.

Unit ratio
AFL Pressure Ratio: About this output

Pressure-rise ratio, equal to r squared, shown explicitly for affinity-law review.

Unit ratio
Scaled pump differential pressure: About this output

Known pressure rise multiplied by the square of the target-to-known speed ratio.

Unit kPa
AFL Scaled Flow Rate: About this output

Known volume flow multiplied by the target-to-known speed ratio under the fixed-geometry affinity-law assumption.

Unit m^3/h

What it is

The Pump and Fan Affinity Law Scaling Calculator takes a known duty point for a rotodynamic pump or fan and scales it to a different shaft speed. Flow scales with the speed ratio, pressure rise with its square, and shaft power with its cube.

It reports the target speed, the target-to-known speed ratio, the three individual ratios so you can see the exponents at work, the scaled flow, pressure rise and shaft power, and an assessment naming the case as a speed reduction, a speed increase, an unchanged point, or a stopped-state extrapolation.

There are two ways to state the target. Enter the target speed and the ratio is formed from it, or enter the ratio directly and the target speed is reconstructed from it. Whichever basis you choose, the other field is hidden and takes no part in the calculation.

The machine type selector switches the wording on the pressure fields between a pump differential pressure and a fan pressure rise. It does not change the arithmetic. The unit selector relabels flow, pressure and power between SI and U.S. customary and converts nothing, and because every relation here is a pure ratio, the unit system never enters the arithmetic at all.

It is a screening scaler. It assumes unchanged geometry and unchanged efficiency, it holds no machine curve and no system curve, and it says nothing about whether the machine can be run at the speed you asked for. The saving it computes for a speed reduction is an upper bound, not a prediction.

Methodology

Purpose and model boundary

This model applies the ideal pump/fan affinity laws to scale one entered operating point to a target rotational speed or speed ratio at unchanged geometry. It returns ideal flow, pressure rise and shaft power. It is a similarity-law extrapolation, not an equipment curve, system-curve intersection or manufacturer-approved operating point.

The spreadsheet remains the calculation authority. The page sends the named inputs to the calculation service and presents workbook outputs, chart and status without calculating the affinity laws in client code.

Inputs and units

Input group	Values used by the model
Basis	SI metric or US customary, pump or fan, and target-speed or target-ratio entry.
Known point	Rotational speed `N1`, flow `Q1`, pressure rise `Δp1`, and shaft power `P1` from one consistent operating point.
Target	Rotational speed `N2` or nonnegative speed ratio `r`, according to the selected basis.

The pump/fan choice changes pressure labels only; the same ideal similarity exponents are used. Pressure is entered directly, so the model performs no head, density or hydraulic-power calculation.

Governing relationships

When target speed is active, r = N2/N1; when target ratio is active, the entered ratio is used and N2 = N1r. For unchanged geometry and comparable dynamically similar conditions, the workbook evaluates

Q2 = Q1r;
Δp2 = Δp1r²;
P2 = P1r³.

The corresponding flow, pressure and power ratios are r, r² and r³. The chart samples P1x³ at seven values of x from zero to max(1,r); it is an explanatory ideal-power curve, not a manufacturer performance map.

Calculation sequence

Validate the listed unit, machine and target-basis selections.
Require positive known speed, flow, pressure rise and shaft power, plus a nonnegative visible target speed or ratio.
Resolve the speed ratio and target speed from the active entry basis.
Apply the first-, second- and third-power affinity relationships to flow, pressure and shaft power.
Confirm nonnegative, finite derived values and consistent zero/nonzero behavior.
Return ratios, the scaling assessment, ideal-power curve and ordered status.

Outputs and interpretation

Primary outputs are scaled flow rate, scaled pressure rise and scaled shaft power. Details show target speed, target-to-known speed ratio, the three scaling ratios and a relationship label: stopped-state ideal extrapolation, unchanged point, ideal speed reduction or ideal speed increase.

The result assumes unchanged efficiency and similarity. It does not predict the actual point where an equipment curve intersects a system curve.

Validation and status logic

The workbook applies these conditions in order:

Condition	Returned status
A selection, known operating-point value, or visible target input is outside the authored domain	`NOT VALID: correct visible selections, known operating point, or target speed basis`
A scaled or chart value is not finite or fails the protected numeric relationships	`NOT VALID: derived scaling result exceeds the supported calculation range`
Target speed ratio is zero	`CHECK: zero target speed is an ideal stopped-state extrapolation`
Target speed ratio is one	`CHECK: target speed equals the known operating point`
None of the preceding conditions applies	`OK`

At r = 0, the workbook returns zero target speed, flow, pressure and power and labels the result explicitly as an ideal stopped-state extrapolation.

Assumptions and limitations

The same rotodynamic machine geometry, impeller diameter, fluid regime and dynamically similar condition are retained.
The entered known speed, flow, pressure and power describe one internally consistent point.
Efficiency is assumed unchanged; the workbook does not infer efficiency at the target state.
Real equipment can depart from the laws because efficiency, Reynolds number, compressibility, cavitation margin, stall, surge, leakage, clearances and the system curve change with speed.
Impeller trimming, mixed-flow corrections, variable geometry, gas-density correction, drive efficiency and transient acceleration are outside scope.
The calculator does not establish allowable speed, mechanical integrity, resonance, critical speed, NPSH, cavitation, surge, stall, controls or code compliance.

Restrictions and non-computing states

Known operating-point quantities must be positive. Target speed or ratio may be zero but not negative. A zero result is a mathematical boundary, not evidence that stopped equipment sustains exactly zero real pressure or power. A NOT VALID status supersedes displayed formula residue.

Errors and warnings

A rejected entry means the request did not satisfy the published input rules. NOT VALID is the workbook's non-computing state. CHECK identifies the stopped or unchanged boundary and must not be read as manufacturer approval. Calculation-service failures are availability errors, not equipment predictions.

References

No pump or fan curve, manufacturer selection table or licensed performance dataset is reproduced. The calculator holds no machine data at all: the known duty point is entirely user-entered, and the shipped values are synthetic demonstration numbers describing no real machine. The workbook implements the ordinary textbook form of the affinity relations, not the method of any single publication. The sources it cites are below.

U.S. Department of Energy, Improving Pumping System Performance: A Sourcebook for Industry, for the pump affinity relations between flow, head or pressure, absorbed power and speed. https://www.energy.gov/sites/prod/files/2014/05/f16/pump.pdf
U.S. Department of Energy, Improving Fan System Performance: A Sourcebook for Industry, for fan similarity and the speed relations among airflow, pressure and power at a fixed geometry. https://www.energy.gov/sites/default/files/2014/05/f16/fan_sourcebook.pdf
U.S. Department of Energy, Variable Speed Pumping: A Guide to Successful Applications, for the linear, square and cube exponents and for the system behaviour this calculator does not model. https://www.energy.gov/sites/prod/files/2014/05/f16/variable_speed_pumping.pdf
NIST Guide to the SI, Appendix B, for the exact foot, pound-force and mechanical-horsepower identities behind the U.S. customary labels. https://www.nist.gov/pml/special-publication-811/nist-guide-si-appendix-b-conversion-factors

The machine curve, the system curve and its static head, efficiency variation with speed, net positive suction head, minimum continuous stable flow and the mechanical speed limits are not supplied here. Take them from the manufacturer's certified curve and from your own system hydraulics before acting on a speed change.

Additional source notes migrated from Methodology

Manufacturer curves, the system curve and qualified rotating-equipment review govern actual operating-point and speed decisions.

Frequently asked questions

Will I really save the power this calculator predicts?

Only if the system is pure friction. The affinity laws scale the machine, not the operating point. If the system has static lift, the duty point moves to wherever the scaled machine curve crosses the system curve, and that crossing shifts much less than the speed ratio implies: flow falls by less than the ratio and power by very much less than its cube. On the shipped defaults the ideal saving is 18.82 kilowatts, from 31.47 down to 12.647; on a system with significant static head the real saving can be a fraction of that. Treat it as an upper bound.

How far from the known speed can I trust this?

The relations assume unchanged geometry and unchanged efficiency, and degrade as the ratio moves away from one. Real efficiency drifts with speed as the Reynolds number and the relative clearances change, and it also falls away from the best efficiency point, so a large speed reduction gives a true power above the ideal cube. There is no efficiency field in this calculator and no warning when the ratio has grown large enough to matter. For anything beyond a modest speed change, check the manufacturer's curve at the new speed.

Does the unit system selector convert my numbers?

No, and it is the most dangerous thing on the page. It relabels the flow, pressure and power fields and converts nothing. Because the relations are dimensionless, the unit system never enters the arithmetic: the ratio is a speed over a speed and every scaled value is a known value times that pure number. Entering metric numbers with the selector on U.S. customary gives results that are self-consistent, correctly scaled and wrongly labelled, and nothing in the model can detect it. Check the selector before reading the answer.

Does selecting Fan instead of Pump change the calculation?

No. The exponents are identical for both machine types, so the selector changes only the wording on the pressure fields. The same inputs return the same numbers either way. Fans also carry a density assumption the calculator does not apply: the pressure and power relations hold at constant density, and there is no density, temperature or altitude input, so a speed change that comes with a density change needs a separate correction.

Can I use this for trimming an impeller instead of changing speed?

No. There is no impeller diameter input in the calculator. The diameter relations are a separate set, and although they are often written with the same exponents they are considerably less reliable, because trimming alters the blade geometry rather than scaling it, so the similarity the laws rest on is broken instead of preserved. Applying the speed relations to a trim will overstate the effect. Use the manufacturer's trim curves.

Why did I get a CHECK rather than an answer?

Neither CHECK is an error. If the target speed equals the known speed, every ratio is 1, the scaled values equal the known values, and the assessment reads KNOWN POINT UNCHANGED. If the target speed or ratio is zero, you get STOPPED-STATE IDEAL EXTRAPOLATION with all three scaled values at zero, which is the honest limit of the relations and not a prediction about a stopped machine. A zero known speed is different and returns NOT VALID, because no ratio can be formed from it.

Does it know my motor rating or my machine's speed limit?

No. It holds no motor rating, no maximum continuous speed, no critical speed and no drive limit, and the speed ratio field declares no upper bound at all. Ask for a 12.5 percent speed increase on the shipped defaults and shaft power rises 42.4 percent, from 31.47 to 44.808 kilowatts, with the status reading OK. The status line judges the arithmetic, not the equipment.

What does the shaft power figure include?

Mechanical power at the shaft, and nothing else. Motor efficiency, variable-speed drive losses, belt or coupling losses and standby draw are all outside the ideal scaling relation. If you are estimating electrical input for an energy calculation, add those separately, and note that drive and motor efficiency themselves fall at reduced speed and load, working against the saving the cube law suggests.

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