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TILAK BHUSAL / ENGINEERING TOOLS

Pump & fan
affinity laws.

Change the speed. Explore the curve. Understand the savings.

Flow Q₂80

m³/h -20%

Head H₂19.2

m -36%

Shaft power P₂7.68

kW -48.8%

Affinity predictions at corresponding points · Q₂/Q₁ = r^1 · H₂/H₁ = r^2 · P₂/P₁ = r^3

02 / EXPLORE THE DUTY POINT

Performance meets demand

80% speed
┄ Baseline━ Proposed━ System● Operating point
Pump/fan curve and system curveQuadratic model. Operating flow 80 m³/h at 19.2 m.00339.126618.249927.3613236.4816545.6HEAD / m FLOW / m³/hQUADRATIC PERFORMANCE MODEL
MODELED OPERATING FLOW80 m³/h
OPERATING HEAD19.2 m

Intersection of the scaled machine curve and the unchanged system curve.

03 / VFD & ENERGY ECONOMICS

Estimated annual savings

$3,655

30,462.3 kWh/year · 4,000 operating hours

Baseline input16.129 kWProposed input8.51347 kW

Uses modeled operating flow and head with constant local hydraulic efficiency. Includes motor losses and proposed VFD losses. Negative savings indicate added cost.

1,440 RPM

Illustrative rotation, scaled to speed

0%75%150%+

Engineering checks

No screening thresholds exceeded. Confirm the actual operating envelope using manufacturer curves.

BEP departure indicates a possible efficiency change; efficiency loss is not calculable from affinity laws alone. Approximate proposed NPSHr: 1.92 m; entered NPSHa: 6 m. A positive NPSH difference alone does not establish an adequate margin.

THE ENGINEERING BEHIND THE NUMBERS

One ratio. Three relationships.

01 / Flow

Q₂ = Q₁ × r

At constant diameter, flow at a corresponding point varies directly with rotational speed.

02 / Head & pressure

H₂ = H₁ × r²

Head or pressure scales with the square of speed at constant fluid density.

03 / Shaft power

P₂ = P₁ × r³

At similar efficiency, shaft power follows the cube of speed. Electrical input also includes motor and drive losses.

Model assumptions, diameter rules & references

The baseline curve is H(Q) = H₀ − aQ², with a = (H₀ − H₁)/Q₁². The system curve is Hstatic + KQ², with K = (H₁ − Hstatic)/Q₁². Their proposed intersection is calculated analytically and checked with an independent numerical solver. These idealized curves cannot represent unstable or non-monotonic fan behavior.

Speed changes use 1/2/3 exponents. Same-casing pump trims approximately use 1/2/3. Geometrically similar machines use diameter exponents 3/2/5. Density stays constant. Manufacturer curves govern actual operation; custom calibration is only as reliable as its supporting measurements.

Operating shaft power is estimated as scaled shaft power × (operating flow / scaled flow) × (operating head / scaled head). This assumes constant local hydraulic efficiency. The savings estimate covers a single duty for the entered hours; actual savings need a duty profile and measured efficiencies.

References: Wilo affinity laws · Hydraulic Institute pump FAQs · AMCA fan engineering.