Skip to main content
CalcStack

Centrifugal Pump Affinity Laws Calculator (Flow, Head, Power)

The centrifugal pump affinity laws mathematically describe how flow rate, head, and shaft power vary as impeller rotational speed or diameter changes.

Baseline operational pump rotational speed in RPM.

Adjusted pump speed (e.g., 1440 RPM represents an 80% speed modulation via VFD).

Volumetric discharge flow rate at baseline speed in m³/h (or GPM).

Baseline developed pump head pressure in meters (or feet).

Baseline electric motor brake horsepower or shaft power in kW.

Baseline impeller outer diameter in mm (default 250 mm).

Trimmed impeller diameter (keep equal to D₁ if speed modulation only).

Calculated Result
7.68 kW

New Shaft Power (Cube Law)

New Flow Rate (Q₂)

80 m³/h (80% of baseline)

New Head Pressure (H₂)

28.8 m (64.0% of baseline)

New Shaft Power (P₂)

7.68 kW (51.2% of baseline)

VFD Power Savings

7.32 kW (48.8% reduction)

Speed Adjustment Ratio (N₂ / N₁)

0.8x

Calculation Breakdown

  1. 1. Speed Scaling RatioSpeed Ratio = 1440 RPM / 1800 RPM = 0.8
  2. 2. Affinity Laws ApplicationFlow Q₂ = Q₁ · (0.8) = 80 m³/h; Head H₂ = H₁ · (0.8)² = 28.8 m; Power P₂ = P₁ · (0.8)³ = 7.68 kW
  3. 3. Energy Efficiency Impact (Cube Law)A 20% speed reduction reduces brake power from 15 kW to 7.68 kW, saving 7.32 kW.

Pump Power vs Speed Ratio (% Baseline)

Interactive visualization based on your current inputs

Power (%)
0.025507510060% Speed70% Speed80% Speed90% Speed100% SpeedSpeed Ratio (% N₁)Power (% P₁)

What Is the Centrifugal Pump Affinity Laws Calculator (Flow, Head, Power)?

The pump affinity laws are hydraulic similitude relationships predicting performance changes in rotodynamic pumps subjected to speed or impeller geometry adjustments.

How Does the Centrifugal Pump Affinity Laws Calculator (Flow, Head, Power) Work?

Rooted in Euler’s turbomachinery equations, fluid velocity scales linearly with tip speed, static pressure with dynamic head (v²), and energy transfer with rate of momentum change.

Centrifugal Pump Affinity Laws Calculator (Flow, Head, Power) Formula & Variables

The core mathematical equation utilized by this calculator is expressed as:

\frac{Q_2}{Q_1} = \frac{N_2}{N_1}, \quad \frac{H_2}{H_1} = \left(\frac{N_2}{N_1}\right)^2, \quad \frac{P_2}{P_1} = \left(\frac{N_2}{N_1}\right)^3

Flow scales linearly with speed ratio. Pressure head scales quadratically with speed ratio. Shaft power scales with the cube of speed ratio.

How to Use the Centrifugal Pump Affinity Laws Calculator (Flow, Head, Power)

  1. Enter baseline pump speed, flow, head, and shaft power.
  2. Specify target operating speed or trimmed diameter.

Step-by-Step Example Calculation

20% Speed Reduction on 15 kW Pump (1800 to 1440 RPM)

Input Values:

initialSpeedRpm:1800
targetSpeedRpm:1440
initialFlowM3H:100
initialHeadMeters:45
initialPowerKw:15
initialDiameterMm:250
targetDiameterMm:250
Worked Steps: Dropping speed to 80% reduces flow to 80 m³/h, head to 28.8 m, and slashes power consumption from 15 kW down to 7.68 kW (48.8% energy savings!).

Understanding Your Result

Target Flow (Q₂): New volumetric discharge capacity.

Target Head (H₂): New pressure head delivered across pump suction and discharge.

Target Power (P₂): New brake shaft kilowatt requirement.

Power Savings: Realized kilowatt reduction and percentage energy conserved.

Factors That Affect the Result

  • Speed adjustment ratio has cubic impact on electricity demand.

When Should You Use This Calculator?

  • HVAC hydronic chilled water systems, municipal wastewater lift stations, industrial process cooling, and energy audit retrofits.

Assumptions & Limitations

  • Assumes constant hydraulic efficiency and negligible static lift (friction-dominated piping circuits).

Frequently Asked Questions

Calculation Accuracy & Reference Note

Standard Hydraulic Institute (HI) centrifugal pump affinity relationships.

Related Calculators

Explore more tools and calculators in Math Calculators

Soil Nail Wall Pullout & Tendon Sizing Calculator

Calculates ultimate and allowable pullout resistance along the grout-ground interface, steel tendon yield strength, and governing limit state per FHWA GEC 7.

Helical Screw Pile Ultimate Axial Capacity Calculator

Calculates ultimate and allowable compressive axial capacity of multi-helix screw anchors using individual plate bearing method in cohesive and frictional soils.

Culvert Outlet Riprap Apron Erosion Protection Calculator (HEC-14)

Calculates median stone size (D₅₀), apron length, downstream width, and blanket thickness for culvert outlet scour protection per FHWA HEC-14.

Dry Extended Detention Basin Drawdown Orifice Calculator

Calculates the required release orifice diameter, average discharge rate, and drawdown velocity for stormwater dry extended detention basins.

Broad-Crested Rectangular Weir Discharge Calculator (ISO 3846)

Calculates open channel discharge capacity, critical depth, crest flow velocity, and discharge coefficient for broad-crested rectangular weirs.

SWMM Urban Catchment Peak Runoff & Infiltration Calculator

Calculates peak stormwater runoff, Horton infiltration abstraction, depression storage losses, and composite runoff coefficients for urban subcatchments.