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Pump Affinity Laws Calculator - VFD Savings, Impeller Trim & Speed Change Analysis

Calculate flow, head, and power changes from pump speed or impeller diameter adjustments

Apply the pump affinity laws to predict how changes in pump speed or impeller diameter affect flow rate, total dynamic head, and brake horsepower. Enter current operating conditions and new speed (from VFD or sheave change) or trimmed impeller diameter to see the resulting performance shift. Calculates energy savings from speed reduction, annual cost comparison, simple payback period for VFD installation, and overlays new operating points on the system curve. Supports centrifugal pumps in HVAC, process, and municipal water applications.

Pro Tip: The cube law is why VFDs save so much money on pumps. Reducing speed by just 20% cuts power consumption by nearly 50%. But affinity laws only apply accurately on the pump curve - not across different pump sizes or designs. If you trim an impeller more than 10-15% from the maximum diameter, the volute mismatch degrades efficiency and the affinity law predictions become unreliable. At that point, select a smaller pump instead of over-trimming.

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Pump Affinity Laws Calculator
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How It Works

  1. Enter Current Operating Conditions

    Input the pump's current flow rate (GPM), total dynamic head (feet), brake horsepower (BHP), and operating speed (RPM). These values come from the pump curve at the current operating point or from field measurements.

  2. Choose Speed Change or Impeller Trim

    Select whether you are changing speed (via VFD, sheave change, or engine throttle) or trimming the impeller diameter. Enter the new speed in RPM or new impeller diameter in inches.

  3. Review Predicted Performance

    See the new flow, head, and BHP calculated using the affinity laws. Flow changes linearly with speed, head changes with the square, and power changes with the cube. Results show both absolute values and percentage change.

  4. Calculate Energy Savings

    Enter electricity cost per kWh and annual operating hours to see the dollar savings from reduced power consumption. The calculator shows simple payback period if you enter VFD or sheave replacement cost.

  5. Verify System Curve Intersection

    The new operating point must still intersect the system curve at a reasonable efficiency. If you reduce speed too much, the pump may not overcome static head. The calculator warns when predicted head drops below your entered static head requirement.

Built For

  • Plant engineers justifying VFD purchases with energy savings payback analysis
  • Pump technicians predicting performance after impeller trimming to reduce excess head
  • HVAC engineers sizing VFDs for chilled water and condenser water pump systems
  • Municipal water operators optimizing pump station speed for varying demand
  • Reliability engineers analyzing pump performance changes from speed adjustments
  • Energy auditors calculating potential savings from variable-speed pump retrofits
  • Process engineers evaluating flow control by speed change versus throttling valve

Features & Capabilities

Affinity Law Equations

Applies all three affinity law relationships simultaneously: Q2/Q1 = N2/N1 for flow, H2/H1 = (N2/N1)^2 for head, and P2/P1 = (N2/N1)^3 for power. Works for both speed changes and impeller diameter changes using the same mathematical relationships.

VFD Energy Savings Calculator

Computes annual energy savings in kWh and dollars from reducing pump speed with a variable frequency drive. Includes motor efficiency derating at reduced speed and accounts for VFD drive losses (typically 2-3% of rated power).

Payback Period Analysis

Enter VFD installed cost (equipment, wiring, programming) and the calculator determines simple payback in months. Most pumping applications over 10 HP with variable flow achieve payback in 12-24 months.

Impeller Trim Predictor

Calculate the trimmed impeller diameter needed to hit a target flow or head. Warns when trim exceeds 15% of maximum impeller diameter, where affinity law accuracy degrades due to volute mismatch and recirculation effects.

Static Head Warning System

Flags operating conditions where reduced speed may not overcome system static head. Essential for systems with significant elevation change or pressurized discharge, where slowing the pump too much causes zero flow.

Comparison

Flow Control Method Energy Efficiency Precision Capital Cost Best Application
VFD Speed Control Excellent (cube law savings) Very high $2,000-15,000 Variable flow systems, HVAC, process
Throttling Valve Poor (wastes energy as heat) High $200-2,000 Small pumps, constant-speed systems
Impeller Trim Good (permanent reduction) Moderate $300-1,000 labor Fixed oversized pumps, one-time correction
Bypass/Recirculation Very poor Low $500-3,000 Minimum flow protection only
Sheave Change Good (fixed speed change) Moderate $200-800 Belt-driven pumps, fixed ratio change

Frequently Asked Questions

The affinity laws are three relationships that predict how centrifugal pump performance changes with speed or impeller diameter. Flow varies linearly with speed (double speed = double flow). Head varies with the square of speed (double speed = 4x head). Power varies with the cube of speed (double speed = 8x power). These laws assume the pump is operating on its curve and the system curve shape does not change.
Energy savings depend on how much you reduce speed. A 20% speed reduction saves about 49% of power consumption (0.8^3 = 0.512). A 50% speed reduction saves about 87% (0.5^3 = 0.125). In practice, savings are somewhat less because motor and VFD efficiency decrease at low speed, and systems with high static head see diminishing returns. Most variable-flow pump VFD installations achieve 30-60% annual energy savings.
No. Affinity laws apply only to centrifugal (rotodynamic) pumps, including end-suction, split-case, vertical turbine, and submersible centrifugal designs. Positive displacement pumps (gear, piston, diaphragm, progressive cavity) have a nearly linear relationship between speed and flow, but head is independent of speed. Power for PD pumps varies linearly with speed, not with the cube.
Most pump manufacturers recommend trimming no more than 10-15% from the maximum impeller diameter. Beyond this, the impeller-to-volute clearance becomes excessive, causing recirculation, reduced efficiency, and increased radial thrust on the bearings. The affinity laws also become less accurate with large trims. If you need more than a 15% reduction, select a smaller pump or use a VFD for speed control.
Because power varies with the cube of speed, small speed reductions yield large power savings. Contrast this with a throttling valve, which dissipates excess energy as heat and pressure drop. A pump running at 80% speed through a VFD uses about 51% power. The same pump throttled to 80% flow at full speed might use 90% power. The difference is pure waste converted to heat across the valve. This is why VFDs on pumps over 10 HP typically pay for themselves in 1-2 years.
No. Affinity laws only apply to a single pump design operating at different speeds or with trimmed impellers. You cannot use them to predict performance of a different pump model, size, or specific speed. Different pumps have different efficiencies, curve shapes, and NPSH characteristics. Use manufacturer pump curves for selection and affinity laws only for predicting changes to an existing pump's operating point.
If you reduce pump speed until the shut-off head drops below the system static head, flow stops completely. The pump churns at shutoff, converting all input energy to heat. This damages the pump rapidly through overheating, seal failure, and bearing damage. Always verify that the minimum operating speed produces enough head to overcome static head plus a reasonable friction margin. Systems with high static head (tall buildings, elevated tanks) have less speed reduction range.
Fans follow the same affinity laws as pumps because both are centrifugal machines. Flow varies with speed, static pressure varies with speed squared, and power varies with speed cubed. Fan VFDs are even more effective than pump VFDs because most fan systems have zero static head (unlike pumps with elevation), meaning the entire system curve is friction-based and responds fully to the cube law savings.
Disclaimer: Affinity law predictions assume the pump operates on its design curve with no significant changes to system geometry. Accuracy decreases for impeller trims exceeding 15%, very low speed operation, or systems with high static head relative to friction head. Actual VFD savings depend on load profile, motor efficiency, and drive losses. Consult the pump manufacturer for performance data outside the range of affinity law applicability.

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