Slowing a pump down with a VFD or trimming its impeller both change performance in predictable ways — but the relationships aren’t linear, and using the wrong scaling assumption leads to inaccurate energy savings estimates or a mis-trimmed impeller. The Pump Affinity Laws Excel Sheet from GrowMechanical applies the standard affinity law relationships so you can scale flow, head, and power correctly for speed or diameter changes.
It is built for mechanical and process engineers evaluating VFD retrofits, impeller trims, or any scenario where a pump’s operating speed or diameter changes from its rated condition.
What This Sheet Calculates
- Flow rate scaling: Q2/Q1 = N2/N1 (or D2/D1 for diameter changes)
- Head scaling: H2/H1 = (N2/N1)²
- Power scaling: P2/P1 = (N2/N1)³
- New performance point at a target speed or trimmed impeller diameter
- Estimated energy savings from reduced-speed VFD operation
The Pump Affinity Laws
| Parameter |
Relationship (Speed or Diameter Change) |
| Flow Rate |
Q2 = Q1 × (N2/N1) |
| Head |
H2 = H1 × (N2/N1)² |
| Power |
P2 = P1 × (N2/N1)³ |
Because power scales with the cube of speed, even modest speed reductions can produce significant energy savings — which is the basis for most VFD retrofit energy justifications.
Why Use This Sheet
- Evaluate VFD Savings Accurately: Quantify expected energy savings from reduced-speed operation using the correct cubic power relationship.
- Confirm Impeller Trims: Estimate new flow, head, and power before committing to a physical impeller trim.
- Save Engineering Time: Apply the affinity laws without re-deriving the scaling relationships for every evaluation.
Key Features
- Flow, head, and power scaling for both speed and diameter changes
- VFD energy savings estimation at reduced speed
- Impeller trim performance projection
- Fully editable formulas — no hidden cells
- Works offline in Microsoft Excel
Technical Specifications
| Parameter |
Details |
| File Format |
Microsoft Excel (.xlsx) |
| Core Relationships |
Q ∝ N; H ∝ N²; P ∝ N³ (affinity laws) |
| Applicable Changes |
Pump speed (VFD) or impeller diameter (trim) |
| Key Outputs |
Scaled flow, head, power; estimated VFD energy savings |
| Editable |
Yes — all formulas open for review |
| Internet Required |
No — works fully offline |
Typical Applications
- VFD retrofit energy savings evaluations
- Impeller trim sizing and performance projection
- Matching an oversized pump to actual system requirements
- Energy audits comparing fixed-speed vs. variable-speed operation
Who Should Use This Sheet
- Mechanical and process engineers evaluating VFD projects
- Energy engineers building pump energy-savings business cases
- Maintenance engineers planning impeller trims
- Engineering students learning pump affinity law fundamentals
What You’ll Receive
- Editable Excel sheet with full affinity law scaling calculations
- VFD energy savings estimation module
- Lifetime access with a single, one-time purchase
Compatibility
- Microsoft Excel 2010 or later (Windows or Mac)
- No macros or add-ins required
- Works fully offline once downloaded
How to Use This Sheet
- Enter your pump’s known flow, head, and power at the current speed or diameter.
- Enter the target speed (or impeller diameter) you want to evaluate.
- Review the scaled flow, head, and power at the new condition.
- Use the energy savings module to estimate VFD operating cost reduction.
- Confirm the new operating point still meets your system curve requirements.
For complete pump sizing, see our Centrifugal Pump Design & Selection Excel Tool and Pump Power Calculation Excel Sheet. Check suction margin with our NPSHA Calculation Excel Sheet. Explore the Engineering Design & Calculation Master Excel Bundle, or browse the complete product catalog.
Frequently Asked Questions
Why does power scale with the cube of speed, not linearly?
Because both head and flow increase with speed (flow linearly, head with the square of speed), and power is proportional to flow × head, power ends up scaling with the cube of speed. This is why modest speed reductions can yield large energy savings.
Do the affinity laws apply exactly, or are they an approximation?
They’re a close approximation for moderate speed changes and small impeller trims on the same pump. Efficiency can shift slightly at very different operating points, so always verify against the actual pump curve where precision matters.
Can I use this sheet for impeller trims instead of speed changes?
Yes, the same relationships apply using diameter ratio (D2/D1) instead of speed ratio (N2/N1), though trims are generally limited to a modest percentage of the original diameter.
How accurate are the estimated VFD energy savings?
The savings estimate is based on the cubic power-speed relationship and your input operating hours/load profile; actual savings depend on your system curve and how much of the time the pump runs at reduced speed.
Does this replace a VFD vendor’s sizing software?
No. This sheet provides an engineering estimate for evaluation and business-case purposes; final VFD selection should be confirmed with the drive manufacturer’s sizing tools.
Evaluating a VFD retrofit or impeller trim? Get the Pump Affinity Laws Excel Sheet today and quantify the flow, head, power, and energy impact before you commit.
