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Affinity Laws Calculator
Calculate new flow, head/pressure, and power when pump or fan speed (or impeller diameter) changes. Based on the centrifugal pump affinity laws.
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The Three Affinity Laws
The affinity laws relate flow rate, head (pressure), and power to changes in rotational speed or impeller diameter for centrifugal pumps, fans, and blowers:
Where the ratio can be either n₂/n₁ (speed change) or D₂/D₁ (diameter change).
Speed Change vs. Diameter Change
The same mathematical relationships apply for both speed changes and impeller diameter changes:
| Parameter | Speed Change | Diameter Change |
|---|---|---|
| Flow Q | Q₂ = Q₁ × (n₂/n₁) | Q₂ = Q₁ × (D₂/D₁) |
| Head H | H₂ = H₁ × (n₂/n₁)² | H₂ = H₁ × (D₂/D₁)² |
| Power P | P₂ = P₁ × (n₂/n₁)³ | P₂ = P₁ × (D₂/D₁)³ |
VFD Energy Savings
Key Insight: Power varies as the cube of speed. A 20% speed reduction saves approximately 49% of power (0.8³ = 0.512). This is why Variable Frequency Drives (VFDs) are one of the most cost-effective energy saving measures for pumps and fans.
| Speed Reduction | Flow Reduction | Head Reduction | Power Savings |
|---|---|---|---|
| 10% | 10% | 19% | 27% |
| 20% | 20% | 36% | 49% |
| 30% | 30% | 51% | 66% |
| 40% | 40% | 64% | 78% |
| 50% | 50% | 75% | 88% |
Practical Example
Given: n₁ = 1450 RPM, n₂ = 1750 RPM, Q₁ = 100 m³/h, H₁ = 25 m, P₁ = 7.5 kW
Speed ratio r = 1750 / 1450 = 1.2069
Q₂ = 100 × 1.2069 = 120.7 m³/h
H₂ = 25 × 1.2069² = 36.4 m
P₂ = 7.5 × 1.2069³ = 13.2 kW
⚠️ Limitations: Affinity laws assume constant efficiency, geometrically similar conditions, and incompressible flow. For speed changes beyond ±30%, actual performance may deviate significantly. Impeller trimming laws are less accurate than speed change laws — always verify with manufacturer curves.
The affinity laws (also called fan laws or pump laws) are three relationships for centrifugal machines:
- Flow varies linearly with speed: Q₂ = Q₁ × (n₂/n₁)
- Head/Pressure varies as the square: H₂ = H₁ × (n₂/n₁)²
- Power varies as the cube: P₂ = P₁ × (n₂/n₁)³
The same ratios apply when impeller diameter changes instead of speed.
Affinity laws apply to:
- Centrifugal pumps, fans, blowers, and turbines
- Operating on a fixed system curve
- With geometrically similar flow conditions
- Incompressible fluids (liquids, low-velocity air)
They work best for speed changes of up to ±30% from the design point. They do not apply to positive displacement pumps or reciprocating compressors.
Key limitations:
- They assume constant efficiency — in reality, efficiency changes at off-design points
- Large speed changes (>30%) can cause significant deviation
- Impeller trimming laws are less accurate than speed change laws
- Not valid for compressible flow at high Mach numbers
- Do not account for cavitation (NPSH) effects
- System curve changes (e.g. valve throttling) invalidate the predictions
Because power varies as the cube of speed, even small speed reductions yield large energy savings:
- 10% speed reduction → 27% power savings
- 20% speed reduction → 49% power savings
- 30% speed reduction → 66% power savings
- 50% speed reduction → 88% power savings
VFDs (Variable Frequency Drives) exploit this cubic relationship, making them far more efficient than throttling valves for flow control. Typical payback periods are 6–18 months.
For a given speed change ratio r:
- Flow changes by r (linear)
- Pressure/head changes by r² (quadratic)
So if you double the speed (r=2), flow doubles but pressure quadruples (4×). If you halve the speed (r=0.5), flow halves but pressure drops to 25%. This non-linear relationship is key to understanding pump and fan system behavior.
The procedures described on this page were developed and field-tested by the Vibromera team using the Balanset-1A, a portable dual-channel balancer and vibration analyzer for on-site rotor balancing.
Professional field balancing instruments and software. Achieve optimal pump and fan performance on-site. Used in 50+ countries.
