Pump · calculator
Pump Affinity Laws Calculator (RPM, Flow, Head & Power)
Estimate centrifugal-pump flow, head, and power after a rotational speed change.
Method record
What this calculator measures
Affinity laws scale a known centrifugal-pump curve for a speed change. Power changes fastest, making motor capacity and NPSH checks essential when speed increases.
Q₂/Q₁=N₂/N₁; H₂/H₁=(N₂/N₁)²; P₂/P₁=(N₂/N₁)³ Use it correctly
Calculation steps
- Start from a known curve point.
- Enter the proposed speed ratio.
- Check the scaled curve against system head, motor power, efficiency, and NPSH.
Applicability
Use the model within its limits
Use only for dynamically similar operation over a reasonable range. The manufacturer curve governs final selection.
What this result represents
- System
- Pump
- Formula
- Q₂/Q₁=N₂/N₁; H₂/H₁=(N₂/N₁)²; P₂/P₁=(N₂/N₁)³
- Review
- Verify safety-sensitive work with qualified guidance.
Worked Field Example
Worked Example: VFD Speed Reduction Power Savings
Field Scenario: Predicting flow, head, and brake horsepower when installing a Variable Frequency Drive (VFD) to reduce pump speed from 3,500 RPM down to 2,800 RPM.
Given Input Parameters
Step-by-Step Mathematical Solution
- Flow changes linearly: Q2 = 150 × (0.80) = 120.0 GPM.
- Head changes with square: H2 = 120 × (0.80)² = 120 × 0.64 = 76.8 feet.
- Power changes with cube: BHP2 = 6.5 × (0.80)³ = 6.5 × 0.512 ≈ 3.33 BHP.
Operating at 80% speed delivers 120 GPM at 76.8 ft head while slashing power from 6.5 to 3.33 BHP (49% energy reduction)!
Professional Guidance: Affinity laws assume impeller diameter remains constant and hydraulic efficiency remains approximately equal.
Engineering FAQs
Frequently Asked Questions
What are the three Pump Affinity Laws?
Law 1: Flow rate varies directly with speed (Q ∝ N). Law 2: Head varies with the square of speed (H ∝ N²). Law 3: Brake horsepower varies with the cube of speed (P ∝ N³).
Can the affinity laws be used for positive displacement pumps?
The flow law applies (flow is proportional to speed), but head and power laws do not apply. In positive displacement pumps (gear, piston, diaphragm), head is determined by downstream system resistance, not pump rotational velocity.
Why is trimming an impeller slightly less efficient than using a VFD?
Impeller trimming reduces diameter permanently, increasing clearance between the impeller tip and pump casing volute, which can slightly degrade hydraulic efficiency (by 1–3%).