What Does This Affinity Laws Calculator Do?
Boiler feed pump duty changes a lot with speed. If you slow the pump by 15%, flow drops by 15%, head drops by about 28% and power drops by about 38%. That is why VFD saves so much energy.
This calculator uses pump affinity laws to find new flow, new head and new power when you change speed or trim the impeller. It also shows power saved, energy saved per year and money saved per year for a VFD run.
Pump Affinity Laws Formula
Flow: Q2 = Q1 × (N2 / N1)Head: H2 = H1 × (N2 / N1)²Power: P2 = P1 × (N2 / N1)³
Same for impeller: Q2 = Q1 × (D2 / D1), H2 = H1 × (D2 / D1)², P2 = P1 × (D2 / D1)³
N = speed RPM, D = impeller diameter mm, Q = flow m³/h, H = head m, P = power kW
Savings = P1 - P2, Energy saved = Savings × hours per year
Ratio r = N2 / N1. If r is 0.85, flow is 0.85 times, head is 0.7225 times and power is 0.614 times original.
How to Use the Calculator
- Pick speed change or impeller trim. Speed change is for VFD. Impeller trim is for permanent diameter cut.
- Enter original duty. Use nameplate speed and pump curve point at that speed: flow, head and power.
- Enter new speed or diameter. For VFD, enter target RPM. For trim, enter new impeller diameter.
- Add hours and electricity price. This gives yearly savings. Leave default 8000 hours and $0.12 per kWh if you do not know.
- Click Calculate New Duty. You get new flow, head, power and savings.
Understanding Results
New Flow Rate
Flow changes in direct line with speed. Halve speed, halve flow. This works well for boiler feed where feed demand follows steam load.
New Head
Head changes with square. So 10% speed cut cuts head by 19%. Check that new head still beats boiler pressure plus line loss. If head falls too low, pump cannot feed boiler.
New Power and Savings
Power changes with cube. A 15% speed cut from 2950 to 2500 RPM cuts power by about 39%. For 22 kW pump, new power is about 13.5 kW, saving 8.5 kW. At 8000 hours, that is 68,000 kWh per year.
Worked Example
Boiler feed pump at 2950 RPM: 50 m³/h, 120 m head, 22 kW. Reduce to 2500 RPM with VFD.
| Step | Calc | Result |
|---|---|---|
| Ratio r | 2500 / 2950 | 0.847 |
| New flow Q2 | 50 × 0.847 | 42.4 m³/h |
| New head H2 | 120 × 0.847² | 86.1 m |
| New power P2 | 22 × 0.847³ | 13.4 kW |
| Power saved | 22 - 13.4 | 8.6 kW (39.1%) |
| Energy per year | 8.6 × 8000 | 68,800 kWh |
| Cost saved | 68,800 × $0.12 | $8,256 / year |
So at lower steam load, pump still delivers 42.4 m³/h but uses far less power than throttling at full speed.
Affinity Laws and Boiler Feed System
Before you change speed, you need correct base head. Our boiler feed pump calculation tool gives you flow, TDH, NPSH and power for your boiler at full load. Use that duty point as Q1, H1 and P1 here, then test lower speed for part load.
- VFD vs throttling: Throttling keeps power high and wastes energy as pressure drop. VFD cuts power by cube law.
- Part load: Boiler rarely runs at 100% all day. VFD lets feed pump follow steam demand.
- Impeller trim: If pump is always oversized, trim impeller by 5-10% for permanent saving. Do not trim more than 10% or efficiency falls.
- NPSH: NPSH required also falls with speed square: NPSHr2 = NPSHr1 × r². That helps at low speed.
When Affinity Laws Do Not Work Well
- Large speed change: Below 50% speed, efficiency drops and laws are less accurate.
- System with high static head: If most head is boiler pressure (static), flow will fall more than law predicts. Law is best when friction is main head.
- Positive displacement pump: Laws are only for centrifugal pumps, not piston or gear pumps.
- Viscosity change: Laws assume same liquid, same temperature. Hot feedwater at 105°C behaves same for affinity, but check NPSH.
Frequently Asked Questions
What are pump affinity laws?
Three rules for centrifugal pump when speed or impeller diameter changes. Flow changes with ratio, head with ratio square, power with ratio cube.
How much power does VFD save?
If you cut speed by 20%, power falls by about 48.8% because 0.8³ = 0.512. Actual saving depends on hours at part load.
Can I use affinity laws for impeller trimming?
Yes, same formulas with diameter ratio D2/D1 instead of speed ratio. Keep trim within 10% to avoid big efficiency loss.
Does efficiency stay same?
For small change up to 10-15% speed, efficiency is almost same. For large change, efficiency drops and actual power is a bit higher than law predicts.
Basis: Centrifugal pump affinity laws per Hydraulic Institute, Grundfos, KSB and Sulzer pump handbooks. Power relation P = rho × g × Q × H / efficiency. Valid for same pump, same impeller, same fluid. For final VFD selection check pump curve at new speed and system curve intersection.