🔄 Pump Affinity Laws Calculator

Calculate Flow, Head & Power Changes for Speed and Impeller Diameter Variations

Overview

Speed Change

Diameter Change

Power Sizing

VFD Savings

Reference

🔄 Centrifugal Pump Operation

The rotating impeller adds energy to the fluid, converting velocity to pressure in the volute.

📐 The Three Affinity Laws

The Affinity Laws describe how centrifugal pump performance changes with speed (N) or impeller diameter (D):

Flow ∝ Speed/Diameter

Q₂/Q₁ = N₂/N₁ = D₂/D₁

Flow changes linearly with speed or diameter

↑ 10% speed = ↑ 10% flow

Head ∝ (Speed/Diameter)²

H₂/H₁ = (N₂/N₁)² = (D₂/D₁)²

Head changes with the square of speed or diameter

↑ 10% speed = ↑ 21% head

Power ∝ (Speed/Diameter)³

P₂/P₁ = (N₂/N₁)³ = (D₂/D₁)³

Power changes with the cube of speed or diameter

↑ 10% speed = ↑ 33% power

📊 Visual Relationship - How Changes Scale

Key Insight: The Cube Law is Powerful!

A 20% speed reduction cuts power by nearly 50% (0.8³ = 0.512). This is why VFDs on pumps and fans provide such dramatic energy savings.

⚡ Speed Change Calculator

Initial Speed (N₁)

RPM

New Speed (N₂)

RPM

Initial Flow (Q₁)

GPM

Initial Head (H₁)

Initial Power (P₁)

Speed Ratio (N₂/N₁)

0.80

↓ 20% reduction

New Flow (Q₂)

400

GPM

↓ 20%

New Head (H₂)

↓ 36%

New Power (P₂)
12.8
HP
↓ 49%

Formulas Used

Q₂ = Q₁ × (N₂/N₁)

H₂ = H₁ × (N₂/N₁)²

P₂ = P₁ × (N₂/N₁)³

🔄 Speed Comparison Visualization

ORIGINAL SPEED

1750 RPM

NEW SPEED

1400 RPM

Speed Change Applications

VFD Control: Vary motor frequency to adjust pump speed
Pulley/Sheave Change: Mechanical speed adjustment
Gear Reducers: Fixed speed reduction
Motor Replacement: Different pole count motors

⚠️ Important Considerations

Speed changes are more accurate than diameter changes
Check motor nameplate for speed limits
NPSH requirements change with speed
Verify pump curve at new operating point

🔌 Common Motor Synchronous Speeds

Poles	60 Hz Sync	60 Hz Typical FL	50 Hz Sync	50 Hz Typical FL
2	3600 RPM	3450-3550 RPM	3000 RPM	2850-2950 RPM
4	1800 RPM	1725-1770 RPM	1500 RPM	1425-1475 RPM
6	1200 RPM	1140-1175 RPM	1000 RPM	950-980 RPM
8	900 RPM	850-880 RPM	750 RPM	710-740 RPM

Synchronous Speed = (120 × Frequency) / Poles. Actual speed is slightly less due to slip.

⭕ Impeller Diameter Change Calculator

Initial Diameter (D₁)

New Diameter (D₂)

Initial Flow (Q₁)

GPM

Initial Head (H₁)

Initial Power (P₁)

Diameter Ratio (D₂/D₁)

0.875

↓ 12.5% trim

New Flow (Q₂)

437.5

GPM

↓ 12.5%

New Head (H₂)

76.6

↓ 23.4%

New Power (P₂)
16.7
HP
↓ 33%

🔧 Impeller Trimming Visualization

⚠️ Impeller Trim Limitations

Accuracy decreases beyond 10-20% trim
Efficiency may decrease with large trims
Trimming is permanent - cannot be reversed
Consult manufacturer for maximum trim allowance

📋 Typical Maximum Impeller Trim Guidelines

Pump Type	Max Trim	Notes
End suction (small)	15-20%	Most common industrial pumps
End suction (large)	10-15%	Check with manufacturer
Vertical turbine	10-15%	Bowl efficiency sensitive
Split case	10-20%	Depends on specific gravity
Multistage	5-10%	Limited by stage matching

⚡ Pump Power Calculator

Calculate the brake horsepower (BHP) required to pump fluid at a given flow rate and head. Use this for motor sizing and pump selection.

Flow Rate (Q)

GPM

Total Head (H)

Specific Gravity (SG)

Custom SG Value

Pump Efficiency (η)

Hydraulic Power (Water HP)

7.58

Brake Horsepower (BHP)
10.82
HP

Recommended Motor

Shaft Power

8.07

Motor Load

72.1

Pump Power Formula

BHP = (Q × H × SG) / (3960 × η)

Where: Q = GPM, H = ft, SG = specific gravity, η = efficiency (decimal)

🔌 Motor Size Selection

Standard NEMA motor sizes. Select a motor with HP ≥ calculated BHP. Allow 10-15% margin for safety.

Motor Sizing Guidelines

Minimum: Motor HP ≥ Calculated BHP
Recommended: Next standard size above BHP (10-15% margin)
Avoid: Running motors continuously above 85% load
VFD: May require motor derating at low speeds

⚠️ Important Considerations

End of curve operation increases power draw
Worn impellers reduce efficiency (increase BHP)
Cold starts may require higher torque
Account for future capacity increases

📊 Power Flow Diagram

Motor Input

11.2 kW

Shaft Power (BHP)

8.1 kW

Hydraulic Output

5.7 kW

📈 Typical Pump Efficiencies

Pump Type	Small (<50 GPM)	Medium (50-500 GPM)	Large (>500 GPM)
End Suction	50-65%	65-80%	75-87%
Vertical Turbine	55-70%	70-82%	78-88%
Split Case	60-70%	72-85%	80-90%
Multistage	50-65%	65-78%	72-85%
Submersible	45-60%	55-72%	65-80%
Positive Disp.	60-75%	70-85%	80-92%

💡 Efficiency Tips

Best efficiency at design point (BEP)
Efficiency drops 10-20% at 50% or 120% of BEP flow
Worn wear rings can reduce efficiency 5-15%

📋 Quick Power Reference

STANDARD NEMA MOTOR SIZES (HP)

0.5 0.75 1 1.5 2 3 5 7.5 10 15 20 25 30 40 50 60 75 100 125 150 200

COMMON SPECIFIC GRAVITIES

Fluid	SG	Fluid	SG
Gasoline	0.72-0.78	Water	1.00
Diesel	0.82-0.95	Seawater	1.02-1.03
Lube Oil	0.85-0.95	Glycol 50%	1.06
Ethanol	0.79	H₂SO₄ 98%	1.84

Alternative Power Formulas

BHP = (Q × ΔP) / (1714 × η)

Q = GPM, ΔP = PSI

kW = (Q × H × SG) / (5308 × η)

Q = GPM, H = ft

kW = (m³/h × m × SG) / (367 × η)

Metric units

💰 VFD Energy Savings Calculator

Motor Power

Motor Efficiency

Operating Hours

hrs/yr

Electricity Cost

$/kWh

Average Operating Speed

80%

Power at Full Speed

40.1

Power at Reduced Speed

20.5

Annual Cost (Full Speed)

$32,080

Annual Cost (VFD)

$16,384

💵 Annual Savings
$15,696
(48.9% reduction)

📈 Speed vs Power Relationship

Speed	Flow	Head	Power
100%	100%	100%	100%
90%	90%	81%	72.9%
80%	80%	64%	51.2%
70%	70%	49%	34.3%
60%	60%	36%	21.6%
50%	50%	25%	12.5%

📊 VFD Payback Calculator

VFD Cost (Installed)

Annual Maintenance

$/yr

Simple Payback

6.3

months

5-Year Net Savings

$69,480

✓ VFD Benefits Beyond Energy Savings

Soft start/stop: Reduces mechanical stress and water hammer
Extended equipment life: Lower speeds mean less wear
Process control: Precise flow/pressure control without valves
Reduced maintenance: Less wear on seals, bearings, impellers

📐 Complete Affinity Law Formulas

Law 1: Flow

Q₂ = Q₁ × (N₂/N₁) × (D₂/D₁)

Law 2: Head/Pressure

H₂ = H₁ × (N₂/N₁)² × (D₂/D₁)²

Law 3: Power

P₂ = P₁ × (N₂/N₁)³ × (D₂/D₁)³

Specific Speed (Ns)

Ns = N × √Q / H^0.75

Where N=RPM, Q=GPM, H=ft (single stage, at BEP)

⚠️ Limitations & Accuracy

When Affinity Laws Are Less Accurate

Large diameter changes (>20%): Vane geometry changes significantly
High viscosity fluids: Laws assume water-like fluids
Systems with static head: Only friction losses follow the laws
Operating far from BEP: Efficiency changes significantly
Very low speeds: Reynolds number effects become significant

Best Accuracy

Speed changes (vs diameter changes)
Changes less than ±20%
Operating near BEP
Low viscosity fluids
Systems dominated by friction head

📋 Quick Reference Table

Change	Flow (Q)	Head (H)	Power (P)	Example
+50%	+50%	+125%	+237.5%	1750→2625 RPM
+25%	+25%	+56.3%	+95.3%	1750→2188 RPM
+10%	+10%	+21%	+33.1%	1750→1925 RPM
0% (baseline)	100%	100%	100%	1750 RPM
-10%	-10%	-19%	-27.1%	1750→1575 RPM
-20%	-20%	-36%	-48.8%	1750→1400 RPM
-30%	-30%	-51%	-65.7%	1750→1225 RPM
-50%	-50%	-75%	-87.5%	1750→875 RPM

📚 Related Standards & Resources

Standard/Resource	Description
Hydraulic Institute Standards	Pump testing, performance, and application guidelines
API 610	Centrifugal pumps for petroleum, petrochemical, and natural gas industries
ANSI/HI 1.3	Rotodynamic centrifugal pumps for design and application
ISO 9906	Rotodynamic pumps - Hydraulic performance acceptance tests
DOE Pump Systems	US Department of Energy pump system assessment resources