Fan Pump Affinity Laws

What Are Fan and Pump Affinity Laws?

Fan Pump Affinity Laws are a set of mathematical relationships that describe how:

• Flow rate
• Head or pressure
• Power consumption

change when the rotational speed of a fan or pump changes, while the impeller size and fluid remain the same.

These laws apply to:

• Centrifugal fans
• Centrifugal pumps
• Axial fans (within limits)

They are especially useful when using variable frequency drives (VFDs) or adjusting motor RPM.

Why Fan Pump Affinity Laws Matter

Understanding affinity laws helps you:

• Predict system performance accurately
• Reduce energy consumption
• Select the right motor size
• Avoid overloading equipment
• Improve system efficiency
• Save operational costs

In short, they turn speed changes into predictable outcomes.

The Three Fan Pump Affinity Laws Explained

The affinity laws compare a known operating condition with a new operating condition after a speed change.

Let’s define the terms first:

• N₁ = Known speed (RPM)
• N₂ = New speed (RPM)
• Q₁ = Known flow rate (GPM or CFM)
• Q₂ = New flow rate
• H₁ = Known head or pressure
• H₂ = New head or pressure
• P₁ = Known power (HP)
• P₂ = New power

1️⃣ First Affinity Law: Flow Rate vs Speed

Formula:

Q₂ / Q₁ = N₂ / N₁

What it means in simple terms:
When speed changes, flow changes in direct proportion.

Example:
If speed increases by 20%, flow also increases by 20%.

Key takeaway:
✔ Flow ∝ Speed

This law is extremely useful for airflow and water flow predictions.

2️⃣ Second Affinity Law: Head / Pressure vs Speed

Formula:

H₂ / H₁ = (N₂ / N₁)²

What it means:
Pressure or head increases with the square of speed.

Example:
A 20% speed increase results in:

1.2² = 1.44 → 44% increase in head

Key takeaway:
✔ Head ∝ Speed²

This explains why small speed increases can create much higher pressure.

3️⃣ Third Affinity Law: Power vs Speed

Formula:

P₂ / P₁ = (N₂ / N₁)³

What it means:
Power demand rises with the cube of speed.

Example:
A 20% speed increase results in:

1.2³ = 1.728 → 72.8% increase in power

Key takeaway:
⚠ Power ∝ Speed³

This is why motors can overload quickly if speed is increased carelessly.

Understanding the Speed Ratio

At the heart of all affinity laws is the speed ratio:

Speed Ratio = N₂ / N₁

This single value controls:

• Flow (linear)
• Head (square)
• Power (cube)

Your calculator smartly computes this ratio first and then applies it across all three laws.

How the Fan & Pump Affinity Laws Calculator Works

The calculator you provided follows the affinity laws step-by-step:

User Inputs

• Known speed (N₁)
• Known flow rate (Q₁)
• Known head or pressure (H₁)
• Known power (P₁)
• New speed (N₂)

Internal Calculations

• Speed Ratio = N₂ / N₁
• New Flow (Q₂) = Q₁ × Speed Ratio
• New Head (H₂) = H₁ × (Speed Ratio)²
• New Power (P₂) = P₁ × (Speed Ratio)³

Output Results

• Updated flow rate
• Updated head or pressure
• Updated power requirement
• Speed ratio for quick comparison

This approach ensures fast, accurate, and practical predictions.

Real-World Applications of Affinity Laws

Fan and pump affinity laws are widely used in:

• HVAC system optimization
• Water distribution systems
• Cooling towers
• Industrial process pumps
• Ventilation and exhaust systems
• Energy audits and retrofits

They are especially valuable when VFDs are used to control speed instead of throttling valves or dampers.

Energy Efficiency and Cost Savings

One of the most powerful insights from affinity laws is this:

Reducing speed slightly can save a lot of energy.

For example:

• Reducing speed by 20%
• Power drops to:

0.8³ = 0.512 → Nearly 49% energy savings

This is why speed control is far more efficient than mechanical throttling.

Limitations of Fan Pump Affinity Laws

While very useful, affinity laws assume:

• Same impeller diameter
• Same fluid properties
• Same system efficiency
• Operation near the design point

They may not be accurate for:

• Very large speed changes
• Cavitation conditions
• Non-Newtonian fluids
• Highly turbulent systems

Always validate results with manufacturer curves when precision is critical.

Best Practices When Using Affinity Laws

• Always check motor power limits
• Watch for cavitation at high speeds
• Confirm pressure ratings of piping
• Use affinity laws for estimation, not final design
• Combine with system curves for accuracy