Learn & Understand

The Square Law, the Fan Affinity Laws, and Why Speed Control Saves So Much Energy

The companion calculator uses a powerful shortcut: for a fixed flow path, pressure drop scales with the square of flow, so doubling the flow roughly quadruples the resistance. That square relationship is not a burner curiosity, it is one corner of the fan affinity laws, and its cousin, a cube law for power, explains one of the biggest energy-saving opportunities in any system that moves air or fluid: variable-speed control.

Why Pressure Drop Follows Flow Squared

Pushing fluid faster through a fixed restriction, an orifice, a nozzle, a length of pipe, meets resistance that rises steeply, not proportionally. The reason is that the energy lost to friction and turbulence depends on the fluid's velocity squared, so as flow increases, the pressure needed to drive it climbs with the square. This is exactly the relationship the calculator exploits to predict pressure drop at a new flow from a single reference measurement: measure once, and the square law extends it across the operating range.

The Affinity Laws: A Family of Relationships

For fans and pumps, this square law is part of a set called the affinity laws, which relate flow, pressure, and power to fan speed.

The pressure-squared law the calculator uses is the middle row. But the real headline is the bottom row: power scales with the cube of speed. Slow a fan to half its speed and it delivers half the flow while drawing only about an eighth of the power. This cube relationship is where enormous energy savings hide.

Two Ways to Reduce Flow, Two Very Different Bills

Suppose a combustion air fan needs to deliver less air at low fire. There are two ways to reduce the flow, and they cost wildly different amounts of energy.

Throttling with a damper is like driving with the brakes on: you get less flow, but the fan is still working near full power and wasting most of it across the restriction. A variable-speed drive instead slows the motor, and because of the cube law, a modest speed reduction produces a dramatic power reduction. This is why fitting variable-speed drives to combustion air fans (and pumps everywhere) is one of the highest-return energy measures available, especially on burners that spend much of their time below full fire.

Why This Matters for Burners Specifically

A modulating burner spends most of its life below full fire, moving less than maximum air. If its fan runs at constant speed and the air is throttled by dampers, the fan wastes energy across the damper the entire time. Driving the fan with a variable-speed drive so it slows at part load captures the cube-law savings continuously. Over a year of part-load operation, the difference is substantial, real electricity saved for the same combustion result.

Using the Pressure-Drop Estimate Well

Take the calculator's square-law prediction as an accurate way to scale pressure drop from a reference point to a new flow. Then carry the bigger lesson: the same physics gives fans a cube-law relationship between speed and power, so reducing flow by slowing the fan (a variable-speed drive) uses far less energy than choking it with a damper. On any burner that runs at part load, speed control of the combustion air fan is where the square law turns into real money saved.