BIZOMAT MAKEOS · Power Transmission
Fan Duty, Fan Laws and Belt Drive
What power does this fan need, how fast must it run for more air, and what pulleys and motor does that take?
Fan drive sizing: air power and shaft power from flow, fan total pressure and efficiency; the fan speed, pressure and power for a new flow by the fan laws (as the affinity tool, on a system without static pressure); motor power with belt losses and margin and the next IEC rating; and the fan pulley diameter for the motor speed and motor pulley.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Present airflow | m³/s | Airflow the fan delivers now. |
| Fan total pressure | Pa | Total pressure rise across the fan at that flow. |
| Fan efficiency | % | Fan total efficiency at that point. |
| Present fan speed | rpm | Fan speed now. |
| Required airflow | m³/s | Airflow you need. |
| Belt drive efficiency | % | Efficiency of the belt drive. |
| Motor margin | % | Margin above the shaft power for the motor. |
| Motor speed | rpm | Motor full-load speed. |
| Motor pulley pitch diameter | mm | Pitch diameter of the motor pulley. |
What each input means
Open an input to see what it is, its units, the worked example and the common mistakes, with a small diagram.
What this means: Present airflow
- What it is
- Airflow the fan delivers now at its present speed, from a measurement or the existing fan duty.
- Units and format
- Enter a number in m³/s: m³/s. The form accepts 0.000001 m³/s to 10000 m³/s. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 5 m³/s as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
What this means: Fan total pressure
- What it is
- Total pressure rise across the fan at the present airflow, from measurement or the design duty.
- Units and format
- Enter a number in Pa: pascals. The form accepts 0.000001 Pa to 100000 Pa. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 800 Pa as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Air and shaft power are proportional to fan pressure.
- Get it right
- Pascals, not kilopascals or millimetres of water.
What this means: Fan efficiency
- What it is
- Fan total efficiency at the present duty point, from the fan maker’s curve.
- Units and format
- Enter a number in %: percent: the number is read as a percentage, so type 8 for 8 %. The form accepts 10% to 95%. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 70% as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Shaft power is inversely proportional to efficiency.
What this means: Present fan speed
- What it is
- Speed the fan impeller runs at now, at the present airflow.
- Units and format
- Enter a number in rpm: revolutions per minute. The form accepts 0.000001 rpm to 100000 rpm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 1000 rpm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- The new fan speed is proportional to it.
What this means: Required airflow
- What it is
- The airflow you need from the same system after the change.
- Units and format
- Enter a number in m³/s: m³/s. The form accepts 0.000001 m³/s to 10000 m³/s. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 6 m³/s as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Fan speed rises in proportion, pressure with the square and power with the cube of the flow ratio.
What this means: Belt drive efficiency
- What it is
- Efficiency of the belt drive between the motor and the fan, from the belt maker or drive design.
- Units and format
- Enter a number in %: percent: the number is read as a percentage, so type 8 for 8 %. The form accepts 50% to 100%. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 95% as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
What this means: Motor margin
- What it is
- Extra motor power allowed above the calculated need, for ageing, dirty filters and duty changes, before rounding up to a standard rating.
- Units and format
- Enter a number in %: percent: the number is read as a percentage, so type 8 for 8 %. The form accepts 0% to 100%. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 15% as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Type the percentage, not a fraction.
What this means: Motor speed
- What it is
- Full-load speed of the drive motor, from its nameplate.
- Units and format
- Enter a number in rpm: revolutions per minute. The form accepts 0.000001 rpm to 100000 rpm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 1450 rpm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- The fan pulley diameter is proportional to motor speed.
What this means: Motor pulley pitch diameter
- What it is
- Pitch diameter of the pulley on the motor shaft, used to work out the fan pulley size.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 2000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 150 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Pitch diameter of the belt groove, not the outside diameter of the pulley.
Method and formulas
- Air power = Q p; shaft power = air power ÷ η.
- Fan laws: speed ∝ Q, pressure ∝ Q², power ∝ Q³ (same system, no static pressure).
- Motor = shaft power ÷ belt efficiency × (1 + margin), next IEC rating.
- Fan pulley = motor pulley × motor speed ÷ fan speed.
- Example: 6 m³/s needs the fan at 1,200 rpm, 9.8743 kW at the shaft and a 15 kW motor.
Limitations
- Fan laws assume the system curve passes through zero; systems with static pressure (filters, dampers held at pressure) need the fan curve.
- Check the fan’s maximum safe speed before speeding it up.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Find the fan speed and motor needed for more airflow
- Size pulleys to change a belt-driven fan’s speed
- Estimate the power saving from slowing a fan
Who it is for
- Plant engineers
- Maintenance engineers
- Process engineers
What you get
- Present air and shaft power
- Speed, pressure and power for the new flow
- Motor rating and fan pulley size
Interpreting the result
- Power rises with the cube of speed: 20% more air needs about 73% more power.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 2487–2536. Topic reference; no source tables or recommended settings are reproduced.
Learn the Concepts Behind This Tool
These BIZOMAT Library readings explain the method this tool uses, with worked examples.
Method explained here · BIZOMAT original book
Burners, turndown and air–fuel ratio control
What it covers: Burner types, turndown, and four ways of controlling a burner's input; why fixed air wastes fuel at low fire, sizing the combustion air fan, and a blocked impulse line found only at low fire.
Method explained here · BIZOMAT original book
Pumps, fans and similarity: affinity laws and specific speed
In Scale Models by the Numbers
What it covers: Derive the affinity laws from dimensionless groups, apply them to a variable-speed pump and a ventilation fan, classify machines by specific speed, and see why model pump efficiency is stepped up.
Method explained here · BIZOMAT original book
Fans, pumps and energy savings
In Variable-Speed Drives by the Numbers
What it covers: How the fan and affinity laws predict the power saved by slowing a fan or pump, why static head cuts the saving, how to measure the before and after, and how to appraise a drive as an investment.
BIZOMAT tools are screening and decision-support utilities. Verify important financial, engineering, safety, legal or operational decisions using appropriate professional standards and your organisation’s approved data.