8.2 Fan Affinity Laws, Pressure, and Power

Fan Laws, Speed Changes, and Power

The three speed relationships

For the same fan, fixed geometry, unchanged system, and constant air density, the fan laws predict:

• Q2 = Q1 × N2/N1
• P2 = P1 × (N2/N1) squared
• BHP2 = BHP1 × (N2/N1) cubed

Q is airflow, P is the same defined fan pressure quantity at both points, N is rotational speed, and BHP is shaft power. These relations describe geometrically similar operation; they do not authorize a change or override a manufacturer limit.

If speed rises 20%, flow is predicted to rise 20%, pressure 44%, and power about 72.8%. The cubic power change is why even a modest speed increase requires a motor, drive, fan, bearing, vibration, and current review before adjustment.

Worked speed example

A fan delivers 8,000 CFM at 900 RPM and requires 3.50 BHP. At 1,080 RPM the ratio is 1.20. Predicted flow is 9,600 CFM, pressure is 1.44 times the original, and power is 3.50 × 1.20 cubed = 6.05 BHP.

If the motor is rated 5 HP, the predicted requirement exceeds nameplate horsepower. Do not assume a specific thermal trip or calculate a universal allowable power as horsepower times service factor. Review nameplate service-factor amperes if listed, manufacturer data, overload protection, temperature, VFD, and driven-equipment limits. Obtain engineering or manufacturer direction.

Pressure example

If the same fan and system produce 1.00 in. w.g. at 800 RPM, the prediction at 1,000 RPM is 1.00 × (1,000/800) squared = 1.5625 in. w.g. Keep the pressure definition consistent: fan total pressure cannot be mixed with a duct static reading.

Mechanical and VFD speed

For an ideal belt drive:

motor RPM × motor-sheave pitch diameter = fan RPM × fan-sheave pitch diameter

Use pitch diameters and verify actual fan speed because motor slip, belt slip, and adjustable-sheave geometry affect the result. Sheave selection, alignment, belt type, minimum groove diameter, shaft load, and guard clearance come from manufacturer data. Qualified authorized workers perform the mechanical change under energy control.

Below base frequency and under the stated motor and drive assumptions, fan speed may be approximately proportional to VFD frequency. Above base frequency, motor torque, voltage, fan speed, and drive limits require specific evaluation. A frequency command is not proof of shaft RPM.

Power estimates

Air horsepower relationships use airflow, a correctly defined pressure rise, and fan efficiency. Three-phase shaft-power estimates use voltage, current, power factor, and motor efficiency. Nameplate nominal power factor or efficiency may not represent part-load values. Treat such calculations as estimates unless measured power data and an applicable method support them.

Always compare like boundaries. Fan total pressure accounts for total-pressure change across the fan; fan static-pressure conventions require the applicable definition. A random downstream duct static pressure is not automatically fan pressure.

Field decision sequence

1. confirm the airflow deficiency is real and the system is in the specified mode;
2. verify rotation, speed, filters, coils, dampers, terminals, and measurement boundary;
3. plot the current point on the correct fan and system curves;
4. calculate predicted flow, pressure, and power at the proposed speed;
5. check every manufacturer, motor, drive, vibration, and pressure limit;
6. obtain authorization and make the controlled change; and
7. remeasure actual airflow, pressure, RPM, and phase currents.

The actual point can differ from the simple prediction if dampers or controls move, density changes, the system curve changes, or the original measurements were not simultaneous. Preserve predicted and measured values so the difference becomes diagnostic evidence rather than hidden error.

Limits of prediction

The first-law flow prediction assumes the operating point follows a similar system curve. If a pressure-control loop moves dampers or resets a setpoint while speed changes, the system is no longer fixed. A dirty-to-clean filter change, economizer movement, VAV diversity change, or opened access door also changes resistance. In those cases, use the laws for a bounded forecast and then measure.

Density has a different effect on pressure and power than on actual volume at the same fan speed. Use the fan manufacturer's correction method when comparing a standard-density curve with field conditions. Do not stack a density correction onto a value that the instrument or software has already corrected. Record the curve basis and field basis beside the calculation.

For exam work, state the ratio first, apply the correct exponent, and check scale. A 10% speed increase cannot produce only a 10% power increase under the cubic assumption.