Fans — Noise Power Generation

Fan Noise Power — Deep Dive (What Drives L_N and How to Use These Formulas)

Fans generate broadband noise as blades interact with moving air, pressure gradients, turbulence, and any flow separations near the housing or duct openings. A quick way to estimate overall sound power level \(L_\mathrm{N}\) is to use empirical relations that tie acoustics to operating point. In SI units \((S\ \text{in kW},\ p\ \text{in Pa},\ Q\ \text{in m}^3/\text{s})\):

• \(L_\mathrm{N} = 67 + 10\log_{10} S + 10\log_{10} p\)   (1a)
• \(L_\mathrm{N} = 40 + 10\log_{10} Q + 20\log_{10} p\)   (1b)
• \(L_\mathrm{N} = 94 + 20\log_{10} S - 10\log_{10} Q\)   (1c)

Each expression uses a different pair of easily measured quantities. (1a) is convenient when you know the motor power and static pressure rise; (1b) emphasizes how both flow and pressure drive noise; (1c) links noise more strongly to power while penalizing very high flow for a given power. These relations produce an overall level in decibels referenced to acoustic power (L_w style). They are meant for screening and planning—for certified values or octave-band data, always rely on the manufacturer’s test reports.

Why the Logs? (Physical Intuition)

Aerodynamic noise scales nonlinearly with operating point. Doubling a driver (e.g., power or pressure) does not simply add a fixed number of decibels; instead the underlying acoustic power tends to scale with a product of flow and pressure terms. Taking \(10\log_{10}\) converts that multiplicative behavior into additive “+dB per decade” rules of thumb—handy when exploring sizing options or comparing fans.

Sound Power vs. Sound Pressure

The calculator estimates sound power level \(L_\mathrm{w}\) (here noted \(L_\mathrm{N}\)). This is a source property. What you hear or measure on site is usually sound pressure level \(L_\mathrm{p}\), which depends on room volume, distance, directivity, duct terminations, and absorption. To move from \(L_\mathrm{w}\) to \(L_\mathrm{p}\), you need a room/duct model (spreading losses, insertion losses, room constants, etc.).

Spectrum, Weighting, and dB Math

Overall levels hide spectral details. Many specifications require octave-band data and A-weighting \(L_\mathrm{A}\) to reflect human hearing. If you need A-weighted totals, apply A-weights to each band and then perform proper dB addition: \(L_\text{total} = 10\log_{10}\!\left(\sum_i 10^{L_i/10}\right)\). Never add decibels arithmetically.

Operating Point & Affinity Laws

For geometrically similar fans: \(Q \propto N\), \(p \propto N^2\), and \(P \propto N^3\) with rotational speed \(N\). Because the formulas include \(p\), \(Q\), and \(S\), noise generally climbs quickly with speed and with throttling that raises static pressure. Moving closer to surge or stall, or operating off the best-efficiency point, often increases tonal components and broadband noise.

Installation Effects (The Hidden Gotchas)

• Inlet/Outlet conditions: Elbows tight to the fan, grilles, or poorly designed transitions introduce swirl and separation that elevate noise.
• Duct breakout and casing radiation: A higher \(L_\mathrm{w}\) at the impeller may not be the only contributor—thin casings and unlined ducts radiate too.
• Vibration & structure-borne paths: Even with the same \(L_\mathrm{w}\), poor isolation can transmit energy into building elements that re-radiate sound.

Practical Use & Limitations

Use (1a)–(1c) for ballpark estimates, option screening, and sanity checks against datasheets. Expect deviations due to blade type (axial vs. centrifugal), tip clearance, Reynolds number, and manufacturing tolerances. For design commitments or code compliance, request certified AMCA/ISO sound power data across octave bands and verify with a full system model (duct losses, silencers, enclosures, and room acoustics).