Ducts Noise Generation

Overview

Engineering reference data for Ducts Noise Generation in acoustics.

Key Formulas

Speed of Sound

$c = \sqrt{\gamma R T}$

Speed of sound in an ideal gas.

Sound Level

$L = 10 \log_{10}(I/I_0)$

Decibel level.

Wavelength

$\lambda = c / f$

Wavelength = speed / frequency.

Variables

Air Flow Noise Formulas

The noise generated by air flow in ducts can be estimated using these empirical formulas.

SI Units: $L_N = 10 + 50 \log(v) + 10 \log(A)$ where:

• $L_N$ = sound power level (dB)
• $v$ = air velocity (m/s)
• $A$ = duct cross-sectional area (m²)

Imperial Units: $L_N = 10 + 50 \log\left(\frac{v_i}{197}\right) + 10 \log\left(\frac{A_i}{1550}\right)$ where:

• $v_i$ = air velocity (ft/min)
• $A_i$ = cross-sectional area (in²)

Practical Example

For a circular duct with diameter $d = 200\text{ mm}$:

1. Calculate cross-sectional area: $A = \pi \left(\frac{0.2\text{ m}}{2}\right)^2 = 0.0314\text{ m}^2$

2. Calculate noise generated at different velocities:

   • At $v = 10\text{ m/s}$: $L_N = 10 + 50 \log(10) + 10 \log(0.0314) \approx 45\text{ dB}$
   • At $v = 20\text{ m/s}$: $L_N = 10 + 50 \log(20) + 10 \log(0.0314) \approx 60\text{ dB}$

Important Note

The noise generated by air flow inside ducts is typically negligible compared to the noise generated by the fan itself. This duct noise is most significant at high velocities or in larger ducts.

References

• Original Source