Noise generated in Air Ducts
Estimate noise generated by air flow in ducts.
Air flow in ducts generates noise. The noise in the duct is determined by
 air velocity
 duct size (cross sectional area)
Generated noise can be calculated with the empirical equation
L_{N} = 10 + 50 log (v) + 10 log (A) (1)
where
L_{N} = sound power level in the duct (dB)
v = air velocity (m/s)
A = air duct cross sectional area (m^{2})
The equation modified for imperial units
L_{N} = 10 + 50 log (v_{i} / 197) + 10 log (A_{i} / 1550) (1b)
where
v_{i} = air velocity (ft/min)
A_{i} = cross sectional area (in^{2})
Example  Generated Noise in Duct by Air Flow
The cross section area of a 200 mm duct can be calculated as
A = π ((0.2 m) / 2)^{2})
= 0.0314 m^{2}
The noise generated in the duct with an air flow velocity 10 m/s can be calculated as
L_{N} = 10 + 50 log (10 m/s) + 10 log (0.0314 m^{2})
= 45 db
The noise generated in the same 200 mm circular duct as above with air flow velocity 20 m/s can be calculated as
L_{N} = 10 + 50 log (20 m/s) + 10 log (π ((0.2 m) / 2)^{2})
= 60 db
Note!  due to the noise generated by fans  noise generated inside ducts by air flow can in general be neglected.
Related Topics

Acoustics
Room acoustics and acoustic properties, decibel A, B and C, Noise Rating (NR) curves, sound transmission, sound pressure, sound intensity and sound attenuation. 
Noise and Attenuation
Noise is usually defined as unwanted sound  noise, noise generation, silencers and attenuation in HVAC systems.
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