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Regenerated Noise from Duct Fittings (Detailed)    1/1, 1/3

Strutt|Mechanical Services|Regenerated Noise|Fitting allows the user to calculate the regenerated noise level from a duct fitting based on its flow characteristics (including the pressure loss factor zeta).

This method can be used for duct fittings (other than duct terminations, for which the Regenerated Noise from Duct Termination/Grille calculation should be used in the absence of detailed manufacturers data). Although derived for rectangular ductwork, it is also applicable to circular ductwork.

Regenerated sound power levels are calculated as follows:

L_W={(-37+20log(K(bbbSbbbt))+20log(zeta)+10log(A)+40log(u) \ " for " f < f_c),(-84+20log(K(bbbSbbbt))+20log(bbbSbbbt)+10log(zeta)-40log(sigma)+10logA+60log(u) \ " for " f ge f_c):}

where:
zeta is the pressure loss factor (from tabulated mechanical data, e.g. CIBSE Guide C)
sigma = (zeta^(1//2)-1)/(zeta-1) is the clear area ratio in the duct
K(bbbSbbbt) is an experimentally-derived factor related to the Strouhal number bbbSbbbt for the duct flow, from Figure 5.A.2.3 of CIBSE Guide B
bbbSbbbt=(fd)/v_c is the Strouhal number. The calculation is valid for bbbSbbbt values from 0.1 to 200
v_c=u/sigma is the velocity through the flow constriction (m/s)
u is the duct flow velocity (entering the fitting) (m/s)
d=b(1-sigma) is the characteristic duct dimension (m)
b is the duct dimension in the dimension of flow constriction (e.g. the dimension of a duct bend) (m)
f is the frequency (Hz)
A is the duct cross-sectional area (m²)
f_c = c/(2l) is the cut-off frequency for plane wave conditions (i.e. at f < f_c plane wave conditions exist)
c is the speed of sound (m/s) [343 m/s by default]
l is the longest duct cross-sectional dimension (m)

Reference: CIBSE Guide B (2005) Appendix 5.A2