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Flow Resistivity Calculation    1/1, 1/3

Strutt|Fundamentals|Flow Resistivity calculates the flow resistivity (in mks rayls) for different types of porous material and inserts it into the current row of the worksheet.

The formulae used are obtained from Table 5.1 of Cox and D'Antonio, as follows:

Parallel to the fibres, all fibres having the same radii:

sigma=(3.94 eta (1 - epsilon)^1.413 [1 + 27(1 - epsilon)^3])/(a^2 epsilon)

Perpendicular to the fibres, all fibres having the same radii:

sigma=(10.56 eta (1-epsilon)^1.531)/(a^2 epsilon^3) 6<=a<=10 mu m

sigma=(6.8 eta (1-epsilon)^1.296)/(a^2 epsilon^3) 20<=a<=30 mu m

Random fibre orientation, all fibres having the same radii:

sigma=(4 eta)/(a^2) [(0.55(1-epsilon)^(4/3))/epsilon + (sqrt(2)(1-epsilon)^2)/epsilon^3]

Random fibre radius distribution with a mean radius of a and random fibre orientation:

Fibreglass: sigma=(3.2 eta (1-epsilon)^1.42)/a^2

Mineral fibre: sigma=(4.4 eta (1-epsilon)^1.59)/a^2

Polyester fibrous materials, where:
18<=2a<=48 mu m
12<= rho_m <= 60 kg//m^3

900<= sigma <= 8,500 rayls//m

sigma = (25.909*10^-9 rho_m^1.404)/(2a)^2

Polyester fibre, where:
6<=2a<=39 mu m
28<= rho_m <= 101 kg//m^3

4,000<= sigma <= 70,000 rayls//m

sigma = (15*10^-9 rho_m^1.53)/(2a)^2

Sheep wool, where:
22<=2a<=35 mu m
13<= rho_m <= 90 kg//m^3
sigma = (490*10^-6 rho_m^1.61)/2a

Wood materials with short fibres:

sigma = 20.8 rho_m^1.57

2a~=30 mu m

Loose granular material:

sigma = (400(1-H^2)(1+H^5)eta)/(HD)

H=1-rho_m/rho_f
Note: Table 5.1 in Cox and D'Antonio has mu in place of eta. This appears to be a typo as the symbol mu is not defined elsewhere in the text. Strutt uses eta.

Where:
a is the radius of the fibres
eta = 1.84*10^-5 is the viscosity of air
epsilon = rho_m/rho_f is the porosity of the material
rho_m is the bulk density of the material
rho_f is the density of the fibres (or granular material)
D is the characteristic particle dimension:
D^2=V_g/0.5233 where V_g is the number of particles per unit volume.

Reference: Cox and D'Antonio Acoustic Absorbers and Diffusers, 2nd Edition, p171