"Self-Flow-Resistance" of Fine Perforated Metal Screens We mentioned above, that, although it is desirable, from the point of view of trying to achieve high transparency from perforated sheet, to aim for tiny perforations closely spaced, there is a danger in over-doing it. First, if the sheet is painted, the fine holes may get clogged and this would spoil the transparency altogether.
Second, if the holes are fine enough, they will act like the fine pores in a glass fiber absorptive blanket, and may introduce unwanted sound absorption. This would be particularly undesirable if all we want from the perforated metal is acoustical transparency.
Therefore, it is a good idea, once you have finished your design for acoustical transparency, to follow through with a calculation of the self-resistance of the perforated sheet that you have chosen, and calculate the absorption coefficient of the sheet without any filling. This is explained below.
Considering that there is a large range of possible perforation patterns, there are two extremes that we could consider, in calculating the self-resistance of the sheet. It depends on whether the holes are wide or narrow, compared with the length of the so- called "viscosity waves" that cause the unwanted absorption.
Since the theory for coping with "in-between" situations is not developed, we must calculate both values and use the higher of the two results. In addition, there is an end correction to be taken into account, as in our calculations of resonance frequency, above.
So our self-resistance is given by:
Rself = Ro + 2~Ro, where the value for Ro is the larger of the two following formulas, depending on whether the flow resistance is dominated by (1) boundary layer effects or (2) laminar flow:
