No worries at all, there was a bit of rambling and ruminating going on in my notes. Much of the design and build was done in something of a blur - it all made sense at the time
the key measurement you are looking for is the cross sectional area of the path through the silencers. The entire design is based on this. This is based on how much airflow you need, and the required air velocity at the outlet. In Rod's book p.135 he says 15 cfm of fresh air per person is required. That's cubic feet per minute.
For pure ventilation, i.e. exchange of stale air with fresh air in the room for breathing and other purposes, I went with Rod's figure of 15 cfm per person. Five people would require 75 cfm.
I muddied the waters a bit by then going on about room volume, and worked out that I could get 6 room air changes per hour (109.4 cfm) while keeping the air velocity at the registers within the speed limit. What mattered was that this was more than 75 cfm. I thought the additional airflow might be useful as the room gets hot in summer due to heat from lots of South facing windows; and in the absence of air conditioning, bringing more cool in air from outside would be useful. It is! In fact I can get up to about 12 room changes per hour with the fan at full speed. This means air exceeding the speed limit at the registers, but it's fine for "surge capacity", e.g. you can run it like this during breaks. Or if some uncouth muso breaks wind
If this is not important to you though, according to Rod, 75 cfm would be enough for 5 people. Adjust according to the maximum amount of people you'll have in your room. You may prefer to base normal airflow on normal use. E.g. one mix engineer, one client, would be 30 cfm. Maybe it only gets busier occasionally, and those occasions would permit exceeding the airflow speed limit at the register. If you let us know what your requirements are it would be useful.
See what I mean about rambling? Anyway!
Assuming 5 people and 75 cfm, the cross section area of the silencer can be calculated:
CSA = CFM/300 = 75/300 =
0.25 ft2 ~=
232 cm2From Gregwor's silencer design for 3 baffles, with X=20 cm, Z=18 (gives 360 cm2 cross section), 25mm duct lining, 25mm walls, silencer outer dimensions are
36mm walls (2 x 18 OSB) is;
Y = 597mm
X' = 1126mm
Z' = 302mm
These were the external dimensions of the entire silencer box design. X' reads X dashed and is something I've retained from my old high school mathematics days. From what I recall, X' is like another version of X that is related to but not the same as X by a formula or transformation.
You're correct that in Gregwor's box design, Y is related to X. This is to preserve the same cross section area throughout as much as possible.
What you have to do next is establish how much airflow you need, then design the silencer in reverse as it were, and try to make it match the required airflow. It seems you have to limits on the external size of the box by the surrounding cavity which is:
Y = 500mm
Z' = 170mm
You'll have to allow fit tolerances for those though, so allowing 20mm on each side, in practice you could end up with;
Y = 460mm
Z' = 150mm (I'm assuming either the bottom or top can be in contact with the leaf it is part of, so only deduct 20mm)
Let's go into imperial units to make it easier to work with Gregwor's box design;
Y = 460mm = 18"
X = (Y - 7) / 2
= (18 - 7) / 2
= 5.5"Z is based on the height, 150mm = 6 inches. The sides of the box will be 2" thick in total, the duct liner will be another 2" thick in total. This leaves
2" height within the box.
This gives the path through the silencer a cross sectional area of 5.5 x 2", i.e. 11 square inches.
This is equivalent to 71 cm2.
But to get the required airflow at less than 300 ft/min at the register, the cross section should be 232 cm2.
So the cross section through the silencer is not big enough for sufficient airflow for 5 people at less than 300 ft/min. It's not even enough for two.
With the above design, your only option would be to have the fan move the air through the silencer quicker than our specification allows. This will increase noise, drafts in the room, and increase the static pressure of the system, requiring the fan to work harder, which will make it noisier....
A small optimisation might be to have the top or bottom of the silencer made from e.g. the actual ceiling leaf itself. This would gain you an additional inch of Z, so cross section is now 5.5 x 3", i.e. 16.5 square inches. Still not enough!
As a last resort you can mitigate some of these problems to some extent with a larger end chamber as per Glenn's diagram, or a plenum inside the actual room. But you'll still be left with the higher static pressure.
Workarounds may be possible, but before that, are you with me so far?
Cheers!
Jennifer