I can't seem to find the instructions on how to calculate the size required for the silencer boxes, and how to construct them. I'm sure there must be a thread, could someone point me to the right one? I found Gregwor's silencer box with the algebraic dimensions, but how do I calculate the what X value I need?
Since plan to use the existing electric heater in the space and not worry about cooling, you only need to replace ~25-30% of the air compared to a ducted system.
Needed flow rate = (at least 8 air changes per hour X cubic feet )/60 min
30% fresh air = Needed flow rate x 0.3
Once you know how many CFM you're pushing/pulling through your system, you can find out roughly how big the duct needs to be to hook up your inline fan by referencing a standard friction rate of .10 inches per 100 feet of lineal duct chart such as this:
Residential Duct Sizing Guide.png
From there, you can calculate the cross sectional area of the duct. Here's a quick list to save you from doing the math yourself:
Duct CSA:
4” RD duct = 12.57 sq in. Double = 25.14 sq in.
5” RD duct = 19.63 sq in. Double = 39.26 sq in.
6” RD duct = 28.27 sq in. Double = 56.54 sq in.
8” RD duct = 50.27 sq in. Double = 100.53 sq in.
9” RD duct = 63.62 sq in. Double = 127.23 sq in.
10” RD duct = 78.54 sq in. Double = 157.08 sq in.
12” RD duct = 113.1 sq in. Double = 226.19 sq in.
Area of a rectangle = width x height
Area of a oval duct = major radius x minor radius x π
This is for a true oval, not a flat oval like HVAC duct though :-S
Area of flat oval = π (minor radius)2 + [(major diameter- minor diameter) x minor diameter)]
OR
[(π minor 2) / 4] + 3 (major - minor)
You can see in the list above that I've indicated what double the CSA would be. This is the minimum cross sectional area that the path inside your silencer box needs to be. If you could quadruple it instead of doubling it, that would be better. Just for fun, let's say you need a 10" round duct from your fan. Your box would then need to be at least 157.08 sq inches inside. So, if you had a simple square air path in your box, you could take the square root of 157.08 sq inches and end up with ~12 1/2".... let's be cool and increase that a bit to play it safe. So, 12 3/4" putting us at a healthy 162.56 sq inches. So, in the silencer box design image I made, 12 3/4" would be the value for "x".
Also, we should make sure that our velocity is good coming out of the box into your room.
In my 10" round duct example, let's say that the air velocity out each baffle will be 162.56 sq inches. In order to calculate the air velocity (which we need to be slower than 300 feet per minute), we need to convert our opening size from square inches to square feet. So, we simply divide our sq inches by 144 to get that value. 162.56 sq in / 144 = 1.1289 sq ft.
So, to get the air velocity, we do this:
30% fresh air CFM / 1.1289 sq ft = velocity in ft per min
If for some reason the air velocity is faster than 300 feet per minute, you will have to increase the size of the opening feeding your room. Or, if you have the space to have a bigger silencer box, simply make the entire thing bigger because it will also improve your insertion loss!
Lastly, you have to find an inline duct fan to push or pull the air in/out of your room. To make life easier (for now until audiomutt, Chris, and I fine tune my static pressure calculator) I would recommend using 0.2 inches water gauge to spec out your fan.
If you use a legit brand such as Fantech, their website has a calculator on it where you can enter your CFM and such and it will show you if the fan will perform as you need it to. Don't worry if the fan is slightly over spec as you can put a speed controller on it to slow it down.
Fan Spec Static Pressure.png
Greg