So, as an example if I used a round 4" duct then the cross sectional area would be 12.56" is that correct? Then the cross-sectional area of the passage way through the silencer baffles needs to be constant (i.e. same width and height?) and at least twice that of the duct... So would I measure the width and height of the passageway to work out the area but not the length of the passageway? I am so confused
I will bet my life savings that your room needs a way bigger duct than a 4" RD feeding your silencer. I didn't look to see how big your room is but you probably need an 8 or bigger.
Here is my answer for your cross sectional area question copy/pasted from my notes:
Cross sectional areas of common duct:
Area of a circle = π r2
Radius = half of the diameter
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)
To answer your question about the path inside your silencer, it needs to at LEAST double in cross sectional area. It certainly does not have to be a square (equal height and width) path. However, the more square it is, the less pressure drop with be introduced which is very important in your design.
Addressing your comment regarding a constant size, the CSA within the silencer can change. Actually, the more changes, the more attenuation. However, realize that with each CSA change, a pressure drop is realized. Remember, the larger the CSA change, the more the attenuation. So, on your Y split type box, I would double the CSA on each half. This would essentially quadruple the CSA of the inlet. This will also really slow down your air velocity, reduce the static pressure drop and reduce the air movement noise within the box.
The noisy ventilator would be in a different room, then the supply and return coming directly off of it would go through their own silencers, then through the 2 leaves without rigid connection in the cavity, then into silencers again, then the control room ducts, then the vents in the room. Is this not correct?
So, you are using a forced air ducted system? Not a ductless mini split? Your statement seems to be correct.
So it seems that I should use rigid duct in the actual rooms, but flex duct in the cavity. What type of rigid ducting would you recommend? Galvanized metal? And would round be better than rectangular?
Once it's in your room, you can use whatever you want. RD always has the least friction coefficients. Rect allows you to maximize space. Remember, inside your room you should always use duct liner.
Also, from what Rod has said, the ducting coming out of the silencers in the control room can be small so long as the silencer brings the velocity down... so would that mean the silencer box needs to double the cross sectional area of the duct work feeding it? (from the ventilator)
You've misunderstood his point. I'll try to explain this better:
The CFM is a constant throughout a duct run.
Air velocity in ft/min = CFM Flow rate in ( ft3/min) / CSA Cross sectional area in ft2
So, if CFM is a constant, then the velocity changes depending on the CSA. So, if you have a smaller duct, your velocity will increase. If you use larger ducts, your velocity decreases.
In your room, you need to achieve a maximum of 300 feet per minute at your register/grille. So yes, you COULD use smaller duct inside your room as long as you make your CSA large enough to reduce the air velocity before it hits your register/grille. However, you will increase your pressure drop and air noise inside those ducts. Duct liner will help with the air noise.
Most importantly, you want to deal with turbulence noise introduced by any change of direction or CSA change. You could use a conical transition which would not allow you to gain the immediate CSA change (insertion loss achieved by a gross impedance mismatch). A gradual change in CSA like a cone (or wave guide) provides will prevent distortion or turbulence, the true rule of thumb is that you need a certain distance between any direction change or CSA change and the mouth of your grille/register. I've heard two values for this distance. It's either 3 or 5 times the diameter of that which is feeding the grille/register. So let's say your have a 4" round duct that goes to a required 6" round grille, you'd need a distance of between 12 and 20" of straight duct to prevent noise at the mouth.
If I say there would be a maximum of 10 people in the control room (more likely it'll only be 5 or 6, but you never know) then how what do I need to look for in terms of specs for either a fan or HRV? I know that it needs to provide enough fresh air for each person (15cfm) with 6 exchanges per hour, so does that mean I need a fan or HRV that is rated at providing 150cfm?
Purely for the required 30% fresh air circulation, you can figure it out like this:
Flow rate in CFM = ft3/min = [# of air changes per hour X cubic volume of room] / 60 min
# of air changes must be at least 6 changers per hour
Air velocity in ft/min = CFM Flow rate in ( ft3/min) / CSA Cross sectional area in ft2
This is actually expressed as v=q/A
Air velocity must be less than 300 ft/min for studios
So, if you need 30% fresh air, take your total CFM and calculate 30% of it. That would be your fresh air CFM. Size your HRV or fan based off of that.
Sizing your actual air handler unit is a different story though as you need to need to figure out your sensible and latent loads.
Then, how does the ducting effect it? If I run it through a ducting calculator it says my ducts should be about 8" for a round duct, but does length of duct effect that?
Typical duct sizing calculators assume a 0.1 friction rate. You can use these to calculate your runs from your air handler to your silencer boxes. From the boxes to your register/grilles you need to size these based on your velocity and CSA changes. Once you've sized everything this way, you need to calculate your total static pressure. If your blower will not run within your system pressure, you may have to change your duct sizing from the air handler to the silencer boxes and then ultimately, that may change everything down the line!
how about if you split it into two ducts at 90 degree angles?
That introduced a pressure drop. These are the things you calculate later to determine your total static pressure. Using 1.5x radius bends instead of 1x can help as well. To be honest with you, I made my own spreadsheet to calculate this because I could find no good resources online. It's a chore and takes hours to calculate
Then, as Rod says, if you make your silencer big enough you can decrease the size.
Again, changing the CSA achieves insertion loss. As I mentioned before, it has negative side effects as well. Another reason to have a large CSA throughout your box is because all of those sharp corners introduce a ton of static pressure. The bigger the path, the less pressure drop!
.. but by how much? These are the types of questions I need help with, so if you could help I'd really be grateful.
If you look at this picture, you'll see that even when we double or halve the CSA, we aren't achieving great levels of insertion loss. That's why I suggest that you double each half of your Y box so that you are quadrupling your CSA!
Insertion Loss Graph from Engineering Acoustics 2009.png
These sort of details are the ones you have to make informed decisions on while designing your studio!
Greg