I'm assuming you are going with at ductless mini-split unit on the wall of the booth? If so, then your math looks good so far. 22.4 FPM is the "make-up" fresh air that you are sucking on from outside, so that's what would be coming in through the register just above the mini-split. (If I got that wrong and you are using a ducted mini-split, then things are different....)
So, what you have now is the size that the REGISTERS need to be: the grill things that let air into the room, and take it back out again. That's the purpose of that part of the math: to figure out the register size, such that the air velocity will be low enough. The reason being: if the air is moving too fast through the register, it creates noise! Keep it slow, and it will be silent.
The next step is to figure out duct size. The ducts can be smaller than the register size: there's no need to restrict the air flow velocity in the ducts to be as slow as through the register. It an be two of three time faster, if you want. So the cross-sectional area of the duct can be 1/2 to 1/3 of the area of the register. Assuming you want round duct, divide the area by pi to get the diameter. So, 17 in2 / pi = 5.4. To get the SAME velocity as the register, the duct would need to be 5.4" diameter. But the duct can be smaller (see above), so a 4" duct would be fine. I wouldn't go smaller than that.
Next step: The silencer box should have at least one sudden transition in cross section, and the difference should be as big as you can make it, but at least twice the area (or half the area). Assuming 4" round duct, the cross-sectional area of that is about 12 in2, so you'd want to have an internal cross-section of at least 24 in2, so 6x4" minimum, but 36in2 would be better, so 6x6": However, perfectly square sections are not such a good idea, so go up another step: make it 5x7, or even 6x7. Don't forget to allow for the fact that the interior surface of your silencer box should be covered with 1" thickness of proper duct liner, which means the internal size of the box itself it needs to be 2" bigger: thus, if you were planning on 6x7 open area, you would need 8x9 internal box size.
2- I'm cooling/heating my house with a central unit...So the air from my house circulate from room to room / floor to floor . Do I need to add ERV/HRV Unit ?
Ahhh! So you won't have any mini-split in the room itself? You will just be bringing in a branch duct from the main HVAC duct for the house, and taking out another branch duct to the main return duct? Great! That makes your job easier.
Do I need to add ERV/HRV Unit ?
No. If you did need one, that would be for the entire house, not just for your room. The house HVAC system would have the HRV on it, if there was a need for one. Your booth just takes a feed from the main house system, and returns the stale air into the main house system as well. You are relying on the main house system to do all of the conditioning for you, so you don't need to do anything additional. Worst case: you might need a small fan in one of the ducts, but even that probably isn't necessary. As long as the house system has enough capacity to handle the extra ducts and silencers, you wouldn't need that.
- Stuart -
