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I watch my dashboard for searches. There have been a few looking for duct size designs.
Supply air duct sizes are determined by how much air (cfm) is to be delivered to a specific area of a civil structure (home). If a bedroom is 12 x 12 feet, or 144 square feet, and the ceiling is 8 feet, the volume is 1152 cubic feet. The velocity of the air, going through the ceiling grill, or floor grille, will affect the amount of air noise in the room. I prefer the more acceptable velocity of 500 feet per minute (fpm). Therefore, if you wish to exchange the volume of air in the room 5 times per hour, at 500 fpm, the diameter of the branch duct feeding the ceiling, or floor grille, would be 9 inches. That’s a little faster (tiny), at .06 friction per 100 foot of duct, but that depends on whether you use round metal, or flexible duct materials. A rectangular branch duct would include sizes from 8 x 9 inches to 4 x 20, and 6 1/4 x 12. Transitioning from round ducts to rectangular ducts, and back, is an acceptable way of adapting to structural elements, and maintaining correct air distribution throughout the air distribution system (ductwork). Since the furnace, or air handler is probably rectangular the first transition might be a plenum, on the furnace, or air handler to round ductwork. The plenum is where most air distribution mistakes occur.
From the ceiling, or floor grill, the main, and other branch, duct sizing back to the furnace, or air handler, is proportionally sized to include volumes of air to be delivered to other spaces along the way back.
I used a Trane Ductulator, I have had for 30 years, to find the numbers above. In the past, I used the equal pressure method for designing air distribution ductwork systems. That’s where the friction per 100 foot of duct comes in. However, it’s quicker to use velocity, and volume to do the designing because of air exchanges between rooms (spaces), and it all seems to balance out ok.
Another example could be; when deciding between a 14 inch and a 16 inch return air duct, choose the 16 inch. The furnace, or air handler generally won’t take in any more air than it can deliver, and won’t deliver any more air than it takes in, and it will slow down the air velocity through air filters located in a return air grille. Filters located in the furnace, or air handler are exposed to higher velocities.
See ya