HVAC register sizing.

There are more scientific ways to look at the problem but the idea of an output register is to diffuse the air flow to both spread the coverage and to reduce noise from excessive air turbulance. It is not uncommon for a register to have twice the aread of its feed duct. There are couplers/adapters made for the change in shape and area or you might need a custom made one depending on your specific needs. Hope this helps.

First- a quick course in terminology.

Any device that expels air in an Jet-Like fashion is a grille. If it has an internal damper, it is a register.

Next issue- What is the ceiling height of the room and is the 9 foot mounting height to the top or the bottom?

Reason for asking is because- if the top of the register/grille is within 12" to 18" of the ceiling the air will tend to "hug" the ceiling and you will get both better spread and throw. If the outlet is much lower than that, it will slow down very quickly (less than 60% of "normal" distribution and you will cause drafts in the occupied zone.

Several HVAC outlet manufacturers have very exact data on how far the throw and how wide the spread will be. You can likely access their catalogs on-line. I recommend the Titus brand- they have a very wide variety of outlets.

The jet outlet from these type of devices travels linearly, meaning that- if a room is 20 feet wide with 10 foot ceilings and you select a throw of 25 feet, that throw will "terminate" (achieve the defined final velocity) 5 feet down the wall.

When you size the outlet, you want the throw to be based on a 50 FPM terminal velocity and you want that velocity to occur about 3 feet from the opposite wall to prevent "drafts" along the wall- humans can generally detect air motion above 35 FPM so you want to keep it slower than that in the occupied zone- especially if it is cool air.

By the way, the nature of grilles is that they induce about 4-5 times more air from the room than is being supplied. Therefore, even "cold" supply air is quickly warmed up (that is how the air cools the room) to within a few degrees of room temperature. But, if there is a draft, the occupant will feel cold even if the air is 72F in a 74F room.

Hope this helps.

for selecting the register /grill /diffuser consider velocity of 500 feet per minute and select. The register shall be a diffuser if it is ceiling mounted or Grill if it is in vertical position.

Ensure return air is at least 1.5 times bigger than supply air. If it is more it will be better.