http://www.lg-vrf.com/indoor-units-ducted.aspx/Index

AC Duct from AHU( Air Handling Unit) in central a.c plants are designed based on Q= AXV;where Q is in flow rate ,A is Area and V is velocity. Higher he velocity( U need to compromise with sound) lesser the duct size. For unitary type a.cs you can check with suppliers catalogue.

The ducts should be sized to accomodate the air quantity required at maximum load unless you can tolerate some uncomfortable spaces during those times. Check your local codes for the minimum head room.

Lou Bindner

The building codes will provide minimum headroom; there are national building codes, but your locality (state, city, etc) may have its own code. I think they also have an exception for projections from the ceiling.

If bar joist construction, the AC ducts can be run thru the openings in the bar joist.