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Sorry, way out of my league. I am not even sure gases work the same as liquids. How big is the rest of the duct work? Even if you are limited to only 4'' at one point, It might be better to run a rectangular duct. I do know with liquids, half as big of a pipe creates 16 times as much pressure drop or more.
There are a ton of factors involved. I think the installation technicians do it scientifically. They set it up and turn it on. They measure the incoming air and the outgoing air. Then they set the blower speed to give the right difference in temperature. If you don't have room for big enough ducts, you may have to use a higher blower speed, a little more noise, and maybe a slightly shorter life for the blower motor.
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