Good math, Katoman... most guys think that you can just add the same amount to one side as you subtract from the other, and keep the perimeter the same a la changing a 20x20 duct to 24x16... obviously you'll lose out on the total area. An example I used to throw out is, "Okay, you have 20x20 with an area of 400 square inches... add/subtract 10 and you'll have 30x10, a 25% loss with area 300 square inches. But hey, why not add/subtract 19 and call it 39x1? Then you'd have 39 square inches... a 90% reduction in area."
BUT as Beenthere pointed out, it's not a raw area calculation. A minor change would be no big deal but the "equal friction loss method" is based on the perimeter length of a cross section of the duct, the amount of metal that comes in contact with the flow of air. (This is why round pipe is the ideal shape for duct: max. area with min. perimeter = min. friction loss. And of course for obvious reasons this never comes up for the transfer of water...) Beenthere used a sliderule device called a "ductulator" which shows how we figure the ductwork. And he's also right that when the length is more than 7 times (or inversely, less than 1/7th) the width, the ductulator isn't very accurate. SO while I have installed 90x10 oval duct spiral pipe, but I do not know how they sized it.
If you absolutely MUST have 4 inches of duct height, you are not out of options, but you'll need a good shopman tinknocker to make this work. In a nutshell, you split the 14x8 duct into TWO 14x4 ducts, keeping the top of the fitting flat. It's a kinnnd-of tough fitting, but doable. I made them back when I was working with my hands in this trade. This type of fitting is called a "pair of pants" because there is one duct "wye-ing" into two (usually smaller) ducts, like a pair of pants has a big hole for the waist then wyes into to smaller sections, like pants legs. [Beenthere: Do you agree with this? Please tell us.]
And yeah, don't exceed 15 degrees taper... I think I was taught to use 21 degrees per SMACNA or whatever, but the longer the fitting is, the shallower the angles are, the more laminar flow you'll have for your air.
I spent 12 years in the field (on the job sites and in the shop fabricating duct, fittings, etc.) so I'm not just talking down from the desk side of a blueprint... if anyone has any other issues with duct, please contact me. I'm always glad to help.
Gugh, it's New Years Eve and I'm here talking about ductwork. Maybe I DO need to get out more!
