An 8" round duct is required from beginning to end (including the termination on the roof or outside wall) for a 600CFM Vent-A-Hood. Alternatively, you can transition from round to rectangular ducting, as long as the rectangular ducting is equivalent in size. An 8" round duct encloses approximately 50 square inches. You don't mention the type of cooktop or range that you will be venting. If it isn't a pro-style gas range, you very likely could go with a 300CFM model which requires a 6" round duct (approx. 28 sq. in.). I have a 600CFM Vent-A-Hood over a 36" Gaggenau gas cooktop. About 95% of the time it runs on the lowest SensaSource setting with only a single blower going. It vents very effectively (and quietly) at that speed. Unless I'm cooking something over very high heat that generates a lot of smoke, I almost never turn on the second blower. Your contractor should be able to find a way to install the appropriate sized ducting. If not, call an HVAC/sheetmetal contractor. Installing a new, properly-sized duct through the attic, through joist spaces, or through a side wall shouldn't pose an insurmountable problem.

Here is the info I gave out to my bible study group when I demonstrated yogurt making: "This yogurt comes out like Dannon plain then you have to drain it for several hours to get a Greek Yogurt. Here's how I do it. I do it exactly the same everytime, this is important. Vary the jar sizes slightly, of course, to suit your needs. 1 small cooler-hard igloo type 2 mayo jars or mason jars- (1 quart size) with lids candy thermometer 2 thick towels 8 cup Pyrex glass measuring cup or similar sized bowl for microwave Milk plain yogurt powdered milk- optional Measure the amount of milk into measuring cup that is the same amount that will fit in your 2 jars. For 2 mason jars this about 8-9 cups. Stir in 1/2 cup or so of powdered milk if using. Bring to a boil in the microwave uncovered. In my microwave this takes about 20 minutes. Doesn't have to be rolling boil but should bubble. Remove from microwave, snap on candy thermometer and let sit until it reaches 120 degrees. About 45 minutes. Meanwhile, put a dollop (tablespoon more or less) in each jar. Have ready a stock pot on stove of water. Don't heat yet. Remove skin on milk and fill each jar with 112-120 degree milk and stir. Place both jars in cooler and close lid. Heat water on stove now, insert candy thermometer and heat to 120 degrees. This only takes a few minutes. If you go over 120, use ice cubes to bring the temperature back down. Pour 120 degree water into cooler to edge of lids. Don't cover lids. Put the top on the cooler, set in a place it will NOT be disturbed for 8-12 hours, cover with 2 thick towels. The next day, remove yogurt jars, refrigerate until ready to drain. To drain, I use a large white plastic colander. You just need a big strainer. Set over a bowl. Line strainer with coffee filters (4) and scoop out all yogurt into strainer. Cover with a dishcloth. Strain as long as you want. I usually use the Pyrex bowl that I microwaved the milk. My white plastic strainer fits nicely on this and I can see how much whey is strained. 2-3 hours produces a Greek yogurt; overnight, almost a cheese. Flop the strainer over into a pan and peel off the coffee filter. Much easier than scooping. Notes: - I have left the jars in the refrigerator for 2 weeks before straining. - Use a good quality yogurt. I use Stonyfield Farms because it has several more active yogurt culture varieties than Dannon and is better for you. -Use whatever milk you want to use. 1%, 2%, whole, organic, etc. I use skim. To give it more body, to the 8-9 cups of milk before microwaving, I stir in 1/2 cup of powdered milk. The taste and texture of the powdered milk will not be discernible. - Moving the cooler while the yogurt is in it will cause it to not set up. - I usually make the yogurt at night while doing chores, watching, tv. etc. Very little hands on time. -The drained whey may be used to make ricotta cheese. - Drained yogurt has less calcium than regular! A lot of the calcium is in the whey. - The Stonyfield Farm yogurt may be frozen in dollops for future use. -Use some of your homemade yogurt next time you make yogurt though. The frozen yogurt is only for when someone eats all the homemade and doesn't leave enough for a starter. - If the milk cools lower than 112 degrees, heat it back up and cool again. Don't have to reboil. Just heat enough to get temp. back up. -Store the candy thermometer carefully! Think of it as a fine piece of crystal. -If making 4 jars, I use 2 coolers. The water, size, ratio is important. - Do not stir the yogurt."

I did. The low profile Broan Elite 36 inch vent fan that I installed can be configured to vent straight back through a 3 1/4"x14" rectangular duct or straight up through a 3 1/4"x14" duct. This rectangular duct is designed to fit completely within a 2x4 framed wall. My ducting enters the wall, and immediately turns straight up, proceeding up until reaching a soffit between the wall and an exposed structural beam. Inside the soffit it transitions to a 8" diameter round duct, turns slightly to match the roof angle, and continues through a hole I cut in the roof, where it is covered by a black metal roof vent cap. I found the local Lowes and even a local HVAC supply store to be unhelpful, and ended up having to order the needed ducting pieces from a couple of places on the interwebs. I don't remember where I ordered the pieces from, but in trying to find where I purchased them from I found an old Gardenweb post by me where I wrote: "I ordered the transition and roof cap from AirShack.com. The 3 1/4 X 14 inch, 90 deg elbow was really hard to find. I ended up ordering 2 of them and a 3 foot stretch of 3 1/4 x 14 inch duct from a different online location (that I won't name because they charged $41 for shipping for those three items) "

The answer to the question is use the larger duct for as much length as possible. From the description, it seems that it could be 6-inches over most of the length, raising the question of why the last bit couldn't be cut larger. Note that duct transitions should be gradual and not abrupt. Your 400 CFM rated blower can only do some lesser flow rate when subjected to pressure loss, some of which is in the hood itself, some of which is in the make-up air path, and the rest in the ducting. Suppose you could actually achieve 200 CFM. Then 4-inch duct would have to be flowing 2300 ft/min, a higher value than desirable and likely to have more pressure loss than the 200 CFM assumption might have assumed. So maybe 100 CFM. You will be in the average condition of 1950s hoods, so all you need is a larger duct to move into th '90s. :)