By careful measurement of wall distances over a path from one side to the other of the duct wall, it should be possible to determine the thickness of the wall. If it is a standard 2 x 4 stud wall, the cavity is 3.5 inches; if a less standard 2 x 6 wall, then the cavity is 5.5 inches. Neither of these will accommodate a 6-inch round duct, so transition to rectangular is likely. The third possibility is a double wall built to accommodate the round duct. It should be possible to distinguish these even with modest error in measurement. kas

Ah! you missed one of the versions of a comment I have added to quite a few threads. Here it is again. Because we do not get to close off parts of the hood not receiving cooking plume impact, all of the hood has to flow the amount needed at the most stressing part of the effluent plume to be contained at the hood baffle space. How much do we need? Well the actual issue is what velocity of air has to be pulled past the baffles to ensure that the rising plume is pulled into the baffles and contained, versus reflecting off of the baffles and potentially curling back into the room, thereby escaping the capture area and hence removal by the hood. Hot cooking plumes over gas burners can rise at velocities of 1.2 m/s, or almost 4 ft/s. The baffle gap is roughly half the baffle assembly area, so to entrain the plume flow, it seems that some portion of 4 ft/s or 4 x 60 CFM per sq. ft. of baffle area is needed for good containment. Actually, there is usually space under the baffles larger than the baffles proper, so adequate flow is needed all across the hood capture aperture. I believe that I have about 900 actual CFM at home, pulled through a 10 sq. ft. Wolf Pro Island hood. This is equivalent to 90 ft/s. This works over induction hobs, including searing and wok cooking with a 3500W Cooktek wok hob. As it happens, Greenheck also looked into the requirements for CFM, perhaps like me doubting that 100 CFM per ft. of hood edge had a mathematical connection to the process of cooking plume containment. They have published a range of values, and I have taken the liberty of copying their relevant table below. So take your hood area, multiply by some value you believe in for actual needed flow, then multiply by another factor to account for blower ratings not actually applying to the conditions in which they are used. (Another topic written about here more than a few times.) http://www.greenheck.com/media/pdf/otherinfo/KVSApplDesign_catalog.pdf No one has complained here that aiming for 90 CFM/sq. ft. of hood aperture allowed smoke and steam to escape into the kitchen, so long as the hood overlapped the cooking area by enough to capture the expanding plumes.

Rerouting the duct to the exterior is the better option to buying an inferior new hood! Recirculating is not a good option for indoor air quality.

@3onthetree is correct, within the assumptions presented. However, so long as you are satisfied with well under 200 CFM, you can transition to 4-inch duct. (With the specified 6-inch duct, the blower would probably only push 300 CFM at best, and this assumes very low pressure loss in whatever method you have of providing make-up air. There will be slightly less overall duct pressure loss if the duct to the ceiling is 6 inches rather than 4 inches, but this difference may be trivial depending on how long the 4-inch duct is to the outside. Impingement grease buildup from too high an air velocity may be compensated by not likely actually achieving a very high velocity. Note that even 200 CFM in a 4-inch duct results in a duct velocity of 2300 ft/min, undesirably high, and quite possibly beyond the capability of the hood blower. Ventilating to the outside will usually beat recirculating, but we don't know enough facts to be sure in this case.