Duct diameter transitions should be gradual, not abrupt. This means generally conical.

Velocities of the air in a grease duct should range between 1000 and 2000 ft/min. Without knowing the rated CFM of your blower, or all the pressure losses of the hood, ducting, and MUA, calculating cannot be done at this distance. What is your blower's rated (zero static pressure) CFM?

Also, 9-inch duct can certainly be made if it will actually fit.

We will be doing similar. Our vent is designed for 7” duct, but 6” is more common for all the fittings we need. We will need to go straight up through hood into the upper level joist, 90° turn, straight out side of house about 6’. Our fan is Broan. They have a help number to talk to techs with exactly these questions - I bet yours does too. I was surprised that they said that the ratings are very flexible when it comes to turns and reductions. They have formulas about all those variables and they do matter, but not quite as rigidly as I thought. I suspect your unit might have similar flexibility. Call the manufacturer and explain your installation situation and they can advise as to requirements and how much latitude you have.

Could you use a rectangular duct?

It's max 1200 CFM...sorry, that was silly not to state lol.

Hmm rectangle vent isn't something I had thought of...I can definitely look into options there!

Does your house have a gas furnace or hot water heater? If so, what are you doing for make up air?

At 1200 CFM in a large, very open and ventilated kitchen, we were not planning to use a make up air system. I know around 1200, people start considering it but I had read generally that would be for smart, more confined spaces. Thoughts?

I believe in some municipalities the code requires make up air be supplied when the vent fan is rated at 400 CFM or higher. If your blower can actually exhaust at a rate of 1200 CFM, then the air to replace it has to come from somewhere. If the windows and exterior doors are tight, then the air may back draft through the hot water and furnace exhaust vents, and fireplace chimney. This is a potentially a dangerous condition which needs to be addressed.

Interesting. Thanks for the heads up. I'll have to look into that one further.

Anyone engaged in hood ventilation definition needs to read the MUA related threads here.

A 1200 CFM blower might be gagged enough to only move 800 CFM. For circular duct, the duct velocity is the CFM divided by the duct sectional area in square feet. [(pi/4)*(diameter_in inches_squared/144)]. For rectangular duct, use (4*sectional_area/perimeter) for the equivalent diameter and then the first equation for velocity (ft/min).

I would strive mightily to use 8-inch duct or larger for a 1200 CFM blower.

Your MUA may need a blower and it will have to be the same size, approximately, depending on how refined your analysis.

While 6, 8, 10 are standard duct sizes, these parts are simple to make and HVAC part distributors that have sheet metal shops can make any other size.

And a point of emphasis for MUA: No air leaves via the hood that wasn't made up by getting into the kitchen somehow. House leakage should not be anywhere near 800 CFM except when windows are open. Edit: The size of the open area appurtenant to the kitchen is not a determinant of whether MUA is required. Further, the amount that the household air pressure can be allowed to drop without back-drafting combustion appliances depends on the appliance type. For passively vented hot water heaters, even window screens may be too much.

Best is to assure that all combustion appliances have their own MUA and are isolated from the kitchen air supply. Then passive MUA (w/o blower) will be sufficient. You will still need heated MUA if winter is more than a season name where you live.