Inch Duct Fan

Inch Duct Fan
reducing duct from 6 to 4 inches?

If I have a 6 inch in duct fan at x CFM what is the formula which will tell me the number of CFM the fan will produce if the duct is reduced in size to 4 inches. The duct run is 1 foot, just through a wall. I want to increase the air flow over what the current 4″ fan provides without disrupting the structure.
Is this formula correct for my application??? Your formula tells me that xyz CFM flows through a 4 inch circle inside the 6 inch pipe. However, I would expect more CFM to flow through the 4 inch pipe created by reducing a 6 inch pipe than flows through a 4 inch circle inside the 6 inch pipe. Is my intuition incorrect on this one?
I believe NotRobinHood also agrees that the formula is incorrect based upon air velocity increasing.

When you reduce the size from 6″ to 4″ you will increase the velocity of the flow. If this helps any.

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