Reducing duct from 6 to 4 inches?

Question

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.

Answer 1

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

Answer 2

CFM1 / (D1 ^ 2) = CFM2 / (D2 ^ 2)

D is diameter of the duct

it is proportional to the diameter squared