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When a vent is less than 10 feet high, the vent should be at least as large as the flue collar outlet.b) Vents for draft hoods or flue collars 12 inches in diameter or less should NOT be reduced more than one pipe size.
Plumbing codes are not the same in every state, but most require the cross-sectional area of the vent pipe to equal at least half of that of the lowest portion of the soil stack. It's common practice in many states to reduce the soil stack to 2 inches, and extend that 2-inch pipe through the roof.