branch arm length if not stack venting

If a shower is directly connected to a 2" vertical vent that goes through the roof, (only fixture using this vent stack) how do I calculate the branch arm length? Can I divide the branch arm diameter by the downward slope? Say 2" diameter divided by 1/8" downward slope = 16' of branch arm? I actually need 10'. Also hypothetically, can a 3" diam branch arm be used for a shower? thanks for enlightening me!

quote; Say 2" diameter divided by 1/8" downward slope = 16' of branch arm?

You cannot install it at 1/8" slope and 2" divided by 1/4" = 8', but most codes err on the conservative side and say 4 to 6 foot maximum. The problem with "oversizing" a drain line is that you lose the "scouring" effect induced by the flow through the proper sized drain line. This can lead to premature stoppage AND difficulty in clearing it properly.

thanks HJ, I now see that the 1/8" slope is only for larger pipe.....

Section 708.0: Horizontal drainage piping shall be run in practical alignment and a uniform slope of not less than one-fourth inch per foot or two percent toward the point of disposal provided that where its impractical due to the depth of the street sewer or to the structural features or to the arrangement of any building or structure to obtain a slope of one-fourth of an inch per foot or two percent, any such pipe or piping three inches or larger in diameter may have a slope of not less than one-eighth of an inch per foot or one percent, when first approved by the Authority Having Jurisdiction.

So you don't get any advantage in terms of the branch arm length you can have by adding a dedicated vent stack to a fixture? My book makes it sound like "stack venting" is allowed, but since the pipe is doing double duty, you have to limit branch arm length. "..but such a stack-vented branch arm is limited. most codes allow 8' for 2" line, and 10' for 3" line."

The distance from the trap to the vent is the part that is limited as far as horizontal length is concerned. Theoretically it is the pipe size divided by 1/4", but since they err on the conservative side, they usually use a smaller number. I.e., 2" equals EIGHT quarters, or 8 feet, but the practical limit is usually around 4 feet.