Sizing branches and stacks

With her tallies done, Maya was ready for the step that turns numbers into pipe. Luis pulled up the sizing tables and explained that a branch and a stack carrying the same number of fixture units can need different sizes, because water behaves differently lying down and falling. A horizontal branch must carry the flow sideways at a gentle slope; a stack lets the water fall but must also carry the air core and survive the pressures at each floor and at the base. The code has separate tables for each, and a few rules that override the tables.

This lesson works through sizing a horizontal branch, sizing a stack, the minimum sizes that apply no matter what the table says, branch intervals, stack offsets and the special zone at the base of a stack. All the numbers come from the course practice tables, which follow the pattern of real code tables. On the job, always size from the adopted code currently in force and the engineer's drawings.

The sizing method in four steps

Every drainage sizing problem follows the same steps:

• Tally the fixture units the pipe carries, as in lesson 3.
• Pick the correct table: horizontal branch, stack, or building drain and sewer.
• Find the smallest pipe whose capacity in that table is equal to or greater than the load.
• Check the overriding rules: minimum sizes for water closets and other fixtures, no reduction downstream, limits on how many water closets a pipe may carry, and the fixture's own outlet size.

The fourth step is where most mistakes happen. A branch carrying only 6 fixture units might pass in a small pipe by the table, but if one of those fixtures is a water closet, the branch must be at least the minimum size for water closets. And a pipe can never be smaller than the outlet of the fixture or trap it serves.

Sizing horizontal branches

A horizontal branch is a drain that runs roughly level, at the minimum slope or steeper, collecting fixture drains on one floor. Its capacity depends on its size and slope. The practice table below gives the maximum fixture units a horizontal branch may carry. Real code tables also distinguish branches by slope or by whether they connect to a building drain, but the pattern is the same.

The Ohio Plumbing Code's horizontal branch table, taken from the IPC, gives separate limits for branches and footnotes that restrict the number of water closets on a 3-inch branch. Check the current table and its footnotes rather than trusting a number learned years ago.

Sizing stacks

A stack has two limits in most sizing tables: the total fixture units it may carry, and the fixture units it may receive from any one branch interval. The total limit protects the stack as a whole and especially its base. The per-interval limit protects each floor: if too much water enters the stack at one level, it can fill the pipe at that point and disturb traps on that floor and the floors around it.

A branch interval is a vertical section of stack, generally at least one story high, into which the horizontal branches from one floor connect. In a typical apartment tower, each floor is one branch interval. Codes define the term precisely, usually by a minimum height, so check the definition when floors are short or branches connect at odd levels.

A stack must satisfy both columns. A stack that carries a modest total but takes a large load from one floor may need to be larger than its total suggests. On Kingsway Tower, the ground floor amenity washrooms connect to some of the residential stacks, and their public fixtures add a large load at one branch interval. Luis showed Maya where the engineer had kept those washrooms on their own stack for exactly that reason.

Codes generally require a stack to be the same size for its full height, at least up to the highest branch that carries water closet waste, rather than tapering it from small at the top to large at the bottom. Some codes allow the upper part of a stack to be smaller where it carries only a small load, but many designers keep stacks uniform for simplicity, and the stack must never be smaller than any branch connecting to it.

# Size a branch and a stack from the course practice tables
BRANCH = [(1.5, 3), (2, 6), (3, 20), (4, 160), (6, 620)]
STACK = [(1.5, 4, 2), (2, 10, 6), (3, 48, 20), (4, 500, 90), (6, 1900, 350)]
WC_MIN = 3

def size_branch(dfu, has_wc):
    for d, cap in BRANCH:
        if dfu <= cap and (not has_wc or d >= WC_MIN):
            return d

def size_stack(total, per_interval, has_wc):
    for d, tot, intv in STACK:
        if total <= tot and per_interval <= intv and (not has_wc or d >= WC_MIN):
            return d

print("suite branch, 7 dfu with a water closet:", size_branch(7, True), "in")
print("kitchen branch, 4 dfu, no water closet:", size_branch(4, False), "in")
print("stack S-5, 168 dfu total, 14 per floor:", size_stack(168, 14, True), "in")
print("waste stack, 48 dfu total, 4 per floor:", size_stack(48, 4, False), "in")

suite branch, 7 dfu with a water closet: 3 in
kitchen branch, 4 dfu, no water closet: 2 in
stack S-5, 168 dfu total, 14 per floor: 4 in
waste stack, 48 dfu total, 4 per floor: 3 in

The kitchen waste stack in the last line carries 48 fixture units but only 4 from each floor, so the table allows the smaller size. In practice an engineer might still choose the larger size for a kitchen stack, because grease and food waste build up over the years and a larger pipe takes longer to restrict.

Minimum sizes that override the tables

Several rules set minimum drain sizes regardless of the fixture unit total:

• Water closets: a drain receiving the discharge of a water closet must be at least 3 inches, and codes limit how many water closets a 3-inch branch or stack may serve.
• Fixture outlets and traps: a fixture drain can never be smaller than the trap it serves, and codes list a minimum trap and fixture drain size for each type of fixture, for example larger for a shower or a floor drain than for a lavatory.
• Underground piping: many codes set a minimum size for drains buried under a floor slab, because they are hard to reach and easy to block.
• No reduction downstream: once a drain reaches a size, every pipe downstream must be at least that size.

In the Ohio Plumbing Code, as in the IPC, footnotes to the sizing tables limit the number of water closets on a 3-inch branch and stack and set other special limits. Rules like these catch designs that would pass on total load alone.

Stack offsets

Kingsway Tower's stacks drop straight through the residential floors, but three of them offset at the ground floor to clear the lobby and amenity rooms. An offset changes how the water flows. A 45-degree offset lets the water slide along the bottom of the pipe and then fall again; many codes treat offsets at 45 degrees or steeper as part of the vertical stack. A horizontal offset is different: the water slows, the pipe may run full, and the air core is interrupted.

Codes therefore set rules for horizontal offsets in stacks. The horizontal part is generally sized like a building drain for the load it carries. Branches are not allowed to connect for a set distance above and below the offset, where the pressures are disturbed. And a relief vent is often required, connecting to the stack below the offset and to the vent stack above it, so that air can move around the offset.

The IPC and the Ohio Plumbing Code include a section on offsets in drainage stacks that sets these rules, with different requirements for offsets above and below the highest horizontal branch. Check the current wording when you meet an offset on the drawings.

The base of the stack

Lesson 1 described the hydraulic jump at the base of a stack, where falling water turns into the building drain and the pressure rises. In tall buildings this zone needs care. A branch connected close to the base of a tall stack can be flooded or have its trap blown out by the surge. Codes restrict horizontal branch connections within a set distance of the base of tall stacks and may require the lower floors to be drained separately or connected through a relief vent.

Detergent suds make it worse. Clothes washers and dishwashers discharge foamy water, and in a tall stack the foam collects at the base and in offsets, where it can push up through the lowest traps. Designers often keep the lowest floors off the main stacks or add relief venting near the base. On Kingsway Tower, the ground floor fixtures drain to separate branches that connect to the building drain downstream of the stack bases, which keeps them out of the high-pressure zone.

The fitting at the base also matters. The turn from vertical to horizontal must use long-turn fittings, as lesson 2 explained. Some engineers specify a larger building drain for the first few meters downstream of the stack base, or a long-radius bend instead of two eighth bends, to soften the hydraulic jump.