2.3 Horizontal Branch & Vertical Stack Sizing

Horizontal Branch & Vertical Stack Sizing

Once the Drainage Fixture Unit (DFU) values for all fixtures have been calculated, the plumber must translate those values into nominal pipe diameters. Sizing horizontal fixture branches and vertical soil and waste stacks requires consulting Florida Plumbing Code Table 710.1(2).

Horizontal branches and vertical stacks operate under radically different hydraulic regimes. In a horizontal branch, wastewater flows as an open-channel stream along the bottom of the pipe. In a vertical stack, wastewater falls rapidly as an annular film clinging to the pipe walls around a central core of air. Consequently, code limits vary significantly between horizontal and vertical piping.

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1. Sizing Horizontal Fixture Branches

Definition of a Horizontal Branch

Under FPC Chapter 2, a horizontal branch is a drain pipe extending laterally from a soil or waste stack or building drain, with or without vertical sections or branches, that receives the discharge from two or more fixture drains and conveys it to the stack or building drain.

Maximum DFU Capacities (FPC Table 710.1(2))

The horizontal branch column of Table 710.1(2) governs the maximum permissible DFU load on any horizontal branch based on its nominal diameter:

How Water Closets Constrain a 3-Inch Branch

Water closets exert large instantaneous hydraulic loads, discharging 1.6 gallons or more in three to four seconds with solids and tissue. Two code rules and one deleted one matter here:

1. Minimum Diameter (3 Inches): a water closet outlet is 3 inches, and FPC Section 704.2 prohibits reducing drainage pipe size in the direction of flow, so the branch receiving a water closet is 3 inches minimum. Section 704.2 lists the narrow exceptions that are not treated as a reduction: a 4-inch by 3-inch water closet flange, a water closet bend with a 4-inch inlet and 3-inch outlet where the 4-inch leg is upright and below but not connected to the flange, and an offset closet flange. Footnote a to Table 710.1(1) adds that the minimum size of any building drain serving a water closet is 3 inches.
2. DFU capacity is the working limit. A 3-inch horizontal branch is capped at 20 dfu by Table 710.1(2). Private 1.6 gpf water closets are 3 dfu each and public ones are 4 dfu each, so a 3-inch branch runs out of capacity well before it runs out of physical room.

[!WARNING] A rule many workbooks still print was deleted. Older IPC editions carried a footnote to the horizontal branch and stack table reading "not more than two water closets or bathroom groups within each branch interval nor more than three water closets or bathroom groups on the stack." That footnote is not in FBC-P 2023 Table 710.1(2). Its three footnotes are: (a) the branch column does not include branches of the building drain, which go to Table 710.1(1); (b) stacks are sized on the total accumulated connected load at each story or branch interval, may be reduced in size as the accumulated load decreases, but shall not be reduced below one-half the diameter of the largest required stack size; and (c) the 15-inch row is sized on design criteria. Size by dfu, and answer a Florida code question from the dfu columns rather than from a deleted water-closet count.

[!TIP] Work it by dfu, every time. A 3-inch horizontal branch carrying two private 1.6 gpf water closets (3 dfu each) and two lavatories (1 dfu each) totals 8 dfu against the 20 dfu that Table 710.1(2) allows on a 3-inch branch. Adding a third private water closet brings it to 11 dfu, still inside the 20 dfu ceiling, so the 3-inch branch remains code-compliant under the 2023 FPC. Change the fixtures to public water closets at 4 dfu each and the same three closets plus two lavatories reach 14 dfu — still inside 20. What actually forces a 4-inch branch is dfu accumulation, adding a third toilet mandates increasing the horizontal branch to 4 inches.

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2. Sizing Soil and Waste Stacks

Soil Stack vs. Waste Stack

• Soil Stack: A vertical pipe that carries wastewater containing human fecal matter or urine (i.e., receives discharges from water closets, clinical sinks, or urinals).
• Waste Stack: A vertical pipe that carries wastewater free of fecal matter (i.e., receives discharges from sinks, lavatories, bathtubs, showers, and clothes washers).

The Concept of a Branch Interval

To properly size vertical stacks in multi-story buildings, plumbers must master the definition and application of a Branch Interval:

Branch Interval (FPC Chapter 2): A vertical length of soil or waste stack, corresponding in general to a story height, but in no case less than 8 feet (2438 mm) in vertical height, within which horizontal branches connect to the stack from one story or floor level.

Why does the code limit the load per branch interval? When a horizontal branch enters a vertical stack, the incoming water forms a sheet across the stack diameter. If too much water enters at one level, it blocks the downward flow of air through the center of the stack, causing severe pressure spikes that blow out trap seals on floors below.

FPC Table 710.1(2) Stack Sizing Matrix

Table 710.1(2) divides stacks into two operational categories: stacks of 3 stories or fewer versus stacks of more than 3 stories.

Understanding Stack Table Application

Notice the dual checks required when sizing tall stacks (> 3 stories):

1. Check the total DFU accumulated down the entire stack against the "Total for Stack" column.
2. Check the DFU entering at any single floor against the "Max per Branch Interval" column.

Example: On a 4-story building, could a 3-inch stack serve a 4th floor that has 24 DFU of sinks and showers? Analysis: No! Even though the total building load might be under 72 DFU, the maximum permitted entering any single branch interval on a 3-inch stack is 20 DFU. If a single floor connects 24 DFU, the stack must be upgraded to 4 inches (which allows up to 90 DFU per branch interval).

Sizing a Stack: Accumulated Load, Not Fixture Counts

Footnote b to Table 710.1(2) is the rule that governs stack sizing, and it is worth quoting: "Stacks shall be sized based on the total accumulated connected load at each story or branch interval. As the total accumulated connected load decreases, stacks are permitted to be reduced in size. Stack diameters shall not be reduced to less than one-half of the diameter of the largest stack size required."

Three consequences:

• Size each story from what is connected above it, not from a single whole-building number. A stack may legitimately be 4 inches at the base and 3 inches at the top floors.
• The reduction floor is one-half the largest required diameter. A stack that needs 6 inches at its base may never be reduced below 3 inches anywhere above.
• The columns are the limits. For a 3-inch stack: 20 dfu may discharge into any one branch interval, 48 dfu total for a stack of three branch intervals or less, and 72 dfu total for a stack greater than three branch intervals.

FPC Section 710.1.2 adds that vertical stack offsets are sized as required for straight stacks under Table 710.1(2), except where Section 711.1.1 requires them to be sized as a building drain, and Section 710.1.1 requires horizontal stack offsets to be sized as building drains under Table 710.1(1), except as required by Section 711.3.

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3. Terminal Velocity & Hydraulic Jumps at Stack Bases

The Physics of Terminal Velocity

When wastewater enters a vertical drainage stack, gravity accelerates it downward. However, as fluid speed increases, the air resistance and friction against the internal pipe wall increase proportionally with the square of velocity. Within 10 to 15 feet of fall (approximately one story), the downward gravitational pull is completely balanced by pipe wall friction.

At this point, the water ceases to accelerate and reaches its terminal velocity, which is approximately 10 to 15 feet per second (fps). Whether a building is 3 stories tall or 50 stories tall, the wastewater will never exceed terminal velocity in a straight vertical stack!

As the water falls, it forms an annular sheet adhering to the pipe walls, leaving an open air cylinder in the center. The falling water drags air downward with it through surface shear, creating an aspirating vacuum at the top of the stack and compressing air toward the bottom.

The Hydraulic Jump at the Stack Base

When the annular water film reaches the base elbow and turns into the horizontal building drain, its vertical velocity is abruptly arrested. The water decelerates from 15 fps to 2 to 4 fps, forcing the flow depth to jump violently. This hydraulic jump creates a wall of solid water that temporarily plugs 100% of the pipe diameter.

Code Prohibitions (FPC Section 711)

Because the hydraulic jump induces extreme positive pressures (which will eject water from toilet bowls and blow sewer gas through trap seals), the Florida Plumbing Code enforces strict connection bans:

1. No connections within 2 feet of the base: No horizontal branch may tie into the vertical stack within 2 feet (610 mm) above the base fitting.
2. No connections within 10 pipe diameters downstream: No horizontal branch may tie into the horizontal drain within 10 pipe diameters downstream from the base fitting (e.g., for a 4-inch drain: $10 \times 4\text{ in} = 40\text{ inches}$ of clear pipe required).

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4. Offsets in Drainage Stacks (FPC Section 711)

In architectural design, structural columns or floor layout changes often prevent a drainage stack from dropping straight down from roof to basement, requiring a horizontal dogleg or offset.

          VERTICAL STACK
                |
                |
                +---\  45° or less: Sized as straight stack
                     \
                      \---
                          |
                          |  VERTICAL STACK CONTINUES

--------------------------------------------------------------

          VERTICAL STACK (Upper Section)
                |
                +-------------+  > 45° (Horizontal Offset):
                              |  Must be sized as HORIZONTAL DRAIN
                              |  (Table 710.1(1))
                              |
                +-------------+
                |
                |  LOWER STACK (Must be at least size of offset)

Offsets of 45 Degrees or Less from Vertical

• Hydraulic Behavior: Wastewater continues to flow smoothly along the lower barrel of the pipe without breaking into a hydraulic jump.
• Sizing Rule: Offsets of 45 degrees or less are treated and sized identically to a straight vertical stack using Table 710.1(2). No special relief vents are required.

Offsets Greater Than 45 Degrees (Horizontal Offsets)

When an offset exceeds 45 degrees from the vertical, it is hydraulically classified as horizontal piping:

1. Offsets Above the Highest Branch: If the offset occurs above the highest horizontal fixture branch connection, it is functioning purely as a vent offset and has no impact on drainage sizing.
2. Offsets With Fixtures Above and Below:
   • Upper Stack: Sized as a vertical stack based on the DFU of fixtures connected above the offset.
   • The Horizontal Offset: Must be sized as a horizontal building drain under FPC Table 710.1(1) based on pipe slope and total DFU from above. It can never be smaller than the upper stack.
   • Lower Stack: Sized based on the total DFU of all fixtures above it (both upper stack and any fixtures connecting to the offset). The lower stack cannot be smaller than the horizontal offset pipe.
3. Yoke & Relief Vents (Buildings with 5+ Branch Intervals): Under FPC Section 711.2, if an offset greater than 45 degrees is installed in a stack serving 5 or more branch intervals, relief vents must be installed. A relief vent must be provided at the upper stack section above the offset, and a yoke vent must connect from the lower stack section below the offset to the main vent stack.