13.1 Roof Drainage Sizing & Michigan Rainfall Rates

13.1 Roof Drainage Sizing & Michigan Rainfall Rates

Exam Focus: Sizing storm drainage systems requires a completely different engineering methodology than sanitary drainage. While sanitary drainage relies on intermittent Fixture Units (DFUs) and Hunter's Probability Curve, storm drainage is governed by continuous hydraulic fluid dynamics, physical roof catchment geometry, and local atmospheric precipitation data. On the Michigan Journeyman Plumber licensing examination, candidates must master Michigan Plumbing Code (MPC) Chapter 11, Appendix B (Rates of Rainfall for Various Cities), the 100-year, 1-hour storm frequency standard, MPC Table 1106.2, Michigan's added MPC 1106.2.1 (Rainfall rate conversion method), Equation 11-1, and the vertical wall addition in MPC Section 1106.4.

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1. Regulatory Authority & The 100-Year, 1-Hour Storm Frequency

Under MPC Section 1106.1, roof drainage systems must be designed to accommodate the maximum volume of rainwater produced by a storm having a return frequency of once every 100 years, sustained over a 1-hour duration (commonly designated as the 100-year, 1-hour storm).

Plumbing systems cannot be sized for average annual rainfall or light precipitation. During severe cloudbursts, intense precipitation falling onto an improperly sized roof drainage network causes rapid hydrostatic water accumulation. If the drainage pipes choke, standing water rapidly exceeds the structural load capacity of the roof framing, leading to catastrophic structural collapse.

+-----------------------------------------------------------------------------+
|              MICHIGAN DESIGN RAINFALL RATES (MPC APPENDIX B)                |
|                   (100-Year, 1-Hour Storm Return Period)                    |
+-----------------------------------------------------------------------------+
|  Michigan City (MPC Appendix B)   | Rainfall Rate (Inches Per Hour - in/hr) |
+-----------------------------------+-----------------------------------------+
|  Alpena                           | 2.5 in/hr                               |
|  Detroit                          | 2.7 in/hr                               |
|  Grand Rapids                     | 2.6 in/hr                               |
|  Lansing                          | 2.8 in/hr                               |
|  Marquette                        | 2.4 in/hr                               |
|  Sault Ste. Marie                 | 2.2 in/hr                               |
+-----------------------------------------------------------------------------+
|  NOTE: Appendix B is informative and lists only these six Michigan cities.   |
|  Appendix B rates are derived from Figures 1106.1(1) through 1106.1(5).      |
|  For any other Michigan location, MPC 1106.1 directs the designer to those   |
|  figures or to other rainfall rates determined from approved local weather   |
|  data. Do NOT assume a single statewide rate.                                |
+-----------------------------------------------------------------------------+

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2. Hydraulic Conversion Principles & Sizing Formulas

Code sizing tables in the Michigan Plumbing Code (and International Plumbing Code) are published using a standardized baseline rainfall rate of 1.0 inch per hour (or in some historic tables, 4.0 inches per hour). Because the Michigan design rainfall rates in Appendix B range from 2.2 to 2.8 inches per hour, plumbers must mathematically adjust either the roof square footage or the pipe carrying capacity.

The Volumetric Flow Rate Constant

To understand the sizing tables, a journeyman must understand the physical relationship between roof area, rainfall depth, and gallons per minute (GPM):

$1\text{ cubic foot of water} = 7.4805\text{ gallons}$

$1\text{ inch of rainfall} = \frac{1}{12}\text{ foot} = 0.08333\text{ feet}$

Over an area of 100 square feet, a rainfall rate of 1.0 inch per hour yields:

$\text{Volume per hour} = 100\text{ sq ft} \times \left(\frac{1}{12}\text{ ft}\right) = 8.333\text{ cu ft/hr}$

$\text{Gallons per hour} = 8.333\text{ cu ft/hr} \times 7.4805\text{ gal/cu ft} = 62.34\text{ gal/hr}$

$\text{Flow Rate (GPM)} = \frac{62.34\text{ gal/hr}}{60\text{ min}} = 1.039\text{ GPM}$

$\mathbf{1.0\text{ GPM} \approx 96.25\text{ square feet of roof area at } 1.0\text{ inch/hour rainfall}}$

$\text{Flow (GPM)} = \frac{\text{Roof Area (sq ft)} \times \text{Rainfall Rate (in/hr)}}{96.25}$

Equation 11-1: The Code's Own Conversion (and Michigan's Added 1106.2.1)

The 2021 code does not ask the plumber to scale square footage against a 1.0-inch-per-hour baseline. It converts roof area directly to a flow rate, and Michigan adds MPC 1106.2.1 (R 408.30755a) to make that step explicit: "The rainfall rate falling on a roof surface shall be converted to a gallon per minute (L/m) flow rate in accordance with equation 11-1."

$\mathbf{Q = \frac{R \times A}{96.23}}$

Where:

• $Q$ = design flow rate in gallons per minute
• $R$ = rainfall rate in inches per hour (from Appendix B, Figures 1106.1(1) to 1106.1(5), or approved local weather data)
• $A$ = horizontal projected roof area in square feet (plus any vertical wall addition from 1106.4)

MPC Table 1106.2 then sizes the piping by flow rate in gpm, listing a capacity for a vertical conductor or leader and capacities for horizontal drainage piping at 1/16, 1/8, 1/4 and 1/2 inch per foot of slope. A 4-inch pipe, for example, is listed at 180 gpm vertical, 81 gpm at 1/16 inch per foot, and 231 gpm at 1/2 inch per foot.

Michigan Exclusion Alert: Part 7 rule R 408.30701 does not adopt MPC Sections 1106.3 or 1106.6, or Tables 1106.3 and 1106.6. That means the separate horizontal-storm-drain table and the roof gutter table in the model code are not part of the Michigan Plumbing Code; Michigan sizes storm piping from the Equation 11-1 flow rate and Table 1106.2, or by approved engineered design.

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3. Sizing Vertical Leaders & Conductors (MPC Table 1106.2)

A conductor is an interior vertical storm drainage pipe; a leader is an exterior vertical downspout. Both are vertical pipes that convey water by gravity downward from the roof surface.

Annular Flow Physics in Vertical Conductors

Water flowing down a vertical conductor does not flow as a solid liquid piston (which would create dangerous vacuum and hydraulic surges). Instead, water adheres to the inner pipe walls by surface tension and gravity, forming a tubular ring of downward-falling water around a central core of atmospheric air—a hydraulic condition called annular flow.

Vertical pipes achieve terminal velocity within approximately two stories of fall (roughly 20 to 30 feet). Once terminal velocity is reached, air resistance balances gravity, and the water sheet travels at a constant speed of roughly 15 to 20 feet per second. Sizing tables limit water flow so that the annular ring does not occupy more than one-third (33%) of the pipe's internal cross-sectional area, ensuring an unobstructed central air path that prevents pulsating slugs and vacuum collapse.

+-----------------------------------------------------------------------------+
|     MPC TABLE 1106.2 IS EXPRESSED IN GALLONS PER MINUTE, NOT SQUARE FEET     |
+-----------------------------------------------------------------------------+
|                                                                             |
|  Step 1  Determine R from Appendix B / Figures 1106.1(1)-(5) or approved    |
|          local weather data.                                                |
|  Step 2  Determine A: the horizontal projected roof area, plus one-half of  |
|          the area of any vertical wall that diverts rain to the roof        |
|          (MPC 1106.4).                                                      |
|  Step 3  Q = (R x A) / 96.23  ->  design flow in gpm (Equation 11-1,        |
|          restated by Michigan's added 1106.2.1).                            |
|  Step 4  Enter Table 1106.2 with Q and read the required pipe size for a    |
|          vertical conductor/leader, or for horizontal piping at the         |
|          installed slope. Select the next size up if Q falls between rows.  |
|                                                                             |
|  Reference point from Table 1106.2: a 4-inch pipe is listed at 180 gpm      |
|  vertical, 81 gpm at 1/16 in/ft, and 231 gpm at 1/2 in/ft.                  |
+-----------------------------------------------------------------------------+

Annular Flow and the One-Third Rule

Water in a vertical conductor clings to the pipe wall as an annular sheet around a central air core. Table 1106.2 limits vertical flow so that the falling sheet occupies roughly one-third or less of the pipe's cross-sectional area, keeping the air core open and preventing pulsating slug flow and vacuum collapse.

Scouring Velocity in Storm Drains

Horizontal storm piping should achieve a self-cleansing velocity of not less than about 2.5 to 3.0 feet per second. Storm water carries roofing granules, atmospheric dust, gravel and biological debris; below scouring velocity, silt settles on the invert, reduces the effective cross-section, and causes chronic blockages in later storms.

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5. Vertical Wall Surface Additions (MPC Section 1106.4)

In urban and multi-story architecture, flat roofs frequently terminate against taller adjacent building walls, parapets, elevator penthouses, or mechanical bulkheads. During severe storms, heavy winds drive falling rain horizontally against these vertical surfaces. Water striking the vertical wall does not disappear; it sheets downward and discharges directly onto the horizontal roof deck below.

Under MPC Section 1106.4, plumbers are legally required to add a specified percentage of adjacent vertical wall surface areas to the horizontal projected roof area prior to pipe sizing.

                   VERTICAL WALL RAIN INTERCEPTION DYNAMICS

           WIND-DRIVEN RAIN
               \  \  \
                \  \  \    +-------------------------+
                 \  \  \   |                         |
                  \  \  v  |                         |
                   ======> |  VERTICAL TOWER WALL    |
                           |  (Projecting Surface)   |
                           |                         |
                           |  Water Sheets Downward  |
                           |  |  |  |  |  |  |  |    |
       +-------------------+--v--v--v--v--v--v--v----+  <--- Roof Flashing
       |                                             |
       |               HORIZONTAL ROOF DECK          |
       |             (Horizontal Projected Area)     |
       +---------------------------------------------+

The Code Rule for Vertical Wall Calculations (MPC 1106.4)

MPC Section 1106.4 states the rule in a single sentence: "In sizing roof drains and storm drainage piping, one-half of the area of any vertical wall that diverts rainwater to the roof shall be added to the projected roof area for inclusion in calculating the required size of vertical conductors, leaders and horizontal storm drainage piping."

$\text{Design Area} = \text{Horizontal Projected Roof Area} + \left(0.50 \times \sum \text{Area of Each Vertical Wall That Diverts Rain to the Roof}\right)$

• One wall: add 50% of that wall's area.
• Two or more walls: the code does not discount for wind direction. Add 50% of the area of each vertical wall that diverts rainwater onto the roof.
• Which walls count: only walls that actually shed water onto the roof in question. A wall on the far side of a parapet, or a wall whose runoff is collected by its own separate drainage, does not divert rainwater to that roof.

Exam Trap Alert: The graduated percentages taught in some study material (35% of two adjacent walls, 50% of only the larger of two opposite walls, zero for an enclosed courtyard) come from the Uniform Plumbing Code, not from the IPC-based Michigan Plumbing Code. Michigan applies the flat one-half of any diverting vertical wall rule in 1106.4.

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6. Realistic Exam Application Scenarios

Scenario A: Warehouse Roof Drain & Conductor Sizing in Grand Rapids

Exam Scenario: A journey plumber in Grand Rapids is roughing in the roof drainage for a new distribution warehouse. The flat horizontal roof measures 120 feet by 100 feet ($12,000\text{ sq ft}$) with no projecting vertical walls. The design specifies four identical, equally spaced vertical conductors connected to individual primary roof drains.

What design flow must each conductor carry?

Code Analysis & Step-by-Step Calculation:

1. Determine the Design Rainfall Rate: MPC Appendix B lists Grand Rapids at 2.6 inches per hour for the 100-year, 1-hour storm.
2. Calculate Roof Catchment per Conductor: $A = \frac{12,000\text{ sq ft}}{4\text{ drains}} = 3,000\text{ sq ft per drain}$
3. Apply Equation 11-1 (and Michigan's added 1106.2.1): $Q = \frac{R \times A}{96.23} = \frac{2.6 \times 3,000}{96.23} = \frac{7,800}{96.23} = 81.1\text{ gpm}$
4. Enter Table 1106.2 with 81 gpm in the vertical conductor column and select the listed size whose capacity equals or exceeds 81.1 gpm, stepping up to the next size where the value falls between rows.
5. Sanity Check: A 4-inch conductor is listed at 180 gpm vertical, so it carries this load comfortably; the exercise is to read the table rather than to memorize a square-footage figure.

Scenario B: Detroit Setback Roof with Vertical Wall Interception

Exam Scenario: An office tower in downtown Detroit has an 8th-floor flat setback roof measuring 50 feet by 60 feet ($3,000\text{ sq ft}$). The east side terminates against the main tower wall, which rises 40 feet above the roofline and is 50 feet wide ($2,000\text{ sq ft}$ of vertical masonry). The entire setback drains into a single horizontal storm drain.

What design flow governs the horizontal storm drain?

Code Analysis & Step-by-Step Calculation:

1. Vertical Wall Addition (MPC 1106.4): One-half of the area of any vertical wall that diverts rainwater to the roof is added to the projected roof area: $0.50 \times 2,000\text{ sq ft} = 1,000\text{ sq ft}$ $A = 3,000 + 1,000 = 4,000\text{ sq ft}$
2. Apply the Detroit Rate (MPC Appendix B): Detroit is listed at 2.7 inches per hour.
3. Apply Equation 11-1: $Q = \frac{2.7 \times 4,000}{96.23} = \frac{10,800}{96.23} = 112.2\text{ gpm}$
4. Select the Pipe: Enter Table 1106.2 at 112 gpm in the column matching the installed slope, and select the listed size whose capacity equals or exceeds that flow. Because Michigan does not adopt Section 1106.3 or Table 1106.3, the horizontal sizing comes from Table 1106.2 at the installed slope or from an approved engineered design - not from the model code's separate horizontal storm drain table.