Every storm drain pipe on a site plan was sized using Manning's Equation, whether the designer ran it by hand, in a spreadsheet, or through software. Manning's Equation relates the flow capacity of a pipe to its size, slope, and roughness. Understanding the equation and how to apply it is fundamental to storm drain design, and it is one of the first things an agency plan checker verifies when reviewing your drainage calculations.

Manning's Equation

The standard form of Manning's Equation for open channel flow (which includes gravity storm drains flowing partially or fully full) is:

Q = (1.486 / n) x A x R^(2/3) x S^(1/2)

Where:

• Q = flow rate in cubic feet per second (cfs)
• n = Manning's roughness coefficient (dimensionless)
• A = cross-sectional flow area in square feet (ft2)
• R = hydraulic radius = A / P, where P is the wetted perimeter (ft)
• S = slope of the energy grade line, approximately equal to the pipe slope for uniform flow (ft/ft)

The constant 1.486 applies to US customary units. For metric (SI) units, the constant is 1.0 and the equation becomes Q = (1/n) x A x R^(2/3) x S^(1/2) with Q in m3/s.

Manning's n Values for Storm Drains

Full-Pipe Capacity for Common Sizes

For a circular pipe flowing full, the cross-sectional area is A = pi x D^2 / 4, and the hydraulic radius is R = D / 4, where D is the pipe diameter in feet. Substituting into Manning's Equation gives the full-pipe capacity. The following table uses n = 0.013 (RCP):

Step-by-Step Sizing Procedure

1. Determine the design storm flow (Q). Use the Rational Method (Q = CiA) for drainage areas under 200 acres, or TR-55/HEC-HMS for larger watersheds. The design storm return period is typically 10-year for on-site storm drains and 25-year or 100-year for trunk lines, per local standards.
2. Establish the pipe slope. The pipe slope is controlled by the upstream and downstream invert elevations, which are dictated by the site grading, cover requirements, and connection points. Minimum slopes for storm drains are typically 0.50% for 12-inch pipe and decrease with larger diameters. Maximum slopes are limited by velocity (typically 15 to 20 ft/s maximum).
3. Select the pipe material and Manning's n. The material is usually dictated by the jurisdiction (most public agencies require RCP for storm drains in public right-of-way; PVC and HDPE are common for private on-site systems).
4. Calculate the required pipe diameter. Rearrange Manning's Equation to solve for diameter, or iterate through standard pipe sizes until the capacity exceeds the design flow. Standard pipe sizes are 12, 15, 18, 21, 24, 27, 30, 36, 42, 48, 54, 60 inches.
5. Check velocity. Calculate the full-pipe velocity (V = Q / A). Minimum velocity should be 2 to 3 ft/s to prevent sediment deposition. Maximum velocity should be 10 to 15 ft/s (varies by material and jurisdiction).
6. Verify headwater depth at inlets. The hydraulic grade line (HGL) must be below the rim of all inlets and manholes for the design storm. If the HGL exceeds the rim, the system is pressurized and water will surface at the inlet, creating a flood hazard.

Worked Example

A parking lot drainage area of 2.5 acres with a runoff coefficient C = 0.90 (impervious) in a location where the 10-year, 15-minute rainfall intensity is 2.5 in/hr.

Q = CiA = 0.90 x 2.5 x 2.5 = 5.6 cfs

The pipe slope is 1.0%, and the jurisdiction requires RCP (n = 0.013). From the capacity table, an 18-inch pipe at 1.0% slope carries 6.2 cfs, which is greater than 5.6 cfs. The full-pipe velocity is V = 6.2 / (pi x 1.5^2 / 4) = 6.2 / 1.767 = 3.5 ft/s, which is within the acceptable range. The 18-inch RCP is adequate.

If the pipe slope were only 0.50%, the 18-inch pipe capacity drops to 4.4 cfs, which is less than 5.6 cfs. You would need to upsize to a 24-inch pipe (9.4 cfs capacity at 0.50% slope) or increase the pipe slope.

Partial Flow Conditions

Manning's Equation can also be used for pipes flowing partially full. This is important because storm drains should be designed to flow full (or nearly full) at the design storm, but they spend most of their life at partial flow. The velocity at partial flow must still meet the minimum to prevent sediment deposition.

At partial flow depths, the actual velocity and capacity differ from full-pipe values. At approximately 82% depth (d/D = 0.82), a circular pipe actually reaches its maximum flow capacity, which is about 8% more than the full-pipe capacity. This is because the hydraulic radius is most efficient at this depth. Below 50% depth, the velocity drops significantly. Most design standards require that the pipe flow at least 2 ft/s at one-third to one-half of the design flow to maintain self-cleansing velocity.

Energy Losses and Headloss Calculations

Manning's Equation gives the friction losses along a straight pipe run. Additional energy losses occur at junctions, bends, manholes, and transitions. These losses are calculated using the energy loss equation:

hL = K x V^2 / (2g)

Where hL is the headloss in feet, K is the loss coefficient (dimensionless), V is the velocity in ft/s, and g is gravitational acceleration (32.2 ft/s2). Typical K values: manhole with straight-through flow = 0.5, 45-degree bend = 0.6, 90-degree bend = 1.0, junction with lateral inflow = 1.0 to 2.0.

These junction losses accumulate along the system and raise the hydraulic grade line. A storm drain system designed without accounting for junction losses will have a higher HGL than predicted, potentially surcharging upstream inlets. Always include junction losses in your HGL calculations.