OpenSpecEngineering

Finds the peak stormwater runoff from a small drainage area by the Rational Method. Civil engineers and site designers use it to size inlets, gutters, storm sewers and ditches for parking lots, streets and small developments.

Equation

Q = C·C_f·I·A     with C·C_f ≤ 1

Q is the peak runoff in ft³/s (cfs). C is the runoff coefficient, the share of the rainfall that runs off. C_f is the frequency factor for the return period. I is the rainfall intensity in in/hr, and A the drainage area in acres [1], [2]. The formula is empirical and works in these US units as written: one acre-inch per hour is 1.008 cfs, and the 0.8 % difference is ignored. The page also converts Q to m³/s.

Inputs

• Choosing a Surface / Land Use fills in the midpoint of its C range from HEC-22 Table 3-1 [2]. Use the high end of the range for steep or tight soils, and type a weighted C for an area with mixed surfaces: the sum of each C times its area, over the total area.
• The Table 3-1 values are for storms of 10 years or less. For rarer storms, Design Storm Return Period applies C_f from Table 3-2 (1.1, 1.2 or 1.25), and C·C_f is capped at 1 [2].
• I is the intensity for a storm whose duration equals the time of concentration of the area, read from the local intensity–duration–frequency (IDF) curve for the chosen return period.

Limits and common mistakes

• HEC-22 limits the method to areas of about 80 hectares (200 acres) or less [2]. For larger or mixed watersheds, use a hydrograph method.
• It gives the peak rate only, not a runoff volume, so it can’t size a detention pond on its own.
• Using a 1-hour or 24-hour intensity instead of the intensity at the time of concentration is the most common error. A short time of concentration means a high intensity.

Worked example

A 3.2-acre neighborhood shopping center drains to one inlet. The local design storm is the 25-year event, and the IDF curve gives 4.8 in/hr at the site’s time of concentration. What peak flow must the inlet and pipe carry?

1. Choose Surface / Land Use Business, neighborhood areas. The coefficient fills in as 0.6.
2. Choose Design Storm Return Period 25 years (Cf = 1.1).
3. Enter Rainfall Intensity 4.8 and Drainage Area 3.2, and press Solve. The Solution shows: Peak Runoff (Q): 10.1376 cfs
   Peak Runoff (Q): 0.287064 m³/s
   Frequency factor Cf: 1.1
   Design coefficient C·Cf (at most 1): 0.66

Check by hand: C·C_f = 0.6 × 1.1 = 0.66, and Q = 0.66 × 4.8 × 3.2 = 10.14 cfs. One cfs is 0.02832 m³/s, so Q is 0.287 m³/s.