#INFOSWMM

# Stormwater Runoff and the Rational Method in InfoSWMM and InfoSWMM SA

Stormwater Runoff and the Rational Method in InfoSWMM and InfoSWMM SA

For storm sewer loading, the focus shifts to hydrologic analysis of excess precipitation and associated runoff. Common techniques for analysis include the rational method and unit hydrograph methods, as well as the use of more advanced hydrologic models.

For small drainage areas, peak runoff is commonly estimated by the rational method. This method is based on the principle that the maximum rate of runoff from a drainage basin occurs when all parts of the watershed contribute to flow and that rainfall is distributed uniformly over the catchment area. Since it neglects temporal and spatial variability in rainfall, and ignores flow routing in the watershed, collection system, and any storage facilities, the rational method should be used with caution only for applications where the assumptions of rational method are valid.

Rational Method

The rational formula is expressed as

where Qp = peak runoff rate (m3/s, ft3/s)

C = dimensionless runoff coefficient (see Table 3-9)

I = average rainfall intensity (mm/hr, in/hr) for a duration of the time of concentration (tc)

A = drainage area (km2, acres)

K = conversion constant (0.28 in SI, 1 in English)

The time of concentration tc used in the rational method is the time associated with the peak runoff from the watershed to the point of interest. Runoff from a watershed usually reaches a peak at the time when the entire watershed is contributing; in this case, the time of concentration is the time for a drop of water to flow from the remotest point in the watershed to the point of interest. Time of concentration, tc (min), for the basin area can be computed using one of the formulas listed in Table 3-10.

Table 3-9: Runoff Coefficients for 2 to 10 Year Return Periods

 Description of drainage area Runoff coefficient Business Downtown 0.70-0.95 Neighborhood 0.50-0.70 Residential Single-family 0.30-0.50 Multi-unit detached 0.40-0.60 Multi-unit attached 0.60-0.75 Suburban 0.25-0.40 Apartment dwelling 0.50-0.70 Industrial Light 0.50-0.80 Heavy 0.60-0.90 Parks and cemeteries 0.10-0.25 Railroad yards 0.20-0.35 Unimproved areas 0.10-0.30 Pavement Asphalt 0.70-0.95 Concrete 0.80-0.95 Brick 0.75-0.85 Roofs 0.75-0.95 Lawns Sandy soils Flat (2%) 0.05-0.10 Average (2-7%) 0.10-0.15 Steep (≥7%) 0.15-0.20 Heavy soils Flat (2%) 0.13-0.17 Average (2-7%) 0.18-0.22 Steep (≥7%) 0.25-0.35

Source: Nicklow et al. (2006)

Table 3-10: Formulas for Computing Time of Concentration

 Method Formula Kirpich (1940) L = length of channel (ft) S = average watershed slope (ft/ft) California Culverts Practice (1942) L = length of the longest channel (mi) H = elevation difference between divide and outlet (ft) Izzard (1946) i = rainfall intensity (in/h) c = Retardance coefficient Retardance factor, c, ranges from 0.007 for smooth pavement to 0.012 for concrete and to 0.06 for dense turf; product i times L should be < 500 Federal Aviation Administration (1970) C = rational method runoff coefficient (see Table 3.9) Kinematic wave n = Manning’s roughness coefficient SCS lag equation CN = SCS runoff curve number (see Table 3.11) SCS average velocity charts V = average velocity (ft/s) Yen and Chow (1983) KY = Coefficient N = Overland texture factor (see Table 3.13) KY ranges from 1.5 for light rain (i<0.8) to 1.1 for moderate rain (0.81.2)

Source: Nicklow et al. (2004)

Table 3-11: Runoff Curve Numbers for Urban Land Uses

 Land use description Soil Group A B C D Lawns, open spaces, parks, golf courses: Good condition: grass cover on 75% or more area 39 61 74 80 Fair condition: grass cover on 50% to 75% of area 49 69 79 84 Poor condition: grass cover on 50% or less of area 68 79 86 89 Paved parking lots, roofs, driveways, etc 98 98 98 98 Streets and roads: Paved with curbs and storm sewers 98 98 98 98 Gravel 76 85 89 91 Dirt 72 82 87 89 Paved with open ditches 83 89 92 93 Commercial and business areas (85% impervious) 89 92 94 95 Industrial districts (72% impervious) 81 88 91 93 Row houses, town houses and residential with lot sizes of 1/8 ac or less (65% impervious) 77 85 90 92 Residential average lot size: 1/4 ac (38% impervious) 61 75 83 87 1/3 ac (30% impervious) 57 72 81 86 1/2 ac (25% impervious) 54 70 80 85 1 ac (20% impervious) 51 68 79 84 2 ac (12% impervious) 46 65 77 82 Developing urban area (newly graded; no vegetation) 77 86 91 94

Adapted from SCS (1985)

Table 3-12: Description of NRCS Soil Classifications

 Group Description Min. infiltration (in/hr) A Deep sand; deep losses; aggregated silts 0.30-0.45 B Shallow loess; sandy loam 0.15-0.30 C Clay loams; shallows sandy loam; soils low in organic content; soils usually high in clay 0.05-0.15 D Soils that swell significantly 0-0.05

Adapted from SCS (1985)

Table 3-13: Overland Texture Factor N

 Overland flow surface Low Medium High Smooth asphalt pavement 0.010 0.012 0.015 Smooth impervious surface 0.011 0.013 0.015 Tar and sand pavement 0.012 0.014 0.016 Concrete pavement 0.014 0.017 0.020 Rough impervious surface 0.015 0.019 0.023 Smooth bare packed soil 0.017 0.021 0.025 Moderate bare packed soil 0.025 0.030 0.035 Rough bare packed soil 0.032 0.038 0.045 Gravel soil 0.025 0.032 0.045 Mowed poor grass 0.030 0.038 0.045 Average grass, closely clipped sod 0.040 0.055 0.070 Pasture 0.040 0.055 0.070 Timberland 0.060 0.090 0.120 Dense grass 0.060 0.090 0.120 Shrubs and bushes 0.080 0.120 0.180 Land use Low Medium High Business 0.014 0.022 0.35 Semi-business 0.022 0.035 0.050 Industrial 0.020 0.035 0.050 Dense residential 0.025 0.040 0.060 Suburban residential 0.030 0.055 0.080 Parks and lawns 0.040 0.075 0.120

Adapted from Yen and Chow (1983)