Saturday, November 5, 2022

Stormwater Runoff and the Rational Method in Innovyze H2OCalc

 

Stormwater Runoff and the Rational  Method

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 (0.8<i<1.2), and to 0.7 for heavy rain (i>1.2)

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)

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