**Aidan Bigham**

**Hydrology and Erosion Management**

Rational Method

Rational Method

We need to:

Choose Runoff Coefficient, C

Estimate Time of Concentration, T

Select a Frequency (Return Period)

Obtain the Intensity-Duration-Frequency Curve (IDF Curve) for the region

Determine the Average Rainfall Intensity from IDF Curve, i

Use Rational Formula to estimate peak runoff, Q

**Q = C**

i

A

i = Rainfall Intensity

i

A

i = Rainfall Intensity

Q =

C

i A

C = Runoff Coefficient

The Rational Method

Activity 2

A ditch will collect runoff from the proposed roadway and an adjacent watershed. The tributary area has a fairly uniform cross-section with 30 feet of bituminous concrete and shoulders, 15 feet of gravel lined ditch (1” stones), and 200 feet of meadow draining to the ditch. The ditch begins at a small summit and drains to a culvert for a length of 1000 ft. The location of this proposed road is near Napier.

Estimate the 50-year storm discharge to the culvert.

Use the rational formula and the given rainfall chart to calculate the peak flow from a catchment with the following characteristics:

Total area; 16.5 ha

12 ha sealed or roofed, c = 0.9

4.5 ha grassed, c = 0.2

Time of concentration = 30 min

Design rainfall exceedance probability = 20%

Once the Rainfall Duration (Tc ) and Frequency (based on general guidelines for a region) are known, we can find the Rainfall Intensity

Local Intensity-Duration-Frequency Curves (IDF Curves) need to be used

Also referred to as Recurrence Interval

Choice of Frequency or Return Period depends on the Nature of the Project being designed

Also depends on the policy of a particular council

A few typical values are tabulated here

For computing Tc several formulae have been developed, and are being used by different councils

However, before choosing a formula, its applicability should be investigated

In Rational Method, Tc is used to determine rainfall intensity, i

Defined as the time required for water to flow from the hydraulically most remote point of the basin to the outlet

Runoff Coefficient , C, represents

The fraction of runoff to rainfall

The integrated effects of infiltration, storage, evaporation, natural retention and interception

Difficult to be determined precisely

The designer must use his experience and judgment in choosing its value

One of the POPULAR methods of estimating

PEAK RATE of RUNOFF

ENGINEERS are interested in

PEAK RATE of RUNOFF

Planning drainage facilities for an area

Designing storm drains

Designing soil conservation structures

RUNOFF VOLUME

Designing water storage structures

Designing irrigation systems

Now using Rational Formula,

with C = 0.53

i = 93.2 mm/h

A = 90 ha = 0.9 km

Runoff Coefficient, C

From Table 2 (NZ Building Code), C for different land uses is as follows:

Residential areas (impervious < 20%) : 0.45

Street : 0.85

Lawn : 0.25

Commercial : 0.65

Weighted Runoff Coefficient

Alternative Guidelines

Estimation of Peak Runoff using Rational Method

We Need to

Choose Runoff Coefficient, C

Estimate Time of Concentration, Tc

Select a Frequency (Return Period)

Obtain the Intensity-Duration-Frequency Curve (IDF Curve) for the region

Determine the Average Rainfall Intensity from IDF Curve, i

Use Rational Formula to estimate peak runoff, Q

Bransby-Williams Formula

Tc = time of concentration, hours

L = maximum flow length, m

A = drainage area, km

H = elevation difference between the highest and lowest points in the area, m

Alternatively, the following formula developed by US Geological Survey could be used:

If the actual catchment slope varies significantly from the value H/L (e.g. with a sudden steepening in the upper reaches), the average slope should be determined using Equal Areas Method

The basin slope for use in Eq. (3) may be calculated as,

H = elevation difference between the hydraulically most remote point of the basin and the outlet, m

10 min to log the answers

Activity 3 on moodle

Determine the runoff coefficient for a 80 ha project site with the following land use:

20% - Residential area (40% impervious)

10% - Streets

10% - Lawns

40% - Cultivated land – medium soaked soil

20% - Bush – heavy clay soil

Weighted Runoff Coefficient

Assumptions

In more conventional units

With

i in mm/h

A in km

Proposed by Mulvaney, an Irish Engineer, in 1851

Rational Formula

Q = C i A

Q = Peak runoff rate (m /s OR cumec)

C = Runoff coefficient (dimensionless)

i = Average rainfall intensity for a duration equal to the time of concentration (m/s)

A = Catchment area (m )

Determine the peak runoff rate for a project site for which the following information is available.

Drainage area: 90 ha

Land use:

40% Residential (impervious < 20%);

20% Streets;

20% Lawns;

20% Commercial

Maximum flow length: 1.0 km

Average slope: 0.5%

The maximum depth of rainfall for a 10-year recurrence interval is tabulated below.

US Soil Conservation Service Formula

Tc = time of concentration, hours

L = maximum flow length, m

A = drainage area, km

H = elevation difference between the highest and lowest points in the area, m

Using Eq. (2), with

C1 = 0.45; A1 = 10

C2 = 0.65; A2 = 4

C3 = 0.85; A3 = 4

C4 = 0.30; A4 = 2

# To be used as a guide for initial calculation of system requirements

Table 1: Runoff Coefficient for the Various Zones

(Source: Hamilton City Development Manual 2008)

A storm drain system consisting of two inlets and pipe is to be designed using rational method. A schematic of the system is shown. Determine the peak flow rates to be used in sizing the two pipes and inlets.

Rainfall intensity (in/h) as a function of t is:

Runoff Coefficient in Table 2 assumes average sloping terrain of 5 – 10%

Shall be adjusted as per Table 3, if needed

Table 3: Slope Correction for Runoff Coefficient

(Source: New Zealand Building Code Clause E1 Surface Water,

Department of Building and Housing, 2006)

Table 2: Runoff Coefficient for Detailed Design

(Source: New Zealand Building Code Clause E1 Surface Water,

Department of Building and Housing, 2006)

Time of Concentration, Tc

Given, L = 1 km = 1000 m

S = 0.5% = 0.005

Using Kirpich Formula

Rainfall Intensity, i

From Table by interpolation,

Maximum depth of rainfall for 30.6 min duration

=

Average Rainfall Intensity, i =

Hydraulically most remote point in the watershed

Compute the runoff coefficient for a 20 ha catchment, with 10 ha under residential areas (impervious area < 30%), 4 ha under industrial and commercial areas, 4 ha under asphalt and concrete surfaces, and 2 ha under grassed parks and playgrounds.

Solution

From Table 2 (NZ Building Code), C for different land uses is as follows:

Residential areas (impervious area < 30%) : 0.45

Industrial and commercial areas : 0.65

Asphalt and concrete surfaces : 0.85

Grassed parks and playgrounds : 0.30

Hydrological Processes

Runoff (flow) measurement

Points of interest

Surface Runoff

Rational method introduced

3

2

Q = CiA

Based on the Rational Formula and Assumptions behind it, try to list the limitations of the Rational Method

Rainfall is uniformly distributed over the catchment

Rainfall is uniformly distributed over the storm duration

The runoff rate resulting from any rainfall event is the maximum when the rainfall lasts for the duration

equal to or greater

than the time of concentration

The return period of peak runoff is the same as that of the rainfall intensity

The fraction of rainfall that becomes runoff is independent of the rainfall intensity or volume

Estimation of Peak Runoff

c

Runoff Co-effiecient

Zoning

Industrial

Commercial

Residential (flat terrain)

Residential (slope > 5%)

Runoff Coefficient

0.75

0.75

0.55

0.60

When working with a complex catchment which has various types of land use, a weighted

Runoff Coefficient

is used.

Computed by multiplying the runoff coefficient of each type of land area by the coefficient for that area and dividing the sum of the product by the total area.

Example 1:

Your turn

Time of concentration T

c

Time of Concentration T

c

There are a few different formulas for calculating Tc

Kirpich Formula (Kirpich 1940)

Tc = time of concentration of a basin, min

L = maximum flow length measured along the drainage line, m

S = basin slope

Basin Slope (S)

Basin Slope (S)

Basin Slope (S)

Kirpich Formula (Kirpich 1940)

Tc = time of concentration of a basin, min

L = maximum flow length measured along the drainage line, m

S = basin slope

2

2

Recall

Frequency (Return Period)

IDF Curves

Note: Some regional councils will prefer particular rainfall intensity tables.

In Hamilton this is the Ruakura Rainfall Gauge.

For consistency in this course we will all use the HIRDS data.

Just be aware that there are differences according to where you are working.

Example 2:

Solution:

Table 2: Runoff Coefficient for Detailed Design

(Source: New Zealand Building Code Clause E1 Surface Water,

Department of Building and Housing, 2006)

2

**Q = CiA**

Your turn

Your turn

Activity 4:

Activity 6:

Activity 5:

Estimation of Peak Runoff using Rational Method

We Need to

Choose Runoff Coefficient, C

Estimate Time of Concentration, Tc

Select a Frequency (Return Period)

Obtain the Intensity-Duration-Frequency Curve (IDF Curve) for the region

Determine the Average Rainfall Intensity from IDF Curve, i

Use Rational Formula to estimate peak runoff, Q

Summary

2

There are multiple ways to find this - the best method is probably to plot a graph of intensity vrs duration and read the graph.

The following is just another method :)