Several methods have been developed for estimating the peak flood discharge that can be expected from small ungaged, wildland watersheds. These procedures are useful for determining the size (diameter) of the culvert that should be installed in a stream crossing that is to be constructed or upgraded.

**Determining the proper size (diameter) culvert requires**

1- Estimating the peak discharge of streamflow which would occur at each stream crossing during the 100-year flood, and then

2- Determining the size of the culvert which would handle that flow using the Federal Highway Administration (FHWA) culvert capacity nomograph (FHWA, 1965).

**The rational method of estimating 100 – year flood discharge**

The most commonly used technique for estimating 100-year flood discharges from small ungaged forested watersheds is the Rational Method. This method is based on the equation:

**Q100 = CIA**

**Where: **

**Q100** = predicted peak runoff from a 100-year runoff event (in cubic feet second)

**C** = runoff coefficient (per cent of rainfall that becomes runoff)

**I** = uniform rate of rainfall intensity (inches/hour)

**A** = drainage area (in acres)

**Assumptions**

1- The 100-year design storm covers the entire basin with uniform constant rainfall intensity until the design discharge at the crossing is achieved.

2.-The design watershed characteristics are homogenous.

3- Overland flow. This method is less accurate or predictable as the per cent impervious surface area in the watershed decreases.

4- The runoff coefficient (C) is constant across the watershed.

5- The 100-year storm event produces the 100-year flood flow.

**Advantages**

1- Frequently used and flexible enough to take into account local conditions

2- Easy to use if local rainfall data is available.

**Disadvantages**

1- Flexibility may lead to misuse or misinterpretation of local conditions.

2- Precipitation factor “I” may be difficult to obtain in remote areas.

3- Less accurate for watersheds greater than 200 acres

**Information needed:**

**A** = area of the watershed (acres)

**C** = runoff coefficient from Table A-1

**H** = elevation difference between the highest point in the watershed and the crossing point (feet)

**L** = length of channel from the head of the watershed to the crossing point (miles)

**I** = uniform rate of rainfall intensity. Obtained from precipitation frequency- duration data for local rain gages as shown in Table A-2.

**Steps**

1- Select runoff coefficient (C) values: Several different publications give a range of “C” values for the rational formula, however, the values given in Table A-1 by Rantz (1971) appear to be the most appropriate for the woodlands and forests around Eureka, California.

2- Select a rainfall intensity (I) value: In selecting an “I” value, two factors are considered: a) the travel time or time of concentration (Tc) for the runoff to reach the crossing, and b) the precipitation conditions for the particular watershed in question.

a. Time of concentration (Tc) can be calculated using the formula:

Tc = [ 11.9L3 H ]0.385

Where: Tc = time of concentration (in hours)

L = length of the channel in miles from the head of the watershed to the crossing point

H = elevation difference between the highest point in the watershed and the crossing point (in feet) (where the culvert is going to be installed). (Note: if the value of Tc is calculated as less than 10 minutes, studies suggest you should use a default value of 10 minutes)

b. Uniform rate of rainfall intensity. Once the time of concentration has been determined, then that value is used to determine which rainfall duration to use (i.e., if Tc = 1 hour, then use 100-year, 1-hour precipitation duration; if Tc = 4 hours, then use 100-year, 4-hour duration).

Rainfall depth duration tables similar to Table A-2 are available for precipitation stations throughout each state. For example, rainfall depth duration frequency data can be obtained from the California Department of Water Resources on-line at ftp://ftp.water. ca.gov/users/dfmhydro/Rainfall%20 Dept Duration-Frequency/. Contact your state’s water resources department (or its equivalent) to obtain rainfall depth duration frequency data for your area.

**Example: Rational Method used to ****calculate 100-year design storm**

1- Area of an example stream crossing watershed (A) = 100 acres.

2- Runoff coefficient (C) = 0.30 (loam woodland soil, from Table A-1)

3- Calculate the time of concentration (Tc)

Tc = [ 11.9L3 H ]0.385

**Where**

L = 1.8 mi., H = 200 ft.

Tc = [ 11.9(1.8)3 200 ]0.385 = 0.67 inches

According to Table A-2, a value of 0.67 inches corresponds to the 15-minute intensity of a 100-year return period storm event.

4- Calculate the rainfall intensity (I)

I =( 0.67 in 15 min )× ( x in 60 min ) = 2.68 in/hr

5- Calculate Q100

Q100 = CIA

Q100 = (0.3)×(2.68)×(100) = 80.4 cubic feet per second (cfs)