The Rational method was developed over 100 years ago and continues to be used for urban watershed modeling, typically on areas less than about 20 acres. While there exists many varieties of the Rational method, Stormwater Studio uses the most popular… the Standard Rational.

## Standard Rational

The Standard Rational method computes the peak discharge as determined by the well-known Rational formula.

Where:

Qp = peak discharge, cfs (cms)

k = 1 English (0.00278 Metric)

C = runoff coefficient

A = basin area, acres (hectares)

i = intensity, in/hr (mm/hr)

Cf = frequency correction factor where C x Cf <= 1.0

The rainfall intensity is computed by one of the following equations:

### FHA Equation

Where:

B, D and E are constants

Tc = time of concentration in minutes subject to the Minimum Tc

### Third Degree Polynomial Equation

Where:

I = rainfall intensity in in/hr (mm/hr)

X = Ln(time duration in minutes)

A = coefficient

B = coefficient

C = coefficient

D = coefficient

Appropriate values for X are 8 to 180 minutes subject to the Minimum Tc.

The B,D and E constants can be pre-computed by the program, or as manually entered, and are based on your geographic location. Polynomial coefficients can be directly entered in to software as well.

### Calculation Procedure

The time of concentration is the time required for water to flow from the remotest point of the drainage area to the point of the system in question. The program computes Tc by choosing the greatest of the following:

- The time of concentration of the upstream Line plus the time of flow through the Line from the upstream run.
- The time of concentration as above for any other connecting Line(s).
- The Inlet Time of the Line under consideration.

For the most upstream run, the time of concentration is the Inlet Time. For all succeeding lines, the time of concentration is computed as the largest value of the three items above.

When computing flows for downstream lines, Stormwater Studio uses a total CxA, that is, CA for the line in question plus CA for the next upstream line plus CA for the next upstream line and so on.

## Tc by TR55

In addition to manual entry, Stormwater Studio can compute Time of Concentration using TR55. With TR55, Tc is broken into 3-components or segments. The final Tc is the sum total of the three components.

- Sheet Flow
- Shallow Concentrated Flow
- Channel Flow

Tc = TSheet + TShallow + TChannel

### Sheet Flow Time

Flow over plane surfaces and typically ranges between 125 to 150 feet (40 to 45 meters).

Where:

n = Manning’s roughness coefficient

L = Flow Length (must be <= 100 ft (30 m) per WinTR55)

P2 = Two-year 24-hr rainfall, inches (mm)

S = Land Slope, ft/ft (m/m) – **Entered as % in the program**

### Shallow Concentrated Flow Time

After about 100 feet, sheet flow becomes shallow concentrated flow. The computed Average Velocity described below is based on the solution of Manning’s equation with different assumptions for n (Manning’s roughness coefficient) and r (hydraulic radius, ft). Per TR55, for for paved areas, n is 0.025 and r is 0.2; unpaved areas, n is 0.05 and r is 0.4.

Where:

L = Flow Length, ft (m)

V = Average velocity, ft/s (m/s) and

Where:

Cp = 20.3282 paved surfaces

Cp = 16.1345 unpaved surfaces

S = Watercourse slope, ft/ft (m/m)

### Channel Flow Time

Occurs within channels, swales, ditches, streams or even piped systems. Manning’s equation is used to compute velocity.

Where:

L = Flow length, ft (m)

V = Average velocity, ft/s (m/s) and

Where:

V = Average velocity, ft/s (m/s)

R = Hydraulic radius, ft (m) = a/wp

S = Channel slope, ft/ft (m/m) – **Entered as % in the program**

n = Manning’s roughness coefficient