The rational method estimates the peak discharge produced in a small catchment by rainfall of constant intensity whose duration equals the time of concentration: the moment at which the whole catchment contributes at once.
How it works
How to use the calculator
- Choose how you obtain the time of concentration: you enter it, or the Kirpich formula calculates it from the length and the elevation drop of the channel.
- Choose how you obtain the intensity: you enter it, or you paste your IDF curve and choose the return period.
- Enter the area and the runoff coefficient, or divide the catchment into sub-areas to obtain a weighted C.
- Press “Calculate”. If the catchment falls outside the usual limits of the method, you will see a notice before buying the report.
Assumptions and limits
- Rainfall of uniform intensity over the whole catchment, with a duration equal to the time of concentration.
- Runoff coefficient constant during the storm.
- The return period of the discharge is that of the design rainfall.
- Small catchments: by default, the calculator gives a notice above 80 ha or with a time of concentration shorter than 5 min. You can adjust these limits to your standards.
- The IDF curve is interpolated on a logarithmic scale between the tabulated durations; it is not extrapolated beyond them.
Formulas and reference values
Rational method formula
Q = C · i · A / 3 600 000
With i in mm/h and A in m², Q is obtained in m³/s. With A in hectares, the equivalent expression is Q = C · i · A / 360.
Kirpich formula
tc = 0.01947 · L0.77 · S−0.385, with S = ΔH / L
With L in metres and S in m/m, t_c is obtained in minutes. It was calibrated on small rural catchments with a defined channel and slopes of 3 % to 10 %.
Interpolation on the IDF curve
log i = log i1 + (log tc − log t1) · (log i2 − log i1) / (log t2 − log t1)
The intensity is taken from the curve of the chosen return period, for a duration equal to the time of concentration, between the two tabulated durations that bracket it.
Indicative values of the runoff coefficient
Usual ranges for return periods of 5 to 10 years (Chow et al., 1988). Choose the value according to the slope, the soil and the condition of the surface; higher values are usually adopted for longer return periods.
| Surface | C |
|---|---|
| Roofs | 0.75 – 0.95 |
| Asphalt pavement | 0.70 – 0.95 |
| Concrete pavement | 0.80 – 0.95 |
| Brick and paving blocks | 0.70 – 0.85 |
| Downtown business areas | 0.70 – 0.95 |
| Industrial areas | 0.50 – 0.90 |
| Single-family residential | 0.30 – 0.50 |
| Multi-family residential | 0.40 – 0.75 |
| Parks and cemeteries | 0.10 – 0.25 |
| Lawns, sandy soil (slope 2–7 %) | 0.10 – 0.15 |
| Lawns, clay soil (slope 2–7 %) | 0.18 – 0.22 |
Frequently asked questions
Up to what catchment size is the rational method valid?
It is a method for small catchments. The calculator gives a notice above 80 ha, a usual limit in the literature; many standards allow somewhat more. You can adjust the limit in the notice.
Why is the rainfall duration equal to the time of concentration?
With that duration the whole catchment contributes at the outlet at once and, since intensity decreases with duration, the largest peak discharge is obtained.
What if the time of concentration falls outside my IDF curve?
The calculator only interpolates between the durations of your table: extend it with a shorter or longer duration, as the case may be.
How is the runoff coefficient weighted?
Each sub-area weighs according to its surface: C = Σ(Cᵢ·Aᵢ) / ΣAᵢ. The report includes the table of sub-areas.
References
- Chow, V. T., Maidment, D. R., and Mays, L. W. (1988). Applied Hydrology. McGraw-Hill.
- Kirpich, Z. P. (1940). Time of concentration of small agricultural watersheds. Civil Engineering, 10(6), 362.