Rational Method — Peak Discharge

Source file: rational_method.html

Purpose

Estimates the peak stormwater runoff discharge from a small catchment/basin for a given rainfall intensity, land-use runoff coefficient, and catchment area. Commonly used for sizing storm drains, culverts, and small conveyance channels.

Governing Equation

Metric form of the Rational Method:

Q = (C × i × A) / 360

Where: - Q — peak discharge (m³/s) - C — dimensionless runoff coefficient (fraction of rainfall that becomes runoff) - i — rainfall intensity (mm/hr), typically taken from an IDF curve at the time of concentration - A — catchment area (hectares) - 360 — unit conversion constant that reconciles mm/hr, hectares, and m³/s

Inputs

Input	Symbol	Notes
Runoff coefficient	`C`	Selected from a preset dropdown by land-use/surface type: • Pavement/roofs/metallic: 0.90 • Asphalt/concrete streets: 0.60 • Residential-suburban/normal soil: 0.30 • Agricultural/cultivated land: 0.15 • Forest/woodland/steep grass: 0.10
Rainfall intensity	`i`	mm/hr — the user must supply this (e.g., from a local IDF curve at the design storm's time of concentration)
Catchment area	`A`	hectares

Method

This is a direct, non-iterative calculation — no numerical solving is required:

User selects C from a preset list (or the last selected value persists).
User enters i and A.
Q is computed directly from the formula above on every input change (oninput), giving real-time feedback.

Outputs

Peak discharge Q (m³/s), displayed to 3 decimal places.

Integration — "Send to Manning's Calculator"

A Send Discharge (Q) to Manning's Calculator button builds a link to manning_calculator.html with the computed Q and an explicit unit flag:

manning_calculator.html?q=<Q_value>&units=metric

The units=metric flag is included because the Rational Method here is hardcoded to the metric form (mm/hr, hectares, m³/s) — this prevents Manning's calculator from misinterpreting the transferred value as cfs if it happens to be set to US Customary units.

Limitations

The Rational Method is only appropriate for small, relatively homogeneous catchments (typically < ~200 ha) where rainfall can be assumed uniform in time and space.
It assumes the storm duration equals or exceeds the time of concentration; the user is responsible for selecting an appropriate i from an IDF curve — this tool does not derive intensity from duration/frequency itself.
A single composite C is used; no weighted-area averaging across mixed land uses is performed (the user must pre-compute a composite coefficient if the catchment has mixed surfaces).