Detailed treatment of the Rational Method (Q = C·i·A) — runoff coefficients by surface type, time of concentration calculation (Kirpich, Manning kinematic, FAA), modified Rational for non-uniform catchments, validity range (catchments < 25 ha for simple, < 200 ha with sub-area weighting), assumptions + limitations, when to switch to SCS-CN or hydrograph methods.
Compute peak design discharge for an urban catchment using the Rational Method. Valid for catchments < 200 ha (with sub-area weighting) or < 25 ha single sub-catchment. Beyond that, use SCS-CN or hydraulic modeling (chapter 4).
Compute the time for runoff to travel from the most-distant catchment point to the design point. Take the maximum of Kirpich + FAA results. Output drives IDF intensity selection in the Rational Method.
The Rational Method is the workhorse of urban drainage design — Q = C·i·A — and probably the most-used (and most-misused) formula in municipal engineering. Its appeal is simplicity: pick a runoff coefficient from a table, get rainfall intensity from an IDF curve, multiply by area, and you have your peak design flow.
Its danger is also simplicity. The Rational assumes uniform rainfall over the entire catchment for the duration of the time of concentration, ignores storage, ignores temporal variability, and breaks down beyond ~25 ha (or ~200 ha with sub-area weighting). Beyond that scale, you need hydrograph methods (SCS-CN unit hydrograph, hydraulic modeling).
Runoff coefficients are the most-debated input. The CPHEEO 2019 tables give reasonable ranges, but Indian cities are densifying — a colony that was 0.50 in 1995 is probably 0.65-0.70 in 2026 because of plot-to-plot densification and paving of every available surface. Always design for future imperviousness, not current. Master plan for 25-year build-out.
Composite C (area-weighted average across surface types) is mandatory for any heterogeneous catchment. Take the example: 60 % paved, 30 % residential, 10 % park gives composite C ≈ 0.72 — not the simple arithmetic average of the three coefficients.
Time of concentration is where engineers regularly get into trouble. tc isn't a single number for the whole catchment — each sub-catchment in a network has its own tc. Using a catchment-wide tc undersizes branch lines. Compute tc independently for each design point, walk through Kirpich or FAA for the overland portion, add pipe time for the buried portion.
Frequency adjustment: high-return-period storms exceed soil infiltration capacity, so the effective C rises. Add 0.05-0.15 to your tabulated C for 25-yr+ designs.
Where this chapter sits: Rational Method gives you peak Q for each design point — the input to pipe sizing in chapter 7. Get C and tc right and the whole network sizes correctly. Get them wrong and you either flood the streets or oversize concrete by 30-50 %.