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CHAPTER 3

Runoff Estimation – Rational Method and C Coefficients

Rational Method & Runoff Coefficients

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.

💦 Runoff EstimationManual on Storm Water Drainage Systems1st Edition (2019), with AMRUT 2.0 + Smart Cities Mission updates referenced

Key formulas

  • Q (m³/s) = C × i × A / 360 (Rational; A in hectares, i in mm/hr)
  • Q (cusec) = C × i × A (Rational; A in acres, i in inch/hr)
  • Time of concentration tc = t_overland + t_pipe
  • Kirpich: tc (min) = 0.0195 × (L^0.77 / S^0.385), L in m, S = slope (m/m)
  • FAA (kinematic): tc (min) = 1.8 × (1.1 − C) × L^0.5 / S^(1/3)
  • Composite C = Σ(Ci × Ai) / Σ Ai (area-weighted)
  • Modified Rational with storage: Q_design = Q_peak × (1 − S/V_storage)

Key values & thresholds

C paved asphalt concrete
0.85 - 0.95
C roof metal concrete
0.85 - 0.95
C gravel compact paved
0.50 - 0.70
C residential dense built
0.65 - 0.80
C residential medium built
0.40 - 0.60
C industrial heavy
0.60 - 0.90
C park lawn clay soil
0.20 - 0.40
C park lawn sandy soil
0.10 - 0.25
C open ground undeveloped
0.10 - 0.30
C forest dense
0.10 - 0.25
C increase per 5yr to 25yr return period
+0.10 (consider for higher return periods)
rational validity simple
< 25 ha (single sub-catchment)
rational validity with subareas
< 200 ha

Clause-level requirements

  • Rational Method assumes uniform rainfall over entire catchment for duration ≥ tc — invalid for catchments > 200 ha or strongly non-uniform.
  • Composite runoff coefficient must be area-weighted average; never arithmetic mean.
  • For higher return periods (25-100 yr), runoff coefficient may be increased by 0.05-0.15 (storm exceeds soil infiltration capacity).
  • Time of concentration shall be the longest hydraulic flow path from catchment boundary to design point, including overland + channel + pipe time.
  • Design intensity i shall be IDF intensity at duration = tc, return period as specified.
  • Where storage exists in the catchment (ponds, depressions), modified Rational with storage adjustment is required — straight peak Rational overestimates.

Practitioner notes — what goes wrong in the field

  • Rational works for small urban catchments (< 25 ha single, < 200 ha with sub-areas) — beyond that, switch to SWMM or MIKE URBAN with proper hydrograph routing.
  • For Indian cities, average residential C is creeping upward (0.50 → 0.65) as paving + buildings densify — re-evaluate periodically, don't assume 1980s coefficients.
  • Composite C example: 60 % paved (C=0.90), 30 % residential (C=0.55), 10 % park (C=0.20) → weighted C = 0.5400+0.165+0.020 = 0.725.
  • Time of concentration in flat urban catchments typically 10-30 min; hilly + small 5-15 min; large flat 30-60 min.
  • Min tc = 5 min (don't use shorter — IDF curves often unreliable for sub-5-min durations).
  • If the IDF is given as 60-min intensity, scale to tc duration using Sherman's equation OR the IDF table directly.
  • Common error: using C for current land use without considering future build-out. Master plan should design for 25-year future imperviousness, not current.
  • Rooftop-to-drain direct connection (downpipe) gives near-100 % runoff — assume C = 0.95 for such areas.
  • For low-density layouts (< 30 % paved), the Rational can overestimate peak; modified Rational with storage adjustment + SCS-CN cross-check.
  • Compute tc separately for each sub-catchment in a network design — using catchment-wide tc is wrong + leads to undersized branches.

FAQs

When is the Rational Method valid?
Small urban catchments < 25 ha (single sub-area) or < 200 ha with proper sub-area weighting. Beyond that, switch to SCS-CN unit hydrograph or full hydraulic modeling (SWMM, MIKE URBAN). Also assumes uniform rainfall + steady-state conditions.
What runoff coefficient should I use for residential areas?
0.40-0.60 for medium-density (typical Indian colony, 30-50 % paved); 0.65-0.80 for dense built-up (apartment blocks, > 60 % paved). Use lower end for greenfield design with mandated open space; upper end for retrofits in dense areas.
How do I calculate time of concentration?
Sum overland time (Kirpich or FAA equation) + pipe travel time (length / velocity). Use longest hydraulic path. For Indian urban, typical tc = 10-30 min for residential catchments, 15-45 min for arterial road catchments.
Should I increase C for higher return periods?
Yes — for 25-yr+ design, increase C by 0.05-0.15 (or use 'frequency factor'). Higher-intensity storms exceed soil infiltration + saturate quickly, raising effective runoff fraction. CPHEEO 2019 recommends this adjustment.
What's the difference between Rational and SCS-CN?
Rational gives peak Q for a single design storm — fast + simple, suited to small catchments. SCS-CN computes runoff volume + temporal hydrograph for any storm — better for storage design, larger catchments, real-time forecasting. CPHEEO 2019 recommends SCS-CN for catchments > 200 ha.

Calculators (2)

Rational Method — Peak Design Discharge (Q = C·i·A / 360)

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).

Inputs
Composite runoff coefficient
Area-weighted; paved 0.85–0.95, residential 0.40–0.80, parks 0.10–0.30
Design rainfall intensitymm/hr
From IDF curve at duration = tc
Catchment areaha
Frequency adjustment (25-yr+)%
+5–15 % to C for return periods 25 yr+
Outputs
Adjusted runoff coefficient
0.65
C × (1 + freq/100); cap at 0.95
Peak design discharge
2.708m³/s
Q = C × i × A / 360
Peak design discharge
2,708L/s
Q (m³/s) × 1000
CPHEEO Reference Values
Paved (asphalt/concrete)C = 0.85 – 0.95
RoofC = 0.85 – 0.95
Dense residentialC = 0.65 – 0.80
Medium residentialC = 0.40 – 0.60
Park / lawn (clay)C = 0.20 – 0.40
Open groundC = 0.10 – 0.30
Validity (single)< 25 ha
Validity (with sub-areas)< 200 ha
Download the Excel version to keep a local copy with live formulas — change inputs in the sheet and outputs recompute automatically.

Time of Concentration (Kirpich + FAA)

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.

Inputs
Hydraulic flow path lengthm
Average slope (m/m)
Rise / run; e.g. 1 % = 0.01
Runoff coefficient (for FAA)
Outputs
Time of concentration (Kirpich)
13.7min
tc = 0.0195 × L^0.77 / S^0.385
Time of concentration (FAA kinematic)
84.1min
tc = 1.8 × (1.1 − C) × L^0.5 / S^(1/3)
Design tc (max + 5 min minimum)
84.1min
max(Kirpich, FAA, 5)
CPHEEO Reference Values
Min tc (per CPHEEO)5 min
Typical urban tc10 – 30 min
Hilly/small catchment tc5 – 15 min
Large flat catchment tc30 – 60 min
Download the Excel version to keep a local copy with live formulas — change inputs in the sheet and outputs recompute automatically.

Cross-references

IS 12251:1987 (surface drains) Annex BIRC SP 50:2013FHWA HEC-22 Urban Drainage (international cross-ref)USDA TR-55 (runoff curve numbers)

Tags

Rational methodrunoff coefficient Ctime of concentrationKirpich formulacomposite Cdesign dischargepeak runoffimperviousnesscatchment area

Engineer's notes

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 %.

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Manual on Storm Water Drainage Systems · 1st Edition (2019), with AMRUT 2.0 + Smart Cities Mission updates referenced · Central Public Health and Environmental Engineering Organisation (CPHEEO), Ministry of Housing and Urban Affairs, Government of India.
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