CivilSolve

Hydrology

Rational Method Peak Flow

Peak stormwater runoff Q = C·i·A for a small catchment, with composite C over multiple subareas. Use for: peak discharge from rainfall intensity and drainage area, storm sewer or inlet sizing problems. Not for: runoff DEPTH or volume (SCS method), large watersheds.

Direct solving is free and needs no account. Have a word problem instead? Submit it as text.

Inputs

Load a sample problem:
subareasOne entry for a simple catchment; multiple entries for a composite-C catchment
subareas 1

Worked examples

These are the solver's own reference problems — the answers come from published sources or independent hand computation, never from the solver itself. The solution below is the live solver output for each.

Example 1

US single catchment: C=0.3, i=2 in/hr, A=5 ac

Given

subareas
  1. 1.runoff coefficient 0.3area 5 ac
intensity
2 in/hr

Assumptions

  • Rational method assumptions: storm duration ≥ time of concentration, uniform rainfall over the catchment, and runoff coefficient constant during the storm.

Solution steps

  1. Rational formula

    Peak flow is runoff coefficient × rainfall intensity × drainage area, in consistent units.

    Qp = C · i · A

    Qp = 0.3 × 2 in/h × 5 ac = 3.025 cfs

    = 3.025 cfs

  2. Handbook form check

    The familiar US form Q(cfs) ≈ C · i(in/hr) · A(ac) treats 1 ac·in/hr as exactly 1 cfs; it is actually 1.008 cfs, which is why the exact answer differs slightly from the shortcut.

    Shortcut: Q ≈ 3 cfs vs exact 3.025 cfs

Results

Peak runoff Qp

3.025cfs

Composite runoff coefficient Cw

0.3

Total drainage area

5ac

Where this answer was checked
source
Rational formula (NCEES FE Reference Handbook); exact unit conversion — Q = C·i·A with ac·in/hr → cfs carrying the 1.00833 factor
verified by
hand-recomputed
derivation
i = 2·0.0254/3600 = 1.41111e-5 m/s; A = 20234.282 m²; Q = 0.3·1.41111e-5·20234.282 = 0.0856583 m³/s = 3.025 cfs (folklore shortcut gives 3.0).

Example 2

SI single catchment: C=0.6, i=80 mm/hr, A=2 ha

Given

subareas
  1. 1.runoff coefficient 0.6area 2 ha
intensity
80 mm/hr

Assumptions

  • Rational method assumptions: storm duration ≥ time of concentration, uniform rainfall over the catchment, and runoff coefficient constant during the storm.

Solution steps

  1. Rational formula

    Peak flow is runoff coefficient × rainfall intensity × drainage area, in consistent units.

    Qp = C · i · A

    Qp = 0.6 × 80 mm/h × 2 ha = 0.2667 m^3/s

    = 0.2667 m^3/s

Results

Peak runoff Qp

0.2667m^3/s

Composite runoff coefficient Cw

0.6

Total drainage area

2ha

Where this answer was checked
source
Rational formula (NCEES FE Reference Handbook) — Q = C·i·A in coherent SI
verified by
hand-recomputed
derivation
i = 0.08/3600 = 2.2222e-5 m/s; A = 20000 m²; Q = 0.6·2.2222e-5·20000 = 0.26667 m³/s.

Example 3

composite catchment: 2 ac at C=0.9 + 8 ac at C=0.3, i=3 in/hr

Given

subareas
  1. 1.runoff coefficient 0.9area 2 ac
  2. 2.runoff coefficient 0.3area 8 ac
intensity
3 in/hr

Assumptions

  • Rational method assumptions: storm duration ≥ time of concentration, uniform rainfall over the catchment, and runoff coefficient constant during the storm.

Solution steps

  1. Composite runoff coefficient

    Weight each subarea's C by its area.

    Cw = Σ(Ci·Ai) / Σ(Ai)

    Cw = (0.9 × 2 ac + 0.3 × 8 ac) / 10 ac = 0.42

    = 0.42

  2. Rational formula

    Peak flow is runoff coefficient × rainfall intensity × drainage area, in consistent units.

    Qp = C · i · A

    Qp = 0.42 × 3 in/h × 10 ac = 12.71 cfs

    = 12.71 cfs

  3. Handbook form check

    The familiar US form Q(cfs) ≈ C · i(in/hr) · A(ac) treats 1 ac·in/hr as exactly 1 cfs; it is actually 1.008 cfs, which is why the exact answer differs slightly from the shortcut.

    Shortcut: Q ≈ 12.6 cfs vs exact 12.71 cfs

Results

Peak runoff Qp

12.71cfs

Composite runoff coefficient Cw

0.42

Total drainage area

10ac

Where this answer was checked
source
Rational formula with area-weighted composite C — Cw = ΣCᵢAᵢ/ΣAᵢ, then Q = Cw·i·A
verified by
hand-recomputed
derivation
Cw = (0.9·2 + 0.3·8)/10 = 4.2/10 = 0.42. Q = 0.42·(3·1.41111e-5·... ) — exact: 0.42·2.11667e-5·40468.564 = 0.359765 m³/s = 12.705 cfs (shortcut: 12.6).