Hydrology and stormwater

Why it matters

When land is paved and roofed, rain that used to soak in runs off faster and in larger volumes. Without drainage design, that means flooded streets, eroded channels, overloaded pipes and polluted streams. Almost every site plan a civil engineer works on needs a stormwater calculation, and the first tool for small sites is the rational method.

The rational method

Q = C * i * A

• Q is the peak runoff rate.
• C is the runoff coefficient: the fraction of rainfall that runs off at the peak (near 0.9 for pavement and roofs, much lower for lawns and woods).
• i is the rainfall intensity for a storm lasting as long as the time of concentration of the drainage area.
• A is the drainage area.

Units matter:

US: Q (cfs) = C * i (in/h) * A (acres)        (the 1.008 conversion is usually dropped)
SI: Q (m^3/s) = C * i (mm/h) * A (ha) / 360

The method assumes rain falls uniformly over the whole area at a constant intensity for at least the time of concentration, so it is meant for small drainage areas. Agencies set their own limits (often somewhere between tens and a couple of hundred acres); larger or complex watersheds use hydrograph methods such as NRCS (TR-55) or software like HEC-HMS and EPA SWMM.

Composite runoff coefficient

Real sites mix surfaces. Weight C by area:

C = sum(A_i * C_i) / sum(A_i)

Agencies publish C values by land cover and often by storm frequency; use the ones your reviewing agency requires. Values in this lesson are illustrative.

Time of concentration and intensity

The time of concentration tc is the time for runoff to travel from the hydraulically most distant point to the outlet. Design intensity is read for a duration equal to tc, because that storm makes the whole area contribute at once. Several empirical formulas exist; the Kirpich formula, developed for small rural watersheds, is a classic:

tc (min) = 0.0078 * L^0.77 * S^-0.385      L in feet, S in ft/ft

Many agencies prescribe a method (often the NRCS velocity method, splitting sheet flow, shallow concentrated flow and channel flow) and a minimum tc, frequently 5 or 10 minutes.

Intensity comes from intensity-duration-frequency (IDF) data for the site and the design return period (for example the 10-year storm for pipes, 100-year for overflow routes). In the US, the source is NOAA's precipitation frequency data (https://hdsc.nws.noaa.gov/pfds/), often packaged into local design manuals. Checked on 2026-10-23.

Worked example (illustrative)

A 2.0 ha site has 0.8 ha of roofs and pavement (C = 0.90) and 1.2 ha of lawn (C = 0.25).

1. Composite C: (0.8 × 0.90 + 1.2 × 0.25) / 2.0 = (0.72 + 0.30) / 2.0 = 0.51.
2. Time of concentration: the longest flow path is 1,000 ft at a 2% slope. Kirpich gives tc = 0.0078 × 1000^0.77 × 0.02^-0.385 = 7.2 min. With an agency minimum of 10 minutes, use 10.
3. Intensity: the local 10-year IDF curve gives about 80 mm/h at 10 minutes (illustrative).
4. Peak flow: Q = 0.51 × 80 × 2.0 / 360 = 0.227 m^3/s (about 8 cfs).

That peak sizes the inlet and pipe (next lesson: Manning's equation). If the same site had been woodland with C = 0.15, the peak would have been about 0.067 m^3/s; the difference is why many jurisdictions require detention to hold post-development peaks to pre-development levels, and water quality measures (bioretention, permeable pavement, ponds) for the first flush of runoff.

Beyond peak flow

• Volume matters for detention and infiltration; the rational method gives peaks, not reliable volumes (the "modified rational method" approximates them for small sites).
• Regulation: the US Clean Water Act drives stormwater permits (NPDES / MS4); states and cities publish design manuals. Always design to the reviewing agency's manual.
• Climate: some agencies now require adjusted or future rainfall depths.

Common mistakes

• Using the wrong units constant (forgetting /360 in SI).
• Reading intensity for the wrong duration, such as a 1-hour value when tc is 10 minutes.
• Applying the rational method to a large watershed.
• Forgetting off-site area draining onto the site.
• Using C for the wrong storm frequency where the manual adjusts it.

Professional responsibility

Drainage reports are reviewed by agencies and sealed by licensed engineers. These numbers are illustrative. Real designs need review and sealing by a licensed professional engineer (PE) under the codes your jurisdiction adopts.

Recap

• Q = C i A gives peak runoff for small areas; watch the unit constant.
• Composite C is area-weighted; intensity is read at a duration equal to tc for the design return period.
• Use the reviewing agency's manual for coefficients, tc method, rainfall data and detention rules.

Try it

Open the Do tab to compute a composite C, a Kirpich time of concentration and the peak runoff in Python.