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watershed TR-55 3-segment North Carolina

Time of concentration the right way: sheet, shallow-concentrated, and channel flow (NC)

Time of concentration drives the design intensity in the Rational method and the unit peak in TR-55 — get it wrong and every downstream peak flow is wrong. This walks the NRCS TR-55 three-segment method along one flow path: sheet flow by the kinematic-wave equation, shallow concentrated flow by velocity, and channel flow by Manning. Real numbers, every step.

Result: For a 100-ft sheet-flow reach, 1,400 ft of shallow concentrated flow, and 2,000 ft of channel, the travel times are 0.225 + 0.197 + 0.139 hr, giving Tc = 0.56 hr (34 min). The sheet-flow segment dominates despite being only 100 ft — which is exactly why TR-55 caps sheet flow at 100 ft. Step-by-step below.

Flow-path inputs

Time of concentration is the travel time of runoff from the hydraulically most distant point to the outlet. Split the longest flow path into three segments:

SegmentLengthSlopeParameter
Sheet flow (overland)100 ft2.0%n = 0.24 (dense grass)
Shallow concentrated1,400 ft1.5%Unpaved
Channel flow2,000 ft0.5%V = 4.0 ft/s (Manning)
2-yr, 24-hr rainfall, P23.6 inNOAA Atlas 14 (sheet-flow term)

Step 1 — Sheet flow (kinematic wave)

TR-55's sheet-flow travel time, valid for L ≤ 100 ft:

$T_t = \frac{0.007\,(nL)^{0.8}}{P_2^{0.5}\, s^{0.4}}$

With n = 0.24, L = 100 ft, P2 = 3.6 in, s = 0.02:

$T_t = \frac{0.007\,(0.24 \times 100)^{0.8}}{3.6^{0.5}\,(0.02)^{0.4}} = \frac{0.007\,(24)^{0.8}}{1.897 \times 0.209} = \frac{0.0890}{0.3965} = 0.225 \text{ hr}$

That's 13.5 minutes for just 100 ft — sheet flow is slow, which is why it usually controls Tc on small sites.

Step 2 — Shallow concentrated flow

Once runoff concentrates into rills, TR-55 gives velocity directly. For unpaved surfaces:

$V = 16.1345\,\sqrt{s} = 16.1345\,\sqrt{0.015} = 1.98 \text{ ft/s}$
$T_t = \frac{L}{3600\,V} = \frac{1{,}400}{3600 \times 1.98} = 0.197 \text{ hr}$

Step 3 — Channel flow

In a defined channel, get velocity from Manning's equation (see the open-channel worked example); here V = 4.0 ft/s:

$T_t = \frac{L}{3600\,V} = \frac{2{,}000}{3600 \times 4.0} = 0.139 \text{ hr}$

Step 4 — Total time of concentration

$T_c = 0.225 + 0.197 + 0.139 = 0.561 \approx 0.56 \text{ hr} \;(34 \text{ min})$
Why it matters: Tc sets the design rainfall intensity in the Rational method and the unit peak in TR-55. A Tc that's too short overstates intensity and oversizes pipes; too long understates the peak and undersizes them. The sheet-flow length is the most-abused input — engineers stretch it past 100 ft to shrink the peak. Don't.

What changes if you tweak the inputs

If you change…The result moves…
Sheet n 0.24 → 0.011 (smooth pavement)Sheet Tt drops to ~0.02 hr; Tc falls to ~0.36 hr
Sheet length 100 → 50 ftSheet Tt ~0.13 hr; post-development paths are shorter and faster
Shallow flow paved (V = 20.33√s)Shallow velocity +26%; its Tt drops to ~0.16 hr
Channel slope 0.5% → 1.0%Higher channel velocity, shorter channel Tt

Compute Tc in HydroComplete

The Hydraflow engine builds Tc from sheet/shallow/channel segments (and Kirpich/FAA as alternatives), then feeds it straight into the peak-flow and routing calculations. Change a segment length or slope and watch Tc — and the design storm intensity — update.

Open in app 14-day free trial

Sources and further reading

— Michael Flynn, PE
This worked example uses HydroComplete's Hydraflow engine for the TR-55 segmented time-of-concentration calculation. Open the scenario in the app to verify or modify any input.

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