What is the TR-55 sheet flow equation?

Tt = 0.007 (nL)^0.8 / (P2^0.5 s^0.4), with Tt in hours, L in feet and P2 the 2-yr 24-hr rainfall in inches. Source: TR-55 (1986) eq. 3-3, p. 3-3.

What is the maximum sheet flow length?

TR-55 (1986) says 300 ft. NRCS NEH 630 Chapter 15 (2010) says 100 ft. The New York design manual caps it at 150 ft pre-development and 100 ft post-development. Source: TR-55 pp. 3-3 and 3-4; NEH 630.15 p. 15-7; NYSDEC DM2024 § 4.6.

What velocity does shallow concentrated flow have?

Unpaved V = 16.1345 √s and paved V = 20.3282 √s, in ft/s with s in ft/ft. Source: TR-55 Appendix F, p. F-1.

What Manning n do I use for sheet flow over grass?

Dense grass 0.24, short grass prairie 0.15, Bermudagrass 0.41. Smooth surfaces such as concrete or asphalt take 0.011. Source: TR-55 Table 3-1, p. 3-3.

What is the minimum Tc?

0.1 hr in TR-55. A shorter sum is raised to 0.1 hr, and the calculator says when it does. Source: TR-55 p. 3-4.

Where does P2 come from?

The 2-yr 24-hr rainfall depth for the site, read from the rainfall source your reviewer accepts, such as NOAA Atlas 14. Source: TR-55 p. 3-3.

Time of concentration calculator

TR-55 Tc from a sheet flow, a shallow concentrated flow and a channel flow segment, in hours and minutes.

PRELIMINARYReference tables are still being checked against their printed sources. How results are checked

1.53hr

Tc 91.7 min: sheet 0.30 hr + shallow 0.24 hr + channel 0.99 hr.

Sheet flow Tt: 0.30 hr
Shallow concentrated Tt: 0.24 hr
Channel Tt: 0.99 hr
Sum of travel times: 1.53 hr
Tc: 91.7 min

The link carries these inputs, not the answer.

Worked example

The default inputs above are a published example: TR-55 Example 3-1 (Fig. 3-2, p. 3-5): published Tc 1.53 hr.

Sheet: Tt = 0.007 (0.24 × 100.00)^0.8 / (3.60^0.5 × 0.0100^0.4) = 0.30 hr
Shallow, unpaved: Tt = 1,400.00 / (3600 V), s 0.0100 = 0.24 hr
Channel: r = 27 / 28.20, V = 1.49 r^(2/3) s^(1/2) / 0.05, Tt = 7,300.00 / (3600 V) = 0.99 hr
Tc = ΣTt = 1.53 hr (91.7 min)

The formula

Tt = 0.007 (nL)^0.8 / (P2^0.5 s^0.4); V = 16.1345 √s unpaved, 20.3282 √s paved; V = 1.49 r^(2/3) s^(1/2) / n; Tt = L / (3600 V); Tc = ΣTt

TR-55 (1986) eq. 3-1 to 3-4, pp. 3-1 to 3-4, and Appendix F p. F-1

Tt: travel time of one segment, hr
n: Manning roughness; TR-55 Table 3-1 for sheet flow
L: flow length of the segment, ft
P2: 2-yr 24-hr rainfall depth for the site, in
s: slope of the land or watercourse, ft/ft
V: average velocity, ft/s
r: hydraulic radius, flow area a over wetted perimeter pw, ft
Tc: time of concentration, the sum of the travel times, hr

How long can sheet flow be?

TR-55 (1986) limits the kinematic sheet-flow equation to 300 ft. NRCS’s newer NEH 630 Chapter 15 (2010) says sheet flow typically lasts no more than 100 ft before it becomes shallow concentrated flow. In New York the design manual caps the sheet-flow length at 150 ft for pre-development and 100 ft for post-development, or 250 ft and 150 ft where the average slope is under 1%. The calculator warns past the NRCS length and refuses past TR-55’s; it never shortens the segment for you.

Manning n for sheet flow

TR-55 (1986) Table 3-1, p. 3-3. For flow depths of about 0.1 ft.
Surface	n
Smooth surfaces (concrete, asphalt, gravel, or bare soil)	0.011
Fallow (no residue)	0.05
Cultivated soils: Residue cover <= 20%	0.06
Cultivated soils: Residue cover > 20%	0.17
Grass: Short grass prairie	0.15
Grass: Dense grasses	0.24
Grass: Bermudagrass	0.41
Range (natural)	0.13
Woods: Light underbrush	0.4
Woods: Dense underbrush	0.8

Questions about this calculation

What is the TR-55 sheet flow equation?: Tt = 0.007 (nL)^0.8 / (P2^0.5 s^0.4), with Tt in hours, L in feet and P2 the 2-yr 24-hr rainfall in inches.; TR-55 (1986) eq. 3-3, p. 3-3
What is the maximum sheet flow length?: TR-55 (1986) says 300 ft. NRCS NEH 630 Chapter 15 (2010) says 100 ft. The New York design manual caps it at 150 ft pre-development and 100 ft post-development.; TR-55 pp. 3-3 and 3-4; NEH 630.15 p. 15-7; NYSDEC DM2024 § 4.6
What velocity does shallow concentrated flow have?: Unpaved V = 16.1345 √s and paved V = 20.3282 √s, in ft/s with s in ft/ft.; TR-55 Appendix F, p. F-1
What Manning n do I use for sheet flow over grass?: Dense grass 0.24, short grass prairie 0.15, Bermudagrass 0.41. Smooth surfaces such as concrete or asphalt take 0.011.; TR-55 Table 3-1, p. 3-3
What is the minimum Tc?: 0.1 hr in TR-55. A shorter sum is raised to 0.1 hr, and the calculator says when it does.; TR-55 p. 3-4
Where does P2 come from?: The 2-yr 24-hr rainfall depth for the site, read from the rainfall source your reviewer accepts, such as NOAA Atlas 14.; TR-55 p. 3-3

The other calculators

Curve number and runoff. Composite CN from cover type and hydrologic soil group, then TR-55 runoff depth for a 24-hr rainfall.
Rational method peak flow. Peak runoff Q = Cf·C·i·A from the runoff coefficient, rainfall intensity and drainage area, with the frequency factor for the storm.
Detention volume estimate. Storage needed to hold post-development runoff to an allowable release rate, by the modified rational critical-duration method.
NY water quality volume. WQv = P·Rv·A/12 from the 90th percentile rainfall, impervious cover and contributing area, per the NYSDEC design manual.

How results are checked Pricing for the full app

The full app runs the whole site: Atlas 14 rainfall frozen for the project, pre and post hydrographs, and the pond routed through its outlets. Then the NYSDEC checks you select, and a PDF report with the SWMM file a reviewer can rerun.

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