# WMS:FHWA Sheet Flow Equation

Sheet flow generally occurs for the first 300 feet at the headwater of streams. The following equation is used to describe sheet flow:

$T_t = \left ( \frac {K}{i^{0.4}} \right ) \left ( \frac {nL}{ \sqrt {S}} \right )^{0.6}$

where:

Tt = travel time for open channel flow segments.
K = emprical coefficient equal to 0.933 for English units and 6.943 for Metric.
i = rainfall intensity (in/hr).
n = Mannings roughness coefficient for overland flow. Suggested values are given in Table 3-2 of the FHWA HEC 22 manual and : arerepeated in the table below.
L = length of the overland flow segment (ft).
S = ground slope of the flow segment (ft/ft).

Manning's Roughness for overland sheet flow
Surface Description $n$
Smooth asphalt 0.011
Smooth concrete 0.012
Ordinary concrete lining 0.013
Good wood 0.014
Brick with cement mortar 0.014
Vitrified clay 0.015
Cast iron 0.015
Corrugated metal pipe 0.024
Cement rubble surface 0.024
Fallow (no residue) 0.05
Cultivated soils
Residue cover £ 20% 0.06
Residue cover > 20% 0.17
Range (natural) 0.13
Grass
Short prairie grass 0.15
Dense grasses 0.24
Bermuda grass 0.41
Woods
Light underbrush 0.40
Dense underbrush 0.80

The rainfall intensity is actually a function of the travel time for the flow segment. In order to iteratively solve for the travel time, define an IDF curve (function) to be used in conjunction with the equation. IDF curves are defined in WMS using Hydro 35, NOAA Atlas 2, or user defined rainfall intensities for specific durations. The IDF Curves dialog used as part of the rational method is used to set up equations relating i to Tt.