# WMS:TR-55 Channel Flow Equation

Open channels are assumed to begin where surveyed cross section information has been obtained, where channels are visible on aerial photographs, or where blue lines (indicating streams) appear on United States Geological Survey (USGS) quadrangle sheets. Manning’s equation or water surface profile information can be used to estimate average flow velocity. Average flow velocity is usually determined for bankfull elevation.

Manning's Equation is:

$V = \frac {1.49 r^{\frac {2}{3}}s^{\frac {1}{2}}}{n}$

where:

V = Average velocity (ft/s).
r = Hydraulic radius (ft) and is equal to a/pw, where:
a = Cross sectional flow area (ft2)
pw = Wetted perimeter (ft)
s = Slope of the hydraulic grade line (channel slope, ft/ft)
n = Manning’s roughness coefficient for open channel flow.

Manning’s n values for open channel flow can be obtained from standard textbooks such as Chow (1959) or Linsley et al. (1982). The FHWA Channel Flow page also lists Manning's n values for various channel and pipe materials.

The hydraulic radius may be computed using the Channel Calculator. In this case, assume an approximate depth of flow or flow rate in order for the channel calculator to be able to compute the appropriate hydraulic radius.

After average velocity is computed using Manning's equation, the travel time Tt for the channel segment can be estimated using the following equation:

$T_t = \frac {L}{3600V}$

where:

Tt = Travel time (hr).
L = Flow path length (ft).
V = Average velocity (ft/s).
3600 = Conversion factor from seconds to hours.

WMS combines Manning's equation and the travel time equation into a single equation to compute the travel time using the TR-55 open channel equation.