# Time of Concentration

The time of concentration, tc, in hours is the sum of the overland flow time, to, and the time of flow in the stormwater conveyance system, td, as follows:

$t_{c}=t_{o}+t_{d}$

The overland flow time to can be estimated using Friend’s Formula below or using the Nomograph in Design Chart 2.A1 (MSMA,2011):

$t_{o}=\frac{107.n^{*}L^{1/3}}{S^{1/5}}$

where

to = Overland sheet flow travel time (minutes)

L = Overland sheet flow path length (m)

N = Manning’s roughness value for the surface (refer Table 2.3 in (MSMA, 2011)

S = Slope of overland surface (%)

And td, the total time of flow in the storm water conveyance system, is given by:

$t_{d}=t_{r}+t_{g}+t_{ch}+t_{p}$

where

tr          = Roof flow time

tg          = Kerbed Gutter flow time

tch        = Channel flow time

tp          = Pipe flow time

$t_{g}=\frac{L}{40\sqrt{S}}$

where

tg          = Kerbed gutter flow time (minutes)

L          = Length of kerbed gutter flow (m)

S          = Longitudinal grade of the kerbed gutter (%)

The time of flow in open channel can be determined by dividing the length of the channel by the average flow velocity which can be calculated from normal hydraulic formula such as Manning’s Formula, given the channel cross section, length, roughness and slope.

where

$t_{ch}=\frac{n.L}{60R^{2/3}S^{1/2}}$

n          = Manning’s roughness coefficient.

S          = Friction slope (m/m)

L          = Length of reach (m)

tch        = Travel time on the channel (minutes)

For natural catchments and mixed flow paths, the time of concentration can be found by using the Brans by-Williams’ Equation which includes the time of overland flow and channel flow:

$t_{c}=\frac{F_{c}.L}{A^{1/10}S^{1/5}}$

where

tc          = Time of concentration (minutes)

Fc         = Conversion factor=92.5

L          = Length of flow path from catchment divide to outlet (km)

A          = Catchment area (ha)

S          = Slope of stream flow path (m/km)

For small catchments up to 0.4 ha in area, the time of concentration can be assumed to be 10 min instead of performing detailed calculation.

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