# 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:

$t_{c}=&space;t_{o}+t_{d}$

The overland flow time to can be estimated using Friend’s Formula below or using the Nomograph in Design Chart 14.1(MSMA, 2000):

$t_{o}=\frac{107.n.L^{1/3}}{S^{1/2}}$

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 14.2 (MSMA, 2000)

S = Slope of overland surface (%)

Table 2.1: Table 14.2 (MSMA, 2000) Values of Manning’s ‘n’ for Overland Flow

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

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

where

$t_{r}$          = Roof flow time

$t_{g}$          = Kerbed Gutter flow time (Design Chart 14.2 (MSMA,2000) or via equation below)

$t_{ch}$        = Channel flow time

$t_{p}$          = Pipe flow time

$t_{g}$          = 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.

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

where

n          = Manning’s roughness coefficient.

S          = Friction slope (m/m)

L          = Length of reach (m)

$t_{ch}$        = Travel time on the channel (minutes)

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

$t_{c}$          = Time of concentration (minutes)

$F_{c}$         = 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 refer Table 14.3 (MSMA, 2000).

Table 2.2:  Table 14.3 (MSMA, 2000) Minimum Times of Concentration

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