# Channel Flow Time of Concentration

The channel flow time of concentration, $$t_{ch}$$, can be computed using the equation

$$t_{ch}=\frac{L_c}{3.6*v_c}$$                                                                  2:1.3.7

where $$L_c$$ is the average flow channel length for the subbasin (km), $$v_c$$ is the average channel velocity (m s$$^{-1}$$), and 3.6 is a unit conversion factor.

The average channel flow length can be estimated using the equation

$$L_c=\sqrt{L*L_{cen}}$$                                                                          2:1.3.8

where $$L$$ is the channel length from the most distant point to the subbasin outlet (km), and $$L_{cen}$$ is the distance along the channel to the subbasin centroid (km). Assuming $$L_{cen}=0.5*L$$, the average channel flow length is

$$L_c=0.71*L$$                                                                        2:1.3.9

The average velocity can be estimated from Manning’s equation assuming a trapezoidal channel with 2:1 side slopes and a 10:1 bottom width-depth ratio.

$$v_c=\frac{0.489*q_{ch}^{0.25}*slp_{ch}^{0.375}}{n^{0.75}}$$                                                          2:1.3.10

where $$v_c$$ is the average channel velocity (m s$$^{-1}$$), $$q_{ch}$$ is the average channel flow rate ($$m^3 s^{-1}$$), $$slp_{ch}$$ is the channel slope (m m$$^{-1}$$), and $$n$$ is Manning’s roughness coefficient for the channel. To express the average channel flow rate in units of mm/hr, the following expression is used&#x20;

$$q_{ch}=\frac{q_{ch}^* *Area}{3.6}$$                                                                  2.1.3.11

where $$^{q^*_{ch}}$$is the average channel flow rate (mm hr$$^{-1}$$), $$Area$$ is the subbasin area (km$$^2$$), and 3.6 is a unit conversion factor. The average channel flow rate is related to the unit source area flow rate (unit source area = 1 ha)

$$q^*_{ch}=q^*_0*(100*Area)^{-0.5}$$                                         2:1.3.12

where $$q_0^*$$ is the unit source area flow rate (mm hr$$^{-1}$$), $$Area$$ is the subbasin area (km$$^2$$), and 100 is a unit conversion factor. Assuming the unit source area flow rate is 6.35 mm/hr and substituting equations 2:1.3.11 and 2:1.3.12 into 2:1.3.10 gives

$$v_c=\frac{0.317*Area^{0.125}*slp_{ch}^{0.375}}{n^{0.75}}$$                                             2:1.3.13

Substituting equations 2:1.3.9 and 2:1.3.13 into 2:1.3.7 gives

$$t_{ch}=\frac{0.62*L*n^{0.75}}{Area^{0.125}*slp_{ch}^{0.375}}$$                                                    2:1.3.14

where $$t_{ch}$$ is the time of concentration for channel flow (hr), $$L$$ is the channel length from the most distant point to the subbasin outlet (km), n is Manning’s roughness coefficient for the channel, Area is the subbasin area (km$$^2$$), and $$slp_{ch}$$ is the channel slope (m m$$^{-1}$$).

![](https://1348478613-files.gitbook.io/~/files/v0/b/gitbook-x-prod.appspot.com/o/spaces%2F-MTFpIHUB1K63DLhLJaf%2Fuploads%2FrXALJiVjX2YTdcK3ptO2%2FTABLE6.jpg?alt=media\&token=dd743697-b314-4609-a0c1-a863bef62926)

Although some of the assumptions used in developing equations 2:1.3.6 and 2:1.3.14 may appear liberal, the time of concentration values obtained generally give satisfactory results for homogeneous subbasins. Since equations 2:1.3.6 and 2:1.3.14 are based on hydraulic considerations, they are more reliable than purely empirical equations.
