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

$q_{ch}=\frac{q_{ch}^* *Area}{3.6}$ 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$^{-1}$).

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.