The overland flow time of concentration, tov, can be computed using the equation

$t_{ov}=\frac{L_{slp}}{3600*v_{ov}}$ 2:1.3.3

where $L_{slp}$ is the subbasin slope length (m), $v_{ov}$ is the overland flow velocity (m s$^{-1}$) and 3600 is a unit conversion factor.

The overland flow velocity can be estimated from Manning’s equation by considering a strip 1 meter wide down the sloping surface:

$v_{ov}=\frac{q_{ov}^{0.4}*slp^{0.3}}{n^{0.6}}$ 2:1.3.4

where $q_{ov}$ is the average overland flow rate ($m^3 s^{-1}$), $slp$ is the average slope in the subbasin (m $m^{-1}$), and $n$ is Manning’s roughness coefficient for the subbasin. Assuming an average flow rate of 6.35 mm/hr and converting units

$v_{ov}=\frac{0.005*L_{slp}^{0.4}*slp^{0.3}}{n^{0.6}}$ 2:1.3.5

Substituting equation 2:1.3.5 into equation 2:1.3.3 gives

$t_{ov}=\frac{L_{slp}^{0.6}*n^{0.6}}{18*slp^{0.3}}$ 2:1.3.6

The time of concentration is the amount of time from the beginning of a rainfall event until the entire subbasin area is contributing to flow at the outlet. In other words, the time of concentration is the time for a drop of water to flow from the remotest point in the subbasin to the subbasin outlet. The time of concentration is calculated by summing the overland flow time (the time it takes for flow from the remotest point in the subbasin to reach the channel) and the channel flow time (the time it takes for flow in the upstream channels to reach the outlet):

$t_{conc}=t_{ov}+t_{ch}$ 2:1.3.2

where $t_{conc}$ is the time of concentration for a subbasin (hr), $t_{ov}$ is the time of concentration for overland flow (hr), and $t_{ch}$ is the time of concentration for channel flow (hr).

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.