Question

The stormwater system of a given site includes the surface overland flow which exits by a rectangular concrete channel to (Manning‘s n = 0.015) drain it. The drainage channel is 100 m long, 20 cm wide, and has a longitudinal slope of 0.6%. The catchment surface of 1950 m2 has an average slope of 0.7%. The site surface is rough asphalt pavement (Manning‘s n = 0.020) and the distance from the upstream catchment boundary to the channel inlet is 100 m. The 25-yr design effective rainfall rate of 78.45 mm/h, which will produce an estimated channel flow rate of 0.034 m3 /s and channel water depth of 0.2 m.

Determine:

a) Estimate the time of concentration of the overland flow over the site using the kinematic wave approach.

b) Estimate the time of concentration from the open channel using the velocity approach and Manning’s equation.

c) Estimate the total time of concentration of the catchment

Answer 1

Ans a) We know, according to Kinematic wave equation,

Tc = 6.92 / ( x )

where, N = Manning roughness coefficient for site = 0.020

L = Length of flow at site = 100 m

i = Rainfall intensity = 78.45 mm/hr

S = Slope = 0.7 % or 0.007

Putting values,

=> Tc = 6.92 / ( x )

=> Tc = 8.11 min

Ans b) We know, according to velocity method,

Tc' = L / V

where, V = Flow velocity

According to0m Manning equation,

V = (1/N)

where, N = Manning roughness coefficient for channel = 0.015

R = Hydraulic depth = Area/Wetted perimeter = A./P

S = Channel slope = 0.6% or 0.006

For rectangular channel , A = BD = 0.2 x 0.2 = 0.04 sq.m

Wetted perimeter, P = B + 2D = 0.2 + 2(0.2) = 0.6 m

=> R = A/P = 0.067 m

=> V = (1 / 0.015)

=> V = 0.85 m/s

Hence, Tc' = (100 m) / (0.85 m/s) = 118 sec or 1.97 min

Ans c) Total time of concentration for catchment ,T

=> T = Tc + Tc'

=> T = 8.11 min + 1.97 min

=> T = 10.08 min