A catchment has an area of $25\ \text{km}^2$. The longest flow path is $6\ \text{km}$ and the average slope of the channel is $0.02$. Using the Kirpich formula $T_c = 0.0195\,L^{0.77}S^{-0.385}$ (where $L$ is in metres, $S$ is dimensionless and $T_c$ is in minutes), calculate:

(a) the time of concentration $T_c$ in hours (rounded to two decimal places);

(b) if a storm delivers rainfall at an intensity of $30\ \text{mm\,h}^{-1}$ for 2 h, and the infiltration capacity of the soil is $15\ \text{mm\,h}^{-1}$, determine the excess runoff depth (in mm) generated by the storm.

Question

A catchment has an area of $25\ \text{km}^2$. The longest flow path is $6\ \text{km}$ and the average slope of the channel is $0.02$. Using the Kirpich formula $T_c = 0.0195\,L^{0.77}S^{-0.385}$ (where $L$ is in metres, $S$ is dimensionless and $T_c$ is in minutes), calculate:

(a) the time of concentration $T_c$ in hours (rounded to two decimal places);

(b) if a storm delivers rainfall at an intensity of $30\ \text{mm\,h}^{-1}$ for 2 h, and the infiltration capacity of the soil is $15\ \text{mm\,h}^{-1}$, determine the excess runoff depth (in mm) generated by the storm.

Accepted Answer

Time of concentration $T_c \approx 1.19$ h; excess runoff depth = 30 mm.

Neco Model Questions Vol1 2023 Geography Question 43

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