Question

The surface of a 2-ha catchment is characterized by a runoff coefficient of 0.5, a Manning n for overland flow of 0.25, an average overland flow length of 60 m, and an average slope of 0.5%. Flow from the catchment drains into a channel. The catchment consists of 0.5 ha of impervious area that directly connects to the channel with a runoff coefficient of 0.9, Manning n of 0.03, average flow length of 15 m, and average slope of 0.5%. The 10-year IDF curve is given by:

i = 150/ (t + 8.96). where i is the average rainfall intensity in cm/h and t is the duration in minutes. Determine the peak runoff rate in the drainage channel.

Answer 1

To determine the peak runoff rate in the drainage channel, we need to calculate the runoff volume from both the impervious and pervious areas of the catchment, and then divide it by the time of concentration. The time of concentration (tc) is the time it takes for water to travel from the furthest point in the catchment to the outlet.

1. Calculate the Time of Concentration (tc):

- For the impervious area: tc_impervious = (L_impervious / V_impervious)^0.6

- For the pervious area: tc_pervious = (L_pervious / V_pervious)^0.6

Where:

- L_impervious is the flow length for the impervious area (15 m)

- V_impervious is the average flow velocity for the impervious area

- L_pervious is the flow length for the pervious area (60 m)

- V_pervious is the average flow velocity for the pervious area

2. Calculate the Average Rainfall Intensity (i) for the given duration (t) using the IDF curve:

i = 150 / (t + 8.96)

3. Calculate the Runoff Volume (Q) for both impervious and pervious areas:

Q_impervious = A_impervious * i * C_impervious

Q_pervious = A_pervious * i * C_pervious

Where:

- A_impervious is the area of impervious surface (0.5 ha)

- C_impervious is the runoff coefficient for impervious area (0.9)

- A_pervious is the area of pervious surface (1.5 ha)

- C_pervious is the runoff coefficient for pervious area (0.5)

4. Calculate the Peak Runoff Rate (Q_peak):

Q_peak = (Q_impervious + Q_pervious) / tc

Now, you need to calculate the flow velocities for both impervious and pervious areas and plug in the values to complete the calculations. After that, substitute the calculated values into the formula for Q_peak to determine the peak runoff rate in the drainage channel.