Question

A rectangular catchment ABCD has an area of 7 hectares. The times of concentration from the four extreme points A, B, C and D to the outlet are 10, 20, 15 and 25 minutes, respectively. The rainfall intensity-duration relationship is given by \(I = \frac{25}{t+20}\), where I = rainfall intensity in cm/hr and t = time of concentration in minutes. The runoff coefficient of the catchment is 0.4. Determine the peak discharge from the catchment. (Enter the numerical value only in m\(^3\)/s.)

Hint:

In the Rational Method, always use the longest time of concentration to calculate the rainfall intensity. Pay close attention to the units of Area and Intensity, as the formula \(Q=CIA\) has different conversion factors depending on the units used.

Answer 1

Step 1: Determine Design Time of Concentration ($t_c$).
Peak discharge occurs when the entire catchment is contributing to the outlet. This is dictated by the longest travel time. $t_c = \max(10, 20, 15, 25) = 25$ minutes.
Step 2: Calculate Rainfall Intensity ($I$).
Using the given equation with $t = 25$ mins: $I = \frac{25}{25 + 20} = \frac{25}{45} = 0.5555$ cm/hr. Convert to mm/hr for the standard Rational formula: $I = 5.555$ mm/hr.
Step 3: Apply Rational Method.
$Q_p = \frac{CIA}{360}$, where $I$ is in mm/hr and $A$ is in hectares. $Q_p = \frac{0.4 \times 5.555 \times 7}{360} = \frac{15.554}{360} = 0.0432$ m$^3$/s.