To determine the peak discharge from a catchment area, the Rational Method is commonly used. This method provides a straightforward way to estimate the maximum rate of runoff from a drainage basin, considering the characteristics of the area and the rainfall event.

Peak Discharge Calculation using Rational Method

The Rational Method is a widely accepted formula for calculating peak discharge in urban or small rural catchments. It assumes that the entire catchment contributes to runoff at the outlet and that the rainfall intensity is uniform over the catchment area for a duration at least equal to the time of concentration.

The formula for the Rational Method is given by:

\( Q = C I A \)

• \( Q \) = Peak discharge (typically in cubic meters per second, m³/sec)
• \( C \) = Run-off coefficient (dimensionless, representing the ratio of runoff to rainfall)
• \( I \) = Rainfall intensity (typically in meters per second, m/sec)
• \( A \) = Catchment area (typically in square meters, m²)

Rational Method Explained for Peak Discharge

The Rational Method is suitable for estimating peak discharge when the storm duration is greater than or equal to the time of concentration of the catchment. This ensures that all parts of the catchment area contribute to the runoff simultaneously, leading to the peak flow.

Catchment Data and Rainfall Parameters Provided

Let's list the values provided in the question for the catchment area and the storm:

The problem statement confirms that the storm duration is larger than the time of concentration, which aligns with the assumptions of the Rational Method for peak discharge calculation.

Unit Conversions for Accurate Discharge Calculation

For the Rational Method formula \( Q = C I A \) to yield peak discharge in m³/sec, the rainfall intensity (\( I \)) must be in m/sec and the catchment area (\( A \)) must be in m². Therefore, we need to convert the given units:

• Converting Catchment Area (\( A \)) from hectares to m²:

  We know that 1 hectare is equal to 10,000 square meters (m²).

  \( A = 80 \text{ hectares} \times 10,000 \frac{\text{m}^2}{\text{hectare}} \)

  \( A = 800,000 \text{ m}^2 \)

• Converting Rainfall Intensity (\( I \)) from cm/hr to m/sec:

  We know that 1 centimeter (cm) is equal to 0.01 meters (m), and 1 hour is equal to 3600 seconds (sec).

  \( I = 3.6 \frac{\text{cm}}{\text{hr}} \times \frac{0.01 \text{ m}}{1 \text{ cm}} \times \frac{1 \text{ hr}}{3600 \text{ sec}} \)

  \( I = \frac{3.6 \times 0.01}{3600} \frac{\text{m}}{\text{sec}} \)

  \( I = \frac{0.036}{3600} \frac{\text{m}}{\text{sec}} \)

  \( I = 0.00001 \frac{\text{m}}{\text{sec}} \)

Discharge Calculation using the Rational Formula

Now, we can substitute the converted values of the run-off coefficient, rainfall intensity, and catchment area into the Rational Method formula:

\( Q = C I A \)

\( Q = 0.5 \times 0.00001 \frac{\text{m}}{\text{sec}} \times 800,000 \text{ m}^2 \)

\( Q = 0.5 \times 8 \frac{\text{m}^3}{\text{sec}} \)

\( Q = 4.0 \frac{\text{m}^3}{\text{sec}} \)

Alternatively, for practical calculations, a simplified form of the Rational Method equation is often used when the catchment area (\( A \)) is in hectares and rainfall intensity (\( I \)) is in cm/hr. The formula becomes:

\( Q (\text{m}^3/\text{sec}) = \frac{C I A}{36} \)

Let's verify our result using this simplified formula:

• \( C = 0.5 \)
• \( I = 3.6 \text{ cm/hr} \)
• \( A = 80 \text{ hectares} \)

\( Q = \frac{0.5 \times 3.6 \times 80}{36} \)

\( Q = \frac{144}{36} \)

\( Q = 4.0 \frac{\text{m}^3}{\text{sec}} \)

Both calculation methods consistently yield the same result, confirming the accuracy of the peak discharge value.

Peak Discharge Result Summary

Based on the detailed calculation using the Rational Method, the peak discharge created by the storm for the given catchment area is 4.00 m³/sec.