Solution: Runoff Coefficient Calculation

The runoff coefficient ($C$) represents the ratio of direct runoff volume to the total rainfall volume over a watershed. It is calculated using the formula:

$C = \frac{\text{Volume of Runoff}}{\text{Volume of Rainfall}}$

Step 1: Calculate Rainfall Volume

First, convert the watershed area and rainfall rate to consistent units.

• Watershed Area ($A$): $100 \text{ ha} = 100 \times 10^4 \text{ m}^2 = 1 \times 10^6 \text{ m}^2$.
• Rainfall Rate: $5 \text{ cm h}^{-1} = 0.05 \text{ m h}^{-1}$.
• Rainfall Duration ($t_{rain}$): $2 \text{ hours}$.

Calculate the total rainfall depth:

$ \text{Rainfall Depth} = \text{Rainfall Rate} \times t_{rain} = 0.05 \text{ m h}^{-1} \times 2 \text{ h} = 0.1 \text{ m} $

Calculate the total volume of rainfall:

$ V_{\text{rainfall}} = A \times \text{Rainfall Depth} = (1 \times 10^6 \text{ m}^2) \times (0.1 \text{ m}) = 1 \times 10^5 \text{ m}^3 $

Step 2: Calculate Runoff Volume

Convert the runoff duration to seconds for consistency with the runoff rate.

• Runoff Rate ($Q_{out}$): $1 \text{ m}^3 \text{ s}^{-1}$.
• Runoff Duration ($t_{run}$): $10 \text{ hours} = 10 \times 3600 \text{ s} = 36000 \text{ s}$.

Calculate the total volume of runoff:

$ V_{\text{runoff}} = Q_{out} \times t_{run} = (1 \text{ m}^3 \text{ s}^{-1}) \times (36000 \text{ s}) = 36000 \text{ m}^3 $

Step 3: Calculate Runoff Coefficient

Now, use the formula for the runoff coefficient:

$ C = \frac{V_{\text{runoff}}}{V_{\text{rainfall}}} = \frac{36000 \text{ m}^3}{1 \times 10^5 \text{ m}^3} $

$ C = \frac{36000}{100000} = 0.36 $

The runoff coefficient for the watershed is $0.36$. This corresponds to Option 3.