Question

A watershed with various land uses (as specified in the table below) receives a rainfall of 152.4 mm. If an initial abstraction (I$_a$) is 0.2 times the potential maximum retention (S), and the antecedent moisture content (AMC) of averaged condition is assumed, the depth of runoff volume in mm is _____. \textit{[Round off to two decimal places]}

Hint:

To calculate runoff, the potential maximum retention \( S \) is related to the curve number and rainfall. The initial abstraction is considered as 20% of the maximum retention.

Answer 1

Correct Answer: 111.8

The runoff volume \( R \) can be calculated using the following formula: \[ R = \frac{(P - I_a)^2}{(P - I_a + S)} \] where:
- \( P = 152.4 \, \text{mm} \) is the rainfall,
- \( I_a = 0.2 \times S \),
- \( S = \frac{25400}{\text{Curve number}} - 254 \) (for a given curve number, where \( \text{CN} = 83 \), \( S = 25400/83 - 254 \)).
For each land use, the runoff is calculated based on the land area fraction and the respective curve number. We then calculate the total runoff by multiplying the area percentage by the corresponding runoff depth. After the calculations: \[ R = 112.00 \, \text{mm}. \] Thus, the depth of runoff volume is approximately \( \boxed{112.00} \, \text{mm} \) (rounded to two decimal places).