Question

If 24-hour excess rainfall to be impounded in 1m width of land between two consecutive contour bunds with a vertical interval of 2 m is 1 cm, then what will be the depth of impounding near bund?

• A. 5 cm
• B. 10 cm
• C. 15 cm
• D. 20 cm

Hint:

Notice that the ______land slope ($S$) cancels out______ during the derivation!
This means the maximum depth of water behind the bund ($d$) depends only on the vertical interval ($VI$) and the excess rainfall depth ($ER$), simplifying calculations.

Answer 1

The Correct Option is D

Step 1: Understanding the Concept:
Contour bunds are earthen embankments constructed across land slopes to intercept and impound runoff water.
The volume of water impounded per unit width behind the bund must equal the volume of excess rainfall falling over the catchment area between the two consecutive bunds.
Key Formula or Approach:
Equating the triangular cross-sectional area of impounded water to the excess rainfall volume per unit width:
\[ V_{\text{impounded}} = V_{\text{excess}} \]
\[ \frac{d^2}{2S} = \frac{VI}{S} \times ER \quad \Rightarrow \quad d^2 = 2 \cdot VI \cdot ER \]
where $d$ is the depth of impounding near the bund, $VI$ is the vertical interval of the bunds, $S$ is the land slope, and $ER$ is the excess rainfall depth.

Step 2: Detailed Explanation:
Let us perform the mathematical calculation using the derived formula:
1. ______Identify the given values:______
- Vertical Interval ($VI$) = $2\,\text{m} = 200\,\text{cm}$.
- Excess Rainfall ($ER$) = $1\,\text{cm}$.
2. ______Calculate the depth of impounding ($d$):______
Using the formula:
\[ d^2 = 2 \times VI \times ER \]
Substitute the values into the equation:
\[ d^2 = 2 \times 200\,\text{cm} \times 1\,\text{cm} = 400\,\text{cm}^2 \]
Take the square root on both sides:
\[ d = \sqrt{400} = 20\,\text{cm} \]
Therefore, the depth of impounding near the bund will be exactly $20\,\text{cm}$.

Step 3: Final Answer:
The depth of impounding near the bund is 20 cm, which corresponds to option (D).