Question

A drainage canal discharges 0.2 m$^3$/s and drains 250 ha. The drainage coefficient of land is

• A. 0.52 cm
• B. 6.90 cm
• C. 0.69 cm
• D. 0.43 cm

Hint:

A handy shortcut formula for Drainage Coefficient (\( D_c \) in cm/day) is:
\( D_c = \frac{8.64 \cdot Q}{A_{\text{ha}}} \times 100 \).
Using our values: \( D_c = \frac{8.64 \cdot 0.2}{250} \times 100 = 0.6912 \text{ cm/day} \).

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
The drainage coefficient ($D_c$) is defined as the equivalent depth of water (usually expressed in cm or mm) drained from a given catchment area in a 24-hour period.
Key Formula or Approach:
1. Volume of water drained in 24 hours ($V$) = $Q \times 24 \text{ hours} \times 3600 \text{ seconds/hour}$
2. Drainage coefficient ($D_c$) = $\frac{V}{\text{Area } (A)}$

Step 2: Detailed Explanation:
Given values:
- Discharge ($Q$) = $0.2 \text{ m}^3\text{/s}$
- Area ($A$) = $250 \text{ ha} = 250 \times 10^4 \text{ m}^2 = 2.5 \times 10^6 \text{ m}^2$
Calculate Volume of water drained in 24 hours ($V$):
\[ V = 0.2 \text{ m}^3\text{/s} \times 86400 \text{ s} = 17280 \text{ m}^3 \] Calculate equivalent water depth drained ($D_c$):
\[ D_c = \frac{17280 \text{ m}^3}{2.5 \times 10^6 \text{ m}^2} = 0.006912 \text{ m} \] Convert the depth to centimeters:
\[ D_c = 0.006912 \times 100 \text{ cm} \approx 0.69 \text{ cm} \]

Step 3: Final Answer:
The drainage coefficient of the land is 0.69 cm, corresponding to option (C).