Question

In a watershed of \(3000\) ha in flat topography, drainage coefficient was found to be \(5\) cm. If the drainage coefficient can be reduced to half by altering cropping pattern, what will be the discharge through drainage channel if both the condition are considered?

• A. \(0.057\) and \(1.52\ \text{m}^3/\text{sec}\)
• B. \(41.66\) and \(2.08\ \text{m}^3/\text{sec}\)
• C. \(0.173\) and \(0.83\ \text{m}^3/\text{sec}\)
• D. \(17.36\) and \(8.68\ \text{m}^3/\text{sec}\)

Hint:

Drainage discharge formula: \[ \boxed{ Q = \frac{A \times d}{864} } \] where:
• \(A\) in hectares
• \(d\) in cm/day Remember: \[ \boxed{ \text{Reducing drainage coefficient reduces discharge proportionally} } \]

Answer 1

The Correct Option is D

Concept: Drainage coefficient represents: \[ \boxed{ \text{Depth of water to be removed from a field within 24 hours} } \] Drainage discharge is calculated using: \[ Q = \frac{A \times d}{864} \] where:
• \(Q\) = drainage discharge in \(\text{m}^3/\text{s}\)
• \(A\) = area in hectares
• \(d\) = drainage coefficient in cm/day The factor \(864\) comes from unit conversion involving:
• hectares to square meters
• centimeters to meters
• day to seconds

Step 1: Writing the given data. Watershed area: \[ A = 3000\ \text{ha} \] Drainage coefficient: \[ d = 5\ \text{cm/day} \] Reduced drainage coefficient: \[ d' = \frac{5}{2} = 2.5\ \text{cm/day} \]

Step 2: Calculating discharge for original condition. Using: \[ Q = \frac{A \times d}{864} \] Substituting values: \[ Q = \frac{3000 \times 5}{864} \] \[ Q = \frac{15000}{864} \] \[ Q \approx 17.36\ \text{m}^3/\text{s} \] Thus: \[ \boxed{ Q_1 = 17.36\ \text{m}^3/\text{s} } \]

Step 3: Calculating discharge after reducing drainage coefficient. Now: \[ d = 2.5\ \text{cm/day} \] Using same formula: \[ Q = \frac{3000 \times 2.5}{864} \] \[ Q = \frac{7500}{864} \] \[ Q \approx 8.68\ \text{m}^3/\text{s} \] Thus: \[ \boxed{ Q_2 = 8.68\ \text{m}^3/\text{s} } \]

Step 4: Matching with the options. Calculated discharges are: \[ 17.36\ \text{m}^3/\text{s} \quad \text{and} \quad 8.68\ \text{m}^3/\text{s} \] This matches: \[ \boxed{ (D)\ 17.36\ \text{and}\ 8.68\ \text{m}^3/\text{s} } \] Final Conclusion: Drainage discharge before and after reducing drainage coefficient are: \[ \boxed{ 17.36\ \text{m}^3/\text{s} \quad \text{and} \quad 8.68\ \text{m}^3/\text{s} } \] Hence the correct answer is: \[ \boxed{ (D) } \]