Question

Estimate the peak rate of runoff from a watershed of 25 ha, having 10 ha under cultivation (C = 0.5), 5 ha under forests (C = 0.4) and 10 ha under grass cover (C = 0.45). The intensity of rainfall is 18 cm/hr.

• A. \(0.575 \mathrm{m}^3/\mathrm{s}\)
• B. \(57.5 \mathrm{m}^3/\mathrm{s}\)
• C. \(5.75 \mathrm{m}^3/\mathrm{s}\)
• D. \(5 \mathrm{m}^3/\mathrm{s}\)

Hint:

Rational Formula: \(Q = \frac{C I A}{360}\).
Always calculate the weighted C for mixed land use.
Units: C (dimensionless), I (cm/hr), A (ha), Q (\(\mathrm{m}^3/\mathrm{s}\)).

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
This question tests the application of the Rational Formula for estimating peak runoff rate from a watershed.
The Rational Formula is given by: \(Q = \frac{C \times I \times A}{360}\), where Q is in \(\mathrm{m}^3/\mathrm{s}\), C is the runoff coefficient, I is rainfall intensity in cm/hr, and A is area in hectares.

Step 2: Key Formula or Approach:
The weighted runoff coefficient for the watershed is calculated as:
\[ C_w = \frac{C_1 A_1 + C_2 A_2 + C_3 A_3}{A_1 + A_2 + A_3} \] Then, peak runoff rate is:
\[ Q = \frac{C_w \times I \times A_{total}}{360} \]

Step 3: Detailed Explanation:
Calculate the weighted runoff coefficient:
\[ C_w = \frac{(0.5 \times 10) + (0.4 \times 5) + (0.45 \times 10)}{10 + 5 + 10} \] \[ C_w = \frac{5 + 2 + 4.5}{25} = \frac{11.5}{25} = 0.46 \] Total area \(A = 25 \text{ ha}\), rainfall intensity \(I = 18 \text{ cm/hr}\).
Now, apply the Rational Formula:
\[ Q = \frac{0.46 \times 18 \times 25}{360} = \frac{207}{360} = 0.575 \times 10 = 5.75 \mathrm{m}^3/\mathrm{s} \]

Step 4: Final Answer:
Thus, the peak rate of runoff is \(5.75 \mathrm{m}^3/\mathrm{s}\), which corresponds to option (C).
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