Question

Using Dicken's formula with the constant C as 12, the flood discharge for a catchment area of 16 km$^2$ is

• A. 1.33 cumecs
• B. 48 cumecs
• C. 96 cumecs
• D. 192 cumecs

Hint:

Memorize the main empirical flood formulas and their exponents:
- Dicken's Formula: $Q_p = C A^{3/4}$
- Ryve's Formula: $Q_p = C A^{2/3}$
- Inglis Formula: $Q_p = \frac{124 A}{\sqrt{A+10.24}}$
Make sure to use the correct area units (usually km$^2$) for each formula.

Answer 1

The Correct Option is C

Step 1: Understanding the Question:
The question asks to calculate the peak flood discharge ($Q_p$) using Dicken's empirical formula, given the catchment area and Dicken's constant.

Step 2: Key Formula or Approach:
Dicken's formula is an empirical formula used for estimating the peak flood discharge from a catchment, particularly in India. The formula is:
\[ Q_p = C A^{3/4} \] where:
$Q_p$ = Peak flood discharge in cumecs (m$^3$/s)
$C$ = Dicken's constant, which depends on the region and catchment characteristics
$A$ = Catchment area in square kilometers (km$^2$)

Step 3: Detailed Explanation:
We are given:
- Dicken's constant ($C$) = 12
- Catchment area ($A$) = 16 km$^2$
Substitute these values into the formula:
\[ Q_p = 12 \times (16)^{3/4} \] To calculate $(16)^{3/4}$, we can first take the fourth root and then cube the result:
\[ (16)^{1/4} = \sqrt{\sqrt{16}} = \sqrt{4} = 2 \] Now, cube this result:
\[ (2)^3 = 8 \] So, $(16)^{3/4} = 8$.
Now, calculate the discharge:
\[ Q_p = 12 \times 8 \] \[ Q_p = 96 \text{ m}^3/\text{s} \text{ (cumecs)} \]

Step 4: Final Answer:
The flood discharge is 96 cumecs.