Dicken's formula for finding discharge is

Question

Examoogle · Accepted Answer

The correct answer is Option B: $Q = C \cdot A^{3/4}$. Dicken's formula is an empirical formula used to estimate the maximum flood discharge from a catchment area. It relates the peak flood discharge ($Q$) to the catchment area ($A$) using a constant ($C_D$) that varies based on the geographical and climatic characteristics of the region.

Step-by-Step Solution & Concepts:
Dicken's formula is an empirical formula used to estimate the maximum flood discharge from a catchment area. It relates the peak flood discharge ($Q$) to the catchment area ($A$) using a constant ($C_D$) that varies based on the geographical and climatic characteristics of the region.

Working Principle: The formula assumes that the peak discharge is proportional to a power of the catchment area. This relationship accounts for the fact that as the catchment size increases, the intensity and duration of rainfall causing peak discharge do not increase linearly, leading to the exponent being less than 1.

Key Formulas: $Q = C_D \cdot A^{3/4}$ — Dicken\'s formula for peak discharge estimation

Key Points: Dicken\'s formula is primarily used for basins in North and Central India.; The constant $C_D$ (Dicken\'s constant) depends on the rainfall intensity, soil type, and catchment characteristics.; It is an empirical method, meaning it is based on historical data rather than derived from physical fluid dynamics laws.; Other similar empirical formulas include Ryves formula ($Q = C \cdot A^{2/3}$) and Inglis formula.

Advantages: Simple to apply; Requires minimal meteorological data

Disadvantages: Regional specificity (limited accuracy outside North India); Does not account for complex watershed parameters

Applications: Estimation of peak flood for small to medium drainage basins; Design of highway culverts and small bridges

Additional Info: Dicken\'s formula: $Q = C_D \cdot A^{3/4}$. Ryves formula: $Q = C_R \cdot A^{2/3}$. Inglis formula: $Q = \frac{124 \cdot A}{\sqrt{A + 10.4}}$. Option A ($A^{3/5}$) and C ($A^{4/5}$) are incorrect exponents for this specific empirical relation.

Answer: B is correct — Dicken\'s formula for finding flood discharge is represented as $Q = C \cdot A^{3/4}$.

Exam Tip: Always remember the exponents: Dicken uses 3/4, Ryves uses 2/3. Examiners frequently test the variation in these empirical coefficients.

Examoogle · Answer

Option A: $Q = C \cdot A^{3/5}$

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Option C: $Q = C \cdot A^{4/5}$

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Option D: none of the above

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