Design flood estimation (regional formula): In Dickens’ formula, the peak flood discharge Q (in m^3/s) is taken proportional to the catchment area A raised to which power (Q ∝ A^n)?

Introduction / Context:
Before wide availability of long hydrologic records, Indian practice often used regional empirical formulae for preliminary design flood estimates. Dickens’ formula is one such classical relation linking peak discharge to drainage area with an exponent less than 1, reflecting non-linear growth of floods with catchment size.

Given Data / Assumptions:

• Dickens’ formula: Q = C * A^(3/4), where Q is in m^3/s, A is catchment area in km^2, and C is a regional coefficient (typically 6 to 30 depending on rainfall and region).
• Question asks only the exponent n in Q ∝ A^n.

Concept / Approach:
Empirical flood formulae (e.g., Ryve’s, Dickens’, Inglis’) use a power-law Q–A relationship. The exponent encapsulates hydrologic scaling: as basin area increases, unit response attenuates, so n is less than 1. Dickens’ established n = 3/4 for Indian conditions historically.

Step-by-Step Solution:
Recall Dickens’ relation: Q = C * A^(3/4).Hence the exponent n = 3/4.

Verification / Alternative check:
Comparison with other formulae shows similar exponents (generally between 0.6 and 0.8) capturing the diminishing incremental increase in floods with larger areas. This cross-check supports n = 3/4 for Dickens’ formula.

Why Other Options Are Wrong:

• 2/3, 4/5, 1/2: Not the classic Dickens exponent.
• 5/4: Greater than 1, which would imply super-linear growth and is inconsistent with attenuation observed in larger basins.

Common Pitfalls:

• Mixing up Dickens with other regional formulae and their exponents.
• Using empirical formulae outside their calibrated regions or without local coefficient C.

Final Answer:
n = 3/4