Flood estimation for catchment shape: For a fan-shaped catchment area, which empirical formula is commonly recommended for estimating high floods in Indian practice?

Introduction / Context:
Peak flood estimation for ungauged basins in India often relies on empirical formulae tailored to regional hydrology and catchment geometry. The plan shape of a catchment (fan-shaped vs elongated) influences concentration time and peak runoff characteristics.

Given Data / Assumptions:

• Fan-shaped catchment, promoting rapid concentration of flow.
• No long-term gauge data available; empirical formula needed.
• Use of classical Indian formulae: Dicken's, Ryve's, Inglis, each with regional context.

Concept / Approach:
Fan-shaped basins tend to yield higher, sharper floods due to short travel times. Traditional Indian practice commonly associates Ryve's formula with catchments in southern regions and situations where quick concentration is expected, making it suitable for fan-shaped basins in standard MCQ conventions.

Step-by-Step Solution:
Identify shape (fan-shaped) ⇒ expect higher peak.Select an empirical relation aligned with quick concentration characteristics.Ryve's formula is generally cited in teaching problems for fan-shaped catchments; hence it is the accepted choice here.

Verification / Alternative check:
Where data permit, regional calibration should be used. In absence of data, shape-based selection using widely taught heuristics is acceptable for preliminary estimates.

Why Other Options Are Wrong:
Dicken's and Inglis are region-specific or tuned differently; they are not the standard selection for a generic fan-shaped-case MCQ.'None of these' is incorrect because a suitable option exists.

Common Pitfalls:
Applying a formula outside its regional validity without adjustment; ignoring catchment lag and storage effects; forgetting to check units and return period consistency.

Final Answer:
Ryve's formula