Pettis empirical flood formula – variables on which it is based The Pettis formula for peak flood discharge, Q = C (P · B)^(5/4) cumecs, relates discharge to which catchment descriptors?

Introduction / Context:
For preliminary hydrologic design in ungauged basins, engineers sometimes employ empirical regional flood formulas. The Pettis formula is one such relation that predicts peak discharge based on rainfall potential and basin scale.

Given Data / Assumptions:

• P denotes a characteristic storm rainfall depth (or index) for the basin and design frequency.
• B denotes the catchment (drainage basin) area.
• C is an empirical coefficient calibrated for region and units.
• Formula is intended for quick estimation, not a substitute for detailed hydrologic modeling.

Concept / Approach:
Empirical flood formulae typically link peak discharge to a measure of storm input and basin size. In Q = C (P · B)^(5/4), the product P · B captures the magnitude of potential runoff volume scaled by area, while the exponent 5/4 reflects observed nonlinearity in peak response with respect to rainfall and basin area.

Step-by-Step Solution:
Identify symbols: P = rainfall metric; B = basin area.Check options: Only option (a) explicitly lists rainfall and drainage area.Therefore, (a) is correct.

Verification / Alternative check:
Comparable regional relations (e.g., Dicken’s, Ryve’s, Inglis) also combine rainfall or a regional constant with basin area to estimate peak flows, lending conceptual support.

Why Other Options Are Wrong:

• (b) “Runoff and area” is not what the stated variables represent; P is rainfall, not measured runoff.
• (c) Shape factor is not present explicitly in the formula.
• (d) Area alone cannot capture storm input variability.

Common Pitfalls:
Using empirical formulas outside their calibrated region; ensure consistent units for P and B so that discharge units emerge correctly with the chosen C.

Final Answer:
Rainfall (P) and drainage basin area (B)