Drainage-basin form factor – compute from given area and axial length A drainage basin has an axial length of 100 km and a plan area of 2,500 sq. km. Using the standard definition (form factor = basin area / axial length^2), determine the basin’s form factor.

Introduction / Context:
The form factor is a popular basin-shape index in hydrology used to infer hydrograph characteristics. A higher form factor suggests a “rounder” basin that tends to yield a sharper flood peak, while a lower value indicates an elongated basin with a flatter hydrograph.

Given Data / Assumptions:

• Basin area A = 2,500 sq. km.
• Axial length L = 100 km.
• Standard definition: form factor Ff = A / L^2.
• Planar (map) measurements; no need for relief corrections.

Concept / Approach:
The form factor is a dimensionless ratio comparing area to the square of the maximum basin length. It normalizes area by length scale so basins of different size can be compared by shape alone. No unit conversion is needed because the km units cancel in the ratio.

Step-by-Step Solution:
Compute L^2: L^2 = 100^2 = 10,000 km^2.Apply formula: Ff = A / L^2 = 2,500 / 10,000.Evaluate: Ff = 0.25.Match with the options provided → 0.25.

Verification / Alternative check:
If the basin were a perfect square of side 50 km, its axial length would be 50 km and A/L^2 would be 2,500/2,500 = 1. Here, L is twice that (100 km), so A/L^2 naturally becomes 1/4 = 0.25, consistent with an elongated plan shape.

Why Other Options Are Wrong:

• 0.10, 0.20, 0.30, 0.35 are not equal to A / L^2 with the given numbers.

Common Pitfalls:
Confusing axial length with mean width; or squaring the area instead of length. Always use the exact definition Ff = A / L^2 with consistent units.

Final Answer:
0.25