Form factor – choose the correct formula The drainage-basin form factor is defined in terms of basin area and axial (maximum) length. Which expression is correct?
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AArea of the basin divided by the axial length
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BAverage width divided by axial length
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CArea of the basin divided by the square of the axial length
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DBoth (a) and (b)
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EBoth (b) and (c)
Answer
Correct Answer: Area of the basin divided by the square of the axial length
Explanation
Introduction / Context:Basin shape indices help anticipate runoff timing. The form factor normalizes area by length scale to compare the “roundness” or elongation of catchments of different sizes.
Given Data / Assumptions:
- Axial length is the maximum straight-line length of the basin.
- Area and length are measured at consistent map scale.
- No need for relief corrections for this planimetric index.
Concept / Approach:The correct and widely used formula is: form factor Ff = A / L^2, where A is basin area and L is axial length. This yields a dimensionless number because the units cancel, enabling inter-basin comparison.
Step-by-Step Solution:Identify required terms: A (area) and L (axial length).Apply the standard definition: Ff = A / L^2.Among the options, only (c) matches the formula.
Verification / Alternative check:If two basins have the same A but one has twice the L, the longer one has one-quarter the form factor, reflecting a more elongated shape—exactly what Ff = A / L^2 captures.
Why Other Options Are Wrong:
- (a) and (b) do not square the length, so they do not provide a dimensionless, scale-normalized measure.
- (d) and (e) include incorrect components and thus are not valid definitions.
Common Pitfalls:Using average width or perimeter in place of axial length; different indices (e.g., circularity ratio) use different inputs—do not mix them.
Final Answer:Area of the basin divided by the square of the axial length