In wind erosion, the amount of soil transported varies
Options:
(A) directly as the cube of the threshold wind velocity and inversely as the square of the mean soil particle diameter
(B) directly as the cube of the actual wind velocity and inversely as the square of the mean soil particle diameter
(C) directly as the cube of the difference in actual and threshold wind velocity and the square of the mean soil particle diameter
(D) directly as the cube of the difference in actual and threshold wind velocity and the square root of the mean soil particle diameter
Official Answer Key:
D
Step-by-Step Solution & Explanation
The classical wind-transport relation (Bagnold / Chepil) is:
q ∝ (V − Vₜ)³ · √d
Two physical ideas fix this form:
1. Excess velocity, not absolute velocity. No transport occurs until the wind exceeds the threshold velocity Vₜ needed to initiate particle movement. The driving term is therefore the excess (V − Vₜ), and it appears cubed because transport rate scales with the cube of shear velocity.
2. Direct √d dependence. Coarser grains require more momentum to lift, but once in saltation they travel farther and carry more mass, giving a direct square-root relation to mean particle diameter — not an inverse one.
Options (A) and (B) fail on both counts (absolute velocity, inverse d²); (C) has the correct velocity term but the wrong power of d.
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