Question

In wind erosion, the amount of soil transported varies

• 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

Hint:

Think about which velocity term actually drives particle movement once the threshold is crossed.

Answer 1

The Correct Option is D

Step 1: Identify the driving variable for wind erosion.
Particles start moving only once wind speed exceeds a threshold value $V_t$; the excess $(V - V_t)$ is what actually drives transport, not $V$ or $V_t$ alone.

Step 2: Recall how transport rate scales with that excess velocity.
Field and wind tunnel studies on saltation show the soil transport rate rises with the cube of this excess velocity, $q \propto (V - V_t)^3$.

Step 3: Recall how particle size enters the relation.
Coarser particles need more energy to loft, and the accepted form shows transport varying with the square root of mean particle diameter, $q \propto \sqrt{d}$.

Step 4: Combine the two dependences and match to the options.
$q \propto (V - V_t)^3\sqrt{d}$, which matches the wording of option (D) and rules out the other three.

Final Answer:
Soil transport by wind grows with the cube of the velocity excess and the square root of particle diameter. \[ q \propto (V - V_t)^3\sqrt{d} \]