GATE AG 2011 • Q20 MCQ • 1 Mark

Section 4: Soil and Water Conservation Engineering

Soil and Water Erosion

Subtopic: Mechanics of soil erosion – wind and water erosion

Question Statement:

In wind erosion process, the rate of soil movement (S) depends on wind speed (v), threshold limit of wind speed required to move the soil (vm) and average soil particle size (d). This interrelationship is expressed as

Options:

  • (A) S ∝ (v−vm)² d^(1/2)
  • (B) S ∝ (v−vm)² d
  • (C) S ∝ (v−vm)³ d^(1/2)
  • (D) S ∝ (v−vm)³ d

Official Answer Key:

D

Step-by-Step Solution & Explanation

The standard empirical relationship for wind-driven soil (sediment) transport rate, following Bagnold-type sand-transport theory, expresses the rate of soil movement as proportional to the cube of the excess wind shear velocity above threshold, (v − vm)³, and directly proportional to particle size d (coarser particles move in higher, more energetic saltation trajectories that increase the transport rate per unit width). This matches option (D), S ∝ (v−vm)³·d.

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