What is the relationship between terminal settling velocity and particle diameter as per the provided equation?

The relationship between terminal settling velocity and particle diameter is described by Stokes' Law, which states that the terminal velocity of a particle moving through a fluid is directly related to the square of the diameter of the particle. This means that when the diameter of the particle increases, the terminal settling velocity increases with the square of that diameter, indicating a quadratic relationship.

In practical terms, this means that if you double the diameter of a particle, its terminal settling velocity increases by a factor of four, not just two. This relationship is crucial in industrial hygiene and environmental science, where the understanding of particle behavior in various mediums is essential for risk assessment and control measures.

Understanding that terminal settling velocity is proportional to the square of the diameter provides insights into how larger particles will settle more quickly compared to smaller ones under the influence of gravity, which is a key factor when considering exposure to airborne particulates or sedimentation in occupational health settings.