What is the formula for terminal settling velocity in relation to particle diameter?

The formula for terminal settling velocity is crucial in understanding how particles settle in a fluid, which is often a key consideration in industrial hygiene and environmental science. The correct choice reflects a direct proportionality to the square of the particle diameter. This relationship arises from the physics of particle motion through a fluid, particularly influenced by the balance of gravitational and drag forces acting on the particle.

When analyzing terminal settling velocity, it is recognized that as the diameter of a particle increases, the gravitational force acting on the particle increases as a function of volume, which is proportional to the cube of the diameter. However, the drag force, which affects how quickly a particle settles, is proportional to its cross-sectional area, which is related to the square of the diameter. Therefore, the terminal velocity will depend on the ratio of gravitational force to drag force. The result of this analysis leads to the conclusion that settling velocity is directly related to the square of the particle diameter, making the formula 0.003 * (diameter)^2 accurate and relevant in practical applications.

This understanding is crucial for professionals in fields where sedimentation and particle transport are relevant, allowing them to predict how particles behave in various environments effectively. The other options provided do not accurately reflect this interplay between gravitational