What equation is used for calculating the settling velocity of discrete particles in a sedimentation tank?

The Stokes' Law is used for calculating the settling velocity of discrete particles in a sedimentation tank. This law applies to small particles settling under the influence of gravity in a viscous fluid, typically within a regime where the particle Reynolds number is less than one. It provides a mathematical relationship between the settling velocity, the particle diameter, the fluid's viscosity, and the density difference between the particle and the fluid.

The equation derived from Stokes' Law shows that the settling velocity is directly proportional to the square of the particle diameter and the density difference, while being inversely proportional to the fluid's viscosity. This relationship is fundamental in environmental engineering and water resources management for designing sedimentation tanks, which are essential for water treatment and wastewater management.

Other equations listed in the choices focus on different principles; for instance, Bernoulli's equation addresses fluid dynamics in ideal conditions without considering settling particles, Darcy's law pertains to flow through porous media, and Newton's law may refer to particle motion under different dynamics that are not specifically for sedimentation under the effects of gravity alone. Thus, Stokes' Law is the most applicable and accurate choice for determining the settling velocity in sedimentation processes.