Understanding Stokes' Law

Stokes' Law describes the settling velocity of a small spherical particle falling through a viscous fluid. This terminal velocity is reached when the drag force exerted by the fluid, combined with the buoyant force, perfectly balances the gravitational force acting on the particle.

The Formula

The mathematical expression for Stokes' Law is: v = (g * d² * (ρₚ - ρբ)) / (18 * μ)

• v: Settling velocity (m/s)
• g: Acceleration due to gravity (9.81 m/s²)
• d: Particle diameter (m)
• ρₚ: Density of the particle (kg/m³)
• ρբ: Density of the fluid (kg/m³)
• μ: Dynamic viscosity of the fluid (Pa·s)

Applications of the Stokes Settling Velocity Calculator

This calculator is an essential tool for environmental engineers, geologists, and chemical engineers. It is widely used in wastewater treatment to design sedimentation tanks, in geology to understand soil deposition patterns, and in the pharmaceutical industry to study the stability of suspensions. If you are analyzing silt, clay, or fine sand in water, Stokes' Law provides the theoretical foundation for how fast these particles will sink to the bottom.

Frequently Asked Questions (FAQs)

What are the limitations of Stokes' Law?

Stokes' Law is only valid for laminar flow, typically where the Reynolds number (Re) is less than 0.1. It also assumes particles are perfectly spherical, smooth, and do not interfere with each other (dilute suspensions).

How does temperature affect settling velocity?

Temperature significantly impacts the dynamic viscosity of the fluid. As temperature increases, viscosity usually decreases, causing the settling velocity to increase.