Stokes Law Settling Velocity Calculator

Stokes' Law Equation:

\[ v = \frac{2 r^2 g (\rho_p - \rho_f)}{9 \eta} \]

Radius (r):

Gravity (g):

m/s²

Particle Density (ρₚ):

kg/m³

Fluid Density (ρ𝒇):

kg/m³

Viscosity (η):

Pa·s

Settling Velocity (v):

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1. What is Stokes' Law?

Stokes' Law describes the force of viscosity on a sphere moving through a fluid. It's used to calculate the terminal velocity of a falling sphere in a viscous fluid, which is important in various scientific and engineering applications.

2. How Does the Calculator Work?

The calculator uses the Stokes' Law equation:

\[ v = \frac{2 r^2 g (\rho_p - \rho_f)}{9 \eta} \]

Where:

\( v \) — Settling velocity (m/s)
\( r \) — Particle radius (m)
\( g \) — Gravitational acceleration (m/s²)
\( \rho_p \) — Particle density (kg/m³)
\( \rho_f \) — Fluid density (kg/m³)
\( \eta \) — Dynamic viscosity (Pa·s)

Explanation: The equation calculates the terminal velocity of a spherical particle falling through a viscous fluid under gravity.

3. Applications of Stokes' Law

Details: Stokes' Law is used in sedimentology, aerosol science, chemical engineering, and various industrial processes including water treatment, mineral processing, and pharmaceutical manufacturing.

4. Using the Calculator

Tips: Enter all values in SI units. Radius and viscosity must be positive values. For water at 20°C, viscosity is approximately 0.001 Pa·s and density is 998 kg/m³.

5. Frequently Asked Questions (FAQ)

Q1: What are the assumptions of Stokes' Law?
A: The law assumes: 1) Spherical particles, 2) Laminar flow (Re < 0.3), 3) Homogeneous fluid, 4) No wall effects, 5) No particle interactions.

Q2: When is Stokes' Law not applicable?
A: For non-spherical particles, turbulent flow, high particle concentrations, or when particles are not significantly denser than the fluid.

Q3: How does temperature affect the calculation?
A: Temperature affects both fluid density and viscosity. Higher temperatures typically decrease viscosity, increasing settling velocity.

Q4: Can this be used for air as the fluid?
A: Yes, but note that air has much lower density and viscosity than water, which affects the settling behavior.

Q5: What is the Reynolds number limitation?
A: Stokes' Law is valid for Reynolds numbers less than approximately 0.3, where viscous forces dominate over inertial forces.