Stokes Law Calculator With Solution

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 (ρ_f):

kg/m³

Viscosity (η):

Pa·s

Settling Velocity (v):

Unit Converter ▲

Unit Converter ▼

From:	To:

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 fields like sedimentology, meteorology, and chemical engineering.

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)
\( r \) — Radius of the particle (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 various applications including sedimentation analysis, air pollution studies, paint manufacturing, and determining the size of particles in suspensions.

4. Using the Calculator

Tips: Enter all values in SI units. Radius should be in meters, densities in kg/m³, gravity in m/s² (9.81 m/s² on Earth), and viscosity in Pa·s (0.001 Pa·s for water at 20°C).

5. Frequently Asked Questions (FAQ)

Q1: What are the assumptions of Stokes' Law?
A: Stokes' Law assumes the particle is spherical, the fluid is Newtonian, flow is laminar (Re < 0.1), and the particle is far from boundaries.

Q2: When is Stokes' Law not applicable?
A: It's not applicable for non-spherical particles, turbulent flow, high particle concentrations, or when particles are near container walls.

Q3: How does temperature affect the calculation?
A: Temperature affects fluid density and viscosity. Warmer fluids typically have lower viscosity, increasing settling velocity.

Q4: Can Stokes' Law be used for gases?
A: Yes, but the density difference (ρₚ - ρ_f) is approximately equal to ρₚ since gas density is much lower than solid particle density.

Q5: What is the Reynolds number limitation?
A: Stokes' Law is valid for Reynolds numbers less than 0.1. For higher Reynolds numbers, more complex equations are needed.