Stokes Law Example Calculation

Stokes Law Equation:

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

Radius (r):

Particle Density (ρ_p):

kg/m³

Fluid Density (ρ_f):

kg/m³

Gravity (g):

m/s²

Viscosity (η):

Pa s

Terminal 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 at low Reynolds numbers. It's used to calculate the terminal velocity of small particles settling in a fluid medium under gravity.

2. How Does the Calculator Work?

The calculator uses the Stokes' Law equation:

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

Where:

\( v \) — Terminal velocity (m/s)
\( r \) — Radius of the spherical particle (m)
\( \rho_p \) — Density of the particle (kg/m³)
\( \rho_f \) — Density of the fluid (kg/m³)
\( g \) — Acceleration due to gravity (m/s²)
\( \eta \) — Dynamic viscosity of the fluid (Pa s)

Explanation: The equation calculates the constant velocity that a spherical object reaches when the drag force equals the gravitational force.

3. Importance of Terminal Velocity Calculation

Details: Calculating terminal velocity is crucial in various fields including sedimentology, chemical engineering, aerosol science, and biomedical applications where particle settling is important.

4. Using the Calculator

Tips: Enter all values in SI units. Radius and viscosity must be positive values. Particle density should be greater than fluid density for settling to occur. Standard gravity is 9.81 m/s².

5. Frequently Asked Questions (FAQ)

Q1: What are the limitations of Stokes' Law?
A: Stokes' Law applies only to spherical particles, laminar flow conditions (low Reynolds numbers), and infinite fluid media without wall effects.

Q2: What is the typical range for viscosity values?
A: Viscosity ranges from about 0.00089 Pa s for air to 1.0 Pa s for glycerol. Water has a viscosity of approximately 0.001 Pa s at 20°C.

Q3: How does temperature affect the calculation?
A: Temperature affects fluid density and viscosity significantly. For accurate results, use values measured at the specific temperature of interest.

Q4: What happens if particle density is less than fluid density?
A: The particle will rise rather than settle, resulting in a negative terminal velocity value.

Q5: Can this be used for non-spherical particles?
A: No, Stokes' Law is specifically for spherical particles. For non-spherical particles, shape factors and other corrections are needed.