1. What is Stokes' Law?

Stokes' Law describes the force of viscosity acting on a spherical object moving through a fluid. It's fundamental in fluid dynamics and is used to calculate the drag force experienced by small particles in laminar flow conditions.

2. How Does the Calculator Work?

The calculator uses the Stokes' Law equation:

Where:

• \( F \) — Drag force (N)
• \( \pi \) — Mathematical constant pi (≈3.1416)
• \( \eta \) — Dynamic viscosity of the fluid (Pa·s)
• \( r \) — Radius of the spherical object (m)
• \( v \) — Velocity of the object relative to the fluid (m/s)

Explanation: The equation calculates the frictional force experienced by a sphere moving through a viscous fluid at low Reynolds numbers.

3. Applications of Stokes' Law

Details: Stokes' Law is used in various fields including sedimentology, aerosol science, and microbiology. It helps determine settling velocities of particles, measure fluid viscosity, and analyze particle motion in fluids.

4. Using the Calculator

Tips: Enter viscosity in Pa·s, radius in meters, and velocity in m/s. All values must be valid (positive values, velocity can be zero).

5. Frequently Asked Questions (FAQ)

Q1: What are the limitations of Stokes' Law?
A: Stokes' Law applies only to spherical objects in laminar flow (low Reynolds numbers, typically Re < 0.1) and assumes the fluid is infinite in extent.

Q2: How is viscosity measured?
A: Viscosity is typically measured using viscometers. Common units include Pa·s (SI unit) and poise (CGS unit), where 1 Pa·s = 10 poise.

Q3: Can Stokes' Law be used for non-spherical objects?
A: The standard form applies only to spheres. For non-spherical objects, shape factors and corrections must be applied.

Q4: What is the terminal velocity in Stokes' Law?
A: When drag force equals gravitational force, objects reach terminal velocity: \( v_t = \frac{2r^2g(\rho_p - \rho_f)}{9\eta} \), where ρ are densities and g is gravity.

Q5: How does temperature affect the calculation?
A: Temperature significantly affects viscosity. For accurate calculations, use viscosity values at the appropriate temperature.