1. What is Stokes' Law?

Stokes' Law describes the drag force experienced by a spherical object moving through a viscous fluid at low Reynolds numbers. It provides a way to calculate drag force without needing a drag coefficient, making it particularly useful for small particles in fluids.

2. How Does the Calculator Work?

The calculator uses Stokes' Law equation:

Where:

• \( F_d \) — Drag force (N)
• \( \eta \) — Fluid viscosity (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 drag force on a sphere moving slowly through a viscous fluid, where the flow is laminar and Reynolds number is low (Re < 1).

3. Importance of Drag Force Calculation

Details: Accurate drag force calculation is crucial for understanding particle motion in fluids, designing filtration systems, studying sedimentation processes, and analyzing biological systems like blood flow.

4. Using the Calculator

Tips: Enter viscosity in Pa·s, radius in meters, and velocity in m/s. All values must be valid (viscosity > 0, radius > 0, velocity ≥ 0). Ensure the Reynolds number is low (Re < 1) for accurate results.

5. Frequently Asked Questions (FAQ)

Q1: When is Stokes' Law applicable?
A: Stokes' Law is valid for spherical objects moving at low Reynolds numbers (Re < 1) where viscous forces dominate over inertial forces.

Q2: What are typical viscosity values for common fluids?
A: Water at 20°C: ~0.001 Pa·s, Air at 20°C: ~0.000018 Pa·s, Honey: ~2-10 Pa·s, depending on temperature and type.

Q3: Can Stokes' Law be used for non-spherical objects?
A: No, Stokes' Law is specifically derived for spherical objects. For non-spherical shapes, different equations or empirical corrections are needed.

Q4: What happens at higher Reynolds numbers?
A: At higher Reynolds numbers (Re > 1), the flow becomes turbulent, and Stokes' Law is no longer accurate. A drag coefficient approach must be used instead.

Q5: How is terminal velocity calculated using Stokes' Law?
A: Terminal velocity occurs when drag force equals gravitational force. For a falling sphere: \( v_t = \frac{2r^2g(\rho_p - \rho_f)}{9\eta} \), where \( \rho_p \) and \( \rho_f \) are particle and fluid densities.