1. What is Stokes' Law Equation?

Stokes' law describes the drag force experienced by a spherical object moving through a viscous fluid at low Reynolds numbers. It is fundamental in fluid dynamics and has applications in various fields including engineering, physics, and biology.

2. How Does the Calculator Work?

The calculator uses Stokes' law equation:

Where:

• \( F \) — Drag force (N)
• \( \eta \) — Dynamic 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 frictional force exerted on a sphere moving through a viscous fluid, assuming laminar flow conditions.

3. Importance of Drag Force Calculation

Details: Accurate drag force calculation is crucial for designing fluid systems, analyzing particle motion, sedimentation studies, and understanding biological processes like blood flow and cell movement.

4. Using the Calculator

Tips: Enter viscosity in Pa·s, radius in meters, and velocity in m/s. All values must be positive and valid for accurate results.

5. Frequently Asked Questions (FAQ)

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

Q2: How does viscosity affect drag force?
A: Drag force is directly proportional to viscosity - higher viscosity fluids create greater resistance to motion.

Q3: What is the significance of the 6π factor?
A: The 6π factor comes from the mathematical derivation for a sphere moving through a viscous fluid and represents the geometric factor for spherical objects.

Q4: Can Stokes' law be used for non-spherical objects?
A: No, Stokes' law is specifically derived for spherical objects. Different equations are needed for other shapes.

Q5: What are some practical applications of Stokes' law?
A: Applications include calculating sedimentation rates, designing viscometers, analyzing aerosol particles, and studying blood flow in capillaries.