Stokes Friction Factor Calculator

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Overview

This relationship distinguishes between boundary conditions at the surface of the sphere, where 'no-slip' assumes the fluid velocity at the particle surface matches the particle velocity, and 'free-slip' assumes zero shear stress at the surface. These factors are fundamental in low-Reynolds number fluid dynamics, where inertial forces are negligible compared to viscous forces. The distinction between these two modes is critical when modeling micro-scale particles or biological entities in Stokes flow regimes.

Symbols

Variables

f = f

Apply it well

When To Use

When to use: Use this relationship when determining the drag force on a spherical object moving through a fluid at very low Reynolds numbers (Re << 1).

Why it matters: It establishes the theoretical bounds for hydrodynamic drag based on the surface interaction model, which is essential for calculating sedimentation rates and micro-particle transport.

Avoid these traps

Common Mistakes

• Applying the no-slip factor to systems where surface lubrication or gas bubbles cause slip.
• Assuming the result applies to non-spherical particles, which require different geometric corrections.

One free problem

Practice Problem

If an experiment requires modeling the movement of a gas bubble in a liquid, which friction factor boundary condition is theoretically more appropriate?

Solve for: $f$

Hint: Consider if the fluid at the surface of a gas bubble is constrained to the same velocity as the bubble itself.

The full worked solution stays in the interactive walkthrough.

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Related Formulas

References

Sources

1. Batchelor, G. K. (1967). An Introduction to Fluid Dynamics. Cambridge University Press.
2. Happel, J., & Brenner, H. (1983). Low Reynolds Number Hydrodynamics. Martinus Nijhoff Publishers.
3. [object Object]
4. Wikipedia: Stokes' drag law
5. NIST CODATA: Dynamic viscosity
6. Britannica, Stokes' law
7. IUPAC Gold Book, Stokes' law
8. Wikipedia, Stokes' drag equation