Stoke Formula

Overview

Engineering reference data for Stoke Formula in basics.

Key Formulas

Ohm's Law

$V = IR$

Voltage = Current × Resistance.

Newton's Second Law

$F = ma$

Force = mass × acceleration.

Conservation of Energy

$E_{in} = E_{out} + \Delta E_{stored}$

Energy balance.

Variables

Symbol	Description	Unit
$V$	Voltage	V
$I$	Current	A
$R$	Resistance	Ω
$F$	Force	N
$m$	Mass	kg
$a$	Acceleration	m/s²

Applications

Stokes' law is fundamental in various engineering and scientific fields:

• Fluid mechanics: Analyzing sedimentation rates in wastewater treatment, mineral processing, and centrifuges.
• Aerosol science: Modeling the behavior of fine particles, droplets, and biological agents in air.
• Microfluidics: Designing lab-on-a-chip devices where viscous forces dominate.
• Geophysics: Understanding the settling of volcanic ash or suspended sediments in water bodies.
• Biophysics: Estimating the drag on microscopic organisms or organelles.

Computational Notes

1. Reynolds Number Constraint: Stokes' formula is valid for creeping flow, where the particle Reynolds number is very low ($Re_p = \frac{\rho v d}{\mu} \ll 1$). For typical calculations, a common engineering threshold is $Re_p < 0.1$.
2. Velocity Dependence: The drag force $F$ is linearly proportional to the relative velocity $v$. This linear relationship breaks down at higher velocities where inertial forces become significant.
3. Temperature Sensitivity: The fluid viscosity $\eta$ is strongly dependent on temperature. For liquids, viscosity typically decreases with increasing temperature (e.g., water viscosity halves from 0°C to 50°C).

References

• Original Source