Stokes Law Calculator

Stokes' Law describes the force of viscosity on a sphere moving through a fluid. This law is pivotal in fields like fluid dynamics and hydrometeorology, aiding in the prediction and analysis of particle settling velocities in various mediums.

Historical Background

Sir George Gabriel Stokes first articulated Stokes' Law in 1851. It provides a fundamental understanding of viscous forces for spheres at low Reynolds numbers, where fluid flow is laminar rather than turbulent. This law has broad applications, from determining the viscosity of liquids to studying sedimentation processes.

Calculation Formula

The fall or settling velocity (V_t) of a particle in a fluid is given by the formula:

\[ V_{t} = \frac{gd^{2}(\rho_{p} - \rho_{m})}{18\mu} \]

Where:

• \(g\) = Acceleration due to gravity (\(m/s^2\))
• \(d\) = Particle diameter (m)
• \(\rho_{p}\) = Particle density (\(kg/m^3\))
• \(\rho_{m}\) = Density of the medium (\(g/m^3\))
• \(\mu\) = Dynamic viscosity of the medium (\(kg/m\cdot s\))

Example Calculation

Consider a particle with a diameter of 0.002 m, moving through water (viscosity = 0.001 Pa·s, density = 1000 \(kg/m^3\)), with a density of 2500 \(kg/m^3\) under standard gravity (9.81 \(m/s^2\)):

\[ V_{t} = \frac{9.81 \times (0.002)^{2} \times (2500 - 1000)}{18 \times 0.001} = 0.04356 \, m/s \]

This calculation shows how Stokes' Law can be used to determine the settling velocity of a particle in a fluid.

Importance and Usage Scenarios

Stokes' Law is crucial for engineers and scientists in designing equipment for the separation of particles from fluids, determining particle size in aerosols and emulsions, and in the environmental field for sedimentation analysis.

Common FAQs

1. What limitations does Stokes' Law have?

   • Stokes' Law is accurate only for laminar flow conditions, small Reynolds numbers, and spherical particles.

2. How does the Reynolds number affect the applicability of Stokes' Law?

   • Stokes' Law applies when the Reynolds number (Re) is less than 0.1, indicating laminar flow around the particle.

3. Can Stokes' Law be applied to non-spherical particles?

   • Direct application is challenging. Corrections for shape factors are required for non-spherical particles.