Stokes' Law Calculator

Stokes' Law Calculator - Calculate The terminal velocity

Particle Diameter:

Particle Density:

Medium Density:

Medium Dynamic Viscosity:

Gravity (m/s², optional):

Settling Velocity (m/s): Settling Velocity (km/h): Settling Velocity (ft/s): Settling Velocity (mph): Settling Velocity (kn): Settling Velocity (ft/min):

1. How Does the Stokes' Law Calculator Work?

Calculations are based on Stokes' Law, which describes the settling velocity of a spherical particle in a viscous medium under low Reynolds number conditions:

\[ v = g \times d^2 \times \frac{(\rho_p - \rho_m)}{18 \mu} \]

Where:

\(v\) = Settling velocity
\(g\) = Gravity (m/s², default 9.81 m/s² on Earth)
\(d\) = Particle diameter
\(\rho_p\) = Particle density
\(\rho_m\) = Medium density
\(\mu\) = Medium dynamic viscosity

Unit Conversions:

Parameter	Units
Particle Diameter	mm, cm, m, in, ft, yd (converted to meters)
Particle Density	kg/m³, kg/L, g/L, g/cm³, oz/cu in, lb/cu in, lb/cu ft, mg/L (converted to kg/m³)
Medium Density	kg/m³, kg/L, g/L, g/cm³, oz/cu in, lb/cu in, lb/cu ft, mg/L (converted to kg/m³)
Medium Dynamic Viscosity	Pa·s, P, cP, lbf·s/ft², lb/(ft·s), dyn·s/cm², kg/(m·s) (converted to Pa·s)
Gravity	m/s² (meters per second squared)
Settling Velocity	m/s, km/h, ft/s, mph, kn, ft/min

Explanation: The calculator converts input values to standard SI units (meters, kg/m³, Pa·s), uses Stokes' Law to compute the settling velocity in m/s, and then converts the result to all specified velocity units, assuming laminar flow and low Reynolds number conditions.

2. Importance of Stokes' Law Calculation

Details: Stokes' Law is critical for applications in sedimentology, environmental science, chemical engineering, and particle size analysis, helping to predict particle behavior in fluids like water or air, such as sedimentation rates in rivers or dust settling in the atmosphere.

3. Using the Stokes' Law Calculator

Tips: Enter the Particle Diameter (selecting the unit), Particle Density (selecting the unit), Medium Density (selecting the unit), Medium Dynamic Viscosity (selecting the unit), and optionally customize Gravity (default 9.81 m/s²). Click "Calculate" to get the Settling Velocity in all specified units (m/s, km/h, ft/s, mph, kn, ft/min).

4. Frequently Asked Questions (FAQ)

Q1: What is Stokes' Law used for? A: Stokes' Law is used to calculate the settling velocity of small spherical particles in a viscous medium under low-speed, laminar flow conditions, applicable in sedimentology, fluid dynamics, and particle analysis.

Q2: Can this calculator handle non-spherical particles? A: No, this calculator assumes spherical particles. Non-spherical particles may require adjustments or different models, as Stokes' Law applies strictly to spheres.

Q3: What if the medium is not viscous enough? A: Stokes' Law assumes low Reynolds number (laminar flow). If the medium has low viscosity or high velocity, turbulent flow may occur, and the law may not apply accurately.

Q4: Are the results exact? A: The results are accurate for ideal conditions (spherical particles, laminar flow). Real-world factors like particle shape, medium turbulence, or temperature may introduce deviations, but the calculator uses standard conversion factors for precision.

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