Stokes' Law Calculator

Formula

The formula to calculate the terminal velocity (v) is:

\[ v = \frac{g \cdot d^2 \cdot (P - p)}{18 \cdot u} \]

Where:

\( v \) is the terminal velocity (m/s).
\( g \) is the acceleration due to gravity (m/s²).
\( d \) is the diameter of the particle (m).
\( P \) is the density of the particle (kg/m³).
\( p \) is the density of the fluid (kg/m³).
\( u \) is the viscosity of the fluid (Pa·s).

What is Stokes' Law?

Stokes' law defines the terminal velocity of a falling object through a specific fluid or medium. It is used to describe the motion of spherical particles in a fluid and is crucial in fields such as fluid dynamics and engineering.

Example Calculation

Consider an example where:

Acceleration due to Gravity (g): 9.81 m/s²
Diameter of the Particle (d): 0.01 m
Density of the Particle (P): 2500 kg/m³
Density of the Fluid (p): 1000 kg/m³
Viscosity of the Fluid (u): 0.001 Pa·s

Using the formula to calculate the terminal velocity:

\[ v = \frac{9.81 \cdot 0.01^2 \cdot (2500 - 1000)}{18 \cdot 0.001} = 81.75 \text{ m/s} \]

This means that the terminal velocity for this example is 81.75 m/s.